{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bab 9 — Neural Network Playground\n", "Forward pass, XOR, gradient descent, dan decision boundary dari nol.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#!/usr/bin/env python3\n", "\"\"\"Bab 9 — Neural networks from scratch.\n", "\n", "Portable standard-library lab: activations, perceptrons, XOR network,\n", "forward pass, gradients, training loop, and SVG decision boundary.\n", "\"\"\"\n", "from __future__ import annotations\n", "\n", "import math\n", "from pathlib import Path\n", "from typing import Sequence\n", "\n", "\n", "def sigmoid(z: float) -> float:\n", " return 1 / (1 + math.exp(-z))\n", "\n", "\n", "def relu(z: float) -> float:\n", " return max(0.0, z)\n", "\n", "\n", "def step(z: float) -> int:\n", " return 1 if z >= 0 else 0\n", "\n", "\n", "def dot(a: Sequence[float], b: Sequence[float]) -> float:\n", " return sum(x * y for x, y in zip(a, b))\n", "\n", "\n", "def perceptron(x: Sequence[float], w: Sequence[float], b: float) -> int:\n", " return step(dot(x, w) + b)\n", "\n", "\n", "def xor_network(x1: int, x2: int) -> int:\n", " h1 = step(1 * x1 + 1 * x2 - 0.5) # OR\n", " h2 = step(-1 * x1 + -1 * x2 + 1.5) # NAND\n", " return step(1 * h1 + 1 * h2 - 1.5) # AND\n", "\n", "\n", "def sigmoid_xor_probability(x1: int, x2: int) -> float:\n", " h1 = sigmoid(10 * x1 + 10 * x2 - 5)\n", " h2 = sigmoid(-10 * x1 - 10 * x2 + 15)\n", " return sigmoid(10 * h1 + 10 * h2 - 15)\n", "\n", "\n", "def forward_layer(x: Sequence[float], weights: Sequence[Sequence[float]], bias: Sequence[float], activation=relu) -> list[float]:\n", " # weights is input_dim x output_dim\n", " outputs = []\n", " for j in range(len(bias)):\n", " z = sum(x[i] * weights[i][j] for i in range(len(x))) + bias[j]\n", " outputs.append(activation(z))\n", " return outputs\n", "\n", "\n", "def mse(preds: Sequence[float], targets: Sequence[float]) -> float:\n", " return sum((p - y) ** 2 for p, y in zip(preds, targets)) / len(preds)\n", "\n", "\n", "def train_linear_neuron(xs: Sequence[float], ys: Sequence[float], w: float = 0.0, b: float = 0.0, lr: float = 0.01, epochs: int = 80):\n", " history = []\n", " n = len(xs)\n", " for epoch in range(epochs):\n", " preds = [w * x + b for x in xs]\n", " loss = mse(preds, ys)\n", " grad_w = sum(2 * (p - y) * x for x, y, p in zip(xs, ys, preds)) / n\n", " grad_b = sum(2 * (p - y) for y, p in zip(ys, preds)) / n\n", " w -= lr * grad_w\n", " b -= lr * grad_b\n", " if epoch % 10 == 0 or epoch == epochs - 1:\n", " history.append((epoch, loss, w, b, grad_w, grad_b))\n", " return w, b, history\n", "\n", "\n", "def write_xor_boundary_svg(path: Path) -> None:\n", " cells = []\n", " size = 42\n", " for i in range(11):\n", " for j in range(11):\n", " # map grid to 0..1, threshold for network demonstration\n", " x1 = 1 if i / 10 >= 0.5 else 0\n", " x2 = 1 if j / 10 >= 0.5 else 0\n", " y = xor_network(x1, x2)\n", " color = \"#bbf7d0\" if y else \"#fecaca\"\n", " x = 90 + i * size\n", " yy = 90 + (10 - j) * size\n", " cells.append(f'')\n", " points = [\n", " (90, 90 + 10 * size, \"0\"),\n", " (90, 90, \"1\"),\n", " (90 + 10 * size, 90 + 10 * size, \"1\"),\n", " (90 + 10 * size, 90, \"0\"),\n", " ]\n", " pt_svg = \"\".join(f'{label}' for x, y, label in points)\n", " path.parent.mkdir(parents=True, exist_ok=True)\n", " path.write_text(f'''\n", "\n", "XOR decision boundary dari hidden layer\n", "{''.join(cells)}{pt_svg}\n", "Hijau = prediksi 1, merah = prediksi 0. Pola ini tidak bisa dibuat satu garis lurus.\n", "''', encoding=\"utf-8\")\n", "\n", "\n", "def main() -> None:\n", " print(\"=== Bab 9 Neural Network Playground ===\")\n", " print(\"sigmoid(0)=\", sigmoid(0))\n", " print(\"ReLU(-3), ReLU(4)=\", relu(-3), relu(4))\n", "\n", " print(\"\\nPerceptron AND w=[1,1], b=-1.5\")\n", " for x in [(0, 0), (0, 1), (1, 0), (1, 1)]:\n", " print(x, perceptron(x, [1, 1], -1.5))\n", "\n", " print(\"\\nXOR network step activation\")\n", " xor_outputs = []\n", " for x in [(0, 0), (0, 1), (1, 0), (1, 1)]:\n", " y = xor_network(*x)\n", " xor_outputs.append(y)\n", " print(x, y, \"sigmoid_prob=\", round(sigmoid_xor_probability(*x), 3))\n", " assert xor_outputs == [0, 1, 1, 0]\n", "\n", " print(\"\\nForward layer example\")\n", " h = forward_layer([2, 3], [[1, -1], [2, 1]], [0, 1], relu)\n", " print(\"h=\", h)\n", "\n", " print(\"\\nGradient training linear neuron for y=3x+1\")\n", " xs = [0, 1, 2, 3, 4]\n", " ys = [1, 4, 7, 10, 13]\n", " w, b, history = train_linear_neuron(xs, ys, lr=0.03, epochs=120)\n", " for epoch, loss, ww, bb, gw, gb in history:\n", " print(f\"epoch={epoch:3d} loss={loss:8.4f} w={ww:6.3f} b={bb:6.3f} grad_w={gw:7.3f} grad_b={gb:7.3f}\")\n", " print(\"final approx:\", round(w, 3), round(b, 3))\n", "\n", " out = (Path(__file__).resolve().parent if \"__file__\" in globals() else Path.cwd()) / \"outputs\"\n", " write_xor_boundary_svg(out / \"xor_boundary.svg\")\n", " print(\"SVG written:\", out / \"xor_boundary.svg\")\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jalankan praktikum utama\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "main()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Latihan cepat\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(\"XOR manual:\", [xor_network(*x) for x in [(0,0),(0,1),(1,0),(1,1)]])\n", "print(\"Gradient example final:\", train_linear_neuron([0,1,2], [1,3,5], lr=0.05, epochs=50)[:2])\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "name": "python", "version": "3" } }, "nbformat": 4, "nbformat_minor": 5 }