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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>AI Explainer: How Neural Networks Work</title>
<style>
* {
margin: 0;
padding: 0;
box-sizing: border-box;
}
body {
font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
background: #0a0a0a;
color: #e0e0e0;
line-height: 1.6;
overflow-x: hidden;
}
.container {
max-width: 1200px;
margin: 0 auto;
padding: 20px;
}
header {
text-align: center;
padding: 40px 20px;
background: linear-gradient(135deg, #1e3c72 0%, #2a5298 100%);
margin-bottom: 40px;
border-radius: 20px;
}
h1 {
font-size: clamp(2rem, 5vw, 3rem);
margin-bottom: 10px;
background: linear-gradient(135deg, #fff 0%, #a8dadc 100%);
-webkit-background-clip: text;
-webkit-text-fill-color: transparent;
}
.mode-toggle {
display: flex;
justify-content: center;
gap: 20px;
margin: 30px 0;
flex-wrap: wrap;
}
.mode-btn {
padding: 12px 30px;
background: #2a5298;
color: white;
border: none;
border-radius: 50px;
cursor: pointer;
font-size: 16px;
transition: all 0.3s ease;
font-weight: 600;
}
.mode-btn.active {
background: #4CAF50;
transform: scale(1.05);
}
.mode-btn:hover {
transform: translateY(-2px);
box-shadow: 0 5px 15px rgba(74, 144, 226, 0.3);
}
.section {
background: #1a1a1a;
padding: 30px;
margin-bottom: 30px;
border-radius: 20px;
box-shadow: 0 10px 30px rgba(0, 0, 0, 0.5);
}
.section h2 {
color: #4CAF50;
margin-bottom: 20px;
font-size: clamp(1.5rem, 4vw, 2rem);
}
.section h3 {
color: #81C784;
margin: 20px 0 10px 0;
font-size: clamp(1.2rem, 3vw, 1.5rem);
}
.math-content {
background: #0d0d0d;
padding: 20px;
border-radius: 10px;
overflow-x: auto;
margin: 15px 0;
border: 1px solid #333;
}
.learn-content {
background: #1e3c72;
padding: 20px;
border-radius: 10px;
margin: 15px 0;
line-height: 1.8;
}
#xor-demo {
background: #0d0d0d;
padding: 20px;
border-radius: 15px;
margin: 20px 0;
}
#network-canvas {
width: 100%;
max-width: 800px;
height: 400px;
background: #000;
border-radius: 10px;
margin: 20px auto;
display: block;
}
.controls {
display: flex;
gap: 15px;
justify-content: center;
flex-wrap: wrap;
margin: 20px 0;
}
.control-btn {
padding: 10px 25px;
background: #4CAF50;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
transition: all 0.3s ease;
}
.control-btn:hover {
background: #45a049;
transform: translateY(-2px);
}
.control-btn:disabled {
background: #666;
cursor: not-allowed;
}
.stats {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 15px;
margin: 20px 0;
}
.stat-box {
background: #1a1a1a;
padding: 15px;
border-radius: 10px;
text-align: center;
border: 1px solid #333;
}
.stat-label {
color: #888;
font-size: 14px;
}
.stat-value {
color: #4CAF50;
font-size: 24px;
font-weight: bold;
margin-top: 5px;
}
.loss-chart {
width: 100%;
height: 200px;
background: #000;
border-radius: 10px;
margin: 20px 0;
}
.formula {
font-family: 'Courier New', monospace;
color: #64B5F6;
padding: 10px;
background: rgba(0, 0, 0, 0.5);
border-radius: 5px;
overflow-x: auto;
white-space: nowrap;
margin: 10px 0;
}
.highlight {
background: #4CAF50;
color: #000;
padding: 2px 6px;
border-radius: 3px;
font-weight: bold;
}
@media (max-width: 768px) {
.container {
padding: 10px;
}
.section {
padding: 20px;
}
#network-canvas {
height: 300px;
}
.controls {
gap: 10px;
}
.control-btn {
padding: 8px 20px;
font-size: 14px;
}
}
.mode-content {
display: none;
}
.mode-content.active {
display: block;
}
.animated-number {
transition: all 0.3s ease;
}
@keyframes pulse {
0% { transform: scale(1); }
50% { transform: scale(1.1); }
100% { transform: scale(1); }
}
.pulse {
animation: pulse 0.5s ease;
}
</style>
</head>
<body>
<div class="container">
<header>
<h1>🧠 How AI Really Works</h1>
<p>An Interactive Journey Inside Neural Networks</p>
</header>
<div class="mode-toggle">
<button class="mode-btn active" onclick="setMode('learn')">🎓 Learn Mode</button>
<button class="mode-btn" onclick="setMode('math')">🔢 Math Mode</button>
</div>
<div class="section">
<h2>What is a Neural Network?</h2>
<div class="mode-content learn-mode active">
<div class="learn-content">
<p>Imagine your brain is made of billions of tiny decision-makers called neurons. Each neuron:</p>
<ul style="margin: 15px 0; padding-left: 30px;">
<li>🎯 Takes in information (inputs)</li>
<li>🤔 Thinks about it (processing)</li>
<li>💡 Makes a decision (output)</li>
</ul>
<p>An AI neural network works the same way! It's like a simplified brain made of math. Let's see it in action!</p>
</div>
</div>
<div class="mode-content math-mode">
<div class="math-content">
<p>A neural network is a function approximator that transforms inputs through layers of neurons:</p>
<div class="formula">
f(x) = σ(W₃ · σ(W₂ · σ(W₁ · x + b₁) + b₂) + b₃)
</div>
<p>Where:</p>
<ul style="margin: 15px 0; padding-left: 30px;">
<li>x = input vector</li>
<li>Wᵢ = weight matrix for layer i</li>
<li>bᵢ = bias vector for layer i</li>
<li>σ = activation function (e.g., ReLU, sigmoid)</li>
</ul>
</div>
</div>
</div>
<div class="section">
<h2>🎮 Live XOR Training Demo</h2>
<p>Watch an AI learn the XOR problem in real-time! XOR outputs 1 when inputs are different, 0 when same.</p>
<div id="xor-demo">
<canvas id="network-canvas"></canvas>
<div class="controls">
<button class="control-btn" onclick="startTraining()">▶️ Start Training</button>
<button class="control-btn" onclick="pauseTraining()">⏸️ Pause</button>
<button class="control-btn" onclick="resetNetwork()">🔄 Reset</button>
<button class="control-btn" onclick="stepTraining()">⏭️ Step</button>
</div>
<div class="stats">
<div class="stat-box">
<div class="stat-label">Epoch</div>
<div class="stat-value animated-number" id="epoch">0</div>
</div>
<div class="stat-box">
<div class="stat-label">Loss</div>
<div class="stat-value animated-number" id="loss">1.000</div>
</div>
<div class="stat-box">
<div class="stat-label">Accuracy</div>
<div class="stat-value animated-number" id="accuracy">0%</div>
</div>
<div class="stat-box">
<div class="stat-label">Learning Rate</div>
<div class="stat-value" id="learning-rate">0.1</div>
</div>
</div>
<canvas id="loss-chart" class="loss-chart"></canvas>
</div>
</div>
<div class="section">
<h2>How Does Learning Work?</h2>
<div class="mode-content learn-mode active">
<h3>🎯 Forward Pass: Making Predictions</h3>
<div class="learn-content">
<p>The network makes a prediction by passing data forward through each layer:</p>
<ol style="margin: 15px 0; padding-left: 30px;">
<li><span class="highlight">Input</span>: Feed in the data (like 0,1 for XOR)</li>
<li><span class="highlight">Multiply & Add</span>: Each connection has a "strength" (weight)</li>
<li><span class="highlight">Activate</span>: Decide if the neuron should "fire"</li>
<li><span class="highlight">Output</span>: Get the final prediction</li>
</ol>
</div>
<h3>📉 Backward Pass: Learning from Mistakes</h3>
<div class="learn-content">
<p>When the network is wrong, it learns by adjusting its connections:</p>
<ol style="margin: 15px 0; padding-left: 30px;">
<li><span class="highlight">Calculate Error</span>: How wrong was the prediction?</li>
<li><span class="highlight">Blame Game</span>: Which connections caused the error?</li>
<li><span class="highlight">Adjust Weights</span>: Make connections stronger or weaker</li>
<li><span class="highlight">Repeat</span>: Try again with new weights!</li>
</ol>
</div>
</div>
<div class="mode-content math-mode">
<h3>Forward Propagation</h3>
<div class="math-content">
<p>For each layer l:</p>
<div class="formula">
z[l] = W[l] · a[l-1] + b[l]
</div>
<div class="formula">
a[l] = σ(z[l])
</div>
<p>Where a[0] = x (input) and a[L] = ŷ (output)</p>
</div>
<h3>Backpropagation</h3>
<div class="math-content">
<p>Loss function (Mean Squared Error):</p>
<div class="formula">
L = ½ Σ(y - ŷ)²
</div>
<p>Gradient computation:</p>
<div class="formula">
δ[L] = ∇ₐL ⊙ σ'(z[L])
</div>
<div class="formula">
δ[l] = (W[l+1]ᵀ · δ[l+1]) ⊙ σ'(z[l])
</div>
<p>Weight update:</p>
<div class="formula">
W[l] = W[l] - α · δ[l] · a[l-1]ᵀ
</div>
<div class="formula">
b[l] = b[l] - α · δ[l]
</div>
</div>
</div>
</div>
<div class="section">
<h2>Key Components Explained</h2>
<div class="mode-content learn-mode active">
<h3>🔗 Weights & Biases</h3>
<div class="learn-content">
<p><span class="highlight">Weights</span> are like volume knobs - they control how much each input matters.</p>
<p><span class="highlight">Biases</span> are like thresholds - they decide when a neuron should activate.</p>
</div>
<h3>⚡ Activation Functions</h3>
<div class="learn-content">
<p>These decide if a neuron should "fire" or not:</p>
<ul style="margin: 15px 0; padding-left: 30px;">
<li><span class="highlight">ReLU</span>: If positive, pass it on. If negative, block it!</li>
<li><span class="highlight">Sigmoid</span>: Squash everything between 0 and 1</li>
<li><span class="highlight">Tanh</span>: Squash everything between -1 and 1</li>
</ul>
</div>
<h3>🎯 Gradient Descent</h3>
<div class="learn-content">
<p>Imagine you're blindfolded on a hill, trying to reach the bottom:</p>
<ol style="margin: 15px 0; padding-left: 30px;">
<li>Feel the slope around you (calculate gradient)</li>
<li>Take a small step downhill (adjust weights)</li>
<li>Repeat until you reach the bottom (minimum loss)</li>
</ol>
</div>
</div>
<div class="mode-content math-mode">
<h3>Activation Functions</h3>
<div class="math-content">
<p><strong>ReLU:</strong></p>
<div class="formula">
f(x) = max(0, x)
</div>
<div class="formula">
f'(x) = {1 if x > 0, 0 if x ≤ 0}
</div>
<p><strong>Sigmoid:</strong></p>
<div class="formula">
σ(x) = 1 / (1 + e⁻ˣ)
</div>
<div class="formula">
σ'(x) = σ(x) · (1 - σ(x))
</div>
<p><strong>Tanh:</strong></p>
<div class="formula">
tanh(x) = (eˣ - e⁻ˣ) / (eˣ + e⁻ˣ)
</div>
<div class="formula">
tanh'(x) = 1 - tanh²(x)
</div>
</div>
<h3>Gradient Descent Update Rule</h3>
<div class="math-content">
<div class="formula">
θₜ₊₁ = θₜ - α · ∇θ L(θₜ)
</div>
<p>Where:</p>
<ul style="margin: 15px 0; padding-left: 30px;">
<li>θ = parameters (weights and biases)</li>
<li>α = learning rate</li>
<li>∇θ L = gradient of loss with respect to parameters</li>
</ul>
</div>
</div>
</div>
</div>
<script>
// Global variables
let mode = 'learn';
let network = null;
let training = false;
let epoch = 0;
let lossHistory = [];
const canvas = document.getElementById('network-canvas');
const ctx = canvas.getContext('2d');
const lossCanvas = document.getElementById('loss-chart');
const lossCtx = lossCanvas.getContext('2d');
// Set canvas sizes
function resizeCanvases() {
canvas.width = canvas.offsetWidth;
canvas.height = canvas.offsetHeight;
lossCanvas.width = lossCanvas.offsetWidth;
lossCanvas.height = lossCanvas.offsetHeight;
}
resizeCanvases();
window.addEventListener('resize', resizeCanvases);
// Mode switching
function setMode(newMode) {
mode = newMode;
document.querySelectorAll('.mode-btn').forEach(btn => {
btn.classList.toggle('active', btn.textContent.toLowerCase().includes(newMode));
});
document.querySelectorAll('.mode-content').forEach(content => {
content.classList.toggle('active', content.classList.contains(`${newMode}-mode`));
});
}
// Neural Network Class
class NeuralNetwork {
constructor() {
// Network architecture: 2-25-25-1 (roughly 100 parameters)
this.layers = [2, 25, 25, 1];
this.weights = [];
this.biases = [];
this.activations = [];
this.zValues = [];
this.gradients = [];
this.learningRate = 0.1;
this.initializeNetwork();
}
initializeNetwork() {
// Xavier initialization
for (let i = 1; i < this.layers.length; i++) {
const rows = this.layers[i];
const cols = this.layers[i-1];
const scale = Math.sqrt(2.0 / cols);
// Initialize weights
this.weights[i-1] = [];
for (let r = 0; r < rows; r++) {
this.weights[i-1][r] = [];
for (let c = 0; c < cols; c++) {
this.weights[i-1][r][c] = (Math.random() * 2 - 1) * scale;
}
}
// Initialize biases
this.biases[i-1] = new Array(rows).fill(0);
}
}
sigmoid(x) {
return 1 / (1 + Math.exp(-x));
}
sigmoidDerivative(x) {
const s = this.sigmoid(x);
return s * (1 - s);
}
relu(x) {
return Math.max(0, x);
}
reluDerivative(x) {
return x > 0 ? 1 : 0;
}
forward(input) {
this.activations = [input];
this.zValues = [];
for (let i = 0; i < this.weights.length; i++) {
const z = [];
const a = [];
for (let j = 0; j < this.weights[i].length; j++) {
let sum = this.biases[i][j];
for (let k = 0; k < this.weights[i][j].length; k++) {
sum += this.weights[i][j][k] * this.activations[i][k];
}
z.push(sum);
// Use ReLU for hidden layers, sigmoid for output
if (i < this.weights.length - 1) {
a.push(this.relu(sum));
} else {
a.push(this.sigmoid(sum));
}
}
this.zValues.push(z);
this.activations.push(a);
}
return this.activations[this.activations.length - 1][0];
}
backward(input, target) {
const output = this.forward(input);
const error = output - target;
// Initialize gradients
this.gradients = [];
// Output layer gradients
let delta = [error * this.sigmoidDerivative(this.zValues[this.zValues.length - 1][0])];
this.gradients.unshift(delta);
// Hidden layer gradients
for (let i = this.weights.length - 2; i >= 0; i--) {
const newDelta = [];
for (let j = 0; j < this.weights[i].length; j++) {
let sum = 0;
for (let k = 0; k < delta.length; k++) {
sum += this.weights[i+1][k][j] * delta[k];
}
const activation = i > 0 ?
this.reluDerivative(this.zValues[i][j]) :
this.reluDerivative(this.zValues[i][j]);
newDelta.push(sum * activation);
}
delta = newDelta;
this.gradients.unshift(delta);
}
// Update weights and biases
for (let i = 0; i < this.weights.length; i++) {
for (let j = 0; j < this.weights[i].length; j++) {
for (let k = 0; k < this.weights[i][j].length; k++) {
this.weights[i][j][k] -= this.learningRate * this.gradients[i][j] * this.activations[i][k];
}
this.biases[i][j] -= this.learningRate * this.gradients[i][j];
}
}
return error * error;
}
train(inputs, targets) {
let totalLoss = 0;
for (let i = 0; i < inputs.length; i++) {
totalLoss += this.backward(inputs[i], targets[i]);
}
return totalLoss / inputs.length;
}
predict(input) {
return this.forward(input);
}
}
// XOR training data
const xorInputs = [[0, 0], [0, 1], [1, 0], [1, 1]];
const xorTargets = [0, 1, 1, 0];
// Initialize network
function resetNetwork() {
network = new NeuralNetwork();
epoch = 0;
lossHistory = [];
training = false;
updateStats();
drawNetwork();
drawLossChart();
}
// Training functions
function startTraining() {
training = true;
trainLoop();
}
function pauseTraining() {
training = false;
}
function stepTraining() {
if (!network) resetNetwork();
trainStep();
}
function trainStep() {
const loss = network.train(xorInputs, xorTargets);
epoch++;
lossHistory.push(loss);
if (lossHistory.length > 100) lossHistory.shift();
updateStats();
drawNetwork();
drawLossChart();
}
function trainLoop() {
if (!training) return;
trainStep();
if (epoch < 1000 && lossHistory[lossHistory.length - 1] > 0.001) {
requestAnimationFrame(trainLoop);
} else {
training = false;
}
}
// Update statistics
function updateStats() {
document.getElementById('epoch').textContent = epoch;
const loss = lossHistory.length > 0 ? lossHistory[lossHistory.length - 1] : 1;
document.getElementById('loss').textContent = loss.toFixed(4);
// Calculate accuracy
let correct = 0;
for (let i = 0; i < xorInputs.length; i++) {
const prediction = network ? network.predict(xorInputs[i]) : 0.5;
const rounded = Math.round(prediction);
if (rounded === xorTargets[i]) correct++;
}
const accuracy = (correct / xorInputs.length * 100).toFixed(0);
document.getElementById('accuracy').textContent = accuracy + '%';
// Add pulse animation on high accuracy
if (accuracy >= 100) {
document.getElementById('accuracy').parentElement.classList.add('pulse');
setTimeout(() => {
document.getElementById('accuracy').parentElement.classList.remove('pulse');
}, 500);
}
}
// Visualization functions
function drawNetwork() {
ctx.clearRect(0, 0, canvas.width, canvas.height);
if (!network) return;
const layerSpacing = canvas.width / (network.layers.length + 1);
const neurons = [];
// Calculate neuron positions
for (let i = 0; i < network.layers.length; i++) {
neurons[i] = [];
const layerSize = network.layers[i];
const ySpacing = canvas.height / (layerSize + 1);
for (let j = 0; j < layerSize; j++) {
const x = layerSpacing * (i + 1);
const y = ySpacing * (j + 1);
neurons[i].push({ x, y });
}
}
// Draw connections
for (let i = 0; i < network.weights.length; i++) {
for (let j = 0; j < network.weights[i].length; j++) {
for (let k = 0; k < network.weights[i][j].length; k++) {
const weight = network.weights[i][j][k];
const opacity = Math.min(Math.abs(weight) / 2, 1);
ctx.beginPath();
ctx.moveTo(neurons[i][k].x, neurons[i][k].y);
ctx.lineTo(neurons[i+1][j].x, neurons[i+1][j].y);
if (weight > 0) {
ctx.strokeStyle = `rgba(76, 175, 80, ${opacity})`;
} else {
ctx.strokeStyle = `rgba(244, 67, 54, ${opacity})`;
}
ctx.lineWidth = Math.abs(weight) * 2;
ctx.stroke();
}
}
}
// Draw neurons
for (let i = 0; i < neurons.length; i++) {
for (let j = 0; j < neurons[i].length; j++) {
const neuron = neurons[i][j];
// Get activation value
let activation = 0;
if (network.activations[i] && network.activations[i][j] !== undefined) {
activation = network.activations[i][j];
}
const intensity = Math.min(activation * 255, 255);
ctx.beginPath();
ctx.arc(neuron.x, neuron.y, 15, 0, Math.PI * 2);
ctx.fillStyle = `rgb(${intensity}, ${intensity}, ${255})`;
ctx.fill();
ctx.strokeStyle = '#4CAF50';
ctx.lineWidth = 2;
ctx.stroke();
// Draw activation value for visible neurons
if (network.layers[i] <= 5 || i === 0 || i === network.layers.length - 1) {
ctx.fillStyle = '#fff';
ctx.font = '10px Arial';
ctx.textAlign = 'center';
ctx.textBaseline = 'middle';
ctx.fillText(activation.toFixed(2), neuron.x, neuron.y);
}
}
}
// Draw layer labels
ctx.fillStyle = '#888';
ctx.font = '14px Arial';
ctx.textAlign = 'center';
const labels = ['Input', 'Hidden 1', 'Hidden 2', 'Output'];
for (let i = 0; i < network.layers.length; i++) {
const x = layerSpacing * (i + 1);
ctx.fillText(labels[i], x, 30);
ctx.fillText(`(${network.layers[i]} neurons)`, x, 45);
}
// Draw XOR truth table
ctx.fillStyle = '#4CAF50';
ctx.font = '12px Arial';
ctx.textAlign = 'left';
ctx.fillText('XOR Truth Table:', 20, canvas.height - 80);
ctx.fillStyle = '#888';
ctx.fillText('0 XOR 0 = 0', 20, canvas.height - 60);
ctx.fillText('0 XOR 1 = 1', 20, canvas.height - 45);
ctx.fillText('1 XOR 0 = 1', 20, canvas.height - 30);
ctx.fillText('1 XOR 1 = 0', 20, canvas.height - 15);
// Show current predictions
if (network) {
ctx.fillStyle = '#4CAF50';
ctx.fillText('Network Output:', 150, canvas.height - 80);
ctx.fillStyle = '#888';
for (let i = 0; i < xorInputs.length; i++) {
const prediction = network.predict(xorInputs[i]);
const text = `${xorInputs[i][0]} XOR ${xorInputs[i][1]} = ${prediction.toFixed(3)}`;
ctx.fillText(text, 150, canvas.height - 60 + i * 15);
}
}
}
function drawLossChart() {
lossCtx.clearRect(0, 0, lossCanvas.width, lossCanvas.height);
if (lossHistory.length < 2) return;
// Find min and max for scaling
const maxLoss = Math.max(...lossHistory, 0.5);
const minLoss = 0;
// Draw axes
lossCtx.strokeStyle = '#444';
lossCtx.lineWidth = 1;
lossCtx.beginPath();
lossCtx.moveTo(40, 10);
lossCtx.lineTo(40, lossCanvas.height - 30);
lossCtx.lineTo(lossCanvas.width - 10, lossCanvas.height - 30);
lossCtx.stroke();
// Draw labels
lossCtx.fillStyle = '#888';
lossCtx.font = '12px Arial';
lossCtx.textAlign = 'right';
lossCtx.fillText(maxLoss.toFixed(3), 35, 15);
lossCtx.fillText('0', 35, lossCanvas.height - 30);
lossCtx.textAlign = 'center';
lossCtx.fillText('Loss over Time', lossCanvas.width / 2, lossCanvas.height - 10);
// Draw loss curve
lossCtx.strokeStyle = '#4CAF50';
lossCtx.lineWidth = 2;
lossCtx.beginPath();
const xStep = (lossCanvas.width - 50) / (lossHistory.length - 1);
const yScale = (lossCanvas.height - 50) / (maxLoss - minLoss);
for (let i = 0; i < lossHistory.length; i++) {
const x = 40 + i * xStep;
const y = lossCanvas.height - 30 - (lossHistory[i] - minLoss) * yScale;
if (i === 0) {
lossCtx.moveTo(x, y);
} else {
lossCtx.lineTo(x, y);
}
}
lossCtx.stroke();
// Draw current loss point
if (lossHistory.length > 0) {
const lastX = 40 + (lossHistory.length - 1) * xStep;
const lastY = lossCanvas.height - 30 - (lossHistory[lossHistory.length - 1] - minLoss) * yScale;
lossCtx.beginPath();
lossCtx.arc(lastX, lastY, 4, 0, Math.PI * 2);
lossCtx.fillStyle = '#4CAF50';
lossCtx.fill();
}
}
// Initialize
resetNetwork();
</script>
</body>
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