123 lines
3.4 KiB
Plaintext
123 lines
3.4 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Iteration 0, Loss: 466.56000000000006\n",
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"Iteration 20, Loss: 5.32959636083938\n",
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"Iteration 40, Loss: 0.41191523404899866\n",
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"Iteration 60, Loss: 0.031836212079467595\n",
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"Iteration 80, Loss: 0.002460565465389601\n",
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"Iteration 100, Loss: 0.000190172825660145\n",
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"Iteration 120, Loss: 1.4698126966451542e-05\n",
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"Iteration 140, Loss: 1.1359926717815175e-06\n",
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"Iteration 160, Loss: 8.779889800154524e-08\n",
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"Iteration 180, Loss: 6.7858241357822796e-09\n",
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"Final weights:\n",
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" [[-0.00698895 -0.01397789 -0.02096684 -0.02795579]\n",
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" [ 0.25975286 0.11950572 -0.02074143 -0.16098857]\n",
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" [ 0.53548461 0.27096922 0.00645383 -0.25806156]]\n",
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"Final biases:\n",
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" [-0.00698895 -0.04024714 -0.06451539]\n"
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]
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}
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],
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"source": [
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"import numpy as np\n",
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"\n",
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"# Initial inputs\n",
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"inputs = np.array([1, 2, 3, 4])\n",
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"\n",
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"# Initial weights and biases\n",
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"weights = np.array([\n",
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" [0.1, 0.2, 0.3, 0.4],\n",
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" [0.5, 0.6, 0.7, 0.8],\n",
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" [0.9, 1.0, 1.1, 1.2]\n",
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"])\n",
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"\n",
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"biases = np.array([0.1, 0.2, 0.3])\n",
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"\n",
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"# Learning rate\n",
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"learning_rate = 0.001\n",
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"\n",
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"# ReLU activation function and its derivative\n",
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"def relu(x):\n",
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" return np.maximum(0, x)\n",
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"\n",
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"def relu_derivative(x):\n",
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" return np.where(x > 0, 1, 0)\n",
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"\n",
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"# Training loop\n",
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"for iteration in range(200):\n",
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" # Forward pass\n",
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" z = np.dot(weights, inputs) + biases\n",
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" a = relu(z)\n",
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" y = np.sum(a)\n",
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"\n",
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" # Calculate loss\n",
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" loss = y ** 2\n",
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"\n",
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" # Backward pass\n",
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" # Gradient of loss with respect to output y\n",
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" dL_dy = 2 * y\n",
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"\n",
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" # Gradient of y with respect to a\n",
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" dy_da = np.ones_like(a)\n",
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"\n",
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" # Gradient of loss with respect to a\n",
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" dL_da = dL_dy * dy_da\n",
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"\n",
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" # Gradient of a with respect to z (ReLU derivative)\n",
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" da_dz = relu_derivative(z)\n",
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"\n",
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" # Gradient of loss with respect to z\n",
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" dL_dz = dL_da * da_dz\n",
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"\n",
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" # Gradient of z with respect to weights and biases\n",
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" dL_dW = np.outer(dL_dz, inputs)\n",
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" dL_db = dL_dz\n",
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"\n",
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" # Update weights and biases\n",
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" weights -= learning_rate * dL_dW\n",
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" biases -= learning_rate * dL_db\n",
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"\n",
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" # Print the loss every 20 iterations\n",
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" if iteration % 20 == 0:\n",
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" print(f\"Iteration {iteration}, Loss: {loss}\")\n",
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"\n",
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"# Final weights and biases\n",
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"print(\"Final weights:\\n\", weights)\n",
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"print(\"Final biases:\\n\", biases)\n",
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"\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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