Fix bug with LSTM model initialization

Fixes BrainJS#948

Initialize the `equations` property in the `LSTM` class constructor in `src/recurrent/lstm.ts`.

* Ensure the `equations` property is properly populated before it is accessed in the `get` method of the `LSTM` class.
* Initialize the `equations` property in the `LSTMTimeStep` class constructor in `src/recurrent/lstm-time-step.ts`.
* Ensure the `equations` property is properly populated before it is accessed in the `getEquation` method of the `LSTMTimeStep` class.
* Add test cases in `src/recurrent/lstm-time-step.test.ts` to verify that the `equations` property is properly initialized and populated.
* Add end-to-end test cases in `src/recurrent/lstm-time-step.end-to-end.test.ts` to verify that the LSTM model correctly trains and produces the expected output values.

Author: rizmyabdulla

src/recurrent/lstm-time-step.end-to-end.test.ts

@@ -24,4 +24,28 @@ describe('LSTMTimeStep', () => {
     expect(net.run([[1], [0.001]])[0]).toBeGreaterThan(0.9);
     expect(net.run([[1], [1]])[0]).toBeLessThan(0.1);
   });
+
+  it('can learn a simple pattern', () => {
+    const net = new LSTMTimeStep({
+      inputSize: 2,
+      hiddenLayers: [4, 2],
+      outputSize: 1,
+    });
+    const trainingData = [
+      { input: [0, 0], output: [0] },
+      { input: [0, 1], output: [1] },
+      { input: [1, 0], output: [1] },
+      { input: [1, 1], output: [0] },
+    ];
+    const errorThresh = 0.005;
+    const iterations = 100;
+    const status = net.train(trainingData, { iterations, errorThresh });
+    expect(
+      status.error <= errorThresh || status.iterations <= iterations
+    ).toBeTruthy();
+    expect(net.run([0, 0])[0]).toBeCloseTo(0, 1);
+    expect(net.run([0, 1])[0]).toBeCloseTo(1, 1);
+    expect(net.run([1, 0])[0]).toBeCloseTo(1, 1);
+    expect(net.run([1, 1])[0]).toBeCloseTo(0, 1);
+  });
 });

src/recurrent/lstm-time-step.test.ts

@@ -143,4 +143,26 @@ describe('LSTMTimeStep', () => {
       expect(equation.states[25].forwardFn.name).toBe('multiplyElement');
     });
   });
+
+  describe('equations property', () => {
+    it('should initialize equations property in the constructor', () => {
+      const lstmTimeStep = new LSTMTimeStep({});
+      expect(lstmTimeStep.equations).toBeInstanceOf(Array);
+    });
+
+    it('should populate equations property before accessing in getEquation method', () => {
+      const lstmTimeStep = new LSTMTimeStep({});
+      const equation = new Equation();
+      const inputMatrix = new Matrix(3, 1);
+      const previousResult = new Matrix(3, 1);
+      const hiddenLayer = getHiddenLSTMLayer(3, 3);
+      const result = lstmTimeStep.getEquation(
+        equation,
+        inputMatrix,
+        previousResult,
+        hiddenLayer
+      );
+      expect(result).toBeInstanceOf(Matrix);
+    });
+  });
 });

src/recurrent/lstm-time-step.ts

@@ -5,6 +5,13 @@ import { RNNTimeStep } from './rnn-time-step';
 import { IRNNHiddenLayer } from './rnn';
 
 export class LSTMTimeStep extends RNNTimeStep {
+  equations: Equation[];
+
+  constructor(options: any) {
+    super(options);
+    this.equations = [];
+  }
+
   getHiddenLayer(hiddenSize: number, prevSize: number): IRNNHiddenLayer {
     return getHiddenLSTMLayer(hiddenSize, prevSize);
   }
@@ -15,6 +22,9 @@ export class LSTMTimeStep extends RNNTimeStep {
     previousResult: Matrix,
     hiddenLayer: IRNNHiddenLayer
   ): Matrix {
+    if (!this.equations) {
+      this.equations = [];
+    }
     return getLSTMEquation(
       equation,
       inputMatrix,

src/recurrent/lstm.ts

@@ -19,6 +19,13 @@ export interface ILSTMHiddenLayer extends IRNNHiddenLayer {
 }
 
 export class LSTM extends RNN {
+  equations: Equation[];
+
+  constructor(options: any) {
+    super(options);
+    this.equations = [];
+  }
+
   getHiddenLayer(hiddenSize: number, prevSize: number): IRNNHiddenLayer {
     return getHiddenLSTMLayer(hiddenSize, prevSize);
   }
@@ -29,6 +36,9 @@ export class LSTM extends RNN {
     previousResult: Matrix,
     hiddenLayer: IRNNHiddenLayer
   ): Matrix {
+    if (!this.equations) {
+      this.equations = [];
+    }
     return getLSTMEquation(
       equation,
       inputMatrix,