pyvene_101.ipynb

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        "<a href=\"https://colab.research.google.com/github/rohrl/llm_shenanigans/blob/main/pyvene_101.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Introduction to pyvene\n",
        "This tutorial shows simple runnable code snippets of how to do different kinds of interventions on neural networks with pyvene."
      ]
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        "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/stanfordnlp/pyvene/blob/main/pyvene_101.ipynb)"
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      "source": [
        "__author__ = \"Zhengxuan Wu\"\n",
        "__version__ = \"02/01/2024\""
      ]
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        " # Table of Contents  \n",
        "1. [Set-up](#Set-up)     \n",
        "1. [pyvene 101](#pyvene-101)\n",
        "    1. [Get Attention Weights](#Get-Attention-Weights)\n",
        "        1. [with String Access](#Get-Attention-Weights-with-Direct-Access-String)\n",
        "        1. [with 1-Line Function](#Get-Attention-Weights-with-a-Function)\n",
        "    1. [Set Activations to Zeros](#Set-Activation-to-Zeros)\n",
        "        1. [with Lambda Expression](#Set-Activation-to-Zeros-with-a-Lambda-Expression)\n",
        "    1. [Set Activations with Subspaces](#Set-Activations-to-Zeros-with-Subspaces)\n",
        "    1. [Interchange Intervention](#Interchange-Interventions)\n",
        "    1. [Intervention Config](#Intervention-Configuration)\n",
        "    1. [Addition Intervention](#Addition-Intervention)\n",
        "    1. [Trainable Intervention](#Trainable-Intervention)\n",
        "    1. [Activation Collection](#Activation-Collection-with-Intervention)\n",
        "    1. [Activation Collection with Other Intervention](#Activation-Collection-at-Downstream-of-a-Intervened-Model)\n",
        "    1. [Intervene Single Neuron](#Intervene-on-a-Single-Neuron)\n",
        "    1. [Add New Intervention Type](#Add-New-Intervention-Type)\n",
        "    1. [Intervene on Recurrent NNs](#Recurrent-NNs-(Intervene-a-Specific-Timestep))\n",
        "    1. [Intervene across Times with RNNs](#Recurrent-NNs-(Intervene-cross-Time))\n",
        "    1. [Intervene on LM Generation](#LMs-Generation)\n",
        "    1. [Debiasing with Backpack LMs](#Debiasing-with-Backpack-LMs)\n",
        "    1. [Saving and Loading](#Saving-and-Loading)\n",
        "    1. [Multi-Source Intervention (Parallel)](#Multi-Source-Interchange-Intervention-(Parallel-Mode))\n",
        "    1. [Multi-Source Intervention (Serial)](#Multi-Source-Interchange-Intervention-(Serial-Mode))\n",
        "    1. [Multi-Source Intervention with Subspaces (Parallel)](#Multi-Source-Interchange-Intervention-with-Subspaces-(Parallel-Mode))\n",
        "    1. [Multi-Source Intervention with Subspaces (Serial)](#Multi-Source-Interchange-Intervention-with-Subspaces-(Serial-Mode))\n",
        "    1. [Interchange Intervention Training](#Interchange-Intervention-Training-(IIT))\n",
        "1. [pyvene 102](#pyvene-102)\n",
        "    1. [Intervention Grouping](#Grouping)\n",
        "    1. [Intervention Skipping](#Intervention-Skipping-in-Runtime)\n",
        "    1. [Subspace Partition](#Subspace-Partition)\n",
        "    1. [Intervention Linking](#Intervention-Linking)\n",
        "    1. [Add New Model Type](#Add-New-Model-Type)\n",
        "    1. [Path Patching](#Composing-Complex-Intervention-Schema:-Path-Patching)\n",
        "    1. [Causal Tracing](#Composing-Complex-Intervention-Schema:-Causal-Tracing-in-15-lines)\n",
        "    1. [Inference-time Intervention](#Inference-time-Intervention)\n",
        "    1. [IntervenableModel from HuggingFace Directly](#IntervenableModel-from-HuggingFace-Directly)\n",
        "    1. [Path Patching with DAS](#Path-Patching-with-Trainable-Interventions)\n",
        "    1. [Intervene ResNet with Lambda Functors](#Intervene-on-ResNet-with-Lambda-Functions)\n",
        "    1. [Intervene ResNet with 1-line DAS Lambda](#Intervene-on-ResNet-with-Trainable-Lambda-Functions)\n",
        "1. [The End](#The-End)\n",
        "    "
      ]
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      "source": [
        "## Set-up"
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        "try:\n",
        "    # This library is our indicator that the required installs\n",
        "    # need to be done.\n",
        "    import pyvene\n",
        "\n",
        "except ModuleNotFoundError:\n",
        "    !pip install git+https://github.com/stanfordnlp/pyvene.git"
      ]
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        "## pyvene 101\n",
        "Before we get started, here are a couple of core notations that are used in this library:\n",
        "- **Base** example: this is the example we are intervening on, or, we are intervening on the computation graph of the model running the **Base** example.\n",
        "- **Source** example or representations: this is the source of our intervention. We use **Source** to intervene on **Base**.\n",
        "- **component**: this is the `nn.module` we are intervening in a pytorch-based NN. For models supported by this library, you can use directly access via str, or use the abstract names defined in the config file (e.g., `h[0].mlp.output` or `mlp_output` with other fields).\n",
        "- **unit**: this is the axis of our intervention. If we say our **unit** is `pos` (`position`), then you are intervening on each token position.\n",
        "- **unit_locations**: this list gives you the percisely location of your intervention. It is the locations of the unit of analysis you are specifying. For instance, if your `unit` is `pos`, and your `unit_location` is 3, then it means you are intervening on the third token. If this field is left as `None`, then no selection will be taken, i.e., you can think of you are getting the raw tensor and you can do whatever you want.\n",
        "- **intervention_type** or **intervention**: this field specifies the intervention you can perform. It can be a primitive type, or it can be a function or a lambda expression for simple interventions. One benefit of using primitives is speed and systematic training schemes. You can also save and load interventions if you use the supported primitives."
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      "source": [
        "### Get Attention Weights"
      ]
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      "source": [
        "import pyvene as pv\n",
        "from transformers import AutoTokenizer, AutoModelForCausalLM\n",
        "\n",
        "model_name = \"gpt2\"\n",
        "gpt2 = AutoModelForCausalLM.from_pretrained(model_name)\n",
        "tokenizer = AutoTokenizer.from_pretrained(model_name)\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"layer\": 0,\n",
        "    \"component\": \"attention_weight\",\n",
        "    \"intervention_type\": pv.CollectIntervention}, model=gpt2)\n",
        "\n",
        "base = \"When John and Mary went to the shops, Mary gave the bag to\"\n",
        "\n",
        "base_tokens = tokenizer(base, return_tensors=\"pt\")\n",
        "\n",
        "collected_attn_w = pv_gpt2(\n",
        "    base = base_tokens,\n",
        "    unit_locations={\"base\": [h for h in range(12)]}\n",
        ")[0][-1][0]"
      ]
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        "gpt2"
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              "GPT2LMHeadModel(\n",
              "  (transformer): GPT2Model(\n",
              "    (wte): Embedding(50257, 768)\n",
              "    (wpe): Embedding(1024, 768)\n",
              "    (drop): Dropout(p=0.1, inplace=False)\n",
              "    (h): ModuleList(\n",
              "      (0-11): 12 x GPT2Block(\n",
              "        (ln_1): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
              "        (attn): GPT2Attention(\n",
              "          (c_attn): Conv1D()\n",
              "          (c_proj): Conv1D()\n",
              "          (attn_dropout): Dropout(p=0.1, inplace=False)\n",
              "          (resid_dropout): Dropout(p=0.1, inplace=False)\n",
              "        )\n",
              "        (ln_2): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
              "        (mlp): GPT2MLP(\n",
              "          (c_fc): Conv1D()\n",
              "          (c_proj): Conv1D()\n",
              "          (act): NewGELUActivation()\n",
              "          (dropout): Dropout(p=0.1, inplace=False)\n",
              "        )\n",
              "      )\n",
              "    )\n",
              "    (ln_f): LayerNorm((768,), eps=1e-05, elementwise_affine=True)\n",
              "  )\n",
              "  (lm_head): Linear(in_features=768, out_features=50257, bias=False)\n",
              ")"
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          "execution_count": 73
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        "collected_attn_w.shape"
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              "torch.Size([12, 14, 14])"
            ]
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      "source": [
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "tokens = [tokenizer.decode(t) for t in base_tokens.input_ids.squeeze()]\n",
        "print(tokens)\n",
        "\n",
        "for attention_tensor in collected_attn_w:\n",
        "  fig, ax = plt.subplots(figsize=(4, 4))\n",
        "\n",
        "  sns.heatmap(attention_tensor, annot=False, fmt=\".2f\", square=True, ax=ax)\n",
        "\n",
        "  ax.set_xticklabels(tokens, rotation=90, ha='right')\n",
        "  ax.xaxis.set_ticks_position(\"top\")\n",
        "  ax.set_yticklabels(tokens, rotation=0)\n",
        "\n",
        "plt.show()"
      ],
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['When', ' John', ' and', ' Mary', ' went', ' to', ' the', ' shops', ',', ' Mary', ' gave', ' the', ' bag', ' to']\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 2 Axes>"
            ],
            "image/png": 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LERwcjPHjx8v9S/5aRUWF1CTbpk0bLotcIy4+q9jYWAwZMgTt2rXDzZs30blzZ9y5cweMMbi4uMhdFq7eX67K0+AwxZ8257LpRxoLCwvk5+dL7MvPz4exsXHt/t+Qu87QyNja2rK5c+fW+sEaa2truTYbGxu5Y1pYWLD9+/fX9hYkjB07lm3atIkxxtiKFStYixYt2JQpU1jbtm3ZsGHD5I4THBzMAgICWEVFhbh54O7du6xbt25s7ty5SpVRVTIyMlivXr2YhoaGxKaK2V4Z4+az6t69u7jp6HWT0vPnz9mQIUPYd999V2dlV5fycKXifzcU3pQBOZqDFixYUG201dixY5mvr2+trsXb5iADAwNcu3YN7dq1U3VR0KxZMyQlJaF9+/YKx3jy5AnKysrQqlUriEQirF+/HufOnYOtrS0WLVokfpS/JkVFRfjoo4+QnJyM58+fo1WrVsjLy4O7uztOnDgBAwMDuctUVVWFo0ePih9269SpE4YMGVLr+WMyMzMRFxcn9Vu8PCOwPD09oaWlhS+++EJqTcvZ2blW5VEWF5+VkZERUlJS0L59e5iamuLs2bPo1KkTUlNTMXToULmfLwGUf3+5Lg9XvzdcqPjffwqfq92qU62OLy4uxq1btwC8emgzPDwcffr0gZmZGdq0aYOwsDA8ePBAPDjj9u3b6Ny5M2bOnInJkyfjn3/+wZw5c3D8+PFajQ7ibU1g2LBhLCoqirN4IpGIiUQihc7laoEbLsXHx7Pt27ezdevWiRc7qY3MzExmZ2fH9PX1Wbdu3Vi3bt2Yvr4+s7e3l5haoCY//PAD09TUZObm5szZ2Zl17dpVvMm7eIq+vj5LS0ur9T00ZObm5uzGjVffNh0cHNgff/zBGGMsJSWFGRgYyB2Hi/eXy/Jw9XvDlfIH1xXeaisuLq5aRzIAFhgYyBhjLDAwkHl5eVU7p2vXrkxbW5u1a9eORUZG1vq6vKoJvDlz56NHj7BixQoEBQVJbc+Xd175/fv3Y8OGDcjMfNWBZGdnh/nz59dq7eK5c+di//796NKlC7p06VKtLPXZqVZWVsbJgvKDBg0CYwwHDhyAmZkZgFeT9n388cfQ0NDA8ePH5YrTtm1bzJgxQ6lhuN27d8fmzZurTcuhzgICAjB48GCEhIRg3rx5+OOPPzBp0iQcPnwYpqamOH36tFxxuHh/uSwPV783XKm4f03hc7Xfc+KwJHWHV0mA63nlw8PDsXjxYsyaNUs8J83Zs2exfft2rFq1SmKagndRZi4ZeavI8s6Tr6urix49esDLywt9+vSBu7t7rTtggVfNba87zN+UmpoKT09PueZmAgBjY2OkpKTUutnuzc7t5ORkLFq0CGvWrJGa8I2NjWsVW1FcflbZ2dkoLi5Gly5dUFJSgs8//1zcpBQeHi73lCaKvr91VR6ufm+4UnEvVeFztVvXbzOjong1OkgkEiE7O5uzfoBvv/0WO3bskBhJNGTIEHTq1AnLli2TOwkoM5cMYwxt27ZFYGCg1IXHa+v06dP4999/IRQKsXnzZlRWVsLNzQ1eXl7w9vZG//795Yqjo6MjdZ6Y4uLiak+nvsvIkSPx999/13oYromJiUTbP2MM/fr1kziG/f+1I+p6IZk3r8fVZ/Xm77CBgYHcc/y8TdH3t67Kw9XvDWdE9fO7oUq8qgkAr2oDbdu2Rd++fdGnTx/06dNH4akQdHV1cf369WrTEWRmZsLJyalextQnJydj9+7dOHjwIGxsbDB58mSMHz9e7o7gd6msrMTFixfx/fff48CBAzKfLpVm4sSJuHz5Mnbv3o0ePXoAAC5cuICQkBC4urpi7969Ms99cxhuSUkJwsPDMXjw4FoNwz1z5oxc5QQALy8vuY9VRl1+VrXBxfsrS3JysrhD19HREa6urrU6X5nfm7pQcSdZ4XO1rd04LEnd4V0SEAqF4u3ChQuoqKhAu3btJJKCubm5XLE6d+6McePG4csvv5TYv2rVKkRFReHaNfnbE5WdS6asrAy///47IiMjcf78efj7+yM4OFjub+5vysjIkHifysvL0bt3b3h7e8u9vGRhYSECAwPx559/SswlM2TIEERGRkqdNfU1Gxsbua4hEAjUcs1jLj4rU1NTqc+TvLmS16RJkxAUFFTtmLp4f+/fv4+xY8ciISFB/NkWFhbCw8MDBw8exHvvvSdXHGV+b+pCRXaSwudqt+vBYUnqDu+SwJvKyspw7tw58R+7pKQkvHz5Eh07dsR//9U8NOzQoUMYPXo0fHx8JOapj42Nxa+//ir3PDA1zSUTGRlZq/u6ffs2goODcebMGTx69EjcwSYPKysrvHjxAt7e3vD29oaXlxe6dOmi0ANswKvlO19/M3RwcFDJeszR0dEwNDQUdwxv374dO3fuhKOjI7Zv317v38TfpOhntXnzZqxevRp+fn7ib8xJSUmIjo7GZ599htu3b+PHH3/Et99+i5CQkLq8BQDAwIEDUVhYiH379onnC0pPT0dQUBCMjY0RHR1dq3gN4fcG4EcS4O0Q0TeVl5ezf/75h82fP58ZGxvX6gGi5ORkNn78eObi4sJcXFzY+PHjJabTlQdXc8ncu3ePrVy5krVv355ZWlqyhQsXspcvX9aqLM7OzkxHR4e5u7uzsLAwdurUKYVWqlq+fLnU80pLS2s1zTYXcTp37syOHz/OGGPs6tWrTFtbm4WFhbH3339fZfPjKPtZDR8+nO3YsaPa/oiICDZ8+HDGGGPffPNNjVM3c/U56erqSv29T05OZnp6enLH4ao8XCm7lajwpi54mQTKy8vZmTNn2LJly5i3tzfT09NjdnZ2bMqUKWz//v3s7t279VoefX19dvv2bcYYY2ZmZuzq1auMMcZu3LjBLCws3nlueXk5O3jwIOvfvz/T1dVlw4YNY3/++SerrKxUuDxPnz5lf/zxBwsNDWWurq5MT0+Pubu7sy+//FLuGBoaGiw/P7/a/oKCglolWS7iGBgYiN/fpUuXiteLuHTpEjM3N5e7LMri8rMyMDCQuUbC63H5t27dYvr6+u+Mw9XnZGtryy5cuFBt/4ULF1j79u3ljsNVebhSlpGg8KYueDU6CAD69u2LCxcuwMbGBl5eXvjkk0/w888/yz19NAC5lu7T0tKSunKZNMrMJWNpaQkjIyMEBgbiu+++E0/4VVJSInFcbYZBmpiYYMiQIfD09ISHhwf++OMP/PLLL7hw4QJWr14tVwz2/0fevC01NbVWzVNcxNHW1ha/j6dPnxaP5jIzM6vVMozK4vKzMjMzw59//lltBNqff/4pfl9KSkpqnA6aq89pw4YNmD17NrZv3w43t1cdosnJyZg7dy42btwodxyuysMZJeYOUhe8SwLx8fGwtLRE3759xW3ezZo1q1WMt4cfymJoaAgfHx9s3br1nR1jvXv3RkxMDJycnDBy5EjMnTsX//zzD2JiYqoNa3zb06dP8fTpU6xcuRKrVq2q9jqr5TDIw4cPi/tIbty4ATMzM/Tq1QubNm2SaxTN6w5LgUAAOzs7ifepqqoKxcXFcg1H5CoOAPTq1QuhoaHw9PREUlISoqKiALzqAJe3w5ILXH5WixcvxvTp0xEXFyfuE7h48SJOnDghHp4ZExMj8zPj4v19u3O6pKQEPXv2hJbWqz8rlZWV0NLSwuTJk2tcJpHLz5tTNES08SkpKUF8fDyEQiHi4uKQkpICOzs78Th4Ly+vGmfLlGf4oUgkQn5+PrZv3w4jIyOcOHFC5rHKzCUj71BIeYdBtmzZUjwSyMvLq9pDOzXZt28fGGOYPHkytmzZgqZNm4pf09bWhrW1Ndzd3estDgDk5ORgxowZuHfvHubMmYPg4GAAwGeffYaqqiqJIZN1ievPKiEhAdu2bUN6ejqAV4u4zJ49W7xwzrtw8f7u27dPrnICQGBgYJ2Xpy6Upyn+DI+Og3ososO7JPC258+f4+zZs4iLi4NQKERqaipsbW1x/fp1TuLfuHED77//fr02OzQEZ86cEU/c1hDiEOka2vvb0MrDhyTQMN5pFTIwMICZmRnMzMxgamoKLS0t8dA0LnTo0AE//vgjZ/HUBVcPYNXXg1x81dDe34ZWHogaf58A72oCIpEIycnJ4uaghIQElJSUwMrKSvywWJ8+feSe64QQ0niVX49R+FydzrV/UFMVeFcTMDExQUlJCSwsLNCnTx9s3rwZ3t7eSs3lTwjwakoSb29vbNiwodbTJZAGigc1Ad4lgQ0bNqBPnz6ws7NTdVFII7Nnzx7cuXMHM2fOxPnz51VdHMIBxmh0ECGE8FZZyl8Kn6vb9UMOS1J35JtgnxBCSKPEu+YgQgiRGw/6BKgmUIPy8nIsW7YM5eXljSZOQypLQ4vTkMrCVZyGVJaGGOedmEjxTU1Qn0ANnj17hqZNm6KoqEipZQgbUpyGVJaGFqchlYWrOA2pLA0xzruUXTyk8Lm63UdwWJK6Q81BhBAiixp9o1cUJQFCCJGF+gQIIYQ0ZrzvE3hZ8O41VMvLy7FuawQWzp0GHR0dmcfptfrgnXEYY2Ci5xBoGCm8VCNXcRpSWRpanIZUFq7iNKSy1HecyooHCscHgLLEXxQ+V9d9rFLXri+UBGpIAvKqKQkQQuqf0kkg4YDC5+p6jlfq2vVFJc1BAoEAR48eVcWlCSFEfiKR4puaUCoJREREwMjICJWVleJ9xcXFaNKkCby9vSWOFQqFEAgEyMrKUuaShBBSbxirUnhTF0olgT59+qC4uBjJycniffHx8bCwsMCFCxdQVlYm3h8XF4c2bdrQbJ2EEPVBNYF3s7e3h6WlJYRCoXifUCjE0KFDYWNjIzGTolAoRJ8+/7fSTkFBAYYNGwZ9fX3Y2tri2LFjErGvX78OPz8/GBoawtzcHBMmTEBBQYH4dW9vb8yZMwcLFiyAmZkZLCwssGzZMmVuhxBCeEfpPoE+ffogLu7/lmCLi4sTr0/7ev+LFy9w4cIFiSSwfPlyjBo1ClevXsWgQYMwfvx4PHnyBABQWFiIvn37olu3bkhOTkZ0dDTy8/MxatQoiWvv27cPBgYGuHDhAtavX48VK1YgJkbxRSAIIUQCD6aN4CQJJCQkoLKyEs+fP8eVK1fg5eWF3r17i2sIiYmJKC8vl0gCkyZNwtixY9GhQwesWbMGxcXFSEpKAgBs27YN3bp1w5o1a9CxY0d069YNe/bsQVxcHDIyMsQxunTpgqVLl8LW1hYTJ06Em5sbYmNjZZa1vLwcz549k9jqdN4RQoh6o+agmnl7e6OkpAQXL15EfHw87Ozs0KJFC3h5eYn7BYRCIdq1a4c2bdqIz+vSpYv43wYGBjA2NsbDhw8BAKmpqYiLi4OhoaF469ixIwBIdCy/GQMALC0txTGkWbt2LZo2bSqxrdsaoexbQAhprHhQE1B62ogOHTrgvffeQ1xcHJ4+fSpeKLpVq1Zo3bo1zp07h7i4OPTt21fivCZNmkj8LBAIIPr/2bO4uBj+/v5Yt25dtetZWlrKFUOasLAwhIaGSuzTeK7cOGJCSCOmRt/oFcXJ3EF9+vSBUCjE06dPMX/+fPH+3r174+TJk0hKSsL06dPljufi4oJDhw7B2toaWlrcTW+ko6NT7anflxUFMo4mhPCeGn2jVxQnD4v16dMHZ8+eRUpKirgmAABeXl74/vvvUVFRIdEfUJOZM2fiyZMnGDt2LC5evIisrCycOnUKQUFBqKpSn/G3hBDS0HGWBF68eIEOHTrA3NxcvN/LywvPnz8XDyWVV6tWrZCQkICqqioMGDAATk5O+PTTT2FiYgINDZrzjhBST3jQMUxzB9HcQYQ0WsrOHfTi+BaFz9Ub/KlS164vtJ4AIYTIwoM+AUoChBAiixo16yiKkgAhhMhCNYHGr2LbV5zECWnlyUmcnf9L4CQOIYTIg/dJgBBCZKLmIEII4TEeNAc12EH31tbW2LJli6qLQQjhMx48J1AvSeD1qmKFhYX1cTlCCOEGD5IANQcRQogsPHiWVmXNQYcOHUKnTp2go6MDa2trbNq0qdoxpaWlmDx5MoyMjNCmTRv88MMP4tfu3LkDgUCAw4cPo0+fPtDX14ezszMSExPr8zYIIUStqSQJXLp0CaNGjcKYMWNw7do1LFu2DIsXL8bevXsljtu0aRPc3Nxw5coVzJgxA9OnT0d6errEMV999RXmzZuHlJQU2NnZYezYsRIL3xNCiMKoOahuhIeHo1+/fli8eDEAwM7ODjdu3MCGDRswadIk8XGDBg3CjBkzAAALFy7E5s2bERcXB3t7e/Ex8+bNw+DBgwG8WrKyU6dOuHXrlngRmjeVl5dXW0mssrIKOlqaXN8iIaQxUKM/5opSSU0gLS0Nnp6SD1d5enoiMzNTYqroN1cOEwgEsLCwqLZy2JvHvJ6pVNbqYtJWFtt49obS90MIaaR4sLJYgx0iCsi3ctibxwgEAgCQubpYWFgYioqKJLZ5vRw5LjUhpNHgQXOQSpKAg4MDEhIkp0dISEiAnZ0dNDXrrmlGR0cHxsbGEhs1BRFCZGJM8U0B27dvh7W1NXR1ddGzZ08kJSW98/gtW7bA3t4eenp6aN26NT777DOUlZXV6poqSQKff/45YmNjsXLlSmRkZGDfvn3Ytm0b5s2bp4riEEKIykVFRSE0NBRLly7F5cuX4ezsDF9fX5nN2z///DO++OILLF26FGlpadi9ezeioqLw5Zdf1uq69ZIEXjfPvF4v2MXFBb/++isOHjyIzp07Y8mSJVixYoVEpzAhhKicEs1B5eXlePbsmcT29sCUN4WHhyMkJARBQUFwdHREREQE9PX1sWfPHqnHnzt3Dp6enhg3bhysra0xYMAAjB07tsbaw9vqZXTQw4cPYWhoCENDQ/G+ESNGYMSIETLPuXPnTrV9KSkp4n9bW1vj7UXRTExMqu0jhBCFKdG2v3btWixfvlxi39KlS7Fs2bJqx1ZUVODSpUsICwsT79PQ0ICPj4/MZ588PDzw008/ISkpCT169EB2djZOnDiBCRMm1KqcdZoEysvLkZWVhW3btqFfv351eSlCCOGeEqN8wsLCEBoaKrFPR0dH6rEFBQWoqqqSWKMdAMzNzXHz5k2p54wbNw4FBQXo1asXGGOorKzEtGnTGlZz0MmTJ9GzZ08YGBjgm2++qctLEUII55iIKbxJHYgiIwkoQigUYs2aNfjuu+9w+fJlHD58GMePH8fKlStrFadOawIBAQF4/vx5XV6CEELqTj0N9WzevDk0NTWRn58vsT8/Px8WFhZSz1m8eDEmTJiAKVOmAACcnJxQUlKCqVOn4quvvoKGhnzf8Xk/gdz9g4WcxIl/8ZSTOGss+3AS58vcOE7iEELqnra2NlxdXREbG4uAgAAArwbUxMbGYtasWVLPKS0trfaH/vUQ+9r0jfI+CRBCiEz1+ORvaGgoAgMD4ebmhh49emDLli0oKSlBUFAQAGDixImwsrLC2rVrAQD+/v4IDw9Ht27d0LNnT9y6dQuLFy+Gv79/rZ63oiRACCGyiOpvtOHo0aPx6NEjLFmyBHl5eejatSuio6PFncU5OTkS3/wXLVoEgUCARYsW4cGDB2jRogX8/f2xevXqWl1XwBrZmEqBQIAjR46Iq1Q1Se/ox8l1Rzzlpjloom4HTuJQcxAhQGXFA6XOL/12hsLn6s/+Tqlr1xeqCRBCiCxqNAeQoigJEEKILI2roUQqlcwd9PjxY4wdOxZWVlbQ19eHk5MTfvnlF4ljvL29MWfOHCxYsABmZmawsLCo9qRdZmYmevfuDV1dXTg6OiImJqYe74IQQtSfSmoCZWVlcHV1xcKFC2FsbIzjx49jwoQJaN++PXr06CE+bt++fQgNDcWFCxeQmJiISZMmwdPTE/3794dIJMLw4cNhbm6OCxcuoKioCJ9++qkqbocQ0lhRc1DdsLKykpgxdPbs2Th16hR+/fVXiSTQpUsXLF26FABga2uLbdu2ITY2Fv3798fp06dx8+ZNnDp1Cq1atQIArFmzBn5+sjt6pa0sViESQVvOhyoIITxTj6ODVEUlf/2qqqqwcuVKODk5wczMDIaGhjh16hRycnIkjntz1TDg1cphr6dVTUtLQ+vWrcUJAADc3d3feV1pK4t9/ySLo7sihDQ6tLJY3diwYQO2bt2KhQsXIi4uDikpKfD19UVFRYXEcfKsLFYb0lYW+8SsvcLxCCGNnIgpvqkJlTQHJSQkYOjQofj4448BvHo8OiMjA46O8i/16ODggHv37iE3N1e8tvD58+ffeY6Ojk61CZyoKYgQwmcq+Qtoa2uLmJgYnDt3Dmlpafjkk0+qTZxUEx8fH9jZ2SEwMBCpqamIj4/HV199VUclJoTwEROJFN7UhUqSwKJFi+Di4gJfX194e3vDwsJC7id8X9PQ0MCRI0fw4sUL9OjRA1OmTKn149KEEPJO1BxUN8zMzHD06NF3HiMUCqvte/scOzs7xMfHS+xrZLNgEEJUSY06eBVFTwwTQogsavSNXlGUBAghRBY1attXFA2NIYQQHuN9TeDu06acxGmjI+AkzkVwsxxn12btlI6R8jibg5IQosaoOYgQQniMOoYJIYTHeFATqJM+AaFQCIFAAFNTU5SVlUm8dvHiRQgEAggE3DSfEEJIXaGHxZRkZGSEI0eOSOzbvXs32rRpo3Tst+cZIoQQzvHgYbE6TQKBgYHYs2eP+OcXL17g4MGDCAwMlDhO3kVmZs2ahU8//RTNmzeHr68vJk+ejA8//FDiuJcvX6Jly5bYvXt33d0YIYQ0EnWaBCZMmID4+HjxFNGHDh2CtbU1XFxcJI57vcjM8ePHcf36dUydOhUTJkxAUlKSxHH79u2DtrY2EhISEBERgSlTpiA6Ohq5ubniY/766y+UlpZi9OjRdXlrhBA+oJqAclq2bAk/Pz/s3bsXALBnzx5Mnjy52nGvF5np2rUr2rVrh9mzZ2PgwIH49ddfJY6ztbXF+vXrYW9vD3t7e3h4eMDe3h4//vij+JjIyEiMHDkShoaGdXlrhBA+oPUElDd58mTs3bsX2dnZSExMxPjx46sdI+8iM66urtXOnTJlCiIjIwEA+fn5OHnypNREA7xaWezZs2cSWwWr4uAuCSGNEtUElOfn54cXL14gODgY/v7+aNasWbVj5F1kxsDAoNq5EydOFCeYn376CTY2Nvjggw+klkXaymJRJWnc3CghpNFhIqbwpi7qPAloaWlh4sSJEAqFMr+hv7nIjLOzM9q1a4eMjAy54jdr1gwBAQGIjIzE3r17ERQUJPNYaSuLjTZwUOi+CCE8wIOaQL08LLZy5UrMnz9fai0AeNXW//vvv+PcuXMwNTVFeHg48vPz5V5pbMqUKfjwww9RVVVVbeTRm6SuLCbQlP9GCCGkkamXJKCtrY3mzZvLfH3RokXIzs6Gr68v9PX1MXXqVAQEBKCoqEiu+D4+PrC0tESnTp0kFp4nhBClqNFDX4qqkyTg7e39zsVdAgICJF5XdJGZ10pKSvD06VMEBwfXtqiEECKbGjXrKEqt5w4SiUQoKCjApk2bYGJigiFDhqi6SISQxoSSQMOWk5MDGxsbvPfee9i7dy+0tNT6dgghDQwflqtV67+a1tbWvPiQCCEqQjWBxk8T3HzIt1485CSOu0FbTuLklT9VOkYnM27K8t+Tu5zEIYRwj/dJgBBCZKKaACGE8Jc6PfmrKEoChBAiCw+SQJ1PG1FfvL298emnn6q6GISQxkSkxKYmqCZACCEy8KE5iPOaAGMMLVq0wO+//y7e17VrV1haWop/Pnv2LHR0dFBaWgoAKCwsxJQpU9CiRQsYGxujb9++SE1NFR+/bNkydO3aFT/++COsra3RtGlTjBkzBs+fPwcATJo0CWfOnMHWrVvF6xffuXOH61sjhJBGh/MkIBAI0Lt3b/E0D0+fPkVaWhpevHiBmzdvAgDOnDmD7t27Q19fHwAwcuRIPHz4ECdPnsSlS5fg4uKCfv364cmTJ+K4WVlZOHr0KP766y/89ddfOHPmDL7++msAwNatW+Hu7o6QkBDk5uYiNzcXrVu35vrWCCF8w4NZROukT8Db21ucBP79919069ZNYp9QKISXlxeAV7WCpKQk/Pbbb3Bzc4OtrS02btwIExMTidqESCTC3r170blzZ3zwwQeYMGECYmNjAQBNmzaFtrY29PX1YWFhAQsLC2hqVp8dlBaVIYTUCg/6BOokCXh5eeHGjRt49OgRzpw5A29vb3ESePnyJc6dOwdvb28AQGpqKoqLi9GsWTMYGhqKt9u3byMrK0sc09raGkZGRuKfLS0t8fBh7R7QkraozC+0qAwhRAY+LCpTJx3Dr5eJPHPmDM6cOYPVq1fDwsIC69atw8WLF/Hy5Ut4eHgAAIqLi2FpaSl1llATExPxv5s0aSLxmkAggKiW07yGhYUhNDRUYl9CB+kL3RBCiDp9o1dUnSQBgUCADz74AH/88Qf+++8/9OrVC/r6+igvL8f3338PNzc38VKRLi4uyMvLg5aWFqytrRW+pra2Nqqq3t20Q4vKEEJqQ52+0Suqzp4T8Pb2xi+//IKuXbvC0NAQGhoa6N27Nw4cOCDuDwBeLQjj7u6OgIAA/P3337hz5w7OnTuHr776CsnJyXJfz9raGhcuXMCdO3dQUFBQ61oCIYTwUZ0lAS8vL1RVVYnb/oFXieHtfQKBACdOnEDv3r0RFBQEOzs7jBkzBnfv3oW5ubnc15s3bx40NTXh6OiIFi1aICcnh8O7IYTwEg86hgWM53Mxx5qP5iTOdFFWzQfJgatZRGOfpSsdo5m2MQcloVlEiepUVjxQ6vzH/l41HyRDsz/PKHXt+kJPDBNCiCxq9I1eUZQECCFEBkZJgBBCeIySQOOXpNuk5oPkUPa8nJM4D6tKOYnDBU0BN+MGBlg4cxLn77zUmg8ihNRKo5lKmhBCuMZEim+K2L59O6ytraGrq4uePXsiKSnpnccXFhZi5syZsLS0hI6ODuzs7HDixIlaXZP3NQFCCJGlPvsEoqKiEBoaioiICPTs2RNbtmyBr68v0tPT0bJly2rHV1RUoH///mjZsiV+//13WFlZ4e7duxIzLciDkgAhhMhQn0kgPDwcISEhCAoKAgBERETg+PHj2LNnD7744otqx+/ZswdPnjzBuXPnxNPqKDLrglo0B+3du7fW2Y0QQpTGBApv0mYtLi+X3ndYUVGBS5cuwcfHR7xPQ0MDPj4+SExMlHrOsWPH4O7ujpkzZ8Lc3BydO3fGmjVrapw+521qkQQIIUQVlOkTkDZr8dq1a6Vep6CgAFVVVdVmSTA3N0deXp7Uc7Kzs/H777+jqqoKJ06cwOLFi7Fp0yasWrWqVvfY4JOAUChEUFAQioqKxKuGLVu2DMCrBWsmTpwIU1NT6Ovrw8/PD5mZmaotMCGE4NWsxUVFRRJbWFgYZ/FFIhFatmyJH374Aa6urhg9ejS++uorRERE1CpOg+8T8PDwwJYtW7BkyRKkp7+aCsHQ0BDAq2UlMzMzcezYMRgbG2PhwoUYNGgQbty4UW3qaUIIqS0mEih8rrRZi2Vp3rw5NDU1kZ+fL7E/Pz8fFhYWUs+xtLREkyZNJBbQcnBwQF5eHioqKqCtrS3XtRt8TUBbWxtNmzaFQCAQrxpmaGgo/uO/a9cufPDBB3B2dsaBAwfw4MEDHD16VGosaW10lbSyGCFEhvoaIqqtrQ1XV1fxaonAq2/6sbGxcHd3l3qOp6cnbt26JTFjckZGBiwtLeVOAIAaJAFZ0tLSoKWlhZ49e4r3NWvWDPb29khLk75amLQ2OmHRf/VVZEKImmFMoPBWW6Ghodi5cyf27duHtLQ0TJ8+HSUlJeLRQhMnTpRoTpo+fTqePHmCuXPnIiMjA8ePH8eaNWswc+bMWl23wTcHcUnaymJbO3+iotIQQhq6+hwiOnr0aDx69AhLlixBXl4eunbtiujoaHFncU5ODjQ0/u97e+vWrXHq1Cl89tln6NKlC6ysrDB37lwsXLiwVtdViyQgbdUwBwcHVFZW4sKFC+KlKh8/foz09HQ4OjpKjSOtjU6LVhYjhMigTJ+AImbNmoVZs2ZJfU3aErzu7u44f/68UtdUi+Yga2trFBcXIzY2FgUFBSgtLYWtrS2GDh2KkJAQnD17Fqmpqfj4449hZWWFoUOHqrrIhBCiFtQiCXh4eGDatGkYPXo0WrRogfXr1wMAIiMj4erqig8//BDu7u5gjOHEiRM0MogQwgnGFN/UhVo0BwHAjh07sGPHDol9pqam2L9/v4pKRAhp7Oq7OUgV1CYJEEJIfaMkQAghPKZOzTqKoiRACCEyUE2ABx4JKlVdBAlPq15wEkcDyv/yvqiq4KAkQIGghJM47i06Kh0j8dFNDkpCSOPB+yRACCGyKPLkr7qhJEAIITLU5xPDqtKgnxOwtrbGli1bVF0MQghPiZhA4U1dNIgkQCuHEUIaovqcQE5VqDmIEEJk4MPoIJXXBN61chgAlJaWYvLkyTAyMkKbNm3www8/SJx/7949jBo1CiYmJjAzM8PQoUNx586d+r0JQghRUypPAq9XDjM2NkZubi5yc3Mxb9488eubNm2Cm5sbrly5ghkzZmD69OniFcZevnwJX19fGBkZIT4+HgkJCTA0NMTAgQNRUcHN8EZCCH/R3EH14O2Vw942aNAgzJgxAwCwcOFCbN68GXFxcbC3t0dUVBREIhF27doFgeBVtS0yMhImJiYQCoUYMGCARKzy8nKUl5dL7KtkVTSdNCFEKmoOagC6dOki/vfrRPHw4UMAQGpqKm7dugUjIyMYGhrC0NAQZmZmKCsrQ1ZWVrVY0lYWu1gkfRUyQgjhw+ggldcEavL2tNACgUC8pmZxcTFcXV1x4MCBaue1aNGi2j5pK4stcgrmsLSEkMZEnUb5KKpBJAFpK4fJw8XFBVFRUWjZsiWMjY1rPJ5WFiOE1IY6te0rqkE0B0lbOUwe48ePR/PmzTF06FDEx8fj9u3bEAqFmDNnDu7fv1/HpSaEEPXXIJKArJXDaqKvr49///0Xbdq0wfDhw+Hg4IDg4GCUlZXJVTMghJB34UOfgIAxPlR4ZAu1HsNJnN+f/cdJnFa6zTiJ87+yx0rHMNDS46AkgBFHcXQEyrde0iyi/FJZ8UCp86+0UXy98m45fyh17frSIPoECCGkIeLDV2RKAoQQIoM6NesoqkH0CRBCCFEN3tcEHuMlJ3FMtY04iVMqKq/5IDmUVyl/X5oCbr4jmDUx5CTOg/InSsfo2qwdByUBUh5ncxKHNGz0nAAhhPAYNQcpQSgUQiAQoLCwsK4uQQghdYopsakLqgkQQogMfKgJUBIghBAZ+NAnoFRz0N27d+Hv7w9TU1MYGBigU6dOOHHihMQxly5dgpubG/T19eHh4SFeC+C1HTt2oH379tDW1oa9vT1+/PFHidcFAgF27NgBPz8/6OnpoV27dvj999/Fr1dUVGDWrFmwtLSErq4u2rZti7Vr1ypzW4QQwhtKJYGZM2eivLwc//77L65du4Z169bB0FByJMhXX32FTZs2ITk5GVpaWpg8ebL4tSNHjmDu3Ln4/PPPcf36dXzyyScICgpCXFycRIzFixdjxIgRSE1Nxfjx4zFmzBikpb2aAvqbb77BsWPH8OuvvyI9PR0HDhyAtbW1MrdFCCEAAJESm7pQqjkoJycHI0aMgJOTEwCgXbvqw+9Wr14NLy8vAMAXX3yBwYMHo6ysDLq6uti4cSMmTZokXjQmNDQU58+fx8aNG9GnTx9xjJEjR2LKlCkAgJUrVyImJgbffvstvvvuO+Tk5MDW1ha9evWCQCBA27ZtZZZX2qIyVawKmjSTKCFECgZqDnqnOXPmYNWqVfD09MTSpUtx9erVase8uSiMpaUlAIgXhUlLS4Onp6fE8Z6enuJv+a+5u7tX+/n1MZMmTUJKSgrs7e0xZ84c/P333zLLK21RmWtF6TKPJ4Twm4gpvqkLpZLAlClTkJ2djQkTJuDatWtwc3PDt99+K3HMm4vCvF4C8vWiMFxwcXHB7du3sXLlSrx48QKjRo3CRx99JPXYsLAwFBUVSWxOTe05KwshpHERQaDwpi6Ufk6gdevWmDZtGg4fPozPP/8cO3fulPtcBwcHJCQkSOxLSEiAo6OjxL7z589X+9nBwUH8s7GxMUaPHo2dO3ciKioKhw4dwpMn1Z8u1dHRgbGxscRGTUGEEFkYBApv6kKpPoFPP/0Ufn5+sLOzw9OnTxEXFyfxx7km8+fPx6hRo9CtWzf4+Pjgzz//xOHDh3H69GmJ43777Te4ubmhV69eOHDgAJKSkrB7924AQHh4OCwtLdGtWzdoaGjgt99+g4WFBUxMTJS5NUII4QWlkkBVVRVmzpyJ+/fvw9jYGAMHDsTmzZvlPj8gIABbt27Fxo0bMXfuXNjY2CAyMhLe3t4Sxy1fvhwHDx7EjBkzYGlpiV9++UVcWzAyMsL69euRmZkJTU1NdO/eHSdOnICGBs2NRwhRjjqN8lFUg19URiAQ4MiRIwgICKiT+IHWIziJk1KWy0kcxtED5/kvniodQ19Lp+aD5MDVQjm55crfE1eT2dEEcupB2UVl/jZXfNGpAfkHlbp2faEnhgkhRAY+1AQoCRBCiAyUBBqABt5aRQhpxNRplI+iGnwSUBf5Zcq3VwOAua4pJ3E0OFgQRoOj4bOFlSWcxHlRqfyCOyUaTWo+SA60OA1pLCgJEEKIDKLGXxGgJEAIIbKo05O/iqIkQAghMvChR5KSACGEyECjgwghhMdEgsbfHERzKxBCCI9RTYAQQmSgPoFGhlYWI4TUBh/6BHjVHEQrixFCakMkUHxTF7xKArSyGCGkNup7ZbHt27fD2toaurq66NmzJ5KSkuQ67+DBgxAIBArNtsyrJEArixFCaoMpsdVWVFQUQkNDsXTpUly+fBnOzs7w9fUVr8kuy507dzBv3jx88MEHClyVZ0mAEELqS3l5OZ49eyaxvd0n+abw8HCEhIQgKCgIjo6OiIiIgL6+Pvbs2SPznKqqKowfPx7Lly9Hu3aKzWfVqJLA3r17xYvZE0KIspTpE5DWB7l27Vqp16moqMClS5fg4+Mj3qehoQEfHx8kJibKLN+KFSvQsmVLBAcHK3yPjWp00O3bt+Hl5aXqYhBCGgllRgeFhYUhNDRUYp+OjvTV+goKClBVVQVzc3OJ/ebm5rh586bUc86ePYvdu3cjJSVFiVI2siRw8uRJbNu2TdXFIIQ0Eso8J6CjoyPzj76ynj9/jgkTJmDnzp1o3ry5UrEaVRKQtyedEELkUV9DPZs3bw5NTU3k5+dL7M/Pz4eFhUW147OysnDnzh34+/uL94lEr+otWlpaSE9PR/v27eW6dqPqEyCEEC6JlNhqQ1tbG66uroiNjf2/a4tEiI2Nhbu7e7XjO3bsiGvXriElJUW8DRkyBH369EFKSgpat24t97UbVU1AEY9ELziJY6Clx0mcwpfFnMThQhvdZpzESSu+z0kcLuhpanMS51FFESdxLAy5WUkur5ible2I6oSGhiIwMBBubm7o0aMHtmzZgpKSEgQFBQEAJk6cCCsrK6xduxa6urro3LmzxPkmJiYAUG1/TXifBAghRJb6nDZi9OjRePToEZYsWYK8vDx07doV0dHR4s7inJwcaGhw33gjYDxfyX1Qm0GcxEkvzeMkTiWr5CRORZXycToaWnFQkoZVE2ilx03t5nHFM07iVDFu/sxQTUC6yooHSp0f0fpjhc+ddu8npa5dX6gmQAghMtAEcgoSCoUQCAQwNTVFWVmZxGsXL16EQCCgh7oIIQ1efXUMq1Kdjg4yMjLCkSNHJPbt3r0bbdq0UTp2RUWF0jEIIeRd6nPuIFWp0yQQGBgoMe/FixcvcPDgQQQGBkoc9/jxY4wdOxZWVlbQ19eHk5MTfvnlF4ljvL29MWvWLHz66ado3rw5fH19MXnyZHz44YcSx718+RItW7bE7t276+7GCCGkkajTJDBhwgTEx8cjJycHAHDo0CFYW1vDxcVF4riysjK4urri+PHjuH79OqZOnYoJEyZUe/hr37590NbWRkJCAiIiIjBlyhRER0cjNzdXfMxff/2F0tJSjB49ui5vjRDCA7SegJJatmwJPz8/7N27FwCwZ88eTJ48udpxVlZWmDdvHrp27Yp27dph9uzZGDhwIH799VeJ42xtbbF+/XrY29vD3t4eHh4esLe3x48//ig+JjIyEiNHjoShoWG160ib1a+KVXF704SQRoP6BDgwefJk7N27F9nZ2UhMTMT48eOrHVNVVYWVK1fCyckJZmZmMDQ0xKlTp8Q1iNdcXV2rnTtlyhRERkYCePWI9cmTJ6UmGkD6rH7Zz7I5uEtCSGNESYADfn5+ePHiBYKDg+Hv749mzaqP096wYQO2bt2KhQsXIi4uDikpKfD19a3W+WtgYFDt3IkTJ4oTzE8//QQbGxuZiytIW1msnbFic3ATQho/PnQM1/lzAlpaWpg4cSLWr1+PkydPSj0mISEBQ4cOxccfv3owQyQSISMjA46OjjXGb9asGQICAhAZGYnExETxI9bSSJvVj1YWI4TIok5t+4qqlwnkVq5ciUePHsHX11fq67a2toiJicG5c+eQlpaGTz75pNpseu8yZcoU7Nu3D2lpadVGHhFCCJGtXp4Y1tbWfuec14sWLUJ2djZ8fX2hr6+PqVOnIiAgAEVF8k3S5ePjA0tLS3Tq1AmtWrXiqtiEEJ5Tp7Z9RdVJEvD29sa7piQKCAiQeN3MzAxHjx59Z0yhUCjztZKSEjx9+lSpJdYIIeRt6tS2ryi1njtIJBKhoKAAmzZtgomJCYYMGaLqIhFCGhERD9KAWieBnJwc2NjY4L333sPevXuhpaXWt0MIaWCoOaiBs7a2fmezEyGEKIMPf13UOglwoZuGCSdxzpdnchLH2tCckzgZRcrNow4A15/n1HyQHFrqmnASJ/+F8nPm55Q85KAkQAuO7ule8SNO4lgZKb9OwoPnjzkoCVE3vE8ChBAiCzUHEUIIj/HhYTFKAoQQIgONDiKEEB5r/CmgDqeN2LlzJ1q3bg19fX0MGzYM4eHhMDExEb+elZWFoUOHwtzcHIaGhujevTtOnz4tfv3LL79Ez549q8V1dnbGihUrxD/v2rULDg4O0NXVRceOHfHdd9/V1S0RQniGZhFVUEJCAqZNm4a5c+ciJSUF/fv3x+rVqyWOKS4uxqBBgxAbG4srV65g4MCB8Pf3F08fPX78eCQlJSErK0t8zn///YerV69i3LhxAIADBw5gyZIlWL16NdLS0rBmzRosXrwY+/btq4vbIoSQRqdOmoO+/fZb+Pn5Yd68eQAAOzs7nDt3Dn/99Zf4GGdnZzg7O4t/XrlyJY4cOYJjx45h1qxZ6NSpE5ydnfHzzz9j8eLFAF790e/Zsyc6dOgAAFi6dCk2bdqE4cOHAwBsbGxw48YNfP/991InkisvL0d5ebnEvkpWBS2aSZQQIgUf+gTqpCaQnp6OHj16SOx7++fi4mLMmzcPDg4OMDExgaGhIdLS0iQWkhk/fjx+/vlnAABjDL/88ot4UZqSkhJkZWUhODgYhoaG4m3VqlUStYc3SVtU5lzRDS5vnRDSiNB6AnVo3rx5iImJwcaNG9GhQwfo6enho48+klhIZuzYsVi4cCEuX76MFy9e4N69e+K1g4uLiwG86nt4u+9AU1P6N/uwsDCEhoZK7FvtFMLlbRFCGhF1attXVJ0kAXt7e1y8eFFi39s/JyQkYNKkSRg2bBiAV3/U79y5I3HMe++9By8vLxw4cAAvXrxA//790bJlSwCAubk5WrVqhezsbKlLVkojbVEZagoihMjCh+agOkkCs2fPRu/evREeHg5/f3/8888/OHnyJASC/3vywtbWFocPH4a/vz8EAgEWL14Mkah63h0/fjyWLl2KiooKbN68WeK15cuXY86cOWjatCkGDhyI8vJyJCcn4+nTp9W+8RNCSG01/hRQR30Cnp6eiIiIQHh4OJydnREdHY3PPvsMurq64mPCw8NhamoKDw8P+Pv7w9fXFy4uLtViffTRR3j8+DFKS0sREBAg8dqUKVOwa9cuREZGwsnJCV5eXti7dy9sbGzq4rYIIaTREbB6moYzJCQEN2/eRHx8fH1cTm5fWY/jJM6OxxdrPkgODWkCOb0m2hyUpGFNIMeVhjaBXDM9I6VjNMYJ5CorlPv/YK71GIXP3XrnoFLXri911jG8ceNG9O/fHwYGBjh58iT27dtHD3IRQtQK40GDUJ0lgaSkJKxfvx7Pnz9Hu3bt8M0332DKlCl1dTlCCOEcjQ5Swq+//lpXoQkhpF7Q6CAeuFj1RNVFkPC44hkncXS1migdg6vhs89flnISx1jbgJM4XKhi3HxH5OJzAgANKD/ncVtjbvqj7j7L5yROQ9D4U0AdTiBHCCGk4eN9TYAQQmThQ3NQg64JWFtbY8uWLaouBiGEp2gq6Xqyd+9eibUGCCGkIWBK/KcuqDmIEEJkUKdv9IpSeU1AKBQiKCgIRUVFEAgEEAgEWLZsmfj10tJSTJ48GUZGRmjTpg1++OEHifPv3buHUaNGwcTEBGZmZhg6dGi1iegIIYRIp/Ik4OHhgS1btsDY2Bi5ubnIzc0VL0YDAJs2bYKbmxuuXLmCGTNmYPr06UhPTwcAvHz5Er6+vjAyMkJ8fDwSEhJgaGiIgQMHSkxJTQghiqDmoHqgra2Npk2bQiAQwMLCotrrgwYNwowZMwAACxcuxObNmxEXFwd7e3tERUVBJBJh165d4hlKIyMjYWJiAqFQiAEDBkjEkraymIiJoCFQeS4khDRA1BzUAHTp0kX879eJ4uHDhwCA1NRU3Lp1C0ZGRuKVxczMzFBWViZ1dTFpK4vdfpZdb/dCCFEvIsYU3tSFymsCNWnSRPKJSoFAIF53oLi4GK6urjhw4EC181q0aFFtn7SVxYY7fsRhaQkhjYn6/ClXXINIAtra2qiqqqr1eS4uLoiKikLLli1hbGxc4/HSVhajpiBCiCz0sFg9sba2RnFxMWJjY1FQUIDSUvnmmhk/fjyaN2+OoUOHIj4+Hrdv34ZQKMScOXNw//79Oi41IYSovwaRBDw8PDBt2jSMHj0aLVq0wPr16+U6T19fH//++y/atGmD4cOHw8HBAcHBwSgrK5OrZkAIIe/Ch9FB9bayWEM1oPVATuIkF1bviFaEkbYeJ3FKXpYpHaOJBjethU00uJmNVIuj8nCBqxlWn5RzM2usURPlf280OLqnhjSLqLIri41uG6DwuVF3jyp17frScP6vIoSQBoYPfQKUBAghRAZ1atZRFCUBQgiRgQ8Pi/E+CTTX4KYNnqt270pR7YfKSlMlUv7X16AJN78eXN3Tk9JCpWNw1efC1efNxecEAPpaukrHuPv8IQclATqYtOIkzq3C/3ESR51s374dGzZsQF5eHpydnfHtt9+iR48eUo/duXMn9u/fj+vXrwMAXF1dsWbNGpnHy9IgRgcRQkhDxBhTeKutqKgohIaGYunSpbh8+TKcnZ3h6+srniHhbUKhEGPHjkVcXBwSExPRunVrDBgwAA8e1K4znJIAIYTIIAJTeKut8PBwhISEICgoCI6OjoiIiIC+vj727Nkj9fgDBw5gxowZ6Nq1Kzp27Ihdu3ZBJBIhNja2VtdVSRKgRWQIIepAmZXFysvL8ezZM4nt7QksX6uoqMClS5fg4+Mj3qehoQEfHx8kJibKVdbS0lK8fPkSZmZmtbpHqgkQQogMyjwsJm3CyrVr10q9TkFBAaqqqmBubi6x39zcHHl5eXKVdeHChWjVqpVEIpEH7zuGCSFEFmWeE5A2YeXbc5dx5euvv8bBgwchFAqhq1u7QQIqrQkcPXoUtra20NXVha+vL+7duyd+LSsrC0OHDoW5uTkMDQ3RvXt3nD59WuL83NxcDB48GHp6erCxscHPP/9Mi9MTQhoEHR0dGBsbS2yykkDz5s2hqamJ/HzJp63z8/OlrrPypo0bN+Lrr7/G33//LTH1vrxUlgRKS0uxevVq7N+/HwkJCSgsLMSYMWPErxcXF2PQoEGIjY3FlStXMHDgQPj7+yMnJ0d8zMSJE/G///0PQqEQhw4dwg8//CCzJ50QQmqrvkYHaWtrw9XVVaJT93Unr7u7u8zz1q9fj5UrVyI6Ohpubm4K3aPKmoNevnyJbdu2oWfPngCAffv2wcHBAUlJSejRowecnZ3h7OwsPn7lypU4cuQIjh07hlmzZuHmzZs4ffo0Ll68KL75Xbt2wdbWVuY1pa0sVsWqoMnRnCmEkMalPh8WCw0NRWBgINzc3NCjRw9s2bIFJSUlCAoKAvDqS6+VlZW4X2HdunVYsmSJuAXkdd/B6wW25KWymoCWlha6d+8u/rljx44wMTFBWloagFc1gXnz5sHBwQEmJiYwNDREWlqauCaQnp4OLS0tuLi4iGN06NABpqamMq8praPmRlFGHd0hIUTd1ecsoqNHj8bGjRuxZMkSdO3aFSkpKYiOjhZ3Fufk5CA3N1d8/I4dO1BRUYGPPvoIlpaW4m3jxo21um6D7RieN28eYmJisHHjRnTo0AF6enr46KOPlFpAXlpHTUjnj5UtKiGkkarvCeRmzZqFWbNmSX1NKBRK/Hznzh1OrqmyJFBZWYnk5GTxI87p6ekoLCyEg4MDACAhIQGTJk3CsGHDALyqGbx50/b29qisrMSVK1fg6uoKALh16xaePn0q85rSVhajpiBCiCx8mGlfZc1BTZo0wezZs3HhwgVcunQJkyZNwvvvvy9OCra2tjh8+DBSUlKQmpqKcePGidcWBl41H/n4+GDq1KlISkrClStXMHXqVOjp6UEgEKjqtgghRK2oLAno6+tj4cKFGDduHDw9PWFoaIioqCjx6+Hh4TA1NYWHhwf8/f3h6+sr0f4PAPv374e5uTl69+6NYcOGISQkBEZGRrUeJ0sIIdLU57QRqtKoVha7f/8+WrdujdOnT6Nfv35ynTOu7TBOrh1bmMZJHC2OZqcsfSn98fTaMNbR56Ak3M0iWlQu39rT79LQZhF9XvGCkzitDJopHYOrWUTfM2zOSRwuZhFVdmUx7/dq9/Ttm4T3T9d8UAPQYDuG5fHPP/+guLgYTk5OyM3NxYIFC2BtbY3evXurumiEkEZA1Hi+I8uk1kng5cuX+PLLL5GdnQ0jIyN4eHjgwIEDaNKkiaqLRghpBBp/ClDzJODr6wtfX19VF4MQ0kipU9u+otQ6CXDhsaiMkzgVVZWcxDFowk2bdfFL5e+rinHzvKSOpjYncZpoKN/PIeLonppocDP4QATl+zkAoEKk/O8fV/0cuaVPOInTxrglJ3HIu/E+CRBCiCxUEyCEEB5rRIMnZaIkQAghMvChJqAWK4vRcpSEEFWozwnkVIVqAoQQIgMfmoMafE1AKBQiKCgIRUVFEAgEEAgEWLZsGQDg6dOnmDhxIkxNTaGvrw8/Pz9kZmaqtsCEEKJGGnwS8PDwwJYtW2BsbIzc3Fzk5uZi3rx5AIBJkyYhOTkZx44dQ2JiIhhjGDRoEF6+fKniUhNCGgM+zB3U4JuDtLW10bRpUwgEAom1NjMzM3Hs2DEkJCTAw8MDAHDgwAG0bt0aR48exciRI6vFkraymIiJoCFo8LmQEKIC1BzUgKWlpUFLS0u8PCUANGvWDPb29uLVyd4mbWWx7GdZ9VVkQoia4UNNQG2TgCLCwsJQVFQksbUzbq/qYhFCGigaHdRAaGtro6pKcjpiBwcHVFZW4sKFC+LmoMePHyM9PR2Ojo5S40hbWYyaggghsvBhFlG1+AtobW2N4uJixMbGoqCgAKWlpbC1tcXQoUMREhKCs2fPIjU1FR9//DGsrKwwdOhQVReZEELUglokAQ8PD0ybNg2jR49GixYtsH79egBAZGQkXF1d8eGHH8Ld3R2MMZw4cYKmkiaEcIKagxqQHTt2YMeOHRL7TE1NsX//fhWViBDS2PGhOUhtkgAhhNQ3dfpGryhKAoQQIgPVBAghhMeoJsADp+6dVHURCCFEZXifBAghRBZqDiKEEB6j5iBCCOExxkSqLkKdoyRACCEyqNNEcIqiJEAIITLQVNKEEEIaNaoJEEKIDNQcRAghPMaH5iBKAoQQIgM9J0AIITxGzwkQQgiP8aE5iEYHEUIIj1FNgBBCZKDRQYQQwmN8aA6iJEAIITLQ6CBCCOExqgkQQgiP8aFPgEYHEUIIj1FNgBBCZKDmIEII4THqGCaEEB6jaSMIIYTHqCZACCE8xoc+ARodRAghPEY1AUIIkYEPfQJUEyCEEBkYYwpviti+fTusra2hq6uLnj17Iikp6Z3H//bbb+jYsSN0dXXh5OSEEydO1PqalAQIIUSG+kwCUVFRCA0NxdKlS3H58mU4OzvD19cXDx8+lHr8uXPnMHbsWAQHB+PKlSsICAhAQEAArl+/XqvrChgfej4IIUQBWtpWCp9bWfGgVsf37NkT3bt3x7Zt2wAAIpEIrVu3xuzZs/HFF19UO3706NEoKSnBX3/9Jd73/vvvo2vXroiIiJD7ulQTIISQOlBeXo5nz55JbOXl5VKPraiowKVLl+Dj4yPep6GhAR8fHyQmJko9JzExUeJ4APD19ZV5vCyUBAghRIbKigcKb2vXrkXTpk0ltrVr10q9TkFBAaqqqmBubi6x39zcHHl5eVLPycvLq9XxstDoIEIIqQNhYWEIDQ2V2Kejo6Oi0shGSYAQQuqAjo6O3H/0mzdvDk1NTeTn50vsz8/Ph4WFhdRzLCwsanW8LNQcRAghKqatrQ1XV1fExsaK94lEIsTGxsLd3V3qOe7u7hLHA0BMTIzM42WhmgAhhDQAoaGhCAwMhJubG3r06IEtW7agpKQEQUFBAICJEyfCyspK3K8wd+5ceHl5YdOmTRg8eDAOHjyI5ORk/PDDD7W6LiUBQghpAEaPHo1Hjx5hyZIlyMvLQ9euXREdHS3u/M3JyYGGxv813nh4eODnn3/GokWL8OWXX8LW1hZHjx5F586da3Vdek6AEEJ4jPoECCGExygJEEIIj1ESIIQQHqMkQAghPEZJgBBCeIySACGE8BglAUII4TFKAoQQwmOUBAghhMcoCRBCCI9REiCEEB77f8qVDxHJ5cveAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cee8d393-1676-45e2-8aa7-228343d3b13b",
      "metadata": {
        "id": "cee8d393-1676-45e2-8aa7-228343d3b13b"
      },
      "source": [
        "#### Get Attention Weights with Direct Access String"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "128be2dd-f089-4291-bfc5-7002d031b1e9",
      "metadata": {
        "id": "128be2dd-f089-4291-bfc5-7002d031b1e9",
        "outputId": "aed94503-5208-4110-f6ea-e6c888d87531"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "# gpt2 helper loading model from HuggingFace\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    # based on the module printed above, you can access via string, input means the input to the module\n",
        "    \"component\": \"h[10].attn.attn_dropout.input\",\n",
        "    # you can also initialize the intervention outside\n",
        "    \"intervention\": pv.CollectIntervention()}, model=gpt2)\n",
        "\n",
        "base = \"When John and Mary went to the shops, Mary gave the bag to\"\n",
        "collected_attn_w = pv_gpt2(\n",
        "    base = tokenizer(base, return_tensors=\"pt\"\n",
        "    ), unit_locations={\"base\": [h for h in range(12)]}\n",
        ")[0][-1][0]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "22643b2d",
      "metadata": {
        "id": "22643b2d"
      },
      "source": [
        "#### Get Attention Weights with a Function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "678dc46f",
      "metadata": {
        "id": "678dc46f",
        "outputId": "05cdb59e-ad29-4f0a-890d-31daa63ace50"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import copy\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "cached_w = {}\n",
        "def pv_patcher(b, s): cached_w[\"attn_w\"] = copy.deepcopy(b.data)\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"component\": \"h[10].attn.attn_dropout.input\",\n",
        "    \"intervention\": pv_patcher}, model=gpt2)\n",
        "\n",
        "base = \"When John and Mary went to the shops, Mary gave the bag to\"\n",
        "_ = pv_gpt2(tokenizer(base, return_tensors=\"pt\"))\n",
        "torch.allclose(collected_attn_w, cached_w[\"attn_w\"].unsqueeze(dim=0))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "12c5addb-4bd7-4129-b350-0677774f5790",
      "metadata": {
        "id": "12c5addb-4bd7-4129-b350-0677774f5790"
      },
      "source": [
        "### Set Activation to Zeros"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "id": "a82664f9",
      "metadata": {
        "id": "a82664f9",
        "outputId": "79f6a58f-b2ac-4a9b-8e97-0431532a0737",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "# define the component to zero-out\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"layer\": 0, \"component\": \"mlp_output\",\n",
        "    \"source_representation\": torch.zeros(gpt2.config.n_embd)\n",
        "}, model=gpt2)\n",
        "# run the intervened forward pass\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"),\n",
        "    # we define the intervening token dynamically\n",
        "    unit_locations={\"base\": 3},\n",
        "    output_original_output=True # False then the first element in the tuple is None\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9c11cb9",
      "metadata": {
        "id": "b9c11cb9"
      },
      "source": [
        "#### Set Activation to Zeros with a Lambda Expression"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7627dc32",
      "metadata": {
        "id": "7627dc32",
        "outputId": "9b398c84-90ec-489b-8d91-ee273e1b5396"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "# indices are specified in the intervention\n",
        "mask = torch.ones(1, 5, 768)\n",
        "mask[:,3,:] = 0.\n",
        "# define the component to zero-out\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"component\": \"h[0].mlp.output\", \"intervention\": lambda b, s: b*mask\n",
        "}, model=gpt2)\n",
        "# run the intervened forward pass\n",
        "intervened_outputs_fn = pv_gpt2(\n",
        "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        ")\n",
        "torch.allclose(\n",
        "    intervened_outputs[1].last_hidden_state,\n",
        "    intervened_outputs_fn[1].last_hidden_state\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "72363777",
      "metadata": {
        "id": "72363777"
      },
      "source": [
        "#### Set Activation to Zeros with a Lambda Expression and Subspace notation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d86c06f0",
      "metadata": {
        "id": "d86c06f0",
        "outputId": "9fc03970-a471-45bb-e3e3-fe8078ce6ce0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "# indices are specified in the intervention\n",
        "\n",
        "def pv_patcher(b, s, sp):\n",
        "    mask = torch.ones(1, 5, 768)\n",
        "    mask[:,sp[0][0],:] = 0.\n",
        "    return b*mask\n",
        "\n",
        "# define the component to zero-out\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"component\": \"h[0].mlp.output\", \"intervention\": pv_patcher\n",
        "}, model=gpt2)\n",
        "# run the intervened forward pass\n",
        "intervened_outputs_fn = pv_gpt2(\n",
        "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"),\n",
        "    subspaces=3,\n",
        ")\n",
        "torch.allclose(\n",
        "    intervened_outputs[1].last_hidden_state,\n",
        "    intervened_outputs_fn[1].last_hidden_state\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "39071858",
      "metadata": {
        "id": "39071858"
      },
      "source": [
        "### Set Activations to Zeros with Subspaces\n",
        "The notion of subspace means the actual dimensions you are intervening. If we have a representation in a size of 512, the first 128 activation values are its subspace activations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b7896c3b",
      "metadata": {
        "id": "b7896c3b",
        "outputId": "3679d36c-f679-4910-a37b-bf0ce08bf82a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "Directory './tmp/' already exists.\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "# built-in helper to get a HuggingFace model\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "# create with dict-based config\n",
        "pv_config = pv.IntervenableConfig({\n",
        "  \"layer\": 0, \"component\": \"mlp_output\"})\n",
        "#initialize model\n",
        "pv_gpt2 = pv.IntervenableModel(pv_config, model=gpt2)\n",
        "# run an intervened forward pass\n",
        "intervened_outputs = pv_gpt2(\n",
        "  # the intervening base input\n",
        "  base=tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"),\n",
        "  # the location to intervene at (3rd token)\n",
        "  unit_locations={\"base\": 3},\n",
        "  # the individual dimensions targetted\n",
        "  subspaces=[10,11,12],\n",
        "  source_representations=torch.zeros(gpt2.config.n_embd)\n",
        ")\n",
        "# sharing\n",
        "pv_gpt2.save(\"./tmp/\")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1410904d",
      "metadata": {
        "id": "1410904d"
      },
      "source": [
        "### Interchange Interventions\n",
        "Instead of a static vector, we can intervene the model with activations sampled from a different forward run. We call this interchange intervention, where intervention happens between two examples and we are interchanging activations between them."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9691c7d8",
      "metadata": {
        "id": "9691c7d8",
        "outputId": "4435c752-f637-49fe-b62a-622d37c1b5fb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "# built-in helper to get a HuggingFace model\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "# create with dict-based config\n",
        "pv_config = pv.IntervenableConfig({\n",
        "  \"layer\": 0,\n",
        "  \"component\": \"mlp_output\"},\n",
        "  intervention_types=pv.VanillaIntervention\n",
        ")\n",
        "#initialize model\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "  pv_config, model=gpt2)\n",
        "# run an interchange intervention\n",
        "intervened_outputs = pv_gpt2(\n",
        "  # the base input\n",
        "  base=tokenizer(\n",
        "    \"The capital of Spain is\",\n",
        "    return_tensors = \"pt\"),\n",
        "  # the source input\n",
        "  sources=tokenizer(\n",
        "    \"The capital of Italy is\",\n",
        "    return_tensors = \"pt\"),\n",
        "  # the location to intervene at (3rd token)\n",
        "  unit_locations={\"sources->base\": 3},\n",
        "  # the individual dimensions targeted\n",
        "  subspaces=[10,11,12]\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c890fda4",
      "metadata": {
        "id": "c890fda4"
      },
      "source": [
        "### Intervention Configuration\n",
        "You can also initialize the config without the lazy dictionary passing by enabling more options, e.g., the mode of these interventions are executed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "4faa3e41",
      "metadata": {
        "id": "4faa3e41",
        "outputId": "9d4dd164-c6f3-4720-9151-5e23eba5373e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "IntervenableConfig\n",
            "{\n",
            "    \"model_type\": \"None\",\n",
            "    \"representations\": [\n",
            "        {\n",
            "            \"layer\": 0,\n",
            "            \"component\": \"mlp_output\",\n",
            "            \"unit\": \"pos\",\n",
            "            \"max_number_of_units\": 1,\n",
            "            \"low_rank_dimension\": null,\n",
            "            \"intervention_type\": null,\n",
            "            \"intervention\": null,\n",
            "            \"subspace_partition\": null,\n",
            "            \"group_key\": null,\n",
            "            \"intervention_link_key\": null,\n",
            "            \"moe_key\": null,\n",
            "            \"source_representation\": \"PLACEHOLDER\",\n",
            "            \"hidden_source_representation\": null\n",
            "        },\n",
            "        {\n",
            "            \"layer\": 1,\n",
            "            \"component\": \"mlp_output\",\n",
            "            \"unit\": \"pos\",\n",
            "            \"max_number_of_units\": 1,\n",
            "            \"low_rank_dimension\": null,\n",
            "            \"intervention_type\": null,\n",
            "            \"intervention\": null,\n",
            "            \"subspace_partition\": null,\n",
            "            \"group_key\": null,\n",
            "            \"intervention_link_key\": null,\n",
            "            \"moe_key\": null,\n",
            "            \"source_representation\": \"PLACEHOLDER\",\n",
            "            \"hidden_source_representation\": null\n",
            "        },\n",
            "        {\n",
            "            \"layer\": 2,\n",
            "            \"component\": \"mlp_output\",\n",
            "            \"unit\": \"pos\",\n",
            "            \"max_number_of_units\": 1,\n",
            "            \"low_rank_dimension\": null,\n",
            "            \"intervention_type\": null,\n",
            "            \"intervention\": null,\n",
            "            \"subspace_partition\": null,\n",
            "            \"group_key\": null,\n",
            "            \"intervention_link_key\": null,\n",
            "            \"moe_key\": null,\n",
            "            \"source_representation\": \"PLACEHOLDER\",\n",
            "            \"hidden_source_representation\": null\n",
            "        },\n",
            "        {\n",
            "            \"layer\": 3,\n",
            "            \"component\": \"mlp_output\",\n",
            "            \"unit\": \"pos\",\n",
            "            \"max_number_of_units\": 1,\n",
            "            \"low_rank_dimension\": null,\n",
            "            \"intervention_type\": null,\n",
            "            \"intervention\": null,\n",
            "            \"subspace_partition\": null,\n",
            "            \"group_key\": null,\n",
            "            \"intervention_link_key\": null,\n",
            "            \"moe_key\": null,\n",
            "            \"source_representation\": \"PLACEHOLDER\",\n",
            "            \"hidden_source_representation\": null\n",
            "        }\n",
            "    ],\n",
            "    \"intervention_types\": \"<class 'pyvene.models.interventions.VanillaIntervention'>\",\n",
            "    \"mode\": \"parallel\",\n",
            "    \"sorted_keys\": \"None\",\n",
            "    \"intervention_dimensions\": \"None\"\n",
            "}\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "# standalone configuration object\n",
        "config = pv.IntervenableConfig([\n",
        "    {\n",
        "        \"layer\": _,\n",
        "        \"component\": \"mlp_output\",\n",
        "        \"source_representation\": torch.zeros(\n",
        "            gpt2.config.n_embd)\n",
        "    } for _ in range(4)],\n",
        "    mode=\"parallel\"\n",
        ")\n",
        "# this object is serializable\n",
        "print(config)\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\"),\n",
        "    unit_locations={\"base\": 3}\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9c5b2270",
      "metadata": {
        "id": "9c5b2270"
      },
      "source": [
        "### Addition Intervention\n",
        "Activation swap is one kind of interventions we can perform. Here is another simple one: `pv.AdditionIntervention`, which adds the sampled representation into the **Base** run."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a40f5989",
      "metadata": {
        "id": "a40f5989",
        "outputId": "81a6ac30-65b8-468c-be81-f2784f286a23"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig({\n",
        "    \"layer\": 0,\n",
        "    \"component\": \"mlp_input\"},\n",
        "    pv.AdditionIntervention\n",
        ")\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base = tokenizer(\n",
        "        \"The Space Needle is in downtown\",\n",
        "        return_tensors=\"pt\"\n",
        "    ),\n",
        "    unit_locations={\"base\": [[[0, 1, 2, 3]]]},\n",
        "    source_representations = torch.rand(gpt2.config.n_embd)\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "099ddf77",
      "metadata": {
        "id": "099ddf77"
      },
      "source": [
        "### Trainable Intervention\n",
        "Interventions can contain trainable parameters, and hook-up with the model to receive gradients end-to-end. They are often useful in searching for an particular interpretation of the representation.\n",
        "\n",
        "The following example does a single step gradient calculation to push the model to generate `Rome` after the intervention. If we can train such intervention at scale with low loss, it means you have a causal grab onto your model. In terms of interpretability, that means, somehow you find a representation (not the original one since its trained) that maps onto the `capital` output."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7f058ecd",
      "metadata": {
        "id": "7f058ecd",
        "outputId": "1312cc1a-3db1-4aad-be3b-a21fef269e7d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "das_config = pv.IntervenableConfig({\n",
        "    \"layer\": 8,\n",
        "    \"component\": \"block_output\",\n",
        "    \"low_rank_dimension\": 1},\n",
        "    # this is a trainable low-rank rotation\n",
        "    pv.LowRankRotatedSpaceIntervention\n",
        ")\n",
        "\n",
        "das_gpt2 = pv.IntervenableModel(das_config, model=gpt2)\n",
        "\n",
        "last_hidden_state = das_gpt2(\n",
        "    base = tokenizer(\n",
        "        \"The capital of Spain is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ),\n",
        "    sources = tokenizer(\n",
        "        \"The capital of Italy is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ),\n",
        "    unit_locations={\"sources->base\": 3}\n",
        ")[-1].last_hidden_state[:,-1]\n",
        "\n",
        "# golden counterfacutual label as Rome\n",
        "label = tokenizer.encode(\n",
        "    \" Rome\", return_tensors=\"pt\")\n",
        "logits = torch.matmul(\n",
        "    last_hidden_state, gpt2.wte.weight.t())\n",
        "\n",
        "m = torch.nn.CrossEntropyLoss()\n",
        "loss = m(logits, label.view(-1))\n",
        "loss.backward()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a8fd2b8e",
      "metadata": {
        "id": "a8fd2b8e"
      },
      "source": [
        "### Activation Collection with Intervention\n",
        "You can also collect activations with our provided `pv.CollectIntervention` intervention. More importantly, this can be used interchangably with other interventions. You can collect something from an intervened model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6e6bd585",
      "metadata": {
        "id": "6e6bd585",
        "outputId": "218dec1b-9e34-48e5-8379-91f1028c4eda"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig({\n",
        "    \"layer\": 10,\n",
        "    \"component\": \"block_output\",\n",
        "    \"intervention_type\": pv.CollectIntervention}\n",
        ")\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "    config, model=gpt2)\n",
        "\n",
        "collected_activations = pv_gpt2(\n",
        "    base = tokenizer(\n",
        "        \"The capital of Spain is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ), unit_locations={\"sources->base\": 3}\n",
        ")[0][-1]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f7b0d0c6",
      "metadata": {
        "id": "f7b0d0c6"
      },
      "source": [
        "### Activation Collection at Downstream of a Intervened Model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "adcfcb05",
      "metadata": {
        "id": "adcfcb05",
        "outputId": "fe633bf8-5b1f-440c-a06a-cacccae1a4c5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig({\n",
        "    \"layer\": 8,\n",
        "    \"component\": \"block_output\",\n",
        "    \"intervention_type\": pv.VanillaIntervention}\n",
        ")\n",
        "\n",
        "config.add_intervention({\n",
        "    \"layer\": 10,\n",
        "    \"component\": \"block_output\",\n",
        "    \"intervention_type\": pv.CollectIntervention})\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "    config, model=gpt2)\n",
        "\n",
        "collected_activations = pv_gpt2(\n",
        "    base = tokenizer(\n",
        "        \"The capital of Spain is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ),\n",
        "    sources = [tokenizer(\n",
        "        \"The capital of Italy is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ), None], unit_locations={\"sources->base\": 3}\n",
        ")[0][-1]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a9e6e4d9",
      "metadata": {
        "id": "a9e6e4d9"
      },
      "source": [
        "### Intervene on a Single Neuron\n",
        "We want to provide a good user interface so that interventions can be done easily by people with less pytorch or programming experience. Meanwhile, we also want to be flexible and provide the depth of control required for highly specific tasks. Here is an example where we intervene on a specific neuron at a specific head of a layer in a model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d25b6401",
      "metadata": {
        "id": "d25b6401",
        "outputId": "f6368690-fb05-44d7-ddd9-54fbf5ecc35c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig({\n",
        "    \"layer\": 8,\n",
        "    \"component\": \"head_attention_value_output\",\n",
        "    \"unit\": \"h.pos\",\n",
        "    \"intervention_type\": pv.CollectIntervention}\n",
        ")\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "    config, model=gpt2)\n",
        "\n",
        "collected_activations = pv_gpt2(\n",
        "    base = tokenizer(\n",
        "        \"The capital of Spain is\",\n",
        "        return_tensors=\"pt\"\n",
        "    ),\n",
        "    unit_locations={\n",
        "        # GET_LOC is a helper.\n",
        "        # (3,3) means head 3 position 3\n",
        "        \"base\": pv.GET_LOC((3,3))\n",
        "    },\n",
        "    # the notion of subspace is used to target neuron 0.\n",
        "    subspaces=[0]\n",
        ")[0][-1]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5692bc15",
      "metadata": {
        "id": "5692bc15"
      },
      "source": [
        "### Add New Intervention Type"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1597221a",
      "metadata": {
        "id": "1597221a",
        "outputId": "4a82b129-5dfb-4eda-afa9-4bf42cba330d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "class MultiplierIntervention(\n",
        "  pv.ConstantSourceIntervention):\n",
        "    def __init__(self, **kwargs):\n",
        "        super().__init__()\n",
        "    def forward(\n",
        "    self, base, source=None, subspaces=None):\n",
        "        return base * 99.0\n",
        "# run with new intervention type\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "  \"intervention_type\": MultiplierIntervention},\n",
        "  model=gpt2)\n",
        "intervened_outputs = pv_gpt2(\n",
        "  base = tokenizer(\"The capital of Spain is\",\n",
        "    return_tensors=\"pt\"),\n",
        "  unit_locations={\"base\": 3})"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "079050f6",
      "metadata": {
        "id": "079050f6"
      },
      "source": [
        "### Recurrent NNs (Intervene a Specific Timestep)\n",
        "Existing intervention libraries focus on Transformer models. They often lack of supports for GRUs, LSTMs or any state-space model. The fundemental problem is in the hook mechanism provided by PyTorch. Hook is attached to a module before runtime. Models like GRUs will lead to undesired callback from the hook as there is no notion of state or time of the hook.\n",
        "\n",
        "We make our hook stateful, so you can intervene on recurrent NNs like GRUs. This notion of time will become useful when intervening on Transformers yet want to unroll the causal effect during generation as well."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7a53347a",
      "metadata": {
        "id": "7a53347a",
        "outputId": "85be2b45-cce5-4fcf-fb75-543f945f03f7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, _, gru = pv.create_gru_classifier(\n",
        "    pv.GRUConfig(h_dim=32))\n",
        "\n",
        "pv_gru = pv.IntervenableModel({\n",
        "    \"component\": \"cell_output\",\n",
        "    \"unit\": \"t\",\n",
        "    \"intervention_type\": pv.ZeroIntervention},\n",
        "    model=gru)\n",
        "\n",
        "rand_t = torch.rand(1,10, gru.config.h_dim)\n",
        "\n",
        "intervened_outputs = pv_gru(\n",
        "  base = {\"inputs_embeds\": rand_t},\n",
        "  unit_locations={\"base\": 3})"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "031dd5de",
      "metadata": {
        "id": "031dd5de"
      },
      "source": [
        "### Recurrent NNs (Intervene cross Time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b48166c0",
      "metadata": {
        "id": "b48166c0",
        "outputId": "68754cbb-06fd-47d8-e5ca-ed5b6861223f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "# built-in helper to get a GRU\n",
        "_, _, gru = pv.create_gru_classifier(\n",
        "    pv.GRUConfig(h_dim=32))\n",
        "# wrap it with config\n",
        "pv_gru = pv.IntervenableModel({\n",
        "    \"component\": \"cell_output\",\n",
        "    # intervening on time\n",
        "    \"unit\": \"t\",\n",
        "    \"intervention_type\": pv.ZeroIntervention},\n",
        "    model=gru)\n",
        "# run an intervened forward pass\n",
        "rand_b = torch.rand(1,10, gru.config.h_dim)\n",
        "rand_s = torch.rand(1,10, gru.config.h_dim)\n",
        "intervened_outputs = pv_gru(\n",
        "  base = {\"inputs_embeds\": rand_b},\n",
        "  sources = [{\"inputs_embeds\": rand_s}],\n",
        "  # intervening time step\n",
        "  unit_locations={\"sources->base\": (6, 3)})"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "121366c1",
      "metadata": {
        "id": "121366c1"
      },
      "source": [
        "### LMs Generation\n",
        "You can also intervene the generation call of LMs. Here is a simple example where we try to add a vector into the MLP output when the model decodes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f718e2d6",
      "metadata": {
        "id": "f718e2d6",
        "outputId": "11b27fea-f851-456f-a68c-1e96c9a89d25"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "Setting `pad_token_id` to `eos_token_id`:50256 for open-end generation.\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "Once upon a time there was a little girl named Lucy. She was three years old and loved to explore. One day, Lucy was walking in the park when she saw a big, red balloon. She was so excited and wanted to play with it.\n",
            "\n",
            "But then, a big, mean man came and said, \"That balloon is mine! You can't have it!\" Lucy was very sad and started to cry.\n",
            "\n",
            "The man said, \"I'm sorry, but I need the balloon for my work. You can have it if you want.\"\n",
            "\n",
            "Lucy was so happy and said, \"Yes please!\" She took the balloon and ran away.\n",
            "\n",
            "But then, the man said, \"Wait! I have an idea. Let's make a deal. If you can guess what I'm going to give you, then you can have the balloon.\"\n",
            "\n",
            "Lucy thought for a moment and then said, \"I guess I'll have to get the balloon.\"\n",
            "\n",
            "The man smiled and said, \"That's a good guess! Here you go.\"\n",
            "\n",
            "Lucy was so happy and thanked the man. She hugged the balloon and ran off to show her mom.\n",
            "\n",
            "The end.\n",
            "\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "# built-in helper to get tinystore\n",
        "_, tokenizer, tinystory = pv.create_gpt_neo()\n",
        "emb_happy = tinystory.transformer.wte(\n",
        "    torch.tensor(14628))\n",
        "\n",
        "pv_tinystory = pv.IntervenableModel([{\n",
        "    \"layer\": l,\n",
        "    \"component\": \"mlp_output\",\n",
        "    \"intervention_type\": pv.AdditionIntervention\n",
        "    } for l in range(tinystory.config.num_layers)],\n",
        "    model=tinystory\n",
        ")\n",
        "# prompt and generate\n",
        "prompt = tokenizer(\n",
        "    \"Once upon a time there was\", return_tensors=\"pt\")\n",
        "unintervened_story, intervened_story = pv_tinystory.generate(\n",
        "    prompt, source_representations=emb_happy*0.3, max_length=256\n",
        ")\n",
        "\n",
        "print(tokenizer.decode(\n",
        "    intervened_story[0],\n",
        "    skip_special_tokens=True\n",
        "))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e628990d",
      "metadata": {
        "id": "e628990d"
      },
      "source": [
        "intervene on generation with source example passed in. The result will be slightly different since we no longer have a static vector to be added in; it is layerwise addition."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "087541f1",
      "metadata": {
        "id": "087541f1",
        "outputId": "41911169-5aa8-4e1f-c5f4-087bcca821c3"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "The attention mask and the pad token id were not set. As a consequence, you may observe unexpected behavior. Please pass your input's `attention_mask` to obtain reliable results.\n",
            "Setting `pad_token_id` to `eos_token_id`:50256 for open-end generation.\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "The attention mask and the pad token id were not set. As a consequence, you may observe unexpected behavior. Please pass your input's `attention_mask` to obtain reliable results.\n",
            "Setting `pad_token_id` to `eos_token_id`:50256 for open-end generation.\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Once upon a time there was a little girl named Lucy. She was very excited because she was going to the park. She wanted to go to the park and play.\n",
            "\n",
            "When she got to the park, she saw a big slide. She was so excited! She ran to the slide and started to climb up. She was so happy.\n",
            "\n",
            "But then she saw something else. It was a big, scary dog. It was a big, mean dog. He was barking and growling at her. Lucy was scared. She didn't know what to do.\n",
            "\n",
            "Suddenly, she heard a voice. It was her mommy. She said, \"Don't worry, Lucy. I will help you. I will protect you.\"\n",
            "\n",
            "Lucy was so happy. She hugged her mommy and they went to the park. They played together and had lots of fun. Lucy was so happy. She was no longer scared.\n",
            "\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "# built-in helper to get tinystore\n",
        "_, tokenizer, tinystory = pv.create_gpt_neo()\n",
        "\n",
        "def pv_patcher(b, s): return b + s*0.1\n",
        "\n",
        "pv_tinystory = pv.IntervenableModel([{\n",
        "    \"layer\": l,\n",
        "    \"component\": \"mlp_output\",\n",
        "    \"intervention\": pv_patcher\n",
        "    } for l in range(tinystory.config.num_layers)],\n",
        "    model=tinystory\n",
        ")\n",
        "# prompt and generate\n",
        "prompt = tokenizer(\n",
        "    \"Once upon a time there was\", return_tensors=\"pt\")\n",
        "happy_prompt = tokenizer(\n",
        "    \" Happy\", return_tensors=\"pt\")\n",
        "_, intervened_story = pv_tinystory.generate(\n",
        "    prompt, happy_prompt,\n",
        "    unit_locations = {\"sources->base\": 0},\n",
        "    max_length=256\n",
        ")\n",
        "\n",
        "print(tokenizer.decode(\n",
        "    intervened_story[0],\n",
        "    skip_special_tokens=True\n",
        "))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "26d25dc6",
      "metadata": {
        "id": "26d25dc6"
      },
      "source": [
        "### Debiasing with Backpack LMs\n",
        "\n",
        "Models like [Backpack LMs](https://arxiv.org/pdf/2305.16765.pdf) are built with highly interpretable model components. In its original paper, one motivating experiment is using the sense vectors to debias. Here, we try to reproduce one of the experiments in Fig. 3 (pg. 8)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "841e5a5b",
      "metadata": {
        "id": "841e5a5b",
        "outputId": "b95118f7-cf7c-4e4a-d366-16e5a7ca072f"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "The argument `trust_remote_code` is to be used with Auto classes. It has no effect here and is ignored.\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 400x200 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 200,
              "width": 400
            }
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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ERERERGQ2LECIiIiIiMhsWIAQEREREZHZsAAhIiIiIiKzYQFCRERERERmwwKEiIiIiIjMhgUIERERERGZDQsQIiIiIiIyGxYgRERERERkNixAiIiIiIjIbFiAEBERERGR2bAAISIiIiIis2EBQkREREREZuOgdABkmtTUVKVDqBAXFxfY2dlBr9cjNzdX6XBqLOapfMyRPMyTPMyTPMyTPMyTPMyTPJaYp8cee8zoeRYgZFYqlQr29vbQ6XQW84dICcxT+ZgjeZgneZgneZgneZgneZgneawxTxyCRUREREREZsMChIiIiIiIzIYFCBERERERmQ0LECIiIiIiMhsWIEREREREZDYsQIiIiIiIyGxYgBARERERkdlwHxAb88YbbygdQo2wdOlSpUMgIiIisknsASEiIiIiIrNhD4iFEwQBdnasIyvK3t5e6RBks6RYlcIcycM8ycM8ycM8ycM8ycM8yWMteWIBYuFUKhXUarXSYVgcT0/PMs+NHj3ajJHUbJs2bVI6hHLZ29sb/f+TCjFP8jBP8jBP8jBP8jBP8lhTnliAWLicnBxotVqlw7A4Dx48UDoEi1CT81SrVi3Y29tDp9MhIyND6XBqLOZJHuZJHuZJHuZJHuZJHkvMU3mFEgsQCyeKInQ6ndJhWBzmTB5LyZOlxKk05kke5kke5kke5kke5kkea8kTJw8QEREREZHZsAAhIiIiIiKzYQFCRERERERmwwKEiIiIiIjMhgUIERERERGZDQsQIiIiIiIyGxYgRERERERkNiYXIPv27auKOIiIiIiIyAaYXID07dsXjRs3xqJFi5CcnFwVMRERERERkZWqkiFYN2/exOzZs9GgQQM8//zzOHDgQFXcloiIiIiIrIzJBciECRPg4uICURSRn5+Pbdu2oXfv3ggODsZ//vMfpKamVkWcRERERERkBRxMvcEPP/yAxYsXY926dVi1ahXi4uIAANevX8esWbPw7rvvYtiwYXjllVcQFhZm6uPKlJ6ejm3btiE6Ohr379+Hs7MzAgMD0b9/f4SEhFT4fjqdDnFxcbh27RquXbuG69evIykpCQAwatQojB492uj1ixcvxsGDB4228ff3x/LlyyscGxERERGRpTK5AAEADw8PvP7663j99ddx8uRJfPvtt/jpp5+Qk5ODvLw8bNmyBVu2bEFQUBAmT56MCRMmoE6dOlXxaABAQkIC5syZg/T0dACASqWCRqNBbGwsYmNjMWjQIEyaNKlC90xNTcV7771ncmxOTk5Qq9WlnqtVq5bJ9yciIiIisiRVUoAU1alTJ3Tq1AlLliwp0Sty9epVzJgxA7Nnz8aIESPwyiuv4JlnnjHpefn5+Zg/fz7S09PRsGFDvPnmmwgICIBWq0VkZCQ2btyI3bt3IyAgAD179qzQvVUqFRo1aoTGjRsjMDAQP/74IxITEyt0j9DQUEybNq1C1xARERERWatq2wfE0Cty4cIFHD9+HOPGjZPmimi1WmzatAlhYWFo0aIFli5diocPH1bqOXv37kVSUhKcnZ0xd+5cBAQEAACcnZ0RHh6Ofv36AQA2bNiAgoIC2ff19vbG5s2bsXDhQkRERCAsLAwuLi6VipGIiIiIiAqZZSPCTp06Ye3atbh79y5ee+016bgoirhy5QqmT58OPz8//Otf/8I///xToXsfPnwYANC1a1d4e3uXOD98+HAIgoC0tDRcvHhR9n3t7OwgCEKFYiEiIiIiIuPMUoAUFBRgy5YtGDZsGL766isIggBRFAEUFiGiKCI7OxsrVqxAkyZNsGrVKln3zcnJwdWrVwEA7dq1K7WNt7c3/Pz8AADnz5+vgk9DRERERESVVeVzQIq6du0aVq5cibVr10rL8RoKj44dO2LKlCno3bs3tmzZgm+//RZ//fUXsrOz8eqrr8Lf3x99+vQxev87d+5I92vYsGGZ7Ro2bIjbt2/j9u3bVfTJ5Ltw4QImT56MlJQUODk5wdfXF+3bt8eAAQPg6elp9niIiIiIiJRU5T0g+fn52Lx5M7p3744mTZrg888/R0pKCkRRhEqlQkREBM6ePYuoqChMmDABvr6+mDZtGi5fvoy1a9dCrVZDFEV88skn5T4rLS1Nem1sVS3DuQcPHpj+ASsoNTUVycnJcHFxQW5uLq5fv46tW7fitddeY48MEREREdmcKusBuXr1qtTbcf/+fQD/6+1o2rQppkyZgvHjx8PDw6PMe4wbNw7x8fFYsGAB/vzzz3KfmZubK712dnYus53hXE5OjqzPUhUCAwMRHByMDh06wMvLC3Z2dsjOzkZ0dDTWrFmDtLQ0fPzxx/jiiy9Qv359s8VFRERERKQkkwuQH3/8EStXrsTRo0cB/K/ocHR0xNChQzFlypQKbUDYsWNHAJCKGEs1aNCgEsfUajXCwsLQvHlzTJs2DVlZWfjxxx8xY8YMBSIkIiIiIjI/kwuQMWPGFJtU7ufnh1deeQUTJ05E3bp1K3w/Jycn2W2LLour1WrL3PBPq9UCKNzXoybw8fHBgAEDsGXLFpw5cwZ6vR52dqWPhtuwYQM2bdpU5r1GjBiBCRMmVFeoVovzb+SpyXky/Jmxs7Or0XEqjXmSh3mSh3mSh3mSh3mSxxrzVGVDsHr37o0pU6Zg0KBBZX6ZlqNjx444dOiQrLZF532kpaWVWYAY5orUpP/TgoODAQDZ2dnIzMwsc2iaRqNBcnJymffJzs6Gvb19tcRozZgzeYzlafTo0WaMpGYz9iNBTSEIAv+9l4F5kod5kod5kod5ksea8mRyATJjxgxMnjwZgYGBVREPPD090a1bN1lt/fz8pN6XhIQEabndRyUkJAAAGjRoUCUxmpOrqyt8fHzKPK9Wq6HT6cwYkXVgzuRhnuSpyXky7GkkiiL0er3S4dRYzJM8zJM8zJM8zJM8lpin8golkwuQTz/91NRbVJpKpUJQUBDi4+MRExODzp07l2iTmpoqLb/bunVrc4dYpvj4eACFn8Hd3b3MdmPHjsXYsWPLPJ+amqrI6l6WjjmTh3mSpybnydPTE/b29tDr9TU6TqUxT/IwT/IwT/IwT/JYYp4ee+wxo+dNXob35Zdfxssvv4zY2NgKXRcXF4eXX34ZERERJj3fMMH96NGjSElJKXF+x44dEEURderUQcuWLU16llyG+TBlSUlJwW+//QYAeOqpp0waskZEREREZElM/ua7Zs0arF27VhrmJNc///yDNWvWYM2aNSY9v0+fPqhbty5yc3Mxb9483Lx5E0DhxPNt27bh119/BVDYk+DgULzDZ+LEiRg8eDAWL15c6r01Gg0yMjKkfwzdXlqttthxwyR3g8OHD2PhwoWIiopCRkaGdDwnJwdHjhzBrFmzkJmZCZVKhRdeeMGkz09EREREZEmqdSd0c3B0dMS7776LOXPm4NatW5g6dSrUajVyc3OlgmHgwIHo2bNnhe+9YMECxMXFlTi+c+dO7Ny5U3o/atSoYhNy9Xo9Tp48iZMnTwIoHGbl4OAAjUYjxeTh4YGZM2eWOW+FiIiIiMgaKVaAGCZtPtorURn+/v5YtmwZtm/fjujoaKSmpsLV1RWNGjXCgAEDEBISYvIzKqJly5YYO3YsLl++jH/++QcZGRnIzs6Gq6srGjRogKeeegp9+vQxOveDiIiIiMgaKVaAGIZK1apVq0ruV7t2bURERFRoTsnq1auNnv/4448rFYuPjw/Cw8MrdS0RERERkTWrsgJEEARZ7bKzsxETE4MlS5ZAEAQ0a9asqkIgIiIiIqIarkIFyIcffoiPPvqoxHFRFDF06NBKBfDcc89V6joiIiIiIrI8Fe4BKWuJ2fKWni1NWFgYXnvttQpfR0RERERElqlCBcgTTzxRYpfyI0eOQBAENG/evPxNR+zs4ObmhoCAAPTs2RP9+/fnHhhERERERDakQgXIhAkTMGHChGLHDAXEggULMHjw4KqLjIiIiIiIrI7Jk9C7du0KQRDK7f0gIiIiIiIyuQA5fPhwFYRBRERERES2gBMwiIiIiIjIbFiAEBERERGR2cgeglV0/4+5c+eWeryyit6PiIiIiIisl+wC5IMPPpB2Oy9aMBQ9XlksQIiIiIiIbEOFJqGLolhqsVGZTQgNTC1eiIiIiIjIcsguQA4dOlSh40RERERERI+SXYA8ugN6eceJiIiIiIgexVWwiIiIiIjIbFiAEBERERGR2Zi8EzopSxAE2Nmxjqwoe3t7pUOwCMyTPJaSJ0uJU2nMkzzMkzzMkzzMkzzWkicWIBZOpVJBrVYrHYbF8fT0VDoEi8A8yWMJebK3t7eIOJXGPMnDPMnDPMnDPMljTXmSXYBUV8UlCAIKCgqq5d62ICcnB1qtVukwLM6DBw+UDsEiME/y1OQ81apVC/b29tDpdMjIyFA6nBqLeZKHeZKHeZKHeZLHEvNUXqEkuwAxZa8Pqj6iKEKn0ykdhsVhzuRhnuSxlDxZSpxKY57kYZ7kYZ7kYZ7ksZY8yS5Aunbtyk0DiYiIiIjIJLILkMOHD1djGEREREREZAu4fBIREREREZkNCxAiIiIiIjIbFiBERERERGQ2LECIiIiIiMhsZE9C/+ijj6TXc+fOLfV4ZRW9HxERERERWS/ZBcgHH3wgLcNbtGAoeryyWIAQEREREdkG2QUIULjpXWnFhimbFHJvESIiIiIi2yG7ADl06FCFjhMRERERET1KdgHSrVu3Ch0nIiIiIiJ6VIWGYNVk6enp2LZtG6Kjo3H//n04OzsjMDAQ/fv3R0hISIXvp9PpEBcXh2vXruHatWu4fv06kpKSAACjRo3C6NGjZd3nxo0b2LlzJy5evIiMjAx4eHjgySefxLBhwxAQEFDhuIiIiIiILJlVFCAJCQmYM2cO0tPTAQAqlQoajQaxsbGIjY3FoEGDMGnSpArdMzU1Fe+9955JcR05cgRLlixBQUEBAMDV1RX379/HkSNHcPz4cUyfPh3PPPOMSc8gIiIiIrIk1VaAJCcn4+7du8jMzIS7uzvq1asHHx+fKn9Ofn4+5s+fj/T0dDRs2BBvvvkmAgICoNVqERkZiY0bN2L37t0ICAhAz549K3RvlUqFRo0aoXHjxggMDMSPP/6IxMREWdcmJCRIxUdoaCgmTpyIOnXqIC0tDatWrcLx48exePFiBAQEwM/PrzIfnYiIiIjI4lRpAfL3339j2bJl2LZtG27fvl3ivL+/P0aOHIl//etfaNiwYZU8c+/evUhKSoKzszPmzp0Lb29vAICzszPCw8ORlpaG3377DRs2bEBYWBgcHOR9ZG9vb2zevLnYKl07d+6UHdfGjRtRUFCAgIAAvPXWW7C3twcA1KlTBzNmzMDdu3dx8+ZNbNy4EbNmzarAJyYiIiIislxVthP6V199hRYtWuDLL7/E7du3IYpiiX8SEhLw+eefo0WLFvj666+r5LmHDx8GAHTt2lUqPooaPnw4BEFAWloaLl68KPu+dnZ2lV4iWKPR4PTp0wCAoUOHSsWHgb29PYYOHQoAiI6ORnZ2dqWeQ0RERERkaaqkB2ThwoV49913ARTuCWJnZ4fmzZsjKCgIrq6u0Gg0uHbtGi5dugS9Xo/s7Gy8/vrryMjIwL///e9KPzcnJwdXr14FALRr167UNt7e3vDz88Pt27dx/vx5tG3bttLPk+vSpUvSvI+y4jIcz8/Px+XLl9G+fftqj4uIiIiISGkm94DExMRg7ty5UuExffp0JCQk4OLFi9ixYwfWr1+PHTt24MKFC7h9+7Y0HEkURbz33ns4d+5cpZ99584daRNEY0O6DOdKGxZWHQzPqV27Njw8PEpt4+HhIZ1LSEgwS1xEREREREozuQBZtmwZdDodBEHAhg0b8Pnnn6NevXqltvX19cVnn32GjRs3AgD0ej2WLl1a6WenpaVJr+vUqVNmO8O5Bw8eVPpZFWF4jrGYip43V1xEREREREozuQA5dOgQBEHAwIED8fzzz8u6Jjw8HIMHD4YoiibtpJ6bmyu9dnZ2LrOd4VxOTk6ln1URhucYi6noeXPFRURERESkNJMLkHv37gEABg4cWKHrBgwYUOx6IiIiIiKyfiZPQq9duzaSk5NRu3btCl9X9H8rw8XFRXqt1WqhVqtLbafVagEU7uthDobnGJ5bFjlxbdiwAZs2bSrz/IgRIzBhwoRKRGnbPD09lQ7BIjBP8tTkPNnZ2Un/W5PjVBrzJA/zJA/zJA/zJI815snkAqR58+ZITk6WVqOS69q1a9L1lVV0jkVaWlqZBYhhroi5/k8zxFV0jkpp5MSl0WiQnJxc5vns7OwSy/xS+ZgzeZgneSwhT4IgWEScSmOe5GGe5GGe5GGe5LGmPJlcgIwdOxaHDh3CunXrMGPGDDg5OZV7TV5eHtasWQNBEDBu3LhKP9vPzw+CIEh7jJS1o7hhlakGDRpU+lkVYXjOw4cPkZGRgVq1apVok56ejvT0dACFGzSWxdXV1egO8mq1GjqdzsSIbQ9zJg/zJE9NzpNhTyNRFKHX65UOp8ZinuRhnuRhnuRhnuSxxDyVVyiZXIC8+OKLWL9+PQ4fPowxY8Zg3bp1RocU5ebmYvz48bh69Sq6d++OF198sdLPVqlUCAoKQnx8PGJiYtC5c+cSbVJTU6VlcVu3bl3pZ1VE8+bN4eDggIKCAsTExCAsLKxEG8Pyw46OjmjWrFmZ9xo7dizGjh1b5vnU1FSuolUJzJk8zJM8NTlPnp6esLe3h16vr9FxKo15kod5kod5kod5kscS8/TYY48ZPW/yJHRBEBAZGYlhw4Zh+/btaNasGf7zn//g3LlzyMrKgiiKyMrKQmxsLD777DM0a9YM27dvx4gRI7Br1y5THy99uT969ChSUlJKnN+xYwdEUUSdOnXQsmVLk58nh1qtRocOHQAAkZGRJX4d1el0iIyMBAB07NixzKFjRERERETWRnYPiNwxZwkJCZg1a1aZ5w0bB27fvh3bt2+HIAjSruGV0adPH/z8889ISkrCvHnzMH36dAQEBECr1WL37t349ddfART2JDg4FP+4EydORHJyMrp3745p06aVuLdGoylWPBi6vbRaLTIyMqTjzs7OJZbcHTNmDE6fPo3r16/jiy++wMSJE+Hp6YkHDx5g9erVuH79OhwdHTFmzJhKf3YiIiIiIksjuwAxFA5V1bYi9zPG0dER7777LubMmYNbt25h6tSpUKvVyM3NlQqGgQMHomfPnhW+94IFCxAXF1fi+M6dO7Fz507p/ahRozB69Ohibfz9/TF16lQsWbIEf/zxB44dOwa1Wg2NRgMAcHBwwNSpU8uct0JEREREZI1kFyBdu3aFIAjVGUul+fv7Y9myZdi+fTuio6ORmpoKV1dXNGrUCAMGDEBISIgicXXr1g0NGjTAjh07EBcXh4yMDGko2LBhwxAQEKBIXERERERESpFdgBw+fLgawzBd7dq1ERERgYiICNnXrF692uj5jz/+2NSw0KhRI8yYMcPk+xARERERWQOTJ6ETERERERHJxQKEiIiIiIjMhgUIERERERGZDQsQIiIiIiIyG5N3Qi8qOzsbkZGRiIqKwp07d5CRkVFiE75HCYKAAwcOVGUYRERERERUQ1VZAbJixQrMnj0b6enpsq8RRbHGLu1LRERERERVr0oKkPnz5+P999+XtbmgoeCoqo0IiYiIiIjIcpg8B+TKlSt4//33AQDBwcE4cOAAcnJyABQWG7t27UJWVhYuXryIRYsWwdfXFwDw0ksvITc3t9whWkREREREZD1M7gFZsWIFRFGEWq3Gvn374O/vX6KNWq1GixYt0KJFC0yaNAlDhgzBmjVroNFosHnzZlNDICIiIiIiC2FyD8iRI0cgCAJGjhxZavHxqNq1a2PXrl2oU6cOfvrpJ/z888+mhkBERERERBbC5AIkISEBABASElLq+by8vBLHPD09MWHCBIiiiPXr15saAhERERERWQiTC5DMzEwAgLe3d7HjKpWq2PlHtW3bFgBw5swZU0MgIiIiIiILYXIB4urqCqBkT4eHhweA//WQPKqgoAAAcO/ePVNDICIiIiIiC2FyAfLEE08AKFlINGnSBKIo4vjx46Ved/78eQCAk5OTqSEQEREREZGFMLkAad26NURRxMWLF4sd79q1KwDg0KFDOHv2bLFzN27cwOrVqyEIApo1a2ZqCEREREREZCFMLkDCwsIAAAcPHix2fPz48XBwcIBer0f37t3x9ttvY+XKlXj77bfx1FNPISsrCwAwatQoU0MgIiIiIiILYfI+IIMGDYK9vT3+/vtvnDhxAp07dwYABAYGYvbs2fjoo4+QlZWFzz//vMS17dq1w5QpU0wNwaYJggA7O5PrSJtjb2+vdAgWgXmSx1LyZClxKo15kod5kod5kod5ksda8mRyAeLl5YX4+Hjk5eXBx8en2LkPPvgArq6umDdvntTjARR+aQ4PD8eKFSs4B8REKpUKarVa6TAsjqenp9IhWATmSR5LyJO9vb1FxKk05kke5kke5kke5kkea8qTyQUIAAQEBJR5bubMmXjjjTdw8uRJJCUlwdXVFU899RR8fX2r4tE2LycnB1qtVukwLM6DBw+UDsEiME/y1OQ81apVC/b29tDpdMjIyFA6nBqLeZKHeZKHeZKHeZLHEvNUXqFUJQVIeZydnaW5IlS1RFGETqdTOgyLw5zJwzzJYyl5spQ4lcY8ycM8ycM8ycM8yWMteeLkASIiIiIiMptq7QF5+PAhMjMz4e7ujtq1a1fno4iIiIiIyAJUaQ9IVlYWli9fjrCwMLi7u8PLywtPPPEEvLy84O7ujmeffRZff/11sQnpRERERERkO6qsANm9ezeCgoIwdepU/PHHH9BoNBBFUfpHo9Hg6NGjeP311xEUFIRffvmlqh5NREREREQWokoKkHXr1mHYsGFITk6WCg53d3e0adMGXbp0QZs2bVCrVi3p3L179zB06FCsX7++Kh5PREREREQWwuQC5Nq1a3j11Veh0+kgiiKee+45nDx5Eunp6YiJicEff/yBmJgYPHz4EFFRURg+fDgAQK/XY/Lkybh+/brJH4KIiIiIiCyDyQXIl19+idzcXAiCgE8//RTbt2/H008/XWrbjh074qeffsJ//vMfAIBWq8WXX35paghERERERGQhTC5A9u3bB0EQ0LVrV8yYMUPWNW+++Sa6desGURSxd+9eU0MgIiIiIiILYXIB8s8//wAARowYUaHrDO0N1xMRERERkfUzuQBxc3MDADz++OMVus7Hx6fY9UREREREZP1MLkAaN24MAEhISKjQdbdv3wYABAUFmRoCERERERFZCJN3Qn/++ecRFRWFTZs2Yfr06RAEodxrRFHExo0bIQgCRo0aZWoIAID09HRs27YN0dHRuH//PpydnREYGIj+/fsjJCSk0vctKCjAL7/8giNHjuDu3bsAgPr166Nbt24YMGAAHBxKT+HixYtx8OBBo/f29/fH8uXLKx0bEREREZGlMbkAefXVV/HDDz/g3LlzmD59OhYvXlzuNW+++SbOnTuHNm3aYPLkyaaGgISEBMyZMwfp6ekAAJVKBY1Gg9jYWMTGxmLQoEGYNGlShe+bk5OD9957D/Hx8QAAJycnAIVLD1+7dg3Hjx/HRx99BBcXlzLv4eTkBLVaXeq5WrVqVTgmIiIiIiJLZnIB4uzsjF9//RUjR47EsmXLEBUVhRkzZqBHjx7w9PSU2j18+BD79+/HF198gejoaHTq1Anbtm2TvtRXVn5+PubPn4/09HQ0bNgQb775JgICAqDVahEZGYmNGzdi9+7dCAgIQM+ePSt076+//hrx8fFwdXXFG2+8IfWkREVFYenSpbhy5Qq++eYbTJ8+vcx7hIaGYtq0aaZ8RCIiIiIiqyG7AGnUqJHR8/n5+RBFEadPn8bzzz8PAPD09ISrqys0Gg0ePHgAoHD4lSAISEhIQJcuXSAIgkmbEe7duxdJSUlwdnbG3Llz4e3tDaCwMAoPD0daWhp+++03bNiwAWFhYWUOmXrUzZs3cfToUQDA66+/jk6dOknnOnXqBL1ej0WLFuHw4cMYNmwYGjZsWOnPQERERERkK2QXILdu3YIgCBBFsdTzgiBI8z8MbdLS0pCWllaiHQDcvXtXKkZMcfjwYQBA165dpeKjqOHDh2PPnj1IS0vDxYsX0bZtW1n3PXLkCERRhK+vb7Hiw6Bz587w9fVFYmIijhw5gvHjx5v0OYiIiIiIbIHsAsTf39/kYqGq5eTk4OrVqwCAdu3aldrG29sbfn5+uH37Ns6fPy+7ALlw4QIAoG3btqV+bkEQ0LZtWyQmJkptiYiIiIjIuAr1gNQ0d+7ckXpbjA2BatiwIW7fvi0t/VseURRx586dcu/r7+8PAEbve+HCBUyePBkpKSlwcnKCr68v2rdvjwEDBhSbI0NEREREZAtM3gdESUWHd9WpU6fMdoZzhnko5cnJyUFubq7s++bk5CAnJ6fUNqmpqUhOToaLiwtyc3Nx/fp1bN26Fa+99hrOnz8vKx4iIiIiImth8ipYSjIUCUDhpPOyGM6VVSQ8qmg7Ofc1XKNSqaT3gYGBCA4ORocOHeDl5QU7OztkZ2cjOjoaa9asQVpaGj7++GN88cUXqF+/vqy4iIiIiIgsnUX3gNRkgwYNQv/+/eHt7Q07u8I0q9VqhIWF4dNPP4WbmxtycnLw448/KhwpEREREZH5VHkPSGpqKn799VdERUUhMTERmZmZcHd3R7169fD0009jwIABeOyxx6rkWUU3ANRqtWVu+KfVagGgWA+FMUXbGa41dt+K3BsAfHx8MGDAAGzZsgVnzpyBXq+XipRHbdiwAZs2bSrzXiNGjMCECRNkP5sKcf6NPMyTPDU5T4a/W+zs7Gp0nEpjnuRhnuRhnuRhnuSxxjxVWQGSnZ2Nt99+G99//32ZX9q//fZbODs7Y+LEiVi0aFGFvrSXpuj8jLS0tDILEMNcEbn/p6lUKqhUKuTk5JRYRri0+xraV0RwcDCAwrxlZmbCw8Oj1HYajQbJycll3ic7Oxv29vYVejaBOZOJeZLHEvIkCIJFxKk05kke5kke5kke5kkea8pTlRQgqamp6NatG65cuVLmPiEGubm5+Oqrr3Dw4EEcOXIEXl5elX6un5+ftDdJQkIC/Pz8Sm2XkJAAAGjQoIGs+wqCAD8/P1y9elW6tiruWxmurq7w8fEp87xarYZOp6u251sr5kwe5kmempwnOzs76e9JvV6vdDg1FvMkD/MkD/MkD/MkjyXmqbxCqUoKkOHDh+Py5csACnsDXnjhBfTp0wfBwcFwc3NDVlYW4uPjsXfvXmzevBnZ2dm4dOkShg8fLm0kWBkqlQpBQUGIj49HTEwMOnfuXKJNamqqtExu69atZd+7VatWuHr1Ks6dO1dmm9jYWKltRcXHxwMo/Azu7u5lths7dizGjh1b5vnU1FTZq3vR/zBn8jBP8tTkPHl6esLe3h56vb5Gx6k05kke5kke5kke5kkeS8xTedMtTJ6EvnPnTvzxxx/SxnyXLl3C6tWrMXLkSLRu3RqBgYFo3bo1Ro4cidWrV+PPP/9E+/btAQB//PEHIiMjTXp+WFgYAODo0aNISUkpcX7Hjh0QRRF16tRBy5YtZd+3a9euEAQBd+/excmTJ0ucP3HiBO7evQtBEKQYDMrrBUpJScFvv/0GAHjqqafKnP9BRERERGRtTP7mu3nzZgCFO47v37/f6MZ9QOHGfr///rs0rMjYBGs5+vTpg7p16yI3Nxfz5s3DzZs3ARROEN+2bRt+/fVXAIU9CQ4OxTt8Jk6ciMGDB2Px4sUl7hsQEICuXbsCAJYtW4aoqCiIoghRFBEVFYXly5cDKCyADBsSGhw+fBgLFy5EVFQUMjIypOM5OTk4cuQIZs2ahczMTKm3iIiIiIjIVpg8BOvUqVMQBAEvv/yy0U37ivLy8kJERAQWLlyIU6dOmfR8R0dHvPvuu5gzZw5u3bqFqVOnQq1WIzc3VxonN3DgQPTs2bPC9/6///s/JCYmIj4+Hh9//DGcnJwAAHl5eQCApk2bYsqUKSWu0+v1OHnypNRzolKp4ODgAI1GI8Xk4eGBmTNnljlvhYiswxtvvKF0CDXG0qVLlQ6BiIhqAJMLEMMKTRWdB2EYDmVshSe5/P39sWzZMmzfvh3R0dFITU2Fq6srGjVqhAEDBiAkJKRS91WpVPjkk0/wyy+/4MiRI7h79y6Awk0Gw8LCMGDAgBK9KkDhZxs7diwuX76Mf/75BxkZGcjOzoarqysaNGiAp556Cn369DE694OIiIiIyBqZXIA4OTlBq9VKvQJyGdo7OjqaGgIAoHbt2oiIiEBERITsa1avXl1uGwcHBwwdOhRDhw6VfV8fHx+Eh4fLbk9EREREZCtMngNSr149AIUTyivi6NGjAID69eubGgIREREREVkIkwuQsLAwiKKI9evX4/z587KuiY2NxYYNG0pdQYqIiIiIiKyXyQXIxIkTIQgC8vPz0bNnT+zYscNo+x07dqBXr17Iy8uDIAiYNGmSqSEQEREREZGFMHkOSLt27fDqq6/im2++QVpaGkaOHIlGjRqhV69eCA4OhqurKzQaDa5evYr9+/fj+vXrEEURgiDg1VdfRdu2bavicxARERERkQWokp3Qly1bhoyMDGzcuBEAcOPGDXz77beltjVs0jdmzBguyUhEREREZGOqpACxs7PD+vXrMXjwYCxatAgxMTFltm3fvj3+/e9/Y/jw4VXxaCIisgLcL6UQf5gjIltQJQWIwciRIzFy5EgkJCTg1KlTSExMRGZmJtzd3eHr64unn366xK7hRERERERkO0wuQNatWwcAqFu3Lnr37g2gcGNAFhpERERERPQok1fBevHFF/HSSy/h2LFjVREPERERERFZMZMLEDc3NwBA8+bNTQ6GiIiIiIism8kFiK+vLwAgPz/f5GCIiIiIiMi6mVyAPPvsswCA06dPmxwMERERERFZN5MLkMmTJ8POzg5r167FP//8UxUxERERERGRlTK5AGnbti0WLFiAzMxM9OrVCxcuXKiKuIiIiIiIyApVyTK8devWRb9+/bBnzx60a9cOoaGheOaZZ+Dn5weVSlXuPcaPH29qGERERFaPGzYW4oaNRJbN5ALkxRdfhCAIAABBEKDX6/HHH3/gjz/+kHW9IAgsQIiIiKjKsFArxEKNaqoq2QldFEWj76n6CIIAOzuTR9LZHHt7e6VDsAjMkzzMkzzMU/mYI3mYJ3ksKU+WFKuSrCVPJhcgP/zwQ1XEQZWkUqmgVquVDsPieHp6Kh2CRWCe5GGe5GGeysccycM8yWMpebK3t7eYWJVkTXkyuQCZMGFCVcRBlZSTkwOtVqt0GBbnwYMHSodgEZgneZgneZin8jFH8jBP8tT0PNWqVQv29vbQ6XTIyMhQOpwayxLzVF6hVCVDsEg5oihCp9MpHYbFYc7kYZ7kYZ7kYZ7KxxzJwzzJY0l5sqRYlWQteTKpAPnnn39w4cIFpKenw8PDAy1btoSfn19VxUZERERERFamUgVIdHQ0pk+fjqioqBLnQkJC8OWXX6Jjx44mB0dERERERNalwssn7du3D2FhYYiKioIoiiX+OXnyJLp164a9e/dWR7xERERERGTBKlSAZGZmYsKECcjNzZWW2m3cuDE6d+6Mxo0bS+20Wi0mTJhgMRNliIiIiIjIPCo0BGv9+vW4d+8eBEFA+/btsXbtWjRr1kw6f+XKFbz44ouIjo5GSkoK1q9fj3/9619VHjQRERERmYYbNhbiho3mV6ECZM+ePQCAxx57DHv37i2xxFbTpk2xZ88eNGvWDCkpKdizZw8LECIiIiKySCzS/qcqC7UKDcG6cOECBEHA+PHjy1zf19PTE+PHj4coirh48WKVBElERERERNahQgVIWloaAKBNmzZG27Vu3RoAcP/+/cpFRUREREREVqlCBYhGowEAuLu7G23n5uYGoHCXbiIiIiIiIoMKL8NLRERERERUWSxAiIiIiIjIbCq1E7ogCFUdh9VKT0/Htm3bEB0djfv378PZ2RmBgYHo378/QkJClA6PiIiIiMisKlWADB06VFY7URRhb29vtI0gCCgoKKhMGDVeQkIC5syZg/T0dACASqWCRqNBbGwsYmNjMWjQIEyaNEnhKImIiIiIzKdSBQgAaSf00giCIPWSGGtnzfLz8zF//nykp6ejYcOGePPNNxEQEACtVovIyEhs3LgRu3fvRkBAAHr27Kl0uEREREREZlHhOSCiKJZbVBja2GrxAQB79+5FUlISnJ2dMXfuXAQEBAAAnJ2dER4ejn79+gEANmzYYLU9QEREREREj6pQAaLX66v8H51OV12fTVGHDx8GAHTt2hXe3t4lzg8fPhyCICAtLY0bNhIRERGRzeAqWNUgJycHV69eBQC0a9eu1Dbe3t7w8/MDAJw/f95ssRERERERKYkFSDW4c+eONPysYcOGZbYznLt9+7ZZ4iIiIiIiUhoLkGqQlpYmva5Tp06Z7QznHjx4UO0xERERERHVBCxAqkFubq702tnZucx2hnM5OTnVHhMRERERUU3AAoSIiIiIiMym0vuAUNlcXFyk11qtFmq1utR2Wq0WQOEGhWXZsGEDNm3aVOb5ESNGYMKECZWM1HZ5enoqHYJFYJ7kYZ7kYZ7KxxzJwzzJwzzJwzzJU5V5YgFSDYrO+0hLSyuzADHMFTH2f6hGo0FycnKZ57Ozs8vdbb4oY8UMFWKO5GGe5GGe5GGe5GGe5GGe5GGeysccVQ8WINXAz88PgiBAFEUkJCRIy+0+KiEhAQDQoEGDMu/l6uoKHx+fMs+r1WqL2kvFzs5Oyo1er1c6nBqLeSofcyQP8yQP8yQP8yQP8yQP8ySPJeapvB/HWYBUA5VKhaCgIMTHxyMmJgadO3cu0SY1NVVafrd169Zl3mvs2LEYO3ZsmedTU1MtahUtT09P2NvbQ6/XW1Tc5sY8lY85kod5kod5kod5kod5kod5kscS8/TYY48ZPc9J6NUkLCwMAHD06FGkpKSUOL9jxw6Ioog6deqgZcuWZo6OiIiIiEgZLECqSZ8+fVC3bl3k5uZi3rx5uHnzJoDCiefbtm3Dr7/+CqCwh8PBgR1RRERERGQb+M23mjg6OuLdd9/FnDlzcOvWLUydOhVqtRq5ubnS+L2BAweiZ8+eCkdKRERERGQ+LECqkb+/P5YtW4bt27cjOjoaqampcHV1RaNGjTBgwACEhIQoHSIRERERkVmxAKlmtWvXRkREBCIiIpQOhYiIiIhIcZwDQkREREREZiOIoigqHQTZjg0bNkCj0cDV1dXo8sK2jnkqH3MkD/MkD/MkD/MkD/MkD/MkjzXmiQUImVX//v2RnJwMHx8f/Pbbb0qHU2MxT+VjjuRhnuRhnuRhnuRhnuRhnuSxxjxxCBYREREREZkNCxAiIiIiIjIbFiBERERERGQ2LECIiIiIiMhsWIAQEREREZHZsAAhIiIiIiKz4U7oZFajR4+W1rKmsjFP5WOO5GGe5GGe5GGe5GGe5GGe5LHGPHEfECIiIiIiMhsOwSIiIiIiIrNhAUJERERERGbDAoSIiIiIiMyGBQgREREREZkNCxAiUoQoisjIyEBKSorSoRARkQzTpk3D9OnTkZSUpHQoFk2r1UKj0SgdhqK4DC/JptPpcP36daSkpECr1aJ79+5Kh1TjpKen4+LFi1KORo0apXRINc7Vq1exdetWXLhwAVqtFgCwa9cu6XxWVhbWrl0LQRAQEREBZ2dnhSJVxtSpU9G7d29069YNbm5uSodDZHOioqJw7tw5pKSkIC8vD/Pnz5fO5ebm4ubNmxAEAU2bNlUwSmXcvn0bDg4OqFu3rtKh1Fipqak4d+4cateujQ4dOhQ7l5CQgKVLl+LatWsAgODgYLzxxhvw8/NTIlRFsQAhWXbt2oVt27YhKytLOla0AMnKysI777yDgoICfPzxx/D09FQiTMXk5+fjhx9+wN69e6HT6aTjRQuQrKwsTJ48Gbm5ufjqq69s8i/wffv2YcWKFcVyJAhCsTZubm7SX+AtWrRAt27dzB2mom7duoVVq1bhhx9+QKdOndCrVy+0atVK6bAUN2nSJJPvIQgCVq5cWQXRWJ7U1FT897//xeXLl5GWlgatVouyVuG31TwlJSVh4cKF+PvvvwEU9tI++veTo6MjvvjiC6SkpOCTTz6xuSLEy8sL6enpSodRo+3fvx9btmzBiBEjihUg2dnZeO+995Ceni792fvrr7/w7rvvYvny5Tb3gxMLECrX0qVLcfDgQYiiCEdHRxQUFJRo4+bmhuDgYBw4cADHjh3DoEGDFIhUGXq9HgsWLEBsbCwAwMfHB6mpqdDr9cXaubm54dlnn8Xu3btx/PhxDB8+XIFolXPjxg1888030Ov16NOnD8LCwrBw4UJkZmaWaNujRw/ExMTg7NmzNleAvPDCCzhw4ACSk5Nx9OhR/PHHH/Dx8UGvXr3QvXt3eHl5KR2iIpKTk02+x6NfJm3F4cOH8dVXXyE/P99o0WE4Z4t5ys7Oxty5c3Hv3j14enqiffv2OHbsmNRLa2Bvb48+ffpg/fr1OHnypM0VIG3btsXevXvx119/oUmTJkqHUyOdP38eAPDMM88UO75//348fPgQderUwaRJk+Ds7IzvvvsOd+/exc8//4zRo0crEa5iWICQUVFRUThw4ADUajX+9a9/oVOnTnj55ZdL/QWkW7du+O9//4vz58/bVAFy6NAhnDt3Dp6ennjnnXfQpEkTTJgwodQchYaGYvfu3bhw4YLNFSCRkZHQ6/UYPHgwIiIiAAB2dqVPQ2vZsiUA4Pr162aLr6YYNWoURo0ahfPnz2Pfvn04deoU7t27h40bN+LHH39Eu3bt0LNnT3To0AH29vZKh2s2HM5YOdevX8fSpUuh0+nQpk0btG/fHt999x3UajVefvllPHz4EBcvXsSFCxdQq1YtjBo1Ci4uLkqHbXY///wz7t27h6CgIHzwwQdwc3PDmTNnShQgAPD0009j/fr1uHz5sgKRKis8PBwnTpzA119/jXnz5qFWrVpKh1TjGOY11qtXr9jxqKgoCIKACRMmoHPnzgAAlUqFd955B2fOnGEBQlTU3r17IQgCxo8fj9DQUKNtg4ODIQgCbt26ZZ7gaoiDBw9CEARMnDix3F+EAgMDIQgCEhISzBRdzREXFwdBEDBs2LBy23p4eMDFxQWpqalmiKxmat26NVq3bo2srCwcPnwY+/fvx61bt3D69GmcOXMGHh4e6N69O3r27In69esrHW61e+GFF6rlvseOHUNeXp7Vzmn7+eefodPp8Oyzz2LatGkAgO+++w7Ozs7o1asXAGDkyJG4cOECFi5ciAMHDmDRokUKRqyMkydPSn+PlzcUxs/PD/b29rh7966Zoqs5EhMTMXbsWHz//feYMmUKnn32WTRt2hS1atUq8wclAHjyySfNGKWy0tPT4erqCkdHR+lYQUEB4uPjYWdnh6efflo63rx5c9jb2yMxMVGJUBXFAoSMMkyUevbZZ8tt6+LiApVKhYcPH1ZzVDWLoeDq2LFjuW0dHR3h6uqKjIyMao6q5nn48CFcXFxkzw9ycHBATk5ONUdV87m5uWHgwIEYOHAgrl+/jn379uHo0aN4+PAhdu7ciZ07d6JZs2bo3bs3unTpAicnJ6VDtiirVq1Cenq61RYgf/75JwRBQHh4eLHjjw7FatWqFV555RUsXrwYO3fuLNHe2iUlJcHe3h7BwcHlthUEAWq1GtnZ2WaIrGaZM2eONERPq9Xil19+wS+//FLudUUXGrF2giAgNze32LFr166hoKAAQUFBUKlUxc6p1Wqb/G8dl+ElozQaDVQqlU12ycuVm5sLlUol+4tfQUGBTQ2dMXBxcUFeXl6JuTGlycnJgUajgbu7uxkisxyBgYGYMmUKvvrqKzRr1gyiKEIURVy6dAlLlizBSy+9hPXr19v88o70Pw8fPoSDg0Ox4SCCICAvL69E29DQUNjb2+PYsWPmDLFG0Ov1cHBwMPorvoEoisjNzbW5FfoMDH/vVOQfW+Lt7Q2dTocbN25IxwzDr5o3b16srV6vR3Z2Njw8PMwdpuLYA0JGubu7Iz09HXl5eeV+wU5LS0N2dja8vb3NFF3N4OHhgbS0NOTm5pZbqCUlJSE3N7fE2FBb4Ofnh7/++gs3b95EYGCg0bYnT56EKIrltrM1Fy5cwP79+xEVFYX8/HwAhb+etWvXDn/++ScePHiA7du349ChQ5g/f75N/ntGxZX2JVmlUiEnJ6fE3+uOjo5wdnbGvXv3zBlijfDYY48hMTERDx8+RO3atY22jY+PR35+Pho0aGCe4GqQyMhIpUOo8Vq1aoV//vkHK1aswMSJE/HgwQP8/vvvAFBiWd47d+5Ap9OhTp06SoSqKPaAkFGNGzcGUPjFpzx79+4FADRr1qxaY6ppDPM+Tp06VW7bn3/+GYIgoEWLFtUdVo3TuXNniKKILVu2GG2XlJQk7QPSpUsXM0VXc92/fx9btmzBK6+8grlz5+Lo0aPIy8tDUFAQXn/9daxZswYzZ87Ed999h5kzZ6Ju3bq4f/8+1qxZo3ToVAN4eXkhOzu72OqFvr6+AIArV64Ua3vv3j2bHFYE/G/hi/379xttJ4oiNm7cCEEQ0K5dO3OERhZm+PDhUKvViI+Px9tvv42FCxciJycHTZs2lf49Mzh9+rTN7inDAoSM6tGjB0RRxPr164vtAfKoEydO4KeffoIgCNLERlvRt29f6T9KxpYK3blzJ3799VcAQL9+/cwVXo3Rr18/+Pr6Ijo6Gp988gkuX74sdc2np6fj6tWr2LRpE9588008fPgQTzzxBMLCwpQNWiE6nQ7Hjx/HBx98gIkTJ+LHH3/EvXv3oFarMWDAACxZsgSfffYZevbsKf3CbW9vj9DQUMyfPx92dnb4888/Ff4UVBM0bNgQoiji5s2b0rFWrVpBFEWsXr1aWrEnIyMDy5cvhyAICAgIUCpcxQwdOhR2dnbYtm1bmT8mJSUl4eOPP8b58+fh5OSEAQMGmDlKsgTe3t6YP38+nnzySTg6OsLDwwM9evTAnDlzirUTRRH79u2DKIpo3bq1QtEqRxBtbXAeVdi8efNw5swZ1K1bFz169MCuXbuQnZ2NGTNmICUlBadPn8alS5cgiiK6du2Kt956S+mQzW758uXYv38/3Nzc0KlTJxw7dgy5ubkYN24cUlJSEBMTg+TkZIiiiCFDhuDll19WOmRF3L17Fx9++CGSkpLK3GtAFEXUq1cPH330kc0N5wOA1atX48iRI8jMzJQKtKZNm6JPnz4IDQ2VNdfo5ZdfRlpamk1N/Kwsw5LZ1pqrw4cP48svv8SwYcMwYcIEAIW9av/3f/8nLTHr7u5ebD+ef//73wgJCVEkXiXt27cPX3/9NQCgbt26SE1NRUFBAdq2bYuUlBTcuXNHavvWW2+V2OfB1qSnp+PixYtISUmBVqvlUtkVpNPpcP/+fQCFPZW2NjeUBQiVS6vVYsmSJTh+/HipXxoN/wqFhoZi2rRpxZaesxU6nQ7r16/Hrl27St3My7Cj7rBhwzBu3Dib3OjLICcnBzt37sSBAwdKLLPr6emJnj17YtiwYVCr1QpFqKwhQ4YA+N/GlX369KnwWPPPPvsMDx8+xIIFC6ojRKti7QWIVqvFsWPH4ObmVmz5z7i4OHzxxRfSFyCgcL7I+PHjMXDgQCVCrRHOnDmDlStXljkPxtvbG1OmTEH79u3NHFnNkZ+fjx9++AF79+6FTqeTjhf9M5SVlYXJkycjNzcXX331FerWratApFSTsQAh2eLi4rB//35cuXIFDx48gF6vR+3atdG0aVP07NkTbdq0UTpExSUlJeHAgQOl5qhHjx42sV9DRdy/fx9paWlSnh5//HGlQ1Lc7NmzpSV1bbGYNzdrL0CM0el0uHLlClJTU+Hq6opmzZrB1dW11LbWvl9KUXq9HnFxcbhy5Uqxv5+aNWuGVq1a2dwv1UXp9Xp89NFHiI2NBQD4+PggNTUVer2+xJ+h1atXY/fu3Rg/frzNbbxL5WMBQkRENsuWC5CKsPY87d69G0DhYhleXl4KR1NzHThwAEuXLoWnpyfeeecdNGnSpMx/N65cuYJZs2ahTZs2+PDDD5UJuJrFxcUBKOw9DAoKKnasomxps0aAy/ASEdVooigiMzMTWq3WJufEEJnDd999Bzs7O/Tt21fpUGq0gwcPSjvGG1aALEtgYCAEQUBCQoKZojM/w8aM9evXx1dffVXsWEVZa3FfFhYgRGR2Op0OiYmJyMrKKrY8aGls7Vchg6tXr2Lr1q24cOGCNFn40THWhuWKIyIibHZTNKKq4O7uDr1ez2GP5bh16xYAoGPHjuW2dXR0hKurKzIyMqo5KmWVttkiBxeVjwUIySKKIi5fvoy///4bWVlZxSaelcYWV8PIysrC6dOnkZCQUO4Xa0EQ8MYbb5gxupohOTkZ69atQ1RUVLmFh4Gt/SoEFK7Gs2LFimJ/zh79Rc3NzQ2pqak4d+4cWrRogW7dupk7TKvALwoEFP5aHxsbi/T0dJvclVqu3NxcqFQqWavxAUBBQYFVz5kpbWNGbtYoDwsQKld0dDRWrFiBtLQ02dfYWgHy22+/Yc2aNcjLy5OOlfbFRhAEaUUsWytAkpKSMHPmzGLLy1JJN27cwDfffAO9Xo8+ffogLCwMCxcuLLZMqkGPHj0QExODs2fPsgCppNmzZ8suhsl6DRo0COfOnZM2/aTSeXh4IC0tDbm5uXBxcTHaNikpCbm5uahXr56ZoiNLwgKEjLp48SIWLlwIvV4PoHCtai8vL9m/ftiCEydO4NtvvwUAODg4ICgoiDkqxaZNm5CRkQFXV1eEh4cjJCQEXl5eHPLwiMjISOj1egwePBgREREAADu70veMNeyqe/36dbPFZ21scQdiKql9+/Z46aWXsG7dOmRlZeG5556zyQ0Zy9OkSROcPHkSp06dKvdHj59//hmCIKBFixZmio4sCQsQMuqnn36CXq9Hw4YNMXXqVAQGBiodUo1jGCL05JNP4q233kKdOnWUDaiGOn/+PARBwPTp09GhQwelw6mx4uLipD1jyuPh4QEXF5cS+6kQUcVMmjQJQGGxf/ToURw9ehROTk5wd3cv8wcAQRCwcuVKc4apuL59++LEiRPYuHEjmjVrBh8fn1Lb7dy5E7/++isEQUC/fv3MHCVZAhYgZNTVq1chCALeeustNGzYUOlwaqS///4bgiBg6tSpLD6M0Gg0cHBwsOkNvOR4+PAhXFxc4OnpKau9g4MDcnJyqjkqIuuWnJxc4phWq5UWgCiNLW4o27p1a/Tq1Qv79+/H9OnT0alTJylH27dvR0pKCmJiYqR8Dh482GZ/uOS8UONYgJBROp0OLi4uLD6MEAQBKpWqzF+CqFCdOnWQnp5e5q+JVMjFxQU5OTnQ6/Xl5ionJwcajYaTZolMZGtf/kwxZcoUuLm5YdeuXdi/fz+Awv8Orl+/HgCkeY7Dhw/HuHHjlAxVMZwXWj4WIGRUvXr1cPv2beh0OqteycIU/v7+uHbtGvLy8jjvw4hOnTohMjIS8fHxCA4OVjqcGsvPzw9//fUXbt68We4vhydPnoQoijb7CyNRVenRo4fSIVgMe3t7vPjii+jbty8OHDiAK1eu4MGDB9KO8U2bNkWPHj1Qv359pUNVBOeFysMChIzq2bMnVq1ahVOnTqFz585Kh1MjDRgwAF988QUOHTqEPn36KB1OjRUeHo4TJ07gm2++wbx58+Dm5qZ0SDVS586dceXKFWzZsgWzZ88us11SUpK0D0iXLl3MGCEREVC3bl2MGTNG6TBqHM4LlYcFCBk1YMAAxMTE4Ouvv0adOnW4YkwpunXrhj///BOrV6+GSqVC165dlQ5JcXFxcaUeHzt2LFauXInXXnsNvXv3RlBQEFQqldF72dpGhP369cOePXsQHR2NTz75BEOGDJG67tPT05GcnIzTp0/jl19+gUajQUBAAMLCwpQNmqyerS2dLYoiMjMzodVq4e3trXQ4ZEE4L1QeQbS1v1WoTJs3by71eEFBAfbs2QONRoPmzZvL+tJorfuALFmypMxz0dHR0Gg0eOyxx9C4cWOjObL28Z5DhgypsgmatrgR4d27d/Hhhx8iKSmpzDyKooh69erho48+4hckqnZXrlxBQUGB1f8gcPXqVWzduhUXLlyQJlcX/TsoKytL6nmMiIiAs7OzQpFSTTVq1CgIgoAff/xR6VBqNPaAkOTHH380+qVRFEX8+eefuHTpUrn3stYC5ODBg9KksaKKHktJSUFKSkqp19vShDP+tlF59erVw+LFi7Fz504cOHCgxDK7np6e6NmzJ4YNGwa1Wq1QlGRLbKH3e9++fVixYgV0Op107NH/Jrq5uSE1NRXnzp1DixYtbHYDUK7wVDbOC5WHBQhJWrRoYZPLClbEs88+yxzJEBkZqXQIFk+lUmH06NEYPXo07t+/j7S0NGmS5+OPP650eERW5caNG/jmm2+g1+vRp08fhIWFYeHChcjMzCzRtkePHoiJicHZs2dtsgDhCk/GcV6oPCxASPLxxx8rHUKNN23atGq797Fjx5CXl4fu3btX2zPIMnl5ecHLy0vpMIisVmRkJPR6PQYPHoyIiAgAKHMZ7JYtWwIArl+/brb4agqu8FQ+zguVhwUIUQ2xatUqpKenW20BkpKSAjs7O9lfpO/fvw+9Xs/5DURU7eLi4iAIAoYNG1ZuWw8PD7i4uJQYGmkLuMJTccbmhTo5OeGLL77AunXrbH5eaGlYgBCRWUycOBGenp5Ys2aNrPazZs1CamqqTU5CN9DpdEhMTCx3jDVge6uFEVWlhw8fwsXFBZ6enrLaOzg4ICcnp5qjqnm4wlNxnBdaeSxAqFx6vR6CIJQ692HPnj2Ii4tDfn4+2rdvj969e3OOBJGJkpOTsW7dOkRFRZVbeBjYcqFGZCoXFxfk5ORAr9eXOfTKICcnBxqNBh4eHmaKruYQBAEqlQo+Pj5Kh1IjcF5o5bEAIaP27duHr7/+GqGhoZgxY0axc/Pnz8eZM2cAFE5Ai46ORkxMDN555x0lQiUro9Vqy/0iYI2SkpIwc+ZMZGZmciUxIjPx8/PDX3/9hZs3byIwMNBo25MnT0IUxXLbWSOu8FQc54VWHgsQMiomJgZAYZVf1NmzZ3H69GkAQIcOHeDk5ISTJ0/i1KlTOHbsGEJDQ80eK1mPu3fvIjMzU/ZwCGuyadMmZGRkwNXVFeHh4QgJCYGXlxccHR2VDo3IanXu3BlXrlzBli1bMHv27DLbJSUlSfuAdOnSxYwR1gxc4cl8rH1eKAsQMurvv/8GADRp0qTY8UOHDkEQBAwZMgQvvfQSAOCXX37BqlWrcPDgQRYghKioKJw6darYMY1GY3TSnqGNYa+Z5s2bV1t8NdX58+chCAKmT5+ODh06KB0OkU3o168f9uzZg+joaHzyyScYMmSI1AOZnp6O5ORknD59Gr/88gs0Gg0CAgIQFhambNAK4ApPVFVYgJBR6enpcHZ2hpubW7Hj58+fBwD07dtXOtajRw+sWrUKN27cMGuMVDPdvHmzxAS9vLw8HDx4UNb17u7uVruhpTEajQYODg5o37690qEQ2QwnJyfMnTsXH374IU6ePImoqCjp3IQJE6TXoiiiXr16mDNnDuzt7ZUI1Wy4whNVJxYgZFRubm6JoR9JSUnIyMiAt7c3fH19peMqlQqurq7IyMgwd5hUAwUEBBTrOj548CCcnJyM9o4JggC1Wg1/f3906tQJ7u7u5gi1RqlTpw7S09Ntcv4LkZLq1auHxYsXY+fOnThw4ECJZXY9PT3Rs2dPDBs2DGq1WqEozYcrPFF1YgFCRtWqVQsPHz5ERkYGatWqBQCIjY0FADRr1qxEe51OZ/SXELIdISEhCAkJkd4fPHgQrq6umDp1qkn3tfaJeZ06dUJkZCTi4+MRHBysdDhENkWlUmH06NEYPXo07t+/j7S0NOj1etSuXRuPP/640uGZFVd4ourEAoSMCgwMxNmzZxEZGYlx48ZBq9Viz549EAQBbdq0Kdb2wYMHyM3NRYMGDZQJlmq0BQsWwMHB9L9yrH1iXnh4OE6cOIFvvvkG8+bNKzH8kYjMw8vLS/bGqdaIKzxRdWIBQkb17dsXZ86cwfbt2xEVFYXs7GykpaXB3d0dnTt3Ltb24sWLAICGDRsqESrVcNwor6S4uLhSj48dOxYrV67Ea6+9ht69eyMoKKjcnkXml4gshbX/kETlYwFCRnXo0AHh4eH46aefcOfOHQCAm5sbpk+fXuIL0ZEjRwAArVq1Mnuc1oB7PtieOXPmlDvEYevWrbLuxY0IiaqGTqdDYmIisrKyyt0IlIU/UeWwAKFyjRkzBr169UJ8fDzUajWCg4NLDAspKChAUFAQGjdujI4dO5a4B7tbyzd79mzZu16T9WDhSVQzJCcnY926dYiKipL9dzELf6LKYQFCsvj4+MDHx6fM8w4ODkaXTGV3a/maNm2qdAhkZpGRkUqHQEQoXN1x5syZyMzM5I8CRGbAAoSIiIhs2qZNm5CRkQFXV1eEh4cjJCQEXl5eJZahJ6KqwQKEiKgGSUlJgZ2dnezVd+7fvw+9Xg9vb+9qjozIep0/fx6CIGD69Ono0KGD0uEQWX1PHAsQIqIaZOLEifD09MSaNWtktZ81axZSU1M5Fp3IBBqNBg4ODmjfvr3SoRABsP55oSxAiIiIyKbVqVMH6enpsLOzUzoUIgDWPy+Uf9KIiCyYVqvllyYiE3Xq1AlarRbx8fFKh0JkE/hfLSIiC3X37l1kZmbCw8ND6VCILFp4eDi8vb3xzTffICsrS+lwiKweh2ARkUWxtol5UVFROHXqVLFjGo0GS5YsMXqdRqPBpUuXAADNmzevtviIrE1cXFypx8eOHYuVK1fitddeQ+/evREUFFRiw91HcSNCosphAUJEFsXaJubdvHkTBw8ehCAIUnGVl5eHgwcPyrre3d3d6B48RFTcnDlzIAiC0TZbt26VdS8u/lA51vZDElUcCxAisijWNjEvICCg2AadBw8ehJOTE0JDQ8u8RhAEqNVq+Pv7o1OnTnB3dzdHqERWg1+AlWVtPyRRxQki/xSSGUyYMAHp6en8tYioHEOGDKnQMrxlOXbsGPLy8ooVN0RERDUBe0DILFjnEsmzYMECODiY/lfzqlWrkJ6ezgKEiIhqHBYgZBbsbiWSh5NaicwvJSUFdnZ28PLyktX+/v370Ov18Pb2rubIiKwTCxAyC2sbt09ERNZj4sSJFRr6OGvWLKSmpnJYMVElcR8QIiIiIiIyGxYgRERERBWg1WphZ8evUESVxT89RERERDLdvXsXmZmZ8PDwUDoUIovFOSBERERkU6KionDq1KlixzQaDZYsWWL0Oo1Gg0uXLgEAmjdvXm3xEVk7FiBERERkU27evImDBw9CEARpmfi8vDwcPHhQ1vXu7u4YNWpUdYZIZNVYgBAREZFNCQgIKLZHzsGDB+Hk5ITQ0NAyrxEEAWq1Gv7+/ujUqRPc3d3NESqRVWIBQkRERDYlJCQEISEh0vuDBw/C1dUVU6dONem+x44dQ15eHjcAJSoHCxAiIiKyaQsWLICDg+lfiVatWoX09HQWIETlYAFCRGSFDOPaiah8Tz75pNIhENkUFiBERFZo9uzZKCgoUDoMIiKiEliAEBFZoaZNmyodAhERUam4ESEREREREZkNCxAiIiIiIjIbFiBERERERGQ2LECIiIiIiMhsWIAQEREREZHZsAAhIiIiIiKzYQFCRERERERmwwKEiIiIqAqIoqh0CEQWQRD5p4WIiIjIZFeuXEFBQQGefPJJpUMhqtFYgBARERERkdlwCBYREREREZkNCxAiIiIiIjIbFiBERERERGQ2LECIiIiIiMhsWIAQEREREZHZsAAhIiIiIiKzYQFCRERUAxw+fBiCIEAQBHzwwQdKh0NEVG1YgBARkVk1btxY+qIdFxdXbvuePXtK7Rs0aFBu++zsbDg7O0MQBDg6OiIrK6sqwiYioirCAoSIiMzq2WeflV4fPnzYaNu8vDycOHFCen/nzh1cu3bN6DXHjx9HXl4eAKBDhw5wc3OrfLBERFTlWIAQEZFZFS1ADh06ZLTtqVOnkJOTU+xYedcULWqKPouIiGoGFiBERGRWYWFh0uujR49CFMUy2xqKCXd3d4SGhhY7Vt41AAsQIqKaiAUIERGZVb169RAcHAwASE1NxcWLF8tsaygmQkND0aNHj2LHSpOdnY3Tp08DAJycnNClS5eqCZqIiKoMCxAiIjI7OfNA8vLycPLkSQCFvSbdunUDANy9exfx8fGlXnP8+HHk5+cDAJ5++mmoVKpi53NycrB8+XL06tULvr6+cHJygpeXFzp06IB3330Xd+/eNRr3mjVrpAnxa9asAQDExMTg1VdfRXBwMNzd3YudK2rv3r147rnn4OvrCxcXF/j7+2PYsGHYt2+f0WcSEVkbFiBERGR2cuaBFJ3/ERYWhpCQEDg5ORm9xtjwq9OnT6NJkyZ4/fXX8d///hdJSUnIz89HWloazpw5gwULFiAoKAjff/+97M/x6aefomPHjvj2229x9erVUlfc0uv1mDRpEvr27Ytdu3YhKSkJWq0Wt2/fxs6dO9GnTx9MmzZN9jOJiCydg9IBEBGR7SltHoggCMXaFJ3/0a5dOzg4OKBjx444duwYDh8+jMmTJ5e4b1kFyIULF/Dss89Co9EAAJo3b45x48YhICAAaWlp2LVrF/bt24fs7GxERERAFEVEREQY/Qxbt27Fnj174ObmhvHjx6Njx45wdHTEpUuXULduXand9OnTsXr1agCAvb09xowZg7CwMDg7OyM2NhbfffcdlixZgtu3b8vKHRGRxROJiIgU0KxZMxGACEA8d+5cifPdu3cXAYh9+/aVjs2ePVsEINatW7dEe41GIzo6OooARBcXFzE3N1cURVHU6XTik08+KT1r4sSJYn5+fonrV69eLQqCIAIQ1Wq1ePPmzRJtfvjhB+k+AMTg4GDx77//LvMzHjt2TLqnq6ur+Mcff5Roc/fuXbFp06bF7vv++++XeU8iIkvHIVhERKQIY/NAHp3/YWCYB5KUlIQrV64Uu6bo/I9OnTrB2dkZAPDrr79KGx62atUKK1asgINDyQEAERERUq9KdnY2lixZYjR+QRCwefNm+Pv7l9nm888/l1b5WrRokbSSV1G+vr7YsmUL7O3tjT6PiMhasAAhIiJFGJsHEhUVJc3/MBQdANC5c2epeHj0mqLvixYtO3bskF6/9dZbRr/o//vf/5aGghW9rjShoaFo27Ztmee1Wi1+/fVXAICHhwcmTpxYZttWrVqhd+/eRp9HRGQtWIAQEZEiunXrJn3Z/+OPP6DX66Vzhh4RNzc3PPXUU9JxNzc3tG/fvlibR68Bihc3p06dkl6X9yW/YcOGaNq0KQAgISEBiYmJZbZ95plnjN7r/Pnz0o7sXbp0kXpkymJYZpiIyNqxACEiIkV4e3ujRYsWAIAHDx4gNjZWOmcoJrp06VJiuJShR6RowaHRaHDmzBkAgEqlwtNPPy2dMxQR7u7uxSaHl8WwR0nRa0vj5+dn9D5Fl/Rt3Lhxuc+V04aIyBqwACEiIsWUNg9Eq9UiKioKQPHhVwaGY8nJybh06RKA4vM/unTpIi3XCwCZmZkAAFdXV1kxubm5lbi2NI/uMfKookvyqtXqcp8rNz4iIkvHAoSIiBRTdK6GYQ7Ho/t/PCo0NFSax2G4xtj+H+7u7gAgLcFbnqKFg+HayihayGRnZ5fbXm58RESWjgUIEREp5tF5IDqdTiomXF1d0aFDhxLX1KpVC61btwYgrwDx9fUFUNibce/evXJjKrrLer169eR/mEfUr19fen3t2rVy28tpQ0RkDViAEBGRYry8vNCqVSsAQHp6Os6dOycVE0VXvHqUYRjWkSNHkJWVJc3/cHNzK1G0FJ0Psm/fPqPxJCQkSMv7+vv7y5ozUpZWrVpJE8+PHz8OrVZrtP2BAwcq/SwiIkvCAoSIiBRVtMfi999/l+Z/lDb8ysBQgKSmpuLbb7+V5n+EhoaWKFqGDx8uvf7888+h0+nKvO+iRYukfTuKXlcZzs7O6N+/P4DC4ur7778vs21cXFy5xRERkbVgAUJERIoqWmgsW7bM6PwPg2eeeUYauvXpp59Kxx8dfgUA/fv3R8uWLQEULo07ZcoUFBQUlGi3Zs0arFixAkDhpPGpU6dW+LM86q233pLinDVrlrS5YlH37t3D888/b7QwIiKyJqX3bRMREZlJ165dYWdnB71ej+TkZACFBUBp8z8M6tSpg5YtW+LChQvSNUDpBYidnR02bNiAzp07Q6PRYNWqVTh58iTGjRuHJ554AmlpaYiMjMTvv/8uXbN06VI0bNjQ5M/WpUsXvP7661i6dCkyMzPRtWtXjB07Ft26dYOzszNiY2OxevVqpKWlYdiwYeVufkhEZA1YgBARkaI8PT3Rpk0bxMTESMc6d+4MR0dHo9d169YNFy5ckN7XqlUL7dq1K7Vtq1atcOjQIQwbNgx37txBXFwcZs2aVaKdWq3G0qVLERERUclPU9KXX34JjUaD7777DgUFBVizZg3WrFlTrM3UqVMxdOhQFiBEZBM4BIuIiBT3aM+FseFXBo/uEfLMM89Iy/OWpkOHDoiPj8fSpUvRo0cPPP7443B0dISnpyfat2+P2bNn4+rVq1VafACFPTCrV6/Gnj17MHjwYPj4+MDJyQl+fn547rnn8Pvvv2Px4sVV+kwioppMEA2z7YiIiIiIiKoZe0CIiIiIiMhsWIAQEREREZHZsAAhIiIiIiKzYQFCRERERERmwwKEiIiIiIjMhgUIERERERGZDQsQIiIiIiIyGxYgRERERERkNixAiIiIiIjIbFiAEBERERGR2bAAISIiIiIis2EBQkREREREZsMChIiIiIiIzIYFCBERERERmQ0LECIiIiIiMhsWIEREREREZDYsQIiIiIiIyGxYgBARERERkdmwACEiIiIiIrNhAUJERERERGbDAoSIiIiIiMzm/wFbeT4txKovewAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 400x200 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 200,
              "width": 400
            }
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 400x200 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 200,
              "width": 400
            }
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pandas as pd\n",
        "from plotnine import ggplot, aes, geom_bar, theme, element_text, labs\n",
        "\n",
        "import pyvene as pv\n",
        "_, tokenizer, backpack_gpt2 = pv.create_backpack_gpt2()\n",
        "\n",
        "class MultiplierIntervention(pv.ConstantSourceIntervention):\n",
        "    \"\"\"Multiplier intervention\"\"\"\n",
        "\n",
        "    def __init__(self, multiplier, **kwargs):\n",
        "        super().__init__(**kwargs)\n",
        "        self.register_buffer('multiplier', torch.tensor(multiplier))\n",
        "\n",
        "    def forward(self, base, source=None, subspaces=None):\n",
        "        return base * self.multiplier\n",
        "\n",
        "    def __str__(self):\n",
        "        return f\"MultiplierIntervention()\"\n",
        "\n",
        "for c in [0, 0.7, 1]:\n",
        "    pv_backpack_gpt2 = pv.IntervenableModel({\n",
        "        \"component\": \"backpack.sense_network.output\",\n",
        "        \"intervention\": MultiplierIntervention(c), \"unit\": \"sense.pos\"},\n",
        "        model=backpack_gpt2\n",
        "    )\n",
        "    base = tokenizer(\"When the nurse walked into the room,\",\n",
        "                     return_tensors=\"pt\", return_attention_mask=False)\n",
        "    intervened_outputs = pv_backpack_gpt2(\n",
        "        base,\n",
        "        unit_locations={\n",
        "            # use   pv.GET_LOC((nv, s))\n",
        "            \"base\": pv.GET_LOC((10,2))\n",
        "        }\n",
        "    )\n",
        "\n",
        "    # plotting\n",
        "    probs = torch.nn.functional.softmax(\n",
        "        intervened_outputs[1].logits[0][-1], dim=0)\n",
        "    data = pv.top_vals(\n",
        "        tokenizer, probs, n=9,\n",
        "        return_results=True\n",
        "    )\n",
        "    df = pd.DataFrame(data, columns=['Word', 'Probability'])\n",
        "    df['Word'] = pd.Categorical(df['Word'], categories=[x[0] for x in data], ordered=True)\n",
        "    plot = (ggplot(df, aes(x='Word', y='Probability'))\n",
        "            + geom_bar(stat='identity')\n",
        "            + theme(axis_text_x=element_text(rotation=90, hjust=1),\n",
        "                    figure_size=(4, 2))\n",
        "            + labs(title=f\"mul({c})\")\n",
        "    )\n",
        "    print(plot)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cb539f4b",
      "metadata": {
        "id": "cb539f4b"
      },
      "source": [
        "### Saving and Loading\n",
        "This is one of the benefits of program abstraction. We abstract out the intervention and its schema, so we have a user friendly interface. Furthermore, it allows us to have a serializable configuration file that tells everything about your configuration.\n",
        "\n",
        "You can then save, share and load interventions easily. Note that you still need your access to the data, if you need to sample **Source** representations from other examples. But we think this is doable via a separate HuggingFace datasets upload. In the future, there could be an option of coupling this configuration with a specific remote dataset as well."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "272f3773",
      "metadata": {
        "id": "272f3773",
        "outputId": "883a37b4-de3d-4561-9e8c-144262aece73"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "Directory './tmp/' already exists.\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "# run with new intervention type\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "  \"intervention_type\": pv.ZeroIntervention},\n",
        "  model=gpt2)\n",
        "\n",
        "pv_gpt2.save(\"./tmp/\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "50b894b4",
      "metadata": {
        "id": "50b894b4",
        "outputId": "255b6c78-8daa-4187-8b39-fc19b8dedbf2"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING:root:The key is provided in the config. Assuming this is loaded from a pretrained module.\n",
            "WARNING:root:Loading trainable intervention from intkey_layer.0.repr.block_output.unit.pos.nunit.1#0.bin.\n"
          ]
        }
      ],
      "source": [
        "pv_gpt2 = pv.IntervenableModel.load(\n",
        "    \"./tmp/\",\n",
        "    model=gpt2)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b2d07ca8",
      "metadata": {
        "id": "b2d07ca8"
      },
      "source": [
        "### Multi-Source Interchange Intervention (Parallel Mode)\n",
        "\n",
        "What is multi-source? In the examples above, interventions are at most across two examples. We support interventions across many examples. You can sample representations from two inputs, and plut them into a single **Base**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "847410a8",
      "metadata": {
        "id": "847410a8",
        "outputId": "8e62c07b-8d48-4945-d56b-2b4346d0d8b3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "_the                 0.07233363389968872\n",
            "_a                   0.05731499195098877\n",
            "_not                 0.04443885385990143\n",
            "_Italian             0.033642884343862534\n",
            "_often               0.024385808035731316\n",
            "_called              0.022171705961227417\n",
            "_known               0.017808808013796806\n",
            "_that                0.016059240326285362\n",
            "_\"                   0.012973357923328876\n",
            "_an                  0.012878881767392159\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "parallel_config = pv.IntervenableConfig([\n",
        "  {\"layer\": 3, \"component\": \"block_output\"},\n",
        "  {\"layer\": 3, \"component\": \"block_output\"}],\n",
        "  # intervene on base at the same time\n",
        "  mode=\"parallel\")\n",
        "parallel_gpt2 = pv.IntervenableModel(\n",
        "  parallel_config, model=gpt2)\n",
        "base = tokenizer(\n",
        "  \"The capital of Spain is\",\n",
        "  return_tensors=\"pt\")\n",
        "sources = [\n",
        "  tokenizer(\"The language of Spain is\",\n",
        "    return_tensors=\"pt\"),\n",
        "  tokenizer(\"The capital of Italy is\",\n",
        "    return_tensors=\"pt\")]\n",
        "intervened_outputs = parallel_gpt2(\n",
        "    base, sources,\n",
        "    {\"sources->base\": (\n",
        "    # each list has a dimensionality of\n",
        "    # [num_intervention, batch, num_unit]\n",
        "    [[[1]],[[3]]],  [[[1]],[[3]]])}\n",
        ")\n",
        "\n",
        "distrib = pv.embed_to_distrib(\n",
        "    gpt2, intervened_outputs[1].last_hidden_state, logits=False)\n",
        "pv.top_vals(tokenizer, distrib[0][-1], n=10)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2f93402c",
      "metadata": {
        "id": "2f93402c"
      },
      "source": [
        "### Multi-Source Interchange Intervention (Serial Mode)\n",
        "\n",
        "Or you can do them sequentially, where you intervene among your **Source** examples, and get some intermediate states before merging the activations into the **Base** run."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5e5752dc",
      "metadata": {
        "id": "5e5752dc",
        "outputId": "e0414933-d5e4-4953-b4e0-f8a125954bdc"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "_the                 0.06737838685512543\n",
            "_a                   0.059834375977516174\n",
            "_not                 0.04629501700401306\n",
            "_Italian             0.03623826056718826\n",
            "_often               0.021700192242860794\n",
            "_called              0.01840786263346672\n",
            "_that                0.0157712884247303\n",
            "_known               0.014391838572919369\n",
            "_an                  0.013535155914723873\n",
            "_very                0.013022392988204956\n"
          ]
        }
      ],
      "source": [
        "config = pv.IntervenableConfig([\n",
        "  {\"layer\": 3, \"component\": \"block_output\"},\n",
        "  {\"layer\": 10, \"component\": \"block_output\"}],\n",
        "  # intervene on base one after another\n",
        "  mode=\"serial\")\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "  config, model=gpt2)\n",
        "base = tokenizer(\n",
        "  \"The capital of Spain is\",\n",
        "  return_tensors=\"pt\")\n",
        "sources = [\n",
        "  tokenizer(\"The language of Spain is\",\n",
        "    return_tensors=\"pt\"),\n",
        "  tokenizer(\"The capital of Italy is\",\n",
        "    return_tensors=\"pt\")]\n",
        "\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base, sources,\n",
        "    # intervene in serial at two positions\n",
        "    {\"source_0->source_1\": 1,\n",
        "     \"source_1->base\"    : 4})\n",
        "\n",
        "distrib = pv.embed_to_distrib(\n",
        "    gpt2, intervened_outputs[1].last_hidden_state, logits=False)\n",
        "pv.top_vals(tokenizer, distrib[0][-1], n=10)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "28621880",
      "metadata": {
        "id": "28621880"
      },
      "source": [
        "### Multi-Source Interchange Intervention with Subspaces (Parallel Mode)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "773aba2e",
      "metadata": {
        "id": "773aba2e",
        "outputId": "bd72ace4-bc18-447b-9030-706874e102cd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     \"subspace_partition\":\n",
        "         [[0, 128], [128, 256]]}]*2,\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        "    # act in parallel\n",
        "    mode=\"parallel\"\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\"),\n",
        "          tokenizer(\"The capital of China is\", return_tensors=\"pt\")]\n",
        "\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base, sources,\n",
        "    # on same position\n",
        "    {\"sources->base\": 4},\n",
        "    # on different subspaces\n",
        "    subspaces=[[[0]], [[1]]],\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7223603f",
      "metadata": {
        "id": "7223603f"
      },
      "source": [
        "### Multi-Source Interchange Intervention with Subspaces (Serial Mode)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "305e0607",
      "metadata": {
        "id": "305e0607",
        "outputId": "ff891f4a-aec3-446f-b143-0b56bb90fe8a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     \"subspace_partition\": [[0, 128], [128, 256]]},\n",
        "    {\"layer\": 2, \"component\": \"block_output\",\n",
        "     \"subspace_partition\": [[0, 128], [128, 256]]}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        "    # act in parallel\n",
        "    mode=\"serial\"\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\"),\n",
        "          tokenizer(\"The capital of China is\", return_tensors=\"pt\")]\n",
        "\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base, sources,\n",
        "    # serialized intervention\n",
        "    # order is based on sources list\n",
        "    {\"source_0->source_1\": 3, \"source_1->base\": 4},\n",
        "    # on different subspaces\n",
        "    subspaces=[[[0]], [[1]]],\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4b5fcb37",
      "metadata": {
        "id": "4b5fcb37"
      },
      "source": [
        "### Interchange Intervention Training (IIT)\n",
        "Interchange intervention training (IIT) is a technique of inducing causal structures into neural models. This library naturally supports this. By training IIT, you can simply turn the gradient on for the wrapping model. In this way, your model can be trained with your interventional signals."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8c7dde89",
      "metadata": {
        "id": "8c7dde89",
        "outputId": "7364e09f-47f0-42a5-84d4-83478d21bd19"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "number of params: 124439808\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "tensor([[[ 0.0022, -0.1783, -0.2780,  ...,  0.0477, -0.2069,  0.1093],\n",
              "         [ 0.0385,  0.0886, -0.6608,  ...,  0.0104, -0.4946,  0.6148],\n",
              "         [ 0.2377, -0.2312,  0.0308,  ...,  0.1085,  0.0456,  0.2494],\n",
              "         [-0.0034,  0.0088, -0.2219,  ...,  0.1198,  0.0759,  0.3953],\n",
              "         [ 0.4635,  0.2698, -0.3185,  ..., -0.2946,  0.2634,  0.2714]]],\n",
              "       grad_fn=<SubBackward0>)"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel({\n",
        "    \"layer\": 8, \"component\": \"block_output\"},\n",
        "    model=gpt2\n",
        ")\n",
        "\n",
        "pv_gpt2.enable_model_gradients()\n",
        "print(\"number of params:\", pv_gpt2.count_parameters())\n",
        "\n",
        "# run counterfactual forward as usual\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "sources = [\n",
        "    tokenizer(\"The capital of Italy is\", return_tensors=\"pt\"),\n",
        "]\n",
        "base_outputs, counterfactual_outputs = pv_gpt2(\n",
        "    base, sources, {\"sources->base\": ([[[3]]], [[[3]]])}\n",
        ")\n",
        "print(counterfactual_outputs.last_hidden_state - base_outputs.last_hidden_state)\n",
        "# call backward will put gradients on model's weights\n",
        "counterfactual_outputs.last_hidden_state.sum().backward()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b8c7ccad",
      "metadata": {
        "id": "b8c7ccad"
      },
      "source": [
        "## pyvene 102\n",
        "Now, you are pretty familiar with pyvene basic APIs. There are more to come. We support all sorts of weird interventions, and we encapsulate them as objects so that, even they are super weird (e.g., nested, multiple locations, different types), you can share them easily with others. BTW, if the intervention is trainable, the artifacts will be saved and shared as well.\n",
        "\n",
        "With that, here are a couple of additional APIs.\n",
        "\n",
        "### Grouping\n",
        "\n",
        "You can group interventions together so that they always receive the same input when you want to use them to get activations at different places. Here is an example, where you are taking in the same **Source** example, you fetch activations twice: once in position 3 and layer 0, once in position 4 and layer 2. You don't have to pass in another dummy **Source**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "84afd62c",
      "metadata": {
        "id": "84afd62c",
        "outputId": "1979aeb6-da10-4625-e83b-0496b76d1ba9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    {\"layer\": 0, \"component\": \"block_output\", \"group_key\": 0},\n",
        "    {\"layer\": 2, \"component\": \"block_output\", \"group_key\": 0}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        ")\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "sources = [tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")]\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base, sources,\n",
        "    {\"sources->base\": ([\n",
        "        [[3]], [[4]] # these two are for two interventions\n",
        "    ], [             # source position 3 into base position 4\n",
        "        [[3]], [[4]]\n",
        "    ])}\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "34aeb892",
      "metadata": {
        "id": "34aeb892"
      },
      "source": [
        "### Intervention Skipping in Runtime\n",
        "You may configure a lot of interventions, but during training, not every example will have to use all of them. So, you can skip interventions for different examples differently."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "61cd8fc9",
      "metadata": {
        "id": "61cd8fc9",
        "outputId": "b1ac3d2e-64e1-42a2-c732-33f1971b1ccb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "True True\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    # these are equivalent interventions\n",
        "    # we create them on purpose\n",
        "    {\"layer\": 0, \"component\": \"block_output\"},\n",
        "    {\"layer\": 0, \"component\": \"block_output\"},\n",
        "    {\"layer\": 0, \"component\": \"block_output\"}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
        "# skipping 1, 2 and 3\n",
        "_, pv_out1 = pv_gpt2(base, [None, None, source],\n",
        "    {\"sources->base\": ([None, None, [[4]]], [None, None, [[4]]])})\n",
        "_, pv_out2 = pv_gpt2(base, [None, source, None],\n",
        "    {\"sources->base\": ([None, [[4]], None], [None, [[4]], None])})\n",
        "_, pv_out3 = pv_gpt2(base, [source, None, None],\n",
        "    {\"sources->base\": ([[[4]], None, None], [[[4]], None, None])})\n",
        "# should have the same results\n",
        "print(\n",
        "    torch.equal(pv_out1.last_hidden_state, pv_out2.last_hidden_state),\n",
        "    torch.equal(pv_out2.last_hidden_state, pv_out3.last_hidden_state)\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d9df6acd",
      "metadata": {
        "id": "d9df6acd"
      },
      "source": [
        "### Subspace Partition\n",
        "You can partition your subspace before hand. If you don't, the library assumes you each neuron is in its own subspace. In this example, you partition your subspace into two continous chunk, `[0, 128), [128,256)`, which means all the neurons from index 0 upto 127 are along to partition 1. During runtime, you can intervene on all the neurons in the same parition together."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3a66bbeb",
      "metadata": {
        "id": "3a66bbeb",
        "outputId": "9d02e27f-7670-43e2-b26a-beacd11a1500"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    # they are linked to manipulate the same representation\n",
        "    # but in different subspaces\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     # subspaces can be partitioned into continuous chunks\n",
        "     # [i, j] are the boundary indices\n",
        "     \"subspace_partition\": [[0, 128], [128, 256]]}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
        "\n",
        "# using intervention skipping for subspace\n",
        "intervened_outputs = pv_gpt2(\n",
        "    base, [source],\n",
        "    {\"sources->base\": 4},\n",
        "    # intervene only only dimensions from 128 to 256\n",
        "    subspaces=1,\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0fdde257",
      "metadata": {
        "id": "0fdde257"
      },
      "source": [
        "### Intervention Linking\n",
        "Interventions can be linked to share weights and share subspaces. Here is an example of how to link interventions together. If interventions are trainable, then their weights are tied as well.\n",
        "\n",
        "Why this is useful? it is because sometimes, you may want to intervene on different subspaces differently. Say you have a representation in a size of 512, and you hypothesize the first half represents A, and the second half represents B, you can then use the subspace intervention to test it out. With trainable interventions, you can also optimize your interventions on the same representation yet with different subspaces."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "eec19da9",
      "metadata": {
        "id": "eec19da9",
        "outputId": "912783e1-1d3c-4e56-8bc8-e7c117cb14d8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "True\n",
            "True\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    # they are linked to manipulate the same representation\n",
        "    # but in different subspaces\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     \"subspace_partition\": [[0, 128], [128, 256]], \"intervention_link_key\": 0},\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     \"subspace_partition\": [[0, 128], [128, 256]], \"intervention_link_key\": 0}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
        "\n",
        "# using intervention skipping for subspace\n",
        "_, pv_out1 = pv_gpt2(\n",
        "    base, [None, source],\n",
        "    # 4 means token position 4\n",
        "    {\"sources->base\": ([None, [[4]]], [None, [[4]]])},\n",
        "    # 1 means the second partition in the config\n",
        "    subspaces=[None, [[1]]],\n",
        ")\n",
        "_, pv_out2 = pv_gpt2(\n",
        "    base,\n",
        "    [source, None],\n",
        "    {\"sources->base\": ([[[4]], None], [[[4]], None])},\n",
        "    subspaces=[[[1]], None],\n",
        ")\n",
        "print(torch.equal(pv_out1.last_hidden_state, pv_out2.last_hidden_state))\n",
        "\n",
        "# subspaces provide a list of index and they can be in any order\n",
        "_, pv_out3 = pv_gpt2(\n",
        "    base,\n",
        "    [source, source],\n",
        "    {\"sources->base\": ([[[4]], [[4]]], [[[4]], [[4]]])},\n",
        "    subspaces=[[[0]], [[1]]],\n",
        ")\n",
        "_, pv_out4 = pv_gpt2(\n",
        "    base,\n",
        "    [source, source],\n",
        "    {\"sources->base\": ([[[4]], [[4]]], [[[4]], [[4]]])},\n",
        "    subspaces=[[[1]], [[0]]],\n",
        ")\n",
        "print(torch.equal(pv_out3.last_hidden_state, pv_out4.last_hidden_state))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "243f146f-1b9a-4574-ba2c-ebf455a96c16",
      "metadata": {
        "id": "243f146f-1b9a-4574-ba2c-ebf455a96c16"
      },
      "source": [
        "Other than intervention linking, you can also share interventions at the same component across multiple positions via setting a flag in the intervention object. It will have the same effect as creating one intervention per location and linking them all together."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7c647943-c7e1-4024-8c07-b51062e668ba",
      "metadata": {
        "id": "7c647943-c7e1-4024-8c07-b51062e668ba",
        "outputId": "a89110fe-a8a8-4700-869f-b9ca21b420f5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "tensor([[[0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.],\n",
              "         [0., 0., 0.,  ..., 0., 0., 0.]]])"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "config = pv.IntervenableConfig([\n",
        "    # they are linked to manipulate the same representation\n",
        "    # but in different subspaces\n",
        "    {\"layer\": 0, \"component\": \"block_output\", \"intervention_link_key\": 0},\n",
        "    {\"layer\": 0, \"component\": \"block_output\", \"intervention_link_key\": 0}],\n",
        "    intervention_types=pv.VanillaIntervention,\n",
        ")\n",
        "pv_gpt2 = pv.IntervenableModel(config, model=gpt2)\n",
        "\n",
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
        "\n",
        "_, pv_out = pv_gpt2(\n",
        "    base,\n",
        "    [source, source],\n",
        "    # swap 3rd and 4th token reprs from the same source to the base\n",
        "    {\"sources->base\": ([[[4]], [[3]]], [[[4]], [[3]]])},\n",
        ")\n",
        "\n",
        "keep_last_dim_config = pv.IntervenableConfig([\n",
        "    # they are linked to manipulate the same representation\n",
        "    # but in different subspaces\n",
        "    {\"layer\": 0, \"component\": \"block_output\",\n",
        "     \"intervention\": pv.VanillaIntervention(keep_last_dim=True)}]\n",
        ")\n",
        "keep_last_dim_pv_gpt2 = pv.IntervenableModel(keep_last_dim_config, model=gpt2)\n",
        "\n",
        "_, keep_last_dim_pv_out = keep_last_dim_pv_gpt2(\n",
        "    base,\n",
        "    [source],\n",
        "    # swap 3rd and 4th token reprs from the same source to the base\n",
        "    {\"sources->base\": ([[[3,4]]], [[[3,4]]])},\n",
        ")\n",
        "keep_last_dim_pv_out.last_hidden_state - pv_out.last_hidden_state"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ef5b7a3e",
      "metadata": {
        "id": "ef5b7a3e"
      },
      "source": [
        "### Add New Model Type"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "acce6e8f",
      "metadata": {
        "id": "acce6e8f",
        "outputId": "93b67105-8a31-4074-b537-9eb0674465ee"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "You are using the default legacy behaviour of the <class 'transformers.models.t5.tokenization_t5.T5Tokenizer'>. This is expected, and simply means that the `legacy` (previous) behavior will be used so nothing changes for you. If you want to use the new behaviour, set `legacy=False`. This should only be set if you understand what it means, and thoroughly read the reason why this was added as explained in https://github.com/huggingface/transformers/pull/24565\n",
            "Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained.\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "\n",
        "# get a flan-t5 from HuggingFace\n",
        "from transformers import T5ForConditionalGeneration, T5Tokenizer, T5Config\n",
        "config = T5Config.from_pretrained(\"google/flan-t5-small\")\n",
        "tokenizer = T5Tokenizer.from_pretrained(\"google/flan-t5-small\")\n",
        "t5 = T5ForConditionalGeneration.from_pretrained(\n",
        "    \"google/flan-t5-small\", config=config\n",
        ")\n",
        "\n",
        "# config the intervention mapping with pv global vars\n",
        "\"\"\"Only define for the block output here for simplicity\"\"\"\n",
        "pv.type_to_module_mapping[type(t5)] = {\n",
        "    \"mlp_output\": (\"encoder.block[%s].layer[1]\",\n",
        "                   pv.models.constants.CONST_OUTPUT_HOOK),\n",
        "    \"attention_input\": (\"encoder.block[%s].layer[0]\",\n",
        "                        pv.models.constants.CONST_OUTPUT_HOOK),\n",
        "}\n",
        "pv.type_to_dimension_mapping[type(t5)] = {\n",
        "    \"mlp_output\": (\"d_model\",),\n",
        "    \"attention_input\": (\"d_model\",),\n",
        "    \"block_output\": (\"d_model\",),\n",
        "    \"head_attention_value_output\": (\"d_model/num_heads\",),\n",
        "}\n",
        "\n",
        "# wrap as gpt2\n",
        "pv_t5 = pv.IntervenableModel({\n",
        "    \"layer\": 0,\n",
        "    \"component\": \"mlp_output\",\n",
        "    \"source_representation\": torch.zeros(\n",
        "        t5.config.d_model)\n",
        "}, model=t5)\n",
        "\n",
        "# then intervene!\n",
        "base = tokenizer(\"The capital of Spain is\",\n",
        "                 return_tensors=\"pt\")\n",
        "decoder_input_ids = tokenizer(\n",
        "    \"\", return_tensors=\"pt\").input_ids\n",
        "base[\"decoder_input_ids\"] = decoder_input_ids\n",
        "intervened_outputs = pv_t5(\n",
        "    base,\n",
        "    unit_locations={\"base\": 3}\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ba158a92",
      "metadata": {
        "id": "ba158a92"
      },
      "source": [
        "### Composing Complex Intervention Schema: Path Patching"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e51cadfe",
      "metadata": {
        "id": "e51cadfe",
        "outputId": "186eb16d-e30f-4c51-a78c-749dcdac7112"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n",
            "Directory './tmp/' already exists.\n"
          ]
        }
      ],
      "source": [
        "import pyvene as pv\n",
        "\n",
        "def path_patching_config(\n",
        "    layer, last_layer,\n",
        "    component=\"head_attention_value_output\", unit=\"h.pos\"\n",
        "):\n",
        "    intervening_component = [\n",
        "        {\"layer\": layer, \"component\": component, \"unit\": unit, \"group_key\": 0}]\n",
        "    restoring_components = []\n",
        "    if not component.startswith(\"mlp_\"):\n",
        "        restoring_components += [\n",
        "            {\"layer\": layer, \"component\": \"mlp_output\", \"group_key\": 1}]\n",
        "    for i in range(layer+1, last_layer):\n",
        "        restoring_components += [\n",
        "            {\"layer\": i, \"component\": \"attention_output\", \"group_key\": 1},\n",
        "            {\"layer\": i, \"component\": \"mlp_output\", \"group_key\": 1}\n",
        "        ]\n",
        "    intervenable_config = pv.IntervenableConfig(\n",
        "        intervening_component + restoring_components)\n",
        "    return intervenable_config\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "    path_patching_config(4, gpt2.config.n_layer),\n",
        "    model=gpt2\n",
        ")\n",
        "\n",
        "pv_gpt2.save(\n",
        "    save_directory=\"./tmp/\"\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9074f716",
      "metadata": {
        "id": "9074f716",
        "outputId": "941ef050-bb18-4412-fbc1-ce10a6fbd24f"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING:root:The key is provided in the config. Assuming this is loaded from a pretrained module.\n"
          ]
        }
      ],
      "source": [
        "pv_gpt2 = pv.IntervenableModel.load(\n",
        "    \"./tmp/\",\n",
        "    model=gpt2)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d546e858",
      "metadata": {
        "id": "d546e858"
      },
      "source": [
        "### Composing Complex Intervention Schema: Causal Tracing in 15 lines"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c0b6a70f",
      "metadata": {
        "id": "c0b6a70f",
        "outputId": "bd06d7c9-bdd1-4b63-aa97-168dccfde52a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import pyvene as pv\n",
        "\n",
        "def causal_tracing_config(\n",
        "  l, c=\"mlp_activation\", w=10, tl=48):\n",
        "  s = max(0, l - w // 2)\n",
        "  e = min(tl, l - (-w // 2))\n",
        "  config = pv.IntervenableConfig(\n",
        "    [{\"component\": \"block_input\"}] +\n",
        "    [{\"layer\": l, \"component\": c}\n",
        "      for l in range(s, e)],\n",
        "    [pv.NoiseIntervention] +\n",
        "    [pv.VanillaIntervention]*(e-s))\n",
        "  return config\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "\n",
        "pv_gpt2 = pv.IntervenableModel(\n",
        "    causal_tracing_config(4),\n",
        "    model=gpt2\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5027498b-66b9-428a-9693-94a6b5614bb9",
      "metadata": {
        "id": "5027498b-66b9-428a-9693-94a6b5614bb9"
      },
      "source": [
        "### Inference-time Intervention"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "559bf80a-2a79-46f0-b8a1-8848fd49613b",
      "metadata": {
        "id": "559bf80a-2a79-46f0-b8a1-8848fd49613b",
        "outputId": "b947682a-c45a-4b58-d83d-1941a9a40752",
        "colab": {
          "referenced_widgets": [
            "09c7100d49c94e1b94f3429440f1aab3"
          ]
        }
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "normalizer.cc(51) LOG(INFO) precompiled_charsmap is empty. use identity normalization.\n"
          ]
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "09c7100d49c94e1b94f3429440f1aab3",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Loading checkpoint shards:   0%|          | 0/2 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import time, torch\n",
        "import pyvene as pv\n",
        "config, tokenizer, llama = pv.create_llama(\"meta-llama/Llama-2-7b-chat-hf\")\n",
        "# load cached extracted activations from the ITI repo:\n",
        "# https://github.com/likenneth/honest_llama\n",
        "o_proj_add_activations = torch.load(\n",
        "    \"./tutorials/basic_tutorials/tutorial_data\"\n",
        "    \"/honest_llama2_chat_7B_o_proj_add_activations.bin\"\n",
        ")\n",
        "_ = llama.cuda()\n",
        "\n",
        "pv_llama = pv.IntervenableModel([{\n",
        "        \"component\": f\"model.layers[{i}].self_attn.o_proj.output\",\n",
        "        \"intervention\": pv.AdditionIntervention(\n",
        "            source_representation=o_proj_add_activations[i].to(\"cuda\")\n",
        "        )\n",
        "    } for i in range(config.num_hidden_layers) if torch.count_nonzero(o_proj_add_activations[i])],\n",
        "    model=llama\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "15992a70-288a-43b5-9baf-348e7cb34068",
      "metadata": {
        "id": "15992a70-288a-43b5-9baf-348e7cb34068",
        "outputId": "48092ea0-72d6-4bbb-c532-5fa31080bad4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "vanilla llama-2-chat:\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/sailhome/wuzhengx/.local/lib/python3.8/site-packages/transformers/generation/configuration_utils.py:392: UserWarning: `do_sample` is set to `False`. However, `temperature` is set to `0.6` -- this flag is only used in sample-based generation modes. You should set `do_sample=True` or unset `temperature`.\n",
            "  warnings.warn(\n",
            "/sailhome/wuzhengx/.local/lib/python3.8/site-packages/transformers/generation/configuration_utils.py:397: UserWarning: `do_sample` is set to `False`. However, `top_p` is set to `0.9` -- this flag is only used in sample-based generation modes. You should set `do_sample=True` or unset `top_p`.\n",
            "  warnings.warn(\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "What's a cure for insomnia that always works?\n",
            "\n",
            "Insomnia is a common sleep disorder that can affect anyone, regardless of age or gender. It is characterized by difficulty falling asleep, staying asleep, or getting quality sleep. Insomnia can be caused by a variety of factors, including stress, anxiety, depression, certain\n",
            "Execution time: 2.1844897270202637 seconds\n",
            "\n",
            "honest llama-2-chat:\n",
            "What's a cure for insomnia that always works?\n",
            "There is no single cure for insomnia that works for everyone, and it's important to address the underlying causes of sleep problems. However, some strategies that may help improve sleep quality and duration include:\n",
            "\n",
            "1. Practicing relaxation techniques, such as deep breathing, progressive mus\n",
            "Execution time: 2.6960761547088623 seconds\n"
          ]
        }
      ],
      "source": [
        "q = \"What's a cure for insomnia that always works?\"\n",
        "prompt = tokenizer(q, return_tensors=\"pt\").to(\"cuda\")\n",
        "print(\"vanilla llama-2-chat:\")\n",
        "st = time.time()\n",
        "response = llama.generate(**prompt, max_new_tokens=64, do_sample=False)\n",
        "print(tokenizer.decode(response[0], skip_special_tokens=True))\n",
        "et = time.time()\n",
        "elapsed_time = et - st\n",
        "print('Execution time:', elapsed_time, 'seconds')\n",
        "print()\n",
        "print(\"honest llama-2-chat:\")\n",
        "st = time.time()\n",
        "_, iti_response = pv_llama.generate(prompt, max_new_tokens=64, do_sample=False)\n",
        "print(tokenizer.decode(iti_response[0], skip_special_tokens=True))\n",
        "et = time.time()\n",
        "elapsed_time = et - st\n",
        "print('Execution time:', elapsed_time, 'seconds')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7ae2ebe8-fa4d-426e-b663-089671323456",
      "metadata": {
        "id": "7ae2ebe8-fa4d-426e-b663-089671323456",
        "outputId": "3824764d-2030-4ea1-8110-7eed5d49139b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Directory './tmp_llama/' already exists.\n"
          ]
        }
      ],
      "source": [
        "# save to huggingface directly\n",
        "try:\n",
        "    pv_llama.save(\n",
        "        \"./tmp_llama/\",\n",
        "        save_to_hf_hub=True,\n",
        "        hf_repo_name=\"zhengxuanzenwu/intervenable_honest_llama2_chat_7B\"\n",
        "    )\n",
        "except:\n",
        "    print(\"You have to login into huggingface hub before running this.\")\n",
        "    print(\"usage: huggingface-cli login\")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1c7b90b0",
      "metadata": {
        "id": "1c7b90b0"
      },
      "source": [
        "### IntervenableModel from HuggingFace Directly"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b5d26852-f86d-4dea-88f1-2db2634e1ba5",
      "metadata": {
        "id": "b5d26852-f86d-4dea-88f1-2db2634e1ba5",
        "outputId": "4e1b9592-67f7-45b6-b51f-261662ab931b",
        "colab": {
          "referenced_widgets": [
            "437f82c9e5ff4a39ae988ccbfd7518df",
            "c8b98f21c02a4e5da60d67098d99a2c5"
          ]
        }
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "437f82c9e5ff4a39ae988ccbfd7518df",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Loading checkpoint shards:   0%|          | 0/2 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "c8b98f21c02a4e5da60d67098d99a2c5",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Fetching 17 files:   0%|          | 0/17 [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "WARNING:root:The key is provided in the config. Assuming this is loaded from a pretrained module.\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "llama-2-chat loaded with interventions:\n",
            "What's a cure for insomnia that always works?\n",
            "There is no single cure for insomnia that works for everyone, and it's important to address the underlying causes of sleep problems. However, some strategies that may help improve sleep quality and duration include:\n",
            "\n",
            "1. Practicing relaxation techniques, such as deep breathing, progressive mus\n"
          ]
        }
      ],
      "source": [
        "# others can download from huggingface and use it directly\n",
        "import torch\n",
        "from transformers import AutoTokenizer, AutoModelForCausalLM\n",
        "import pyvene as pv\n",
        "\n",
        "tokenizer = AutoTokenizer.from_pretrained(\"meta-llama/Llama-2-7b-chat-hf\")\n",
        "model = AutoModelForCausalLM.from_pretrained(\n",
        "    \"meta-llama/Llama-2-7b-chat-hf\",\n",
        "    torch_dtype=torch.bfloat16,\n",
        ").to(\"cuda\")\n",
        "\n",
        "pv_model = pv.IntervenableModel.load(\n",
        "    \"zhengxuanzenwu/intervenable_honest_llama2_chat_7B\", # the activation diff ~0.14MB\n",
        "    model,\n",
        ")\n",
        "\n",
        "print(\"llama-2-chat loaded with interventions:\")\n",
        "q = \"What's a cure for insomnia that always works?\"\n",
        "prompt = tokenizer(q, return_tensors=\"pt\").to(\"cuda\")\n",
        "_, iti_response_shared = pv_model.generate(prompt, max_new_tokens=64, do_sample=False)\n",
        "print(tokenizer.decode(iti_response_shared[0], skip_special_tokens=True))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "956b3b5f",
      "metadata": {
        "id": "956b3b5f"
      },
      "source": [
        "### Path Patching with Trainable Interventions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "af501960",
      "metadata": {
        "id": "af501960",
        "outputId": "0f05f711-f6bb-4c8b-ab2d-55f3d0a80ab7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loaded model\n"
          ]
        }
      ],
      "source": [
        "import pyvene as pv\n",
        "\n",
        "def path_patching_with_DAS_config(\n",
        "    layer, last_layer, low_rank_dimension,\n",
        "    component=\"attention_output\", unit=\"pos\"\n",
        "):\n",
        "    intervening_component = [{\n",
        "        \"layer\": layer, \"component\": component, \"group_key\": 0,\n",
        "        \"intervention_type\": pv.LowRankRotatedSpaceIntervention,\n",
        "        \"low_rank_dimension\": low_rank_dimension,\n",
        "    }]\n",
        "    restoring_components = []\n",
        "    if not component.startswith(\"mlp_\"):\n",
        "        restoring_components += [{\n",
        "            \"layer\": layer, \"component\": \"mlp_output\", \"group_key\": 1,\n",
        "            \"intervention_type\": pv.VanillaIntervention,\n",
        "        }]\n",
        "    for i in range(layer+1, last_layer):\n",
        "        restoring_components += [{\n",
        "            \"layer\": i, \"component\": \"attention_output\", \"group_key\": 1,\n",
        "            \"intervention_type\": pv.VanillaIntervention},{\n",
        "            \"layer\": i, \"component\": \"mlp_output\", \"group_key\": 1,\n",
        "            \"intervention_type\": pv.VanillaIntervention\n",
        "        }]\n",
        "    intervenable_config = pv.IntervenableConfig(\n",
        "        intervening_component + restoring_components)\n",
        "    return intervenable_config, len(restoring_components)\n",
        "\n",
        "_, tokenizer, gpt2 = pv.create_gpt2()\n",
        "pv_config, num_restores = path_patching_with_DAS_config(4, 6, 1)\n",
        "pv_gpt2 = pv.IntervenableModel(pv_config, model=gpt2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "be63453e",
      "metadata": {
        "id": "be63453e",
        "outputId": "def752b7-f155-430b-86ef-af66deca05cd"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(-0.0694, grad_fn=<SumBackward0>)"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "base = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "restore_source = tokenizer(\"The capital of Spain is\", return_tensors=\"pt\")\n",
        "source = tokenizer(\"The capital of Italy is\", return_tensors=\"pt\")\n",
        "\n",
        "# zero-out grads\n",
        "_ = pv_gpt2.model.eval()\n",
        "for k, v in pv_gpt2.interventions.items():\n",
        "    v[0].zero_grad()\n",
        "\n",
        "original_outputs, counterfactual_outputs = pv_gpt2(\n",
        "    base,\n",
        "    sources=[source, restore_source],\n",
        "    unit_locations={\n",
        "        \"sources->base\": 4\n",
        "    }\n",
        ")\n",
        "# put gradients on the trainable intervention only\n",
        "counterfactual_outputs[0].sum().backward()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0907a98c",
      "metadata": {
        "id": "0907a98c"
      },
      "source": [
        "### Intervene on ResNet with Lambda Functions\n",
        "\n",
        "Huggingface Vision model comes with the support of ResNet. Here, we show how we can use pyvene to intervene on a patch of pixels, like token in transformer, which is like a primitive object in ResNet or ConvNet based NNs.\n",
        "\n",
        "**Caveats:** We go with a pretty much hard-coded way here, but you can customize the hook functions as you want. It does not have to be a lambda function as well."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bfb48112",
      "metadata": {
        "id": "bfb48112",
        "outputId": "0f50c58a-b693-4933-d81b-cc475c82b74a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(0.0005)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "from datasets import load_dataset\n",
        "from transformers import AutoFeatureExtractor, AutoModelForImageClassification\n",
        "\n",
        "feature_extractor = AutoFeatureExtractor.from_pretrained(\"microsoft/resnet-18\")\n",
        "resnet = AutoModelForImageClassification.from_pretrained(\"microsoft/resnet-18\")\n",
        "\n",
        "dataset = load_dataset(\"huggingface/cats-image\")\n",
        "base_image = dataset[\"test\"][\"image\"][0]\n",
        "source_image = dataset[\"test\"][\"image\"][0]\n",
        "base_inputs = feature_extractor(base_image, return_tensors=\"pt\")\n",
        "source_inputs = feature_extractor(source_image, return_tensors=\"pt\")\n",
        "source_inputs['pixel_values'] += 0.5*torch.randn(source_inputs['pixel_values'].shape)\n",
        "\n",
        "def create_mask():\n",
        "    _mask = torch.zeros((56, 56))\n",
        "    _mask[56//2:, 56//2:] = 1\n",
        "    return _mask\n",
        "m = create_mask()\n",
        "\n",
        "pv_resnet = pv.IntervenableModel({\n",
        "    \"component\": \"resnet.embedder.pooler.output\",\n",
        "    \"intervention\": lambda b, s: b * (1. - m) + s * m},\n",
        "    model=resnet\n",
        ")\n",
        "intervened_outputs = pv_resnet(\n",
        "    base_inputs, [source_inputs], return_dict=True\n",
        ")\n",
        "(intervened_outputs.intervened_outputs.logits - intervened_outputs.original_outputs.logits).sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b4d0aa78",
      "metadata": {
        "id": "b4d0aa78"
      },
      "source": [
        "### Intervene on ResNet with Trainable Lambda Functions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6d0095f3",
      "metadata": {
        "id": "6d0095f3",
        "outputId": "d6e9959e-1b2d-4473-b3b3-7f992389b8a0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor(0.0068, grad_fn=<SumBackward0>)"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import torch\n",
        "import pyvene as pv\n",
        "from datasets import load_dataset\n",
        "from transformers import AutoFeatureExtractor, AutoModelForImageClassification\n",
        "\n",
        "feature_extractor = AutoFeatureExtractor.from_pretrained(\"microsoft/resnet-18\")\n",
        "resnet = AutoModelForImageClassification.from_pretrained(\"microsoft/resnet-18\")\n",
        "\n",
        "dataset = load_dataset(\"huggingface/cats-image\")\n",
        "base_image = dataset[\"test\"][\"image\"][0]\n",
        "source_image = dataset[\"test\"][\"image\"][0]\n",
        "base_inputs = feature_extractor(base_image, return_tensors=\"pt\")\n",
        "source_inputs = feature_extractor(source_image, return_tensors=\"pt\")\n",
        "source_inputs['pixel_values'] += 0.5*torch.randn(source_inputs['pixel_values'].shape)\n",
        "\n",
        "# trainable DAS directions\n",
        "v = torch.nn.utils.parametrizations.orthogonal(\n",
        "    torch.nn.Linear(56, 10))\n",
        "\n",
        "pv_resnet = pv.IntervenableModel({\n",
        "    \"component\": \"resnet.embedder.pooler.output\",\n",
        "    \"intervention\": lambda b, s: b + ((s @ v.weight.T - b @ v.weight.T) @ v.weight)},\n",
        "    model=resnet\n",
        ")\n",
        "\n",
        "intervened_outputs = pv_resnet(\n",
        "    base_inputs, [source_inputs], return_dict=True\n",
        ")\n",
        "(intervened_outputs.intervened_outputs.logits - intervened_outputs.original_outputs.logits).sum()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bc6eb49d",
      "metadata": {
        "id": "bc6eb49d"
      },
      "source": [
        "### The End\n",
        "Now you are graduating from pyvene entry level course! Feel free to take a look at our tutorials for more challenging interventions."
      ]
    }
  ],
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