FirstNN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "08c7604a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8003e8ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "136f8f98",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_parameters(n_x, n_h, n_y):\n",
    "    W1 = np.random.randn(n_h, n_x)\n",
    "    b1 = np.zeros((n_h, 1))\n",
    "    W2 = np.random.randn(n_y, n_h)\n",
    "    b2 = np.zeros((n_y, 1))\n",
    "    \n",
    "    parameters = {\"W1\" : W1, \"b1\": b1,\n",
    "                  \"W2\" : W2, \"b2\": b2}\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dc2f9d7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_propagation(X, Y, parameters):\n",
    "    m = X.shape[1]\n",
    "    W1 = parameters[\"W1\"]\n",
    "    W2 = parameters[\"W2\"]\n",
    "    b1 = parameters[\"b1\"]\n",
    "    b2 = parameters[\"b2\"]\n",
    "    Z1 = np.dot(W1, X) + b1\n",
    "    A1 = sigmoid(Z1)\n",
    "    Z2 = np.dot(W2, A1) + b2\n",
    "    A2 = sigmoid(Z2)\n",
    "    cache = (Z1, A1, W1, b1, Z2, A2, W2, b2)\n",
    "    logprobs = np.multiply(np.log(A2), Y) + np.multiply(np.log(1 - A2), (1 - Y))\n",
    "    cost = -np.sum(logprobs) / m\n",
    "    return cost, cache, A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4355a404",
   "metadata": {},
   "outputs": [],
   "source": [
    "def backward_propagation(X, Y, cache):\n",
    "    m = X.shape[1]\n",
    "    (Z1, A1, W1, b1, Z2, A2, W2, b2) = cache\n",
    "    \n",
    "    dZ2 = A2 - Y\n",
    "    dW2 = np.dot(dZ2, A1.T) / m\n",
    "    db2 = np.sum(dZ2, axis = 1, keepdims=True)\n",
    "    \n",
    "    dA1 = np.dot(W2.T, dZ2)\n",
    "    dZ1 = np.multiply(dA1, A1 * (1- A1))\n",
    "    dW1 = np.dot(dZ1, X.T) / m\n",
    "    db1 = np.sum(dZ1, axis=1, keepdims=True) / m\n",
    "    \n",
    "    gradients = {\"dZ2\": dZ2, \"dW2\": dW2, \"db2\": db2,\n",
    "                 \"dZ1\": dZ1, \"dW1\": dW1, \"db1\": db1}\n",
    "    return gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "76eec306",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_parameters(parameters, grads, learning_rate):\n",
    "    parameters[\"W1\"] = parameters[\"W1\"] - learning_rate * grads[\"dW1\"]\n",
    "    parameters[\"W2\"] = parameters[\"W2\"] - learning_rate * grads[\"dW2\"]\n",
    "    parameters[\"b1\"] = parameters[\"b1\"] - learning_rate * grads[\"db1\"]\n",
    "    parameters[\"b2\"] = parameters[\"b2\"] - learning_rate * grads[\"db2\"]\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f2d7fbd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([[0, 0, 1, 1], [0, 1, 0, 1]])\n",
    "Y = np.array([[0, 1, 1, 0]]) # XOR\n",
    "n_h = 2\n",
    "n_x = X.shape[0]\n",
    "n_y = Y.shape[0]\n",
    "parameters = initialize_parameters(n_x, n_h, n_y)\n",
    "num_iterations = 100000\n",
    "learning_rate = 0.01\n",
    "losses = np.zeros((num_iterations, 1))\n",
    "\n",
    "for i in range(num_iterations):\n",
    "    losses[i, 0], cache, A2 = forward_propagation(X, Y, parameters)\n",
    "    grads = backward_propagation(X, Y, cache)\n",
    "    parameters = update_parameters(parameters, grads, learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d6fedb57",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.00937659 0.98897399 0.49790576 0.50500673]]\n",
      "[[0. 1. 0. 1.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cost, _, A2 = forward_propagation(X, Y, parameters)\n",
    "pred = (A2 > 0.5) * 1.0\n",
    "print(A2)\n",
    "print(pred)\n",
    "plt.figure()\n",
    "plt.plot(losses)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41d4b225",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}