2d:null 2e:["$","title",null,{"children":"Generative Adversarial Network | Mark Keller | Observable"}] 33:T659,render = (ctx) => { ctx.clearRect(0, 0, 400, 400); // various vis hyperparams const orih = 350; const orix0 = 10; const orix1 = 390; const transh = 250; // lower black line ctx.beginPath(); ctx.moveTo(orix0, orih); ctx.lineTo(orix1, orih); ctx.strokeStyle = "#000"; ctx.strokeWidth = 2; ctx.stroke(); // upper black line ctx.beginPath(); ctx.moveTo(orix0, transh); ctx.lineTo(orix1, transh); ctx.strokeStyle = "#000"; ctx.strokeWidth = 2; ctx.stroke(); let t, prevp; // draw the true distribution t = 0; prevp = 0; while(t <= 1) { var p = pdf(t); if(t > 0) { ctx.beginPath(); ctx.moveTo((t-dt)*(orix1-orix0) + orix0, transh - prevp); ctx.lineTo(t*(orix1-orix0) + orix0, transh - p); ctx.strokeStyle = "#00F"; ctx.strokeWidth = 1; ctx.stroke(); } prevp = p; t += dt; } // draw the discriminator t = 0; prevp = 0; while(t <= 1) { let p = disc.forward(t); p = sigmoid(p)*50; // sigmoid if(t > 0) { ctx.beginPath(); ctx.moveTo((t-dt)*(orix1-orix0) + orix0, transh - prevp); ctx.lineTo(t*(orix1-orix0) + orix0, transh - p); ctx.strokeStyle = "#0F0"; ctx.strokeWidth = 1; ctx.stroke(); } prevp = p; t += dt; } // draw the generating distribution arrows t = 0; while(t <= 1) { let x = gen.forward(t); ctx.beginPath(); ctx.moveTo(t*(orix1-orix0) + orix0, orih); ctx.lineTo(x*(orix1-orix0) + orix0, transh); ctx.strokeStyle = "#F00"; ctx.strokeWidth = 1; ctx.stroke(); t += dt; } return ctx; }34:T798,// a simple 2-layer net, // except we have to be careful because our inputs are 1D scalars. class Net { constructor(nh, wscale) { this.nh = nh; // number of hidden units let param = {}; let grad_param = {}; param.w1 = []; param.b1 = []; param.w2 = []; param.b2 = 0; grad_param.w1 = []; grad_param.b1 = []; grad_param.w2 = []; grad_param.b2 = 0.5; for(let i = 0; i < nh; i++) { let c = i/nh; let w = 14.7; // 10 * atanh(0.9) let b = -w * c; if(Math.random() < 0.5) { w = -w; } param.w1.push(w); param.b1.push(b); param.w2.push((Math.random()-0.5)*wscale); grad_param.w1.push(0); grad_param.b1.push(0); grad_param.w2.push(0); } this.param = param; this.grad_param = grad_param; this.hcache = []; for(let i = 0; i < nh; i++) { this.hcache[i] = 0; } } forward(t) { let param = this.param; let x = param.b2; for(let i = 0; i < this.nh; i++) { let h = Math.tanh(param.w1[i] * t + param.b1[i]); this.hcache[i] = h; // store for backward pass x += param.w2[i] * h; } this.t = t; return x; } backward(dx) { let grad_param = this.grad_param; let param = this.param; grad_param.b2 += dx; let dt = 0; for(let i = 0; i < this.nh; i++) { let h = this.hcache[i]; grad_param.w2[i] += h * dx; let dh = param.w2[i] * dx; let ds = (1.0 - h*h) * dh; // backprop through tanh grad_param.b1[i] += ds; grad_param.w1[i] += this.t * ds; dt += param.w1[i] * ds; } return dt; } update() { // do param update and reset gradients to zero let nh = this.nh; // dont learn 1st layer. 1D is finicky, lets just fix it let p = this.param.w2; let g = this.grad_param.w2; for(var i=0;itrue data distribution, \ngenerator network from uniform noise in U[0,1], \ndiscriminator network\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":144,"value":"viewof vis = {\n const ctx = DOM.context2d(400, 400);\n yield render(ctx).canvas;\n while(true) {\n await Promises.delay(20);\n for(let i=0;i<20;i++) { step(); }\n yield render(ctx).canvas;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"viewof reset = button(\"Reset\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"viewof lrPow = slider({\n min: -10, \n max: 10, \n step: 1, \n value: 0,\n description: \"Learning rate exponent\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"viewof currD = radio({\n options: [\n \"1D\",\n \"2D\"\n ],\n value: \"1D\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"// do a single training step\nstep = () => {\n // forward and backward a generated (negative) example\n for(let k = 0; k < 5; k++) {\n let t = Math.random();\n let xgen = gen.forward(t);\n let sgen = disc.forward(xgen);\n let dsgen = sigmoid(sgen);\n let dxgen = disc.backward(dsgen);\n // forward and backward a real (positive) example\n let xdata = sample();\n let sdata = disc.forward(xdata);\n let dsdata = sigmoid(sdata) - 1;\n let dxdata = disc.backward(dsdata);\n disc.update();\n }\n // backward the generator\n let t = Math.random();\n let xgen = gen.forward(t);\n let sgen = disc.forward(xgen);\n let dsgen = sigmoid(sgen);\n let dxgen = disc.backward(dsgen);\n let dt = gen.backward(-dxgen);\n gen.update();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"gen = {\n reset;\n return new Net(30, 0.5); // generator\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"disc = {\n reset;\n return new Net(30, 0.5); // discriminator\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"// learning rate\nlr = { \n return 0.0001*Math.pow(2,lrPow); \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"// various learning hyperparams\ndt = 0.02","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"// various learning hyperparams\nreg = 0.00001","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":103,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"pdf = {\n return (currD === \"2D\" ? Stats.pdf2 : Stats.pdf1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":91,"value":"sample = {\n return (currD === \"2D\" ? Stats.sample2 : Stats.sample1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"sigmoid = (x) => {\n return 1.0/(1.0 + Math.exp(-x));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"import {radio, button, slider} from \"@jashkenas/inputs\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 32:"$31:body"