On a recent Winter weekend, I was snowed-in in my house. To use some time productively, I dusted off some old JavaScript code I wrote. The code implements a complete neural network classifier from scratch. The goal of the demo multi-class classifier NN is to predict the size of the company (small, medium, large) that a student works for after graduation, based on their sex (M, F), science units taken, major (finance, geology, history), and parents income.
The data is synthetic. It looks like:
-1 0.39 0 0 1 0.3570 0 1 0 1 0.51 1 0 0 0.8610 0 1 0 -1 0.19 0 0 1 0.6550 1 0 0 1 0.24 0 1 0 0.5700 0 0 1 1 0.22 1 0 0 0.8970 0 1 0 . . .
The first column is sex (M = -1, F = 1), the next column is number of science units taken, normalized by dividing by 100. The next three columns are the college major, one-hot encoded (finance = 100, geology = 010, history = 001), the sixth column is parent’s income, normalized by dividing by 100,000. The last three columns are the company size to predict (small = 100, medium = 010, large = 001).
The code is complex and involves every aspect of neural networks: network architecture, input-output, activation functions, mean squared error/loss, gradient descent training, softmax, classification accuracy, saving model weights and biases, and many other sub-topics. But the point is that neural networks aren’t magic — they’re just ideas and code, even if the ideas and code are complicated.
My demo runs in a shell and is based on the node.js framework. The demo code could be adapted to run in a browser, by replacing console.log() statements with some sort of display on a Web page in an HTML element.
A mildly annoying aspect of node.js file IO is that there is no easy way to do syncronous text file read. At first I though I must be completely missing something, but in node.js you just can’t read a file line-by-line without working at a very low level and buffering characters or bytes. Ugh.
Here are a few representative code snippets. The complete demo code is listed below.
. . .
class NeuralNet
{
constructor(numInput, numHidden, numOutput, seed)
{
this.rnd = new U.Erratic(seed);
this.ni = numInput;
. . .
this.iNodes = U.vecMake(this.ni, 0.0);
this.hNodes = U.vecMake(this.nh, 0.0);
. . .
this.initWeights();
}
. . .
}
. . .
// compute output node signals
for (let k = 0; k < this.no; ++k) { // softmax
let derivative = (1 - this.oNodes[k]) * this.oNodes[k];
// E=(t-o)^2
oSignals[k] = derivative * (this.oNodes[k] - Y[k]);
}
. . .
// compute hidden-to-output weight gradients using output signals
for (let j = 0; j < this.nh; ++j) {
for (let k = 0; k < this.no; ++k) {
hoGrads[j][k] = oSignals[k] * this.hNodes[j];
}
}
. . .
Good fun!
There are several roller coaster model kits you can buy (CoasterDynamix, Lego, Thames and Kosmos, etc.) But Adam Throgmorton has created beautiful working model roller coasters from scratch — more interesting and beautiful than a kit model.
Demo code below. Very long. Replace “lt” (less-than), “gt”, “lte”, “gte” with symbols — my blog editor chokes on those symbols.
// students_nn.js
// ES6, node.js
// predict company size (S,M,L) from sex, science units, major, parents income.
let U = require("../Utilities/utilities_lib.js");
let FS = require("fs");
// =============================================================================
class NeuralNet
{
constructor(numInput, numHidden, numOutput, seed)
{
this.rnd = new U.Erratic(seed);
this.ni = numInput;
this.nh = numHidden;
this.no = numOutput;
this.iNodes = U.vecMake(this.ni, 0.0);
this.hNodes = U.vecMake(this.nh, 0.0);
this.oNodes = U.vecMake(this.no, 0.0);
this.ihWeights = U.matMake(this.ni, this.nh, 0.0);
this.hoWeights = U.matMake(this.nh, this.no, 0.0);
this.hBiases = U.vecMake(this.nh, 0.0);
this.oBiases = U.vecMake(this.no, 0.0);
this.initWeights();
}
initWeights()
{
let lo = -0.01;
let hi = 0.01;
for (let i = 0; i "lt" this.ni; ++i) {
for (let j = 0; j "lt" this.nh; ++j) {
this.ihWeights[i][j] = (hi - lo) * this.rnd.next() + lo;
}
}
for (let j = 0; j "lt" this.nh; ++j) {
for (let k = 0; k "lt" this.no; ++k) {
this.hoWeights[j][k] = (hi - lo) * this.rnd.next() + lo;
}
}
}
eval(X)
{
let hSums = U.vecMake(this.nh, 0.0);
let oSums = U.vecMake(this.no, 0.0);
this.iNodes = X;
for (let j = 0; j "lt" this.nh; ++j) {
for (let i = 0; i "lt" this.ni; ++i) {
hSums[j] += this.iNodes[i] * this.ihWeights[i][j];
}
hSums[j] += this.hBiases[j];
this.hNodes[j] = U.hyperTan(hSums[j]);
}
for (let k = 0; k "lt" this.no; ++k) {
for (let j = 0; j "lt" this.nh; ++j) {
oSums[k] += this.hNodes[j] * this.hoWeights[j][k];
}
oSums[k] += this.oBiases[k];
}
this.oNodes = U.softmax(oSums);
let result = [];
for (let k = 0; k "lt" this.no; ++k) {
result[k] = this.oNodes[k];
}
return result;
} // eval()
setWeights(wts)
{
// order: ihWts, hBiases, hoWts, oBiases
let p = 0;
for (let i = 0; i "lt" this.ni; ++i) {
for (let j = 0; j "lt" this.nh; ++j) {
this.ihWeights[i][j] = wts[p++];
}
}
for (let j = 0; j "lt" this.nh; ++j) {
this.hBiases[j] = wts[p++];
}
for (let j = 0; j "lt" this.nh; ++j) {
for (let k = 0; k "lt" this.no; ++k) {
this.hoWeights[j][k] = wts[p++];
}
}
for (let k = 0; k "lt" this.no; ++k) {
this.oBiases[k] = wts[p++];
}
} // setWeights()
getWeights()
{
// order: ihWts, hBiases, hoWts, oBiases
let numWts = (this.ni * this.nh) + this.nh +
(this.nh * this.no) + this.no;
let result = U.vecMake(numWts, 0.0);
let p = 0;
for (let i = 0; i "lt" this.ni; ++i) {
for (let j = 0; j "lt" this.nh; ++j) {
result[p++] = this.ihWeights[i][j];
}
}
for (let j = 0; j "lt" this.nh; ++j) {
result[p++] = this.hBiases[j];
}
for (let j = 0; j "lt" this.nh; ++j) {
for (let k = 0; k "lt" this.no; ++k) {
result[p++] = this.hoWeights[j][k];
}
}
for (let k = 0; k "lt" this.no; ++k) {
result[p++] = this.oBiases[k];
}
return result;
} // getWeights()
shuffle(v)
{
// Fisher-Yates
let n = v.length;
for (let i = 0; i "lt" n; ++i) {
let r = this.rnd.nextInt(i, n);
let tmp = v[r];
v[r] = v[i];
v[i] = tmp;
}
}
train(trainX, trainY, lrnRate, maxEpochs)
{
let hoGrads = U.matMake(this.nh, this.no, 0.0);
let obGrads = U.vecMake(this.no, 0.0);
let ihGrads = U.matMake(this.ni, this.nh, 0.0);
let hbGrads = U.vecMake(this.nh, 0.0);
let oSignals = U.vecMake(this.no, 0.0);
let hSignals = U.vecMake(this.nh, 0.0);
let n = trainX.length; // 160
let indices = U.arange(n); // [0,1,..,159]
let freq = Math.trunc(maxEpochs / 10);
for (let epoch = 0; epoch "lt" maxEpochs; ++epoch) {
this.shuffle(indices); //
for (let ii = 0; ii "lt" n; ++ii) { // each item
let idx = indices[ii];
let X = trainX[idx];
let Y = trainY[idx];
this.eval(X); // output stored in this.oNodes
// compute output node signals
for (let k = 0; k "lt" this.no; ++k) {
let derivative = (1 - this.oNodes[k]) * this.oNodes[k]; // softmax
oSignals[k] = derivative * (this.oNodes[k] - Y[k]); // E=(t-o)^2
}
// compute hidden-to-output weight gradients using output signals
for (let j = 0; j "lt" this.nh; ++j) {
for (let k = 0; k "lt" this.no; ++k) {
hoGrads[j][k] = oSignals[k] * this.hNodes[j];
}
}
// compute output node bias gradients using output signals
for (let k = 0; k "lt" this.no; ++k) {
obGrads[k] = oSignals[k] * 1.0; // 1.0 dummy input can be dropped
}
// compute hidden node signals
for (let j = 0; j "lt" this.nh; ++j) {
let sum = 0.0;
for (let k = 0; k "lt" this.no; ++k) {
sum += oSignals[k] * this.hoWeights[j][k];
}
let derivative = (1 - this.hNodes[j]) * (1 + this.hNodes[j]); // tanh
hSignals[j] = derivative * sum;
}
// compute input-to-hidden weight gradients using hidden signals
for (let i = 0; i "lt" this.ni; ++i) {
for (let j = 0; j "lt" this.nh; ++j) {
ihGrads[i][j] = hSignals[j] * this.iNodes[i];
}
}
// compute hidden node bias gradients using hidden signals
for (let j = 0; j "lt" this.nh; ++j) {
hbGrads[j] = hSignals[j] * 1.0; // 1.0 dummy input can be dropped
}
// update input-to-hidden weights
for (let i = 0; i "lt" this.ni; ++i) {
for (let j = 0; j "lt" this.nh; ++j) {
let delta = -1.0 * lrnRate * ihGrads[i][j];
this.ihWeights[i][j] += delta;
}
}
// update hidden node biases
for (let j = 0; j "lt" this.nh; ++j) {
let delta = -1.0 * lrnRate * hbGrads[j];
this.hBiases[j] += delta;
}
// update hidden-to-output weights
for (let j = 0; j "lt" this.nh; ++j) {
for (let k = 0; k "lt" this.no; ++k) {
let delta = -1.0 * lrnRate * hoGrads[j][k];
this.hoWeights[j][k] += delta;
}
}
// update output node biases
for (let k = 0; k "lt" this.no; ++k) {
let delta = -1.0 * lrnRate * obGrads[k];
this.oBiases[k] += delta;
}
} // ii
if (epoch % freq == 0) {
let mse = this.meanSqErr(trainX, trainY).toFixed(4);
let acc = this.accuracy(trainX, trainY).toFixed(4);
let s1 = "epoch: " + epoch.toString().padStart(6, ' ');
let s2 = " MSE = " + mse.toString().padStart(8, ' ');
let s3 = " acc = " + acc.toString();
console.log(s1 + s2 + s3);
}
} // epoch
} // train()
meanCrossEntErr(dataX, dataY)
{
let sumCEE = 0.0; // sum of the cross entropy errors
for (let i = 0; i "lt" dataX.length; ++i) { // each data item
let X = dataX[i];
let Y = dataY[i]; // target output like (0, 1, 0)
let oupt = this.eval(X); // computed like (0.23, 0.66, 0.11)
let idx = U.argmax(Y); // find location of the 1 in target
sumCEE += Math.log(oupt[idx]);
}
sumCEE *= -1;
return sumCEE / dataX.length;
}
meanSqErr(dataX, dataY)
{
let sumSE = 0.0;
for (let i = 0; i "lt" dataX.length; ++i) { // each data item
let X = dataX[i];
let Y = dataY[i]; // target output like (0, 1, 0)
let oupt = this.eval(X); // computed like (0.23, 0.66, 0.11)
for (let k = 0; k "lt" this.no; ++k) {
let err = Y[k] - oupt[k] // target - computed
sumSE += err * err;
}
}
return sumSE / dataX.length;
}
accuracy(dataX, dataY)
{
let nc = 0; let nw = 0;
for (let i = 0; i "lt" dataX.length; ++i) { // each data item
let X = dataX[i];
let Y = dataY[i]; // target output like (0, 1, 0)
let oupt = this.eval(X); // computed like (0.23, 0.66, 0.11)
let computedIdx = U.argmax(oupt);
let targetIdx = U.argmax(Y);
if (computedIdx == targetIdx) {
++nc;
}
else {
++nw;
}
}
return nc / (nc + nw);
}
saveWeights(fn)
{
let wts = this.getWeights();
let n = wts.length;
let s = "";
for (let i = 0; i "lt" n-1; ++i) {
s += wts[i].toString() + ",";
}
s += wts[n-1];
FS.writeFileSync(fn, s);
}
loadWeights(fn)
{
let n = (this.ni * this.nh) + this.nh + (this.nh * this.no) + this.no;
let wts = U.vecMake(n, 0.0);
let all = FS.readFileSync(fn, "utf8");
let strVals = all.split(",");
let nn = strVals.length;
if (n != nn) {
throw("Size error in NeuralNet.loadWeights()");
}
for (let i = 0; i "lt" n; ++i) {
wts[i] = parseFloat(strVals[i]);
}
this.setWeights(wts);
}
} // NeuralNet
// =============================================================================
function main()
{
process.stdout.write("\033[0m"); // reset
process.stdout.write("\x1b[1m" + "\x1b[37m"); // bright white
console.log("\nBegin Students Data demo with JavaScript ");
console.log("Goal is to predict size of company after graduation ");
// 1. load data
// raw data looks like: male 29 finance 38400.00 medium
// norm data looks like: -1 0.29 1 0 0 0.3840 0 1 0
let trainX = U.loadTxt(".\\Data\\students_train.txt", "\t", [0,1,2,3,4,5]);
let trainY = U.loadTxt(".\\Data\\students_train.txt", "\t", [6,7,8]);
let testX = U.loadTxt(".\\Data\\students_test.txt", "\t", [0,1,2,3,4,5]);
let testY = U.loadTxt(".\\Data\\students_test.txt", "\t", [6,7,8]);
// 2. create network
console.log("\nCreating a 6-40-3 tanh, softmax NN for Students dataset ");
let seed = 1;
let nn = new NeuralNet(6, 40, 3, seed);
// 3. train network
let lrnRate = 0.005;
let maxEpochs = 4000;
console.log("\nStarting training with learning rate = 0.005 ");
nn.train(trainX, trainY, lrnRate, maxEpochs);
console.log("Training complete ");
// 4. evaluate model
let trainAcc = nn.accuracy(trainX, trainY);
let testAcc = nn.accuracy(testX, testY);
console.log("\nAccuracy on training data = " +
trainAcc.toFixed(4).toString());
console.log("Accuracy on test data = " +
testAcc.toFixed(4).toString());
// 5. save trained model
fn = ".\\Models\\students_wts.txt";
console.log("\nSaving model weights and biases to: ");
console.log(fn);
nn.saveWeights(fn);
// 6. use trained model
let unknownRaw = ["male", 46, "finance", 66400.00];
// sex, science units, major, parents income
let unknownNorm = [-1, 0.46, 0, 0, 1, 0.6640];
let predicted = nn.eval(unknownNorm);
console.log("\nRaw features of student to predict: ");
console.log(unknownRaw);
console.log("\nNormalized features of student to predict: ");
U.vecShow(unknownNorm, 4, 12);
console.log("\nPredicted pseudo-probabilities: ");
U.vecShow(predicted, 4, 12);
let companySizes = ["small", "medium", "large"];
let predIdx = U.argmax(predicted);
let predSize = companySizes[predIdx];
console.log("Predicted company size = " + predSize);
process.stdout.write("\033[0m"); // reset
console.log("\nEnd demo");
} // main()
main();
File students_train.txt. Original is tab-delimited, this has three spaces.
-1 0.39 0 0 1 0.3570 0 1 0 1 0.51 1 0 0 0.8610 0 1 0 1 0.52 0 0 1 0.6530 0 1 0 -1 0.36 0 1 0 0.7300 0 1 0 1 0.24 0 1 0 0.5700 0 0 1 1 0.27 1 0 0 0.7610 0 0 1 -1 0.19 0 0 1 0.6550 1 0 0 1 0.22 1 0 0 0.8970 0 1 0 -1 0.39 0 0 1 0.8230 0 0 1 1 0.63 1 0 0 0.2120 1 0 0 1 0.34 0 1 0 0.3780 0 1 0 -1 0.22 0 1 0 0.8500 1 0 0 1 0.35 0 0 1 0.8660 0 0 1 -1 0.33 1 0 0 0.8330 0 1 0 1 0.45 1 0 0 0.7680 0 1 0 1 0.42 1 0 0 0.4130 0 1 0 -1 0.33 1 0 0 0.2980 0 1 0 1 0.25 0 0 1 0.6010 0 1 0 -1 0.31 1 0 0 0.4370 1 0 0 1 0.27 0 1 0 0.5750 0 0 1 1 0.48 0 1 0 0.7570 0 1 0 -1 0.64 1 0 0 0.5740 0 0 1 1 0.61 1 0 0 0.2970 1 0 0 1 0.54 0 0 1 0.4170 1 0 0 1 0.29 0 1 0 0.8570 1 0 0 1 0.51 0 0 1 0.8000 0 1 0 1 0.55 0 0 1 0.2160 1 0 0 1 0.42 0 1 0 0.5610 1 0 0 1 0.22 0 1 0 0.2760 0 0 1 1 0.68 1 0 0 0.6810 1 0 0 -1 0.61 0 1 0 0.3940 0 0 1 -1 0.34 0 0 1 0.2550 0 1 0 -1 0.25 0 0 1 0.6230 1 0 0 -1 0.31 1 0 0 0.4300 0 1 0 1 0.43 0 0 1 0.8510 0 1 0 1 0.58 1 0 0 0.8850 0 0 1 -1 0.55 1 0 0 0.7180 0 0 1 -1 0.43 1 0 0 0.7370 0 1 0 -1 0.43 0 0 1 0.8130 0 1 0 -1 0.21 0 1 0 0.7700 1 0 0 1 0.55 0 0 1 0.7330 1 0 0 1 0.64 1 0 0 0.5460 1 0 0 -1 0.41 0 1 0 0.5250 0 1 0 1 0.64 0 0 1 0.4540 1 0 0 -1 0.56 0 0 1 0.4040 0 0 1 1 0.31 0 0 1 0.2050 0 1 0 -1 0.65 0 0 1 0.6860 0 0 1 1 0.55 0 0 1 0.3180 1 0 0 -1 0.25 0 1 0 0.7050 1 0 0 1 0.46 0 0 1 0.8180 0 1 0 -1 0.36 0 1 0 0.5260 1 0 0 1 0.52 1 0 0 0.5820 0 1 0 1 0.61 0 0 1 0.6940 1 0 0 1 0.57 0 0 1 0.5740 1 0 0 -1 0.46 1 0 0 0.2240 0 1 0 -1 0.62 0 1 0 0.2460 0 0 1 1 0.55 0 0 1 0.8530 1 0 0 -1 0.22 0 0 1 0.6800 0 1 0 -1 0.51 0 1 0 0.3750 1 0 0 -1 0.32 1 0 0 0.4800 0 1 0 -1 0.21 0 0 1 0.6710 1 0 0 1 0.44 1 0 0 0.6000 0 1 0 1 0.46 1 0 0 0.5290 0 1 0 1 0.62 1 0 0 0.2320 1 0 0 1 0.57 1 0 0 0.6740 1 0 0 -1 0.67 0 0 1 0.3930 0 0 1 1 0.29 0 1 0 0.4860 0 0 1 1 0.53 0 1 0 0.6190 1 0 0 -1 0.44 0 1 0 0.8680 0 1 0 1 0.46 1 0 0 0.2300 0 1 0 -1 0.21 1 0 0 0.3250 0 1 0 -1 0.38 0 1 0 0.7450 0 1 0 1 0.52 1 0 0 0.5980 0 1 0 1 0.33 1 0 0 0.7070 0 1 0 -1 0.33 1 0 0 0.7810 0 1 0 1 0.26 1 0 0 0.3690 1 0 0 1 0.58 0 1 0 0.2750 1 0 0 1 0.43 0 0 1 0.8880 0 1 0 -1 0.46 0 1 0 0.8900 1 0 0 1 0.61 0 1 0 0.5990 1 0 0 -1 0.42 0 1 0 0.6630 0 1 0 -1 0.56 0 0 1 0.2700 0 0 1 -1 0.62 1 0 0 0.3720 0 0 1 -1 0.51 0 1 0 0.2990 0 1 0 1 0.47 0 0 1 0.8090 0 1 0 -1 0.67 1 0 0 0.3080 0 0 1 -1 0.41 0 0 1 0.6850 0 1 0 1 0.42 1 0 0 0.5000 0 1 0 1 0.64 0 1 0 0.8040 1 0 0 -1 0.47 0 1 0 0.2580 0 0 1 1 0.45 1 0 0 0.8300 0 1 0 -1 0.25 0 0 1 0.6980 1 0 0 1 0.38 0 1 0 0.8280 1 0 0 1 0.55 0 0 1 0.2040 0 1 0 -1 0.44 0 1 0 0.7880 0 1 0 1 0.33 0 1 0 0.6400 0 1 0 1 0.34 0 0 1 0.6130 0 1 0 1 0.27 1 0 0 0.7360 0 0 1 1 0.32 1 0 0 0.2340 0 1 0 1 0.42 0 0 1 0.5350 0 1 0 -1 0.24 0 0 1 0.5490 1 0 0 1 0.42 1 0 0 0.8570 0 1 0 1 0.25 0 0 1 0.2920 0 0 1 1 0.51 1 0 0 0.8000 0 1 0 -1 0.55 1 0 0 0.6180 0 0 1 1 0.44 0 1 0 0.4510 0 0 1 -1 0.18 0 1 0 0.4430 1 0 0 -1 0.67 1 0 0 0.4860 0 0 1 1 0.45 0 0 1 0.8700 0 1 0 1 0.48 0 1 0 0.4830 0 1 0 -1 0.25 1 0 0 0.2170 0 1 0 -1 0.67 0 1 0 0.7670 0 1 0 1 0.37 0 0 1 0.2670 0 1 0 -1 0.32 0 1 0 0.7700 0 1 0 1 0.48 0 1 0 0.2260 0 1 0 -1 0.66 0 0 1 0.2990 0 0 1 1 0.61 0 1 0 0.3030 1 0 0 -1 0.58 0 0 1 0.6770 0 1 0 1 0.19 0 1 0 0.3010 0 0 1 1 0.38 0 0 1 0.6840 0 1 0 -1 0.27 0 1 0 0.6120 0 1 0 1 0.42 0 1 0 0.5140 0 1 0 1 0.61 0 1 0 0.7200 1 0 0 -1 0.27 0 0 1 0.8620 1 0 0 1 0.29 1 0 0 0.6460 1 0 0 -1 0.43 0 1 0 0.5990 0 1 0 1 0.48 0 1 0 0.8250 0 1 0 1 0.27 0 0 1 0.6140 0 0 1 -1 0.44 0 1 0 0.8910 1 0 0 1 0.23 1 0 0 0.4550 0 0 1 -1 0.36 1 0 0 0.8190 0 0 1 1 0.64 0 0 1 0.3130 1 0 0 1 0.29 0 0 1 0.7660 0 0 1 -1 0.33 0 1 0 0.2010 0 1 0 -1 0.66 1 0 0 0.2350 0 0 1 -1 0.21 0 0 1 0.6740 1 0 0 1 0.27 0 1 0 0.6540 0 0 1 1 0.29 0 1 0 0.6900 0 0 1 -1 0.31 0 1 0 0.8330 0 1 0 1 0.36 0 0 1 0.8130 0 1 0 1 0.49 1 0 0 0.8170 0 1 0 -1 0.28 0 1 0 0.2110 1 0 0 -1 0.43 0 0 1 0.7810 0 1 0 -1 0.46 1 0 0 0.7460 0 1 0 1 0.57 0 1 0 0.2330 1 0 0 -1 0.52 0 0 1 0.8910 0 1 0 -1 0.31 0 0 1 0.8700 0 1 0 -1 0.55 0 1 0 0.5860 0 0 1 1 0.51 0 1 0 0.5340 0 1 0 1 0.48 1 0 0 0.4510 0 1 0 -1 0.22 0 0 1 0.2970 1 0 0 1 0.59 0 0 1 0.5920 1 0 0 1 0.34 0 1 0 0.8240 0 0 1 -1 0.64 0 1 0 0.6300 0 0 1 1 0.29 0 0 1 0.8700 0 0 1 -1 0.34 1 0 0 0.7480 0 1 0 -1 0.61 0 1 0 0.2100 0 0 1 1 0.64 0 0 1 0.4450 1 0 0 -1 0.29 0 1 0 0.6360 1 0 0 1 0.63 1 0 0 0.4700 1 0 0
File students_test.txt
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