2f:Tab8,class Value { constructor(value, label = "", operator = "", children = [], exponent = 1) { this.value = value; this.label = label; this.operator = operator; this.gradient = 0; this.exponent = exponent; this.children = children; } add(other) { if (typeof other === "number") other = new Value(other); const newValue = this.value + other.value; return new Value(newValue, "", "+", [this, other]); } sub(other) { if (typeof other === "number") other = new Value(other); return this.add(other.mul(-1)); } mul(other) { if (typeof other === "number") other = new Value(other); const newValue = this.value * other.value; return new Value(newValue, "", "*", [this, other]); } div(other) { if (typeof other === "number") other = new Value(other); return this.mul(other.pow(-1)); } neg() { return this.mul(-1); } pow(x) { const newValue = Math.pow(this.value, x); this.exponent = x; return new Value(newValue, "", "^", [this], x); } exp() { const newValue = Math.exp(this.value); return new Value(newValue, "", "exp", [this]); } tanh() { const newValue = Math.tanh(this.value); return new Value(newValue, "", "tanh", [this]); } backward() { this.gradient = 1; let topo = []; let visited = new Set(); const buildTopo = (v) => { if (!visited.has(v)) { visited.add(v); for (let child of v.children) { buildTopo(child); } topo.push(v); } }; buildTopo(this); for (let node of topo.reverse()) { node._setChildGradients(); } } _setChildGradients() { const saved = this.children.map(c => ({ v: c.value, g: c.gradient, op: c.operator })); switch (this.operator) { case "+": { const [left, right] = this.children; left.gradient += this.gradient; right.gradient += this.gradient; break; } case "*": { const [left, right] = this.children; left.gradient += this.gradient * right.value; right.gradient += this.gradient * left.value; break; } case "^": { const [c] = this.children; c.gradient += this.exponent * (Math.pow(c.value, this.exponent - 1)) * this.gradient; break; } case "tanh": { const [c] = this.children; c.gradient += this.gradient * (1 - Math.pow(this.value, 2)); break; } case "exp": { const [c] = this.children; c.gradient += this.gradient * this.value; break; } case "": break; default: throw new Error(`Operator '${this.operator}' not implemented!`); break; } } }30:[] 2d:{"title":"micrograd.js","cells":[{"id":0,"value":"# micrograd.js\n\nA JavaScript implementation of Andrej Karpathy's micrograd engine.\n\nJust like the original micrograd, this is an educational tool not meant for production use. I wrote it to understand backpropagation better.","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"$2f","pinned":true,"hidden":false,"mode":"ojs"},{"id":53,"value":"function preventInfinity(x) {\n if (isFinite(x)) return x;\n if (x > 0) return Number.MAX_VALUE;\n return Number.MIN_VALUE;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"function visualize(value) {\n const children = value.children.map(c => visualize(c)).reduce((curr, prev) => html`${prev}${curr}`, html``);\n return html`\n

${value.label}(${value.value}, grad = ${value.gradient})

\n\t

\n \t \t

${value.operator === \"exp\" ? \"eˣ\" : value.operator}${value.exponent !== 1 ? value.exponent : \"\"}

\n ${children}\n

\n\t

\n `;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":9,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":11,"value":"{\n const a = new Value(2, \"a\");\n const b = new Value(3, \"b\");\n const c = a.add(b); c.label = \"c\";\n const d = new Value(5, \"d\");\n const e = d.mul(b); e.label = \"e\";\n const f = c.mul(e); f.label = \"f\";\n f.backward();\n return visualize(f)\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":17,"value":"class Neuron {\n constructor(nin) {\n this.w = [];\n for (let i = 0; i < nin; i++)\n this.w.push(new Value((Math.random() * 2) - 1))\n this.b = new Value((Math.random() * 2) - 1);\n }\n\n call(x) {\n const z = x.map((x, i) => this.w[i].mul(x)).reduce((sum, p) => sum.add(p), new Value(0)).add(this.b);\n return z.tanh();\n }\n\n parameters() {\n return [...this.w, this.b];\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":19,"value":"class Layer {\n constructor(nin, nout) {\n this.neurons = [];\n for (let i = 0; i < nout; i++) {\n this.neurons.push(new Neuron(nin));\n }\n }\n\n call(x) {\n const outs = this.neurons.map(n => n.call(x));\n return outs.length === 1 ? outs[0] : outs;\n }\n\n parameters() {\n return this.neurons.reduce((p, n) => p.concat(n.parameters()), []);\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":21,"value":"class MLP {\n constructor(nin, nouts) {\n const sizes = [nin].concat(nouts);\n this.layers = [];\n for (let i = 0; i < nouts.length; i++) {\n this.layers.push(new Layer(sizes[i], sizes[i + 1]));\n }\n }\n\n call(x) {\n for (const layer of this.layers) {\n x = layer.call(x);\n }\n return x;\n }\n\n parameters() {\n return this.layers.reduce((p, n) => p.concat(n.parameters()), []);\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"{\n const n = new MLP(3, [4, 4, 1]);\n const xs = [\n [2.0, 3.0, -1.0],\n [3.0, -1.0, 0.5],\n [0.5, 1.0, 1.0],\n [1.0, 1.0, -1.0],\n ];\n const ys = [1.0, -1.0, -1.0, 1.0];\n let ypred;\n let loss;\n const iterations = 1000;\n const learningRate = 0.1;\n \n for (let k = 0; k < iterations; k++) {\n // forward pass\n ypred = xs.map(x => n.call(x));\n loss = ys.reduce((acc, ygt, index) => {\n const yout = ypred[index];\n return yout.sub(ygt).pow(2).add(acc);\n }, 0);\n\n // backward pass\n for (const p of n.parameters()) {\n p.gradient = 0;\n }\n loss.backward();\n\n // learning\n for (const p of n.parameters()) {\n p.value -= p.gradient * learningRate;\n }\n }\n return { loss, ypred };\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}