particles/gradient-descent.html at main · danlex/particles · GitHub

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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>Gradient Descent — Particles</title>
  <meta name="description" content="Particles are learners descending a procedural loss landscape using simulated SGD with momentum — overshooting minima, oscillating in narrow valleys, escaping saddle points.">
  <meta name="author" content="Alexandru DAN">
  <meta name="theme-color" content="#050505">
  <link rel="canonical" href="https://particles.alexandrudan.com/gradient-descent.html">
  <link rel="icon" type="image/svg+xml" href="favicon.svg">

  <!-- Open Graph -->
  <meta property="og:type" content="website">
  <meta property="og:url" content="https://particles.alexandrudan.com/gradient-descent.html">
  <meta property="og:title" content="Gradient Descent — Particles">
  <meta property="og:description" content="Particles are learners descending a procedural loss landscape using simulated SGD with momentum — overshooting minima, oscillating in narrow valleys, escaping saddle points.">
  <meta property="og:image" content="https://particles.alexandrudan.com/og-image.svg">
  <meta property="og:site_name" content="Particles">

  <!-- Twitter -->
  <meta name="twitter:card" content="summary_large_image">
  <meta name="twitter:title" content="Gradient Descent — Particles">
  <meta name="twitter:description" content="Particles are learners descending a procedural loss landscape using simulated SGD with momentum — overshooting minima, oscillating in narrow valleys, escaping saddle points.">
  <meta name="twitter:image" content="https://particles.alexandrudan.com/og-image.svg">
  <style>
    * { margin: 0; padding: 0; box-sizing: border-box; }
    body { background: #000; overflow: hidden; font-family: 'Courier New', monospace; }
    canvas { display: block; }
    #controls {
      position: fixed;
      bottom: 24px;
      left: 50%;
      transform: translateX(-50%);
      display: flex;
      gap: 20px;
      background: rgba(0,0,0,0.6);
      backdrop-filter: blur(12px);
      border: 1px solid rgba(255,255,255,0.08);
      border-radius: 12px;
      padding: 14px 28px;
      z-index: 10;
      align-items: center;
    }
    .ctrl-group {
      display: flex; flex-direction: column; align-items: center; gap: 4px;
    }
    .ctrl-group label {
      color: rgba(255,255,255,0.4); font-size: 9px;
      text-transform: uppercase; letter-spacing: 1.5px;
    }
    .ctrl-group input[type="range"] {
      -webkit-appearance: none; width: 100px; height: 3px;
      background: rgba(255,255,255,0.15); border-radius: 2px; outline: none;
    }
    .ctrl-group input[type="range"]::-webkit-slider-thumb {
      -webkit-appearance: none; width: 12px; height: 12px;
      border-radius: 50%; background: #fff; cursor: pointer;
    }
    #info {
      position: fixed; top: 24px; left: 28px; z-index: 10;
    }
    #info h1 {
      color: rgba(255,255,255,0.7); font-size: 14px; font-weight: 400;
      letter-spacing: 3px; text-transform: uppercase;
    }
    #info p {
      color: rgba(255,255,255,0.25); font-size: 10px;
      margin-top: 6px; letter-spacing: 1px;
    }
    #fps {
      position: fixed; top: 24px; right: 28px;
      color: rgba(255,255,255,0.2); font-size: 10px;
      letter-spacing: 1px; z-index: 10;
    }
    #back {
      position: fixed; top: 24px; left: 50%; transform: translateX(-50%);
      z-index: 10;
    }
    #back a {
      color: rgba(255,255,255,0.2); font-size: 9px; text-decoration: none;
      letter-spacing: 2px; text-transform: uppercase;
      transition: color 0.3s;
    }
    #back a:hover { color: rgba(255,255,255,0.5); }
      .zoom-btn {
      width: 32px; height: 32px; border-radius: 50%;
      background: rgba(255,255,255,0.06); border: 1px solid rgba(255,255,255,0.12);
      color: rgba(255,255,255,0.5); font-size: 18px; cursor: pointer;
      display: flex; align-items: center; justify-content: center;
      transition: background 0.2s;
      font-family: monospace;
    }
    .zoom-btn:hover { background: rgba(255,255,255,0.12); }
  </style>
</head>
<body>
  <div id="info">
    <h1>Gradient Descent</h1>
    <p id="particle-count"></p>
  </div>
  <div id="fps"></div>
  <div id="back"><a href="index.html">Gallery</a></div>
  <div id="controls">
    <div class="ctrl-group">
      <input type="range" id="speed" min="0.1" max="5" step="0.1" value="1">
      <label>Speed</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="bloom" min="0" max="3" step="0.1" value="0.5">
      <label>Bloom</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="size" min="0.5" max="4" step="0.1" value="1.0">
      <label>Size</label>
    </div>
    <div class="ctrl-group">
      <input type="range" id="hueShift" min="0" max="1" step="0.01" value="0">
      <label>Hue</label>
    </div>
    <button class="zoom-btn" id="zoomOut">−</button>
    <button class="zoom-btn" id="zoomIn">+</button>
  </div>

  <script type="importmap">
  {
    "imports": {
      "three": "https://cdn.jsdelivr.net/npm/three@0.160.0/build/three.module.js",
      "three/addons/": "https://cdn.jsdelivr.net/npm/three@0.160.0/examples/jsm/"
    }
  }
  </script>
  <script type="module">
    import * as THREE from 'three';
    import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
    import { EffectComposer } from 'three/addons/postprocessing/EffectComposer.js';
    import { RenderPass } from 'three/addons/postprocessing/RenderPass.js';
    import { UnrealBloomPass } from 'three/addons/postprocessing/UnrealBloomPass.js';
    import { GPUComputationRenderer } from 'three/addons/misc/GPUComputationRenderer.js';

    const WIDTH = 256;
    const PARTICLE_COUNT = WIDTH * WIDTH;

    // Scene
    const scene = new THREE.Scene();
    const camera = new THREE.PerspectiveCamera(60, innerWidth / innerHeight, 0.1, 2000);
    camera.position.set(0, 10, 16);

    const renderer = new THREE.WebGLRenderer({ antialias: false, powerPreference: 'high-performance' });
    renderer.setSize(innerWidth, innerHeight);
    renderer.setPixelRatio(1);
    document.body.appendChild(renderer.domElement);

    const orbitControls = new OrbitControls(camera, renderer.domElement);
    orbitControls.enableDamping = true;
    orbitControls.dampingFactor = 0.05;
    orbitControls.autoRotate = true;
    orbitControls.autoRotateSpeed = 0.5;

    // Post-processing
    const composer = new EffectComposer(renderer);
    composer.addPass(new RenderPass(scene, camera));
    const bloomPass = new UnrealBloomPass(
      new THREE.Vector2(innerWidth / 2, innerHeight / 2),
      0.5, 0.3, 0.8
    );
    composer.addPass(bloomPass);

    // GPU Computation
    const gpuCompute = new GPUComputationRenderer(WIDTH, WIDTH, renderer);
    const posTex0 = gpuCompute.createTexture();

    function seedTexture(tex) {
      const data = tex.image.data;
      for (let i = 0; i < PARTICLE_COUNT; i++) {
        const idx = i * 4;
        data[idx]     = (Math.random() * 2.0 - 1.0) * 7.0; // x position in [-7, 7]
        data[idx + 1] = (Math.random() * 2.0 - 1.0) * 7.0; // y position in [-7, 7]
        data[idx + 2] = 0; // velocity x = 0
        data[idx + 3] = 0; // velocity y = 0
      }
    }

    seedTexture(posTex0);

    const positionShader = `
      uniform vec3 uMouse;
      uniform float uMouseActive;
      uniform float uDt;
      uniform float uSpeed;
      uniform float uFrame;
      uniform float uTime;

      float hash(vec2 p) {
        vec3 p3 = fract(vec3(p.xyx) * 0.1031);
        p3 += dot(p3, p3.yzx + 33.33);
        return fract((p3.x + p3.y) * p3.z);
      }

      // Loss landscape: sum of inverted Gaussians (local minima) + quadratic valley
      float loss(vec2 p) {
        float L = 0.0;
        // Global quadratic bowl
        L += 0.02 * dot(p, p);
        // Local minima (inverted Gaussians)
        L -= 3.0 * exp(-dot(p - vec2(3.0, 2.0), p - vec2(3.0, 2.0)) * 0.3);
        L -= 2.5 * exp(-dot(p - vec2(-4.0, 1.0), p - vec2(-4.0, 1.0)) * 0.4);
        L -= 2.0 * exp(-dot(p - vec2(1.0, -3.0), p - vec2(1.0, -3.0)) * 0.35);
        L -= 1.5 * exp(-dot(p - vec2(-2.0, -4.0), p - vec2(-2.0, -4.0)) * 0.5);
        L -= 3.5 * exp(-dot(p - vec2(-1.0, 3.0), p - vec2(-1.0, 3.0)) * 0.25);
        // Narrow valley (Rosenbrock-like)
        L += 0.1 * (1.0 - p.x) * (1.0 - p.x) + 0.3 * (p.y - p.x*p.x) * (p.y - p.x*p.x);
        return L;
      }

      vec2 gradLoss(vec2 p) {
        float eps = 0.05;
        float dx = (loss(p + vec2(eps, 0.0)) - loss(p - vec2(eps, 0.0))) / (2.0 * eps);
        float dy = (loss(p + vec2(0.0, eps)) - loss(p - vec2(0.0, eps))) / (2.0 * eps);
        return vec2(dx, dy);
      }

      void main() {
        vec2 uv = gl_FragCoord.xy / resolution.xy;
        vec4 state = texture2D(texturePosition, uv);

        // State: x,y = position on loss surface; z = velocity_x; w = velocity_y
        float x = state.x;
        float y = state.y;
        float vx = state.z;
        float vy = state.w;

        float dt = uDt * uSpeed;
        float lr = 0.8; // learning rate
        float momentum = 0.9;

        // Compute gradient
        vec2 grad = gradLoss(vec2(x, y));

        // SGD with momentum
        vx = momentum * vx - lr * grad.x * dt;
        vy = momentum * vy - lr * grad.y * dt;

        // Stochastic noise (SGD noise)
        vec2 seed = uv * 1000.0 + uFrame;
        vx += (hash(seed) - 0.5) * 0.15 * dt;
        vy += (hash(seed + 100.0) - 0.5) * 0.15 * dt;

        x += vx;
        y += vy;

        // Soft boundary
        if (abs(x) > 8.0) { x *= 0.95; vx *= -0.5; }
        if (abs(y) > 8.0) { y *= 0.95; vy *= -0.5; }

        // Mouse attraction (project mouse 3D onto the loss surface XZ plane)
        if (uMouseActive > 0.01) {
          vec2 toMouse = uMouse.xz - vec2(x, y);
          float mouseDist = length(toMouse);
          float mouseForce = uMouseActive * 0.3 / (mouseDist * mouseDist + 1.0);
          x += toMouse.x * mouseForce * dt;
          y += toMouse.y * mouseForce * dt;
        }

        gl_FragColor = vec4(x, y, vx, vy);
      }
    `;

    const posVar = gpuCompute.addVariable('texturePosition', positionShader, posTex0);
    gpuCompute.setVariableDependencies(posVar, [posVar]);

    posVar.material.uniforms.uDt = { value: 0.01 };
    posVar.material.uniforms.uSpeed = { value: 1.0 };
    posVar.material.uniforms.uFrame = { value: 0.0 };
    posVar.material.uniforms.uTime = { value: 0.0 };
    posVar.material.uniforms.uMouse = { value: new THREE.Vector3(0, 0, -1000) };
    posVar.material.uniforms.uMouseActive = { value: 0.0 };

    posVar.wrapS = THREE.RepeatWrapping;
    posVar.wrapT = THREE.RepeatWrapping;

    const err = gpuCompute.init();
    if (err !== null) console.error('GPU Computation init error:', err);

    // Particle Rendering
    const vertexShader = `
      uniform sampler2D uPositionTexture;
      uniform float uHueShift;
      uniform float uPointSize;
      uniform float uScale;
      attribute vec2 aTexCoord;
      varying vec3 vColor;

      vec3 hsl2rgb(float h, float s, float l) {
        float c = (1.0 - abs(2.0 * l - 1.0)) * s;
        float h6 = h * 6.0;
        float x = c * (1.0 - abs(mod(h6, 2.0) - 1.0));
        float m = l - c * 0.5;
        vec3 rgb;
        if (h6 < 1.0) rgb = vec3(c, x, 0.0);
        else if (h6 < 2.0) rgb = vec3(x, c, 0.0);
        else if (h6 < 3.0) rgb = vec3(0.0, c, x);
        else if (h6 < 4.0) rgb = vec3(0.0, x, c);
        else if (h6 < 5.0) rgb = vec3(x, 0.0, c);
        else rgb = vec3(c, 0.0, x);
        return rgb + m;
      }

      void main() {
        vec4 posData = texture2D(uPositionTexture, aTexCoord);
        float px = posData.x;
        float py = posData.y;

        // Compute loss for height
        float L = 0.0;
        L += 0.02 * (px*px + py*py);
        L -= 3.0 * exp(-((px-3.0)*(px-3.0)+(py-2.0)*(py-2.0))*0.3);
        L -= 2.5 * exp(-((px+4.0)*(px+4.0)+(py-1.0)*(py-1.0))*0.4);
        L -= 2.0 * exp(-((px-1.0)*(px-1.0)+(py+3.0)*(py+3.0))*0.35);
        L -= 1.5 * exp(-((px+2.0)*(px+2.0)+(py+4.0)*(py+4.0))*0.5);
        L -= 3.5 * exp(-((px+1.0)*(px+1.0)+(py-3.0)*(py-3.0))*0.25);
        L += 0.1*(1.0-px)*(1.0-px) + 0.3*(py-px*px)*(py-px*px);

        vec3 pos = vec3(px, -L * 1.5, py) * uScale; // invert L so minima are valleys
        float gradMag = length(posData.zw);

        // Coloring: gradient magnitude -> hue (steep=hot red, flat=cool blue settled)
        float hue = fract(0.6 - gradMag * 0.15 + uHueShift);
        float saturation = 0.6;
        float lightness = 0.12 + min(gradMag * 0.2, 0.25);

        vColor = hsl2rgb(hue, saturation, lightness);

        vec4 mvPosition = modelViewMatrix * vec4(pos, 1.0);
        gl_PointSize = uPointSize * (55.0 / -mvPosition.z);
        gl_PointSize = max(gl_PointSize, 0.3);
        gl_Position = projectionMatrix * mvPosition;
      }
    `;

    const fragmentShader = `
      varying vec3 vColor;
      void main() {
        float d = length(gl_PointCoord - 0.5) * 2.0;
        if (d > 1.0) discard;
        // Soft gaussian falloff with bright core
        float glow = exp(-d * d * 3.0);
        float core = exp(-d * d * 12.0);
        float alpha = (glow * 0.15 + core * 0.3);
        // Slight color boost at core (hotter center)
        vec3 col = vColor + core * 0.15;
        gl_FragColor = vec4(col, alpha);
      }
    `;

    const geometry = new THREE.BufferGeometry();
    const texCoords = new Float32Array(PARTICLE_COUNT * 2);
    for (let j = 0; j < WIDTH; j++) {
      for (let i = 0; i < WIDTH; i++) {
        const idx = (j * WIDTH + i) * 2;
        texCoords[idx]     = (i + 0.5) / WIDTH;
        texCoords[idx + 1] = (j + 0.5) / WIDTH;
      }
    }
    const dummyPositions = new Float32Array(PARTICLE_COUNT * 3);
    geometry.setAttribute('position', new THREE.BufferAttribute(dummyPositions, 3));
    geometry.setAttribute('aTexCoord', new THREE.BufferAttribute(texCoords, 2));

    const material = new THREE.ShaderMaterial({
      vertexShader,
      fragmentShader,
      uniforms: {
        uPositionTexture: { value: null },
        uHueShift: { value: 0.0 },
        uPointSize: { value: 1.5 },
        uScale: { value: 1.2 },
      },
      transparent: true,
      blending: THREE.AdditiveBlending,
      depthWrite: false,
    });

    const points = new THREE.Points(geometry, material);
    const pivot = new THREE.Group(); pivot.add(points); scene.add(pivot);

    // UI
    document.getElementById('particle-count').textContent =
      `${PARTICLE_COUNT.toLocaleString()} particles — fully GPU computed`;

    const speedSlider = document.getElementById('speed');
    const bloomSlider = document.getElementById('bloom');
    const sizeSlider = document.getElementById('size');
    const hueSlider = document.getElementById('hueShift');
    const fpsEl = document.getElementById('fps');

    document.getElementById('zoomIn').addEventListener('click', () => {
      material.uniforms.uScale.value *= 1.15;
    });
    document.getElementById('zoomOut').addEventListener('click', () => {
      material.uniforms.uScale.value *= 0.85;
    });

    // Animation Loop
    // Mouse interaction
    const mouse = new THREE.Vector2();
    const mouse3D = new THREE.Vector3();
    const raycaster = new THREE.Raycaster();
    let mouseActive = false;

    renderer.domElement.addEventListener('mousemove', (e) => {
      mouse.x = (e.clientX / innerWidth) * 2 - 1;
      mouse.y = -(e.clientY / innerHeight) * 2 + 1;
      mouseActive = true;
      raycaster.setFromCamera(mouse, camera);
      mouse3D.copy(raycaster.ray.direction).multiplyScalar(15).add(camera.position);
    });
    renderer.domElement.addEventListener('mouseleave', () => { mouseActive = false; });

    let lastTime = performance.now();
    let frameCount = 0;

    function animate(now) {
      requestAnimationFrame(animate);

      frameCount++;
      if (now - lastTime >= 1000) {
        fpsEl.textContent = `${frameCount} FPS`;
        frameCount = 0;
        lastTime = now;
      }

      posVar.material.uniforms.uSpeed.value = parseFloat(speedSlider.value);
      posVar.material.uniforms.uFrame.value += 1.0;
      posVar.material.uniforms.uTime.value += 0.016 * parseFloat(speedSlider.value);
      bloomPass.strength = parseFloat(bloomSlider.value);
      material.uniforms.uHueShift.value = parseFloat(hueSlider.value);
      material.uniforms.uPointSize.value = parseFloat(sizeSlider.value);

      // Update mouse uniforms
      if (mouseActive) {
        posVar.material.uniforms.uMouse.value.copy(mouse3D);
        posVar.material.uniforms.uMouseActive.value = 1.0;
      } else {
        posVar.material.uniforms.uMouseActive.value *= 0.95;
      }


      gpuCompute.compute();

      material.uniforms.uPositionTexture.value =
        gpuCompute.getCurrentRenderTarget(posVar).texture;

      pivot.rotation.x += 0.0008;
      orbitControls.update();
      composer.render();
    }

    animate(performance.now());

    // Resize
    window.addEventListener('resize', () => {
      camera.aspect = innerWidth / innerHeight;
      camera.updateProjectionMatrix();
      renderer.setSize(innerWidth, innerHeight);
      composer.setSize(innerWidth, innerHeight);
    });
  </script>
<script src="shared-ui.js"></script>
</body>
</html>