2f:T110e,class Value { constructor(value, label = "", operator = "", children = [], exponent = 1, ixp = 0) { this.value = value; this.label = label; this.operator = operator; this.gradient = 0; this.exponent = exponent; this.ixp = ixp; 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]); } relu() { const newValue = this.value < 0 ? 0 : this.value; return new Value(newValue, "", "ReLU", [this]); } // softmax cross-entropy loss static sce(xs, ixp) { // xs: predictions, ixp: index of the positive class const xp = xs[ixp]; const xsv = xs.map(x => x.value); const D = -Math.max(...xsv); const exps = xs.map(x => Math.exp(x.value + D)); const sum = exps.reduce((acc, e) => acc + e, 0); const quot = Math.exp(xp.value + D) / sum; const sce = -Math.log(quot); return new Value(sce, "", "SCE", [...xs], 1, ixp); } 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 "ReLU": { const [c] = this.children; c.gradient += this.gradient * (c.value < 0 ? 0 : 1); break; } case "SCE": { const D = -Math.max(...this.children.map(x => x.value)); //throw new Error (`childValues: ${JSON.stringify(this.children.map(c => c.value))}, D: ${D}`); const exps = this.children.map(x => Math.exp(x.value + D)); const sum = exps.reduce((acc, e) => acc + e, 0); //throw new Error (`exps: ${JSON.stringify(exps)}, sum: ${sum}`); const softmax = exps.map(exp => exp / sum); //throw new Error (`softmax: ${JSON.stringify(softmax)}`); softmax.forEach((sm, i) => { const yi = i === this.ixp ? 1 : 0; //throw new Error(`this.children[${i}].gradient === ${this.children[i].gradient}, this.gradient === ${this.gradient}, (sm - yi) === ${sm - yi}, sm === ${sm}, yi === ${yi}`) this.children[i].gradient += this.gradient * (sm - yi); }) break; } case "": break; default: throw new Error(`Operator '${this.operator}' not implemented!`); break; } } }30:T1ad4,colorData = 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31:T695,function train1() { const n = new MLP(3, [16, 4, 4, 4, 3]); const losses = []; let ypred; let loss; let i = 0; const epochs = 3; const batchSize = 32; const learningRate = 0.01; const allData = _.shuffle(colors_2000); const trainingData = allData.slice(0, 4000); const testData = allData.slice(4000); for (let k = 0; k < epochs; k++) { const batches = _.chunk(trainingData, 10); for (const batch of batches) { const xs = batch.map(([x, y]) => x); const ys = batch.map(([x, y]) => y); // forward pass ypred = xs.map(x => n.call(x)); loss = ypred.reduce((sum, yp, i) => Value.sce(yp, getPositiveIndex(ys[i])).add(sum), 0).div(batch.length); losses.push({ i, k, xs, ys, loss: Math.min(loss.value, 2), l: batch.length }); i++; // backward pass for (const p of n.parameters()) { p.gradient = 0; } loss.backward(); // learning for (const p of n.parameters()) { p.value -= p.gradient * learningRate; } } } let cc = 0; for (const [input, expected] of testData) { const actual = n.call(input); if (isCorrect(actual, expected)) { cc++; } } return cc / testData.length * 100; function isCorrect(ygts, yps) { let maxIndexArr1 = 0; let maxIndexArr2 = 0; for (let i = 1; i < ygts.length; i++) { if (ygts[i] > ygts[maxIndexArr1]) { maxIndexArr1 = i; } if (yps[i] > yps[maxIndexArr2]) { maxIndexArr2 = i; } } return maxIndexArr1 === maxIndexArr2; } return Plot.line(losses, { x: "i", y: "loss" }).plot(); //return losses; }32:[{"id":"905eb4c53205cc1c1ac8bb56f83f703600892ad7b6184dd8998d9b98bf2e2cd15456c41051e6a1cf1a894d4177e91040d7fd016dfae3f85e9aef055954695280","href":"https://static.observableusercontent.com/files/905eb4c53205cc1c1ac8bb56f83f703600892ad7b6184dd8998d9b98bf2e2cd15456c41051e6a1cf1a894d4177e91040d7fd016dfae3f85e9aef055954695280","name":"colors_2000.json","type":"application/json","lastModified":1683557513885.724,"size":136712}] 2d:{"title":"micrograd.js optimized","cells":[{"id":0,"value":"# micrograd.js optimized\n\nA version of my previous micrograd.js notebook that implements more complex functions as single operations, and therefore is hopefully more efficient than the original.","pinned":false,"hidden":false,"mode":"md"},{"id":162,"value":"{\n const a = new Value(-5, \"a\");\n const b = new Value(3, \"b\");\n const c = a.mul(b); c.label = \"c\";\n const r = c.relu();\n r.backward();\n return visualize(r);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":227,"value":"{\n const a = new Value(5, \"a\");\n const b = new Value(3, \"b\");\n const c = new Value(1, \"c\");\n let s;\n for (let k = 0; k < 500; k++) {\n s = Value.sce([a, b, c], 0);\n s.backward();\n a.value -= a.gradient * 0.01;\n b.value -= b.gradient * 0.01;\n c.value -= c.gradient * 0.01;\n }\n return visualize(s);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":244,"value":"5 - (-0.015376131670486492 * 0.01)","pinned":true,"hidden":false,"mode":"ojs"},{"id":5,"value":"$2f","pinned":true,"hidden":false,"mode":"ojs"},{"id":390,"value":"{\n const childValues = [-3, 25, 7];\n return -Math.max(...childValues.map(c => c))\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":53,"value":"function preventInfinity(x) {\n if (isFinite(x)) return x;\n if (x > 0) return Number.MAX_VALUE;\n return Number.MIN_VALUE;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"function visualize(value) {\n const children = value.children.map(c => visualize(c)).reduce((curr, prev) => html`${prev}${curr}`, html``);\n return html`\n

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

\n\t

\n \t \t

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

\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, isOutput) {\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 this.isOutput = isOutput;\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 this.isOutput ? z : z.relu();\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, isOutput) {\n this.neurons = [];\n for (let i = 0; i < nout; i++) {\n this.neurons.push(new Neuron(nin, isOutput));\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], i === nouts.length - 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":116,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":356,"value":"colors_2000 = FileAttachment(\"colors_2000.json\").json()","pinned":true,"hidden":false,"mode":"ojs"},{"id":121,"value":"xs = colors_2000.map(([color, _]) => color.map(c => c / 255));","pinned":true,"hidden":false,"mode":"ojs"},{"id":123,"value":"ys = colors_2000.map(([_, y]) => y);","pinned":true,"hidden":false,"mode":"ojs"},{"id":126,"value":"function getPositiveIndex(ygt) {\n return ygt.findIndex(i => i === 1);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":177,"value":"{\n // const n = new MLP(3, [4, 4, 3]);\n // const iterations = 20;\n // const learningRate = 0.5;\n // let ypred, loss;\n // for (let k = 0; k < iterations; k++) {\n // ypred = n.call([255, 0, 0]);\n // const positiveIndex = 1;\n // loss = Value.sce(ypred, positiveIndex);\n // console.log(\"loss:\", loss.value, \"ypred\", ypred.map(p => p.value).join(\":\"));\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: loss.value, ypred: ypred.map(y => y.value).join(\":\") };\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":363,"value":"train1()","pinned":true,"hidden":false,"mode":"ojs"},{"id":321,"value":"_.shuffle([1, 2, 3, 4, 5, 6, 7])","pinned":true,"hidden":false,"mode":"ojs"},{"id":293,"value":"{\n const a = new Value(-3, \"a\");\n const b = new Value(25, \"b\");\n const c = new Value(7, \"c\");\n const L = Value.sce([a, b, c], 0); L.label = \"L\";\n L.backward();\n return visualize(L);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":377,"value":"outputLayerGradients([-3, 25, 7], 0, 1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":375,"value":"function outputLayerGradients(outputValues, positiveClassIndex, parentGradient) {\n const maxOutputValue = Math.max(...outputValues);\n const exps = outputValues.map(value => Math.exp(value - maxOutputValue));\n const sumExps = exps.reduce((sum, exp) => sum + exp, 0);\n const softmaxOutputs = exps.map(exp => exp / sumExps);\n\n const gradients = softmaxOutputs.map((softmaxOutput, index) =>\n parentGradient * (index === positiveClassIndex ? softmaxOutput - 1 : softmaxOutput)\n );\n\n return gradients;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":310,"value":"{\n const data = [];\n for (let x = -10; x <= 10; x++) {\n data.push({ x, y: Math.pow(x, 2) });\n }\n return Plot.line(data, {x: \"x\", y: \"y\"}).plot()\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":422,"value":"function showData([color, [isBlue, isRed, isYellow]]) {\n return html`\n

\n rgb(${color.join(\", \")})\n ${isBlue ? \"blue\" : (isRed ? \"red\" : \"yellow\")}\n

`\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":426,"value":"{\n const sc = _.shuffle(colors_2000);\n return sc.slice(0, 20).reduce((acc, c) => html`${acc}${showData(c)}`, html``);\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W32","stdlib":"1","titling":"auto"}