{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "metadata": {}, "source": "# 실습 05 · XOR 신경망 — 역전파를 손으로\n\n> **연계 강의자료:** M5 「신경망과 역전파」 · 9~10주차\n> **목표:** 프레임워크 없이 numpy로 2-2-1 신경망의 순전파·역전파를 구현하고, Gradio UI로 학습률을 바꿔 가며 수렴/발산을 관찰한다.\n>\n> 강의자료 M5 실습 2(XOR 실시간 학습)의 구현 원본. 다시 실행할 때마다 서로 다른 해로 수렴하지만 결과는 같다는 점이 관찰 포인트다.\n" }, { "cell_type": "code", "source": [ "!pip install gradio" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "2rKXoxxyP_r8", "outputId": "7a190a2c-51c7-42d0-f141-246127f0eebe" }, "execution_count": 2, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Collecting gradio\n", " Downloading gradio-5.5.0-py3-none-any.whl.metadata (16 kB)\n", "Collecting aiofiles<24.0,>=22.0 (from gradio)\n", " Downloading aiofiles-23.2.1-py3-none-any.whl.metadata (9.7 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Automatically setting `share=True` (you can turn this off by setting `share=False` in `launch()` explicitly).\n", "\n", "Colab notebook detected. To show errors in colab notebook, set debug=True in launch()\n", "* Running on public URL: https://f01bcba1d3ccc69585.gradio.live\n", "\n", "This share link expires in 72 hours. For free permanent hosting and GPU upgrades, run `gradio deploy` from the terminal in the working directory to deploy to Hugging Face Spaces (https://huggingface.co/spaces)\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "text/html": [ "
" ] }, "metadata": {} } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import networkx as nx\n", "import gradio as gr\n", "from PIL import Image\n", "from io import BytesIO\n", "\n", "class XORNetwork:\n", " def __init__(self, learning_rate=0.3):\n", " self.learning_rate = learning_rate\n", " self.epoch = 0\n", " self.error_history = []\n", " self.weight_history = []\n", " self.initialize_weights()\n", "\n", " def initialize_weights(self):\n", " init_scale = np.sqrt(2.0 / (2 + 2))\n", " self.weights = {\n", " 'w11': (np.random.rand() * 2 - 1) * init_scale,\n", " 'w12': (np.random.rand() * 2 - 1) * init_scale,\n", " 'w21': (np.random.rand() * 2 - 1) * init_scale,\n", " 'w22': (np.random.rand() * 2 - 1) * init_scale,\n", " 'v1': (np.random.rand() * 2 - 1) * init_scale,\n", " 'v2': (np.random.rand() * 2 - 1) * init_scale,\n", " 'b1': (np.random.rand() * 2 - 1) * init_scale,\n", " 'b2': (np.random.rand() * 2 - 1) * init_scale,\n", " 'bo': (np.random.rand() * 2 - 1) * init_scale\n", " }\n", "\n", " def sigmoid(self, x):\n", " return 1 / (1 + np.exp(-x))\n", "\n", " def forward_pass(self, inputs):\n", " hidden1_sum = inputs[0] * self.weights['w11'] + inputs[1] * self.weights['w21'] + self.weights['b1']\n", " hidden1 = self.sigmoid(hidden1_sum)\n", "\n", " hidden2_sum = inputs[0] * self.weights['w12'] + inputs[1] * self.weights['w22'] + self.weights['b2']\n", " hidden2 = self.sigmoid(hidden2_sum)\n", "\n", " output_sum = hidden1 * self.weights['v1'] + hidden2 * self.weights['v2'] + self.weights['bo']\n", " output = self.sigmoid(output_sum)\n", "\n", " return {\n", " 'hidden1': hidden1,\n", " 'hidden2': hidden2,\n", " 'output': output,\n", " 'hidden1_sum': hidden1_sum,\n", " 'hidden2_sum': hidden2_sum,\n", " 'output_sum': output_sum\n", " }\n", "\n", " def backward_pass(self, inputs, target):\n", " forward_result = self.forward_pass(inputs)\n", " hidden1 = forward_result['hidden1']\n", " hidden2 = forward_result['hidden2']\n", " output = forward_result['output']\n", "\n", " output_error = target - output\n", " output_delta = output_error * output * (1 - output)\n", "\n", " hidden1_delta = output_delta * self.weights['v1'] * hidden1 * (1 - hidden1)\n", " hidden2_delta = output_delta * self.weights['v2'] * hidden2 * (1 - hidden2)\n", "\n", " self.weights['v1'] += self.learning_rate * output_delta * hidden1\n", " self.weights['v2'] += self.learning_rate * output_delta * hidden2\n", "\n", " self.weights['w11'] += self.learning_rate * hidden1_delta * inputs[0]\n", " self.weights['w12'] += self.learning_rate * hidden2_delta * inputs[0]\n", " self.weights['w21'] += self.learning_rate * hidden1_delta * inputs[1]\n", " self.weights['w22'] += self.learning_rate * hidden2_delta * inputs[1]\n", "\n", " self.weights['b1'] += self.learning_rate * hidden1_delta\n", " self.weights['b2'] += self.learning_rate * hidden2_delta\n", " self.weights['bo'] += self.learning_rate * output_delta\n", "\n", " # Record weight history for visualization\n", " self.weight_history.append(self.weights.copy())\n", "\n", " error = (output_error ** 2) / 2\n", " return error\n", "\n", " def train(self, training_data, max_epochs=10000, error_threshold=0.001):\n", " self.epoch = 0\n", " self.error_history = []\n", " self.weight_history = []\n", " running = True\n", "\n", " while running and self.epoch < max_epochs:\n", " total_error = 0\n", " for example in training_data:\n", " inputs = example['inputs']\n", " target = example['target']\n", " error = self.backward_pass(inputs, target)\n", " total_error += error\n", "\n", " avg_error = total_error / len(training_data)\n", " self.error_history.append(avg_error)\n", " self.epoch += 1\n", "\n", " if avg_error < error_threshold:\n", " running = False\n", "\n", " def visualize_training(self):\n", " plt.figure(figsize=(10, 5))\n", " plt.plot(range(1, len(self.error_history) + 1), self.error_history, color='b', label='Average Error')\n", " plt.xlabel('Epoch')\n", " plt.ylabel('Error')\n", " plt.title('Training Error over Epochs')\n", " plt.legend()\n", " plt.grid(True)\n", " buf = BytesIO()\n", " plt.savefig(buf, format='png')\n", " buf.seek(0)\n", " plt.close()\n", " return Image.open(buf)\n", "\n", " def visualize_network(self):\n", " G = nx.DiGraph()\n", " G.add_nodes_from([\"Input 1\", \"Input 2\", \"Hidden 1\", \"Hidden 2\", \"Output\", \"Bias 1\", \"Bias 2\", \"Bias Output\"])\n", "\n", " # Adding edges with weights\n", " G.add_edge(\"Input 1\", \"Hidden 1\", weight=self.weights['w11'])\n", " G.add_edge(\"Input 1\", \"Hidden 2\", weight=self.weights['w12'])\n", " G.add_edge(\"Input 2\", \"Hidden 1\", weight=self.weights['w21'])\n", " G.add_edge(\"Input 2\", \"Hidden 2\", weight=self.weights['w22'])\n", " G.add_edge(\"Hidden 1\", \"Output\", weight=self.weights['v1'])\n", " G.add_edge(\"Hidden 2\", \"Output\", weight=self.weights['v2'])\n", " G.add_edge(\"Bias 1\", \"Hidden 1\", weight=self.weights['b1'])\n", " G.add_edge(\"Bias 2\", \"Hidden 2\", weight=self.weights['b2'])\n", " G.add_edge(\"Bias Output\", \"Output\", weight=self.weights['bo'])\n", "\n", " pos = {\n", " \"Input 1\": (0, 2), \"Input 2\": (0, 0),\n", " \"Hidden 1\": (1, 2.5), \"Hidden 2\": (1, -0.5),\n", " \"Output\": (2, 1),\n", " \"Bias 1\": (0.5, 3.5), \"Bias 2\": (0.5, -1.5), \"Bias Output\": (1.5, 3.5)\n", " }\n", "\n", " plt.figure(figsize=(10, 6))\n", " edge_labels = {(u, v): f\"{d['weight']:.2f}\" for u, v, d in G.edges(data=True)}\n", " nx.draw(G, pos, with_labels=True, node_size=3000, node_color='lightblue', font_size=10, font_weight='bold')\n", " nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_color='red')\n", " plt.title(\"Neural Network Visualization with Weights and Biases\")\n", " buf = BytesIO()\n", " plt.savefig(buf, format='png')\n", " buf.seek(0)\n", " plt.close()\n", " return Image.open(buf)\n", "\n", " def visualize_weight_changes(self):\n", " plt.figure(figsize=(12, 8))\n", " for key in self.weights.keys():\n", " weights_over_time = [w[key] for w in self.weight_history]\n", " plt.plot(weights_over_time, label=key)\n", " plt.xlabel('Epoch')\n", " plt.ylabel('Weight Value')\n", " plt.title('Weight Changes Over Training')\n", " plt.legend()\n", " plt.grid(True)\n", " buf = BytesIO()\n", " plt.savefig(buf, format='png')\n", " buf.seek(0)\n", " plt.close()\n", " return Image.open(buf)\n", "\n", " def predict(self, inputs):\n", " forward_result = self.forward_pass(inputs)\n", " hidden1_sum = forward_result['hidden1_sum']\n", " hidden2_sum = forward_result['hidden2_sum']\n", " output_sum = forward_result['output_sum']\n", " output = forward_result['output']\n", "\n", " hidden1_equation = f\"({inputs[0]} * {self.weights['w11']:.3f}) + ({inputs[1]} * {self.weights['w21']:.3f}) + {self.weights['b1']:.3f} = {hidden1_sum:.3f}\"\n", " hidden2_equation = f\"({inputs[0]} * {self.weights['w12']:.3f}) + ({inputs[1]} * {self.weights['w22']:.3f}) + {self.weights['b2']:.3f} = {hidden2_sum:.3f}\"\n", " output_equation = f\"({forward_result['hidden1']:.3f} * {self.weights['v1']:.3f}) + ({forward_result['hidden2']:.3f} * {self.weights['v2']:.3f}) + {self.weights['bo']:.3f} = {output_sum:.3f}\"\n", "\n", " return (f\"Input: {inputs}\\n\"\n", " f\"Hidden Layer 1 Calculation: {hidden1_equation}, Activation: {forward_result['hidden1']:.3f}\\n\"\n", " f\"Hidden Layer 2 Calculation: {hidden2_equation}, Activation: {forward_result['hidden2']:.3f}\\n\"\n", " f\"Output Layer Calculation: {output_equation}, Output (after sigmoid): {output:.3f}\")\n", "\n", " def gradio_interface(self):\n", " def train_and_visualize(learning_rate, max_epochs):\n", " self.learning_rate = learning_rate\n", " self.train(training_data, max_epochs=max_epochs)\n", " training_plot = self.visualize_training()\n", " network_plot = self.visualize_network()\n", " weight_change_plot = self.visualize_weight_changes()\n", " predictions = \"\\n\\n\".join([self.predict(example['inputs']) for example in training_data])\n", " return f\"Training complete. Check the graphs for details.\\n\\nPredictions:\\n{predictions}\", training_plot, network_plot, weight_change_plot\n", "\n", " def reset_network():\n", " self.initialize_weights()\n", " self.error_history = []\n", " self.weight_history = []\n", " return \"Network reset complete. Ready for new training.\"\n", "\n", " training_data = [\n", " {'inputs': [0, 0], 'target': 0},\n", " {'inputs': [0, 1], 'target': 1},\n", " {'inputs': [1, 0], 'target': 1},\n", " {'inputs': [1, 1], 'target': 0}\n", " ]\n", "\n", " with gr.Blocks() as demo:\n", " gr.Markdown(\"# XOR Neural Network Training\")\n", " with gr.Row():\n", " learning_rate = gr.Slider(0.01, 1.0, step=0.01, label=\"Learning Rate\")\n", " max_epochs = gr.Slider(100, 10000, step=100, label=\"Max Epochs\")\n", " train_button = gr.Button(\"Train Network\")\n", " reset_button = gr.Button(\"Reset Network\")\n", " output_text = gr.Textbox(label=\"Training Output\")\n", " training_plot = gr.Image(type=\"pil\", label=\"Training Error Plot\")\n", " network_plot = gr.Image(type=\"pil\", label=\"Network Visualization\")\n", " weight_change_plot = gr.Image(type=\"pil\", label=\"Weight Changes Over Time\")\n", "\n", " train_button.click(train_and_visualize, inputs=[learning_rate, max_epochs], outputs=[output_text, training_plot, network_plot, weight_change_plot])\n", " reset_button.click(reset_network, outputs=output_text)\n", "\n", " demo.launch()\n", "\n", "if __name__ == \"__main__\":\n", " training_data = [\n", " {'inputs': [0, 0], 'target': 0},\n", " {'inputs': [0, 1], 'target': 1},\n", " {'inputs': [1, 0], 'target': 1},\n", " {'inputs': [1, 1], 'target': 0}\n", " ]\n", "\n", " network = XORNetwork(learning_rate=0.3)\n", " network.gradio_interface()\n", "\n" ] } ] }