41:null 42:["$","title",null,{"children":"Research Replication: Unsupervised Learning of Digit Recognition Using STDP (Part 2) | Steve Oney | Observable"}] 48:T4bb,weightCanvas = { const EX_PIXEL_SIZE = 1; const WIDTH = EX_PIXEL_SIZE * NUM_NEURON_COLS * DIGIT_WIDTH; const HEIGHT = EX_PIXEL_SIZE * NUM_NEURON_ROWS * DIGIT_HEIGHT; const canvas = DOM.canvas(WIDTH, HEIGHT); const ctx = canvas.getContext('2d'); const wcolor = d3.scaleLinear().range(["white", "black"]).domain([0, 1]); const selected_wcolor = d3.scaleLinear().range(["#FCC", "red"]).domain([0, 1]); for(let pixelNum = 0; pixelNum < xeae.length; pixelNum++) { const [inpX, inpY] = idx2Coordinates(pixelNum, DIGIT_HEIGHT, DIGIT_WIDTH); for(let neuronNum = 0; neuronNum < xeae[pixelNum].length; neuronNum++) { const [neuronX, neuronY] = idx2Coordinates(neuronNum, NUM_NEURON_ROWS, NUM_NEURON_COLS); const x = (neuronX * DIGIT_WIDTH + inpX) * EX_PIXEL_SIZE; const y = (neuronY * DIGIT_HEIGHT + inpY) * EX_PIXEL_SIZE; if(neuronNum === selectedIndex) { ctx.fillStyle = selected_wcolor(xeae[pixelNum][neuronNum]); } else { ctx.fillStyle = wcolor(xeae[pixelNum][neuronNum]); } ctx.fillRect(x, y, EX_PIXEL_SIZE, EX_PIXEL_SIZE); } } const container = DOM.element('div'); container.append(canvas); return container; };49:T13a9,drawingBoard = { const radius = 15; const WIDTH = 280; const HEIGHT = WIDTH; const canvas = DOM.canvas(WIDTH, HEIGHT); const ctx = canvas.getContext('2d'); ctx.fillStyle = ctx.strokeStyle = 'black'; ctx.lineWidth = radius; let state = 'idle'; const twoPi = 2 * Math.PI; let lastX = false; let lastY = false; function addDot(x, y) { ctx.lineWidth = 0; ctx.beginPath(); ctx.arc(x, y, radius, 0, twoPi, false); ctx.fill(); if(lastX && lastY) { ctx.lineWidth = radius*2; ctx.beginPath(); ctx.moveTo(lastX, lastY); ctx.lineTo(x, y); ctx.closePath(); ctx.stroke(); } lastX = x; lastY = y; } function clear() { ctx.fillStyle = 'white'; ctx.fillRect(0, 0, WIDTH, HEIGHT); ctx.fillStyle = ctx.strokeStyle = 'black'; convertDigit(); } let updateInterval = false; canvas.addEventListener('mousedown', (event) => { if(state === 'idle') { state = 'drawing'; lastX = lastY = false; const bbox = event.target.getBoundingClientRect(); addDot(event.clientX - bbox.left, event.clientY - bbox.top); updateInterval = setInterval(convertDigit, 200); } }); canvas.addEventListener('mousemove', (event) => { if(state === 'drawing') { const bbox = event.target.getBoundingClientRect(); addDot(event.clientX - bbox.left, event.clientY - bbox.top); } }); window.addEventListener('mouseup', (event) => { if(state === 'drawing') { state = 'idle'; clearInterval(updateInterval); convertDigit(); } }); canvas.style.border = '1px solid grey'; canvas.style.display = 'inline-block'; const clearButton = Inputs.button("Clear"); clearButton.addEventListener('click', clear); const inpColor = d3.scaleLinear().range(["white", "black"]).domain([0, 255]); const runButton = Inputs.button("Run"); runButton.addEventListener('click', async () => { convertDigit(); const delta_t = 0.01; const SHOW_NUM_STEPS = Math.round(SHOW_NUM_TIME /delta_t); let endStep = SHOW_NUM_STEPS; const ABSOLUTE_END_STEP = SHOW_NUM_STEPS * 10; let stepNum = 0; let maxFiringRate = DEFAULT_MAX_RATE; const fireCount = times(NUM_NEURONS, 0); let firingNeuron = -1; // ************************************* while(true) { if(stepNum > endStep) { const totalFires = sum(fireCount); if(totalFires > 5) { firingNeuron = largestIndex(fireCount); break; } else if(stepNum >= ABSOLUTE_END_STEP) { break; } else { maxFiringRate += MAX_RATE_INCREASE_INCREMENT; endStep += SHOW_NUM_STEPS; } } const t = delta_t * stepNum; const exOutput = await step(delta_t, t, maxFiringRate); exOutput.forEach((o, i) => { if(o > 0) { fireCount[i]++; } }); stepNum++; } mutable selectedIndex = firingNeuron; if(firingNeuron < 0) { output.textContent = `Classification: No digit`; } else { output.textContent = `Classification: ${neuron_labels[firingNeuron]}`; } }); // ************************************* function convertDigit() { const sampleWindowX = Math.round(WIDTH / DIGIT_WIDTH); const sampleWindowY = Math.round(HEIGHT / DIGIT_HEIGHT); const inputArr = []; let i = 0; for(let startX = 0; startX < WIDTH; startX += sampleWindowX) { for(let startY = 0; startY < HEIGHT; startY += sampleWindowY) { const data = ctx.getImageData(startX, startY, sampleWindowX, sampleWindowY).data.filter((_, i) => i % 4 === 0); // only include red channel (since it's B&W, it's fine to exclude R & B & alpha) const intensity = 255 - avg(data); mutable digitInput[i] = intensity; rects[i].setAttribute('fill', inpColor(intensity)); i++; } } } function avg(arr) { return arr.reduce((x, accum) => x + accum, 0) / arr.length; } const svgns = "http://www.w3.org/2000/svg"; const SVG_WIDTH = WIDTH; const SVG_HEIGHT = SVG_WIDTH; const svg = DOM.svg(SVG_WIDTH, SVG_HEIGHT); const rects = []; for(let i = 0; i new ALIF(0.2, 0, 0.002, 1 + theta[i], 1, 0), NUM_NEURONS); const exPSP = new PSP(excitatory_neurons, 0.2); // Create the inhibitory neurons and post-synaptic potential for them const inhibitory_neurons = new NeuronCollection(() => new LIF, NUM_NEURONS) const inhPSP = new PSP(inhibitory_neurons, 0.2); return async function(t_step, t, maxRate) { await inputLayer.step(t_step, t, maxRate); // Step the input inputPSP.step(t_step); // Step input post-synaptic const weightedInputVals = stdp.weightedOutput(inputPSP.output); // Compute the weighted inputs for the excitatory layer // Compute the output of the inhibitory layer by... const totalInhibitoryOutput = sum(inhPSP.output); // Finding the total inhibitory output // And take the sum *minus* each inhibitory neuron's value to get every other inhibitory neuron's value const inhibitoryOutputs = inhPSP.output.map((v) => totalInhibitoryOutput - v); // Compute the input to the excitatory layer as the sum of the weighted input from the digit and the // inhibitory input const excitatoryInput = addArrays(weightedInputVals, mulArray(negArray(inhibitoryOutputs), 2)); excitatory_neurons.step(excitatoryInput, t_step); // Step excitatory layer exPSP.step(t_step); // Step excitatory post-synaptic inhibitory_neurons.step(excitatory_neurons.output, t_step); // Step inhibitory layer (using excitatory output as its input) inhPSP.step(t_step); // Step inhibitory post-synaptic stdp.step(t_step); // Step STDP // stdp.updateWeights(inputLayer.output, excitatory_neurons.output); // Update STDP weights return excitatory_neurons.output; } }4b:Tcdb,class STDPWeights { constructor(numPre, numPost, tau_plus = 0.03, tau_minus = 0.03, a_plus = 0.08, a_minus = 0.088, g_min = 0, g_max = 1) { this.numPre = numPre; this.numPost = numPost; this.tau_plus = tau_plus; this.tau_minus = tau_minus; this.x = times(numPre, 0); // An array with numPre zeros this.y = times(numPost, 0); // An array with numPost zeros this.a_plus = a_plus; this.a_minus = a_minus; this.g_min = g_min; this.g_max = g_max; this.w = times2d(numPre, numPost, () => randomBetween(this.g_min, 10 * this.g_max/numPre)); // A 2-D array; numPre x numPost random values } updateWeights(preOutputs, postOutputs) { const preSpikeIndices = getIndicesGreaterThan0(preOutputs); // Indices of pre-synaptic spiking neurons const postSpikeIndices = getIndicesGreaterThan0(postOutputs); // Indices of poast-synaptic spiking neurons // Increment x for spiking pre-synaptic neurons preSpikeIndices.forEach((ps_idx) => { this.x[ps_idx] += this.a_plus; }); // Increment y for spiking poast-synaptic neurons postSpikeIndices.forEach((ps_idx) => { this.y[ps_idx] -= this.a_minus; }); const alpha_g = this.g_max - this.g_min; // Scaling factor for weight updates // Loop over the *index* of every pre-synaptic neuron that spiked preSpikeIndices.forEach((ps_idx) => { // And for every post-synaptic neuron connected to this pre-synaptic neuron, update // the connection weight by the `y` value for that post-synaptic neuron for(let i = 0; i this.g_max) { this.w[ps_idx][i] = this.g_max; } // if greater than g_max, set to g_max } }); // Loop over the *index* of every post-synaptic neuron that spiked postSpikeIndices.forEach((ps_idx) => { // And for every pre-synaptic neuron connected to this post-synaptic neuron, update // the connection weight by the `x` value for that pre-synaptic neuron for(let i = 0; i this.g_max) { this.w[i][ps_idx] = this.g_max; } // if greater than g_max, set to g_max } }); return this.w; } step(dt) { // Loop through each value of this.x and decay for(let i = 0; i neuron.output); // Assign our output to be a list of neuron outputs\n }\n\n step(inputs, t_step) {\n // Step every individual neuron\n // Assign this.output to the neurons' outputs\n // Return this.output\n return this.output = this.neurons.map((neuron, i) => neuron.step(inputs[i], t_step));\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":137,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"function addArrays(l1, l2) {\n return l1.map((v, i) => v + l2[i]);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":174,"value":"function mulArray(l, by) {\n return l.map((v) => by*v);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":176,"value":"function negArray(l) {\n return mulArray(l, -1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":169,"value":"function sum(l) {\n return l.reduce((accum, val) => accum + val, 0);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"DEFAULT_MIN_RATE = 0","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"DEFAULT_MAX_RATE = 16","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":334,"value":"MAX_RATE_INCREASE_INCREMENT = 16","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"DIGIT_WIDTH = 28","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"DIGIT_HEIGHT = DIGIT_WIDTH","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"DIGIT_SIZE = DIGIT_WIDTH * DIGIT_HEIGHT","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"NUM_NEURON_ROWS = 20","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"NUM_NEURON_COLS = NUM_NEURON_ROWS","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"NUM_NEURONS = NUM_NEURON_ROWS * NUM_NEURON_COLS;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"neuron_labels = FileAttachment(\"neuron_labels.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"theta = FileAttachment(\"theta.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"xeae = FileAttachment(\"xeae.json\").json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"function times(n, funcVal) {\n const result = [];\n const func = (typeof funcVal === 'function') ? funcVal : (() => funcVal);\n\n for(let i = 0; i 0);\n this.digitPixels = _.times(DIGIT_SIZE, () => 0);\n }\n\n setDigitPixels(pixels) {\n this.digitPixels = pixels;\n }\n \n async step(dt, t, maxFiringRate) {\n digitInput.forEach((intensity, i) => {\n const firingProbability = dt * (this.MIN_FIRING_RATE + (maxFiringRate - this.MIN_FIRING_RATE) * (intensity - this.DATA_MIN_VAL) / (this.DATA_MAX_VAL - this.DATA_MIN_VAL));\n \n const fires = Math.random() < firingProbability;\n\n if(fires) {\n this.output[i] = 1/dt;\n } else {\n this.output[i] = 0;\n }\n });\n return this.output;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"class PSP {\n constructor(collection, tau) {\n this.collection = collection; // NeuronCollection instance\n this.tau = tau; // time constant for decay\n this.output = this.collection.output.map(o => o); // Use the collection's output (but make a clone so we don't mutate the original)\n }\n\n step(t_step) {\n // Loop through my output, decay it, and add the output from the incoming collection.\n for(let i = 0; i= this.v_th + this.inh) {\n this.inh += this.inc_inh;\n this.refractory_time = this.tau_ref; // Set refractory time\n\n this.output = 1 / t_step; // Fire\n this.v = 0; // Reset potential\n } else {\n this.output = 0; // Don't fire\n }\n return this.output;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"class LIF {\n constructor(tau_rc=0.2, v_init=0, tau_ref=0.002, v_th=1){\n this.tau_rc = tau_rc;\n this.tau_ref = tau_ref;\n this.v = v_init;\n this.v_th = v_th;\n \n this.output = 0;\n this.refractory_time = 0;\n }\n\n step(I, t_step) {\n this.refractory_time -= t_step; // Subtract the amount of time thhat passed from our refractory time\n \n if(this.refractory_time < 0) { // If we aren't in our refractory period, update the voltage\n this.v = this.v * (1 - t_step/this.tau_rc) + (I * t_step / this.tau_rc);\n }\n\n if(this.v >= this.v_th) { // Fired\n this.refractory_time = this.tau_ref; // Set refractory time\n\n this.output = 1 / t_step; // Fire\n this.v = 0; // Reset potential\n } else {\n this.output = 0; // Don't fire\n }\n return this.output;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"function randomBetween(low, high) {\n return Math.random() * (high - low) + low;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":151,"value":"function times2d(n1, n2, funcVal) {\n const result = [];\n const func = (typeof funcVal === 'function') ? funcVal : (() => funcVal);\n\n for(let i = 0; i index).filter((index) => arr[index] > 0);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":106,"value":"function idx2Coordinates(idx, rows, cols) {\n const col = idx % cols;\n const row = Math.floor(idx / rows);\n return [col, row];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"INP_DISPLAY_PIXEL_SIZE = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":192,"value":"EX_MARGIN = 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":194,"value":"EX_PIXEL_SIZE = 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"EX_PADDING = 1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":321,"value":"SHOW_NUM_TIME = 0.35;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"function largestIndex(arr) {\n let max = arr[0];\n let maxIndex = 0;\n\n for (let i = 1; i < arr.length; i++) {\n if (arr[i] > max) {\n maxIndex = i;\n max = arr[i];\n }\n }\n\n return maxIndex;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4c","stdlib":"1"}} 47:"$46:body"