Update comments and fix typos

neuralnetwork/neuralnetworkbase/common.go

@@ -58,11 +58,16 @@ func sigmoidPrime(x float64) float64 {
 	return sigmoid(x) * (1 - sigmoid(x))
 }
 
-func makeBackGradien(in mat.Matrix, actual mat.Matrix, alpha float64) *mat.Dense {
+func makeBackGradient(in mat.Matrix, actual mat.Matrix, alpha float64) *mat.Dense {
+	// Gradient change of actual matrix using:
+	// m[l]′ = m[l] − η * ∂C/∂m
+	// Where ∂C/∂m is `in` matrix
 	scaled := &mat.Dense{}
 	result := &mat.Dense{}
 
+	// η * ∂C/∂m
 	scaled.Scale(alpha, in)
+	// m[l] − η * ∂C/∂m
 	result.Sub(actual, scaled)
 	return result
 }

neuralnetwork/neuralnetworkbase/neuralnetwork.go

@@ -148,19 +148,19 @@ func (nn *NeuralNetwork) forward(aIn mat.Matrix) {
 		aSrc := nn.A[i-1]
 		aDst := nn.A[i]
 
-		//Each iteration implements formula bellow for neuron activation values
-		//A[l]=σ(W[l]*A[l−1]+B[l])
+		// Each iteration implements formula bellow for neuron activation values
+		// A[l]=σ(W[l]*A[l−1]+B[l])
 
-		//W[l]*A[l−1]
+		// W[l]*A[l−1]
 		aDst.Mul(nn.Weights[i], aSrc)
 
-		//W[l]*A[l−1]+B[l]
+		// W[l]*A[l−1]+B[l]
 		aDst.Add(aDst, nn.Biases[i])
 
-		//Save raw activation value for back propagation
+		// Save raw activation value for back propagation
 		nn.Z[i] = mat.DenseCopyOf(aDst)
 
-		//σ(W[l]*A[l−1]+B[l])
+		// σ(W[l]*A[l−1]+B[l])
 		aDst.Apply(applySigmoid, aDst)
 	}
 }
@@ -170,75 +170,75 @@ func (nn *NeuralNetwork) backward(aIn, aOut mat.Matrix) {
 
 	lastLayerNum := nn.Count - 1
 
-	//To calculate new values of weights and biases
-	//following formulas are used:
-	//W[l] = A[l−1]*δ[l]
-	//B[l] = δ[l]
+	// To calculate new values of weights and biases
+	// following formulas are used:
+	// W[l] = A[l−1]*δ[l]
+	// B[l] = δ[l]
 
-	//For last layer δ value is calculated by following:
-	//δ = (A[L]−y)⊙σ'(Z[L])
+	// For last layer δ value is calculated by following:
+	// δ = (A[L]−y)⊙σ'(Z[L])
 
-	//Calculate initial error for last layer L
-	//error = A[L]-y
-	//Where y is expected activations set
+	// Calculate initial error for last layer L
+	// error = A[L]-y
+	// Where y is expected activations set
 	err := &mat.Dense{}
 	err.Sub(nn.result(), aOut)
 
-	//Calculate sigmoids prime σ'(Z[L]) for last layer L
+	// Calculate sigmoids prime σ'(Z[L]) for last layer L
 	sigmoidsPrime := &mat.Dense{}
 	sigmoidsPrime.Apply(applySigmoidPrime, nn.Z[lastLayerNum])
 
-	//(A[L]−y)⊙σ'(Z[L])
+	// (A[L]−y)⊙σ'(Z[L])
 	delta := &mat.Dense{}
 	delta.MulElem(err, sigmoidsPrime)
 
-	//B[L] = δ[L]
+	// B[L] = δ[L]
 	biases := mat.DenseCopyOf(delta)
 
-	//W[L] = A[L−1]*δ[L]
+	// W[L] = A[L−1]*δ[L]
 	weights := &mat.Dense{}
 	weights.Mul(delta, nn.A[lastLayerNum-1].T())
 
-	//Initialize new weights and biases values with last layer values
-	newBiases := []*mat.Dense{makeBackGradien(biases, nn.Biases[lastLayerNum], nn.alpha)}
-	newWeights := []*mat.Dense{makeBackGradien(weights, nn.Weights[lastLayerNum], nn.alpha)}
+	// Initialize new weights and biases values with last layer values
+	newBiases := []*mat.Dense{makeBackGradient(biases, nn.Biases[lastLayerNum], nn.alpha)}
+	newWeights := []*mat.Dense{makeBackGradient(weights, nn.Weights[lastLayerNum], nn.alpha)}
 
-	//Save calculated delta value temporary error variable
+	// Save calculated delta value temporary error variable
 	err = delta
 
-	//Next layer Weights and Biases are calculated using same formulas:
-	//W[l] = A[l−1]*δ[l]
-	//B[l] = δ[l]
+	// Next layer Weights and Biases are calculated using same formulas:
+	// W[l] = A[l−1]*δ[l]
+	// B[l] = δ[l]
 
-	//But δ[l] is calculated using different formula:
-	//δ[l] = ((Wt[l+1])*δ[l+1])⊙σ'(Z[l])
-	//Where Wt[l+1] is transponded matrix of actual Weights from
-	//forward step
+	// But δ[l] is calculated using different formula:
+	// δ[l] = ((Wt[l+1])*δ[l+1])⊙σ'(Z[l])
+	// Where Wt[l+1] is transposed matrix of actual Weights from
+	// forward step
 	for l := nn.Count - 2; l > 0; l-- {
-		//Calculate sigmoids prime σ'(Z[l]) for last layer l
+		// Calculate sigmoids prime σ'(Z[l]) for last layer l
 		sigmoidsPrime := &mat.Dense{}
 		sigmoidsPrime.Apply(applySigmoidPrime, nn.Z[l])
 
-		//(Wt[l+1])*δ[l+1]
-		//err bellow is delta from previous step(l+1)
+		// (Wt[l+1])*δ[l+1]
+		// err bellow is delta from previous step(l+1)
 		delta := &mat.Dense{}
 		wdelta := &mat.Dense{}
 		wdelta.Mul(nn.Weights[l+1].T(), err)
 
-		//Calculate new delta and store it to temporary variable err
-		//δ[l] = ((Wt[l+1])*δ[l+1])⊙σ'(Z[l])
+		// Calculate new delta and store it to temporary variable err
+		// δ[l] = ((Wt[l+1])*δ[l+1])⊙σ'(Z[l])
 		delta.MulElem(wdelta, sigmoidsPrime)
 		err = delta
 
-		//B[l] = δ[l]
+		// B[l] = δ[l]
 		biases := mat.DenseCopyOf(delta)
 
-		//W[l] = A[l−1]*δ[l]
-		//At this point it's required to give explanation for inaccuracy
-		//in the formula
+		// W[l] = A[l−1]*δ[l]
+		// At this point it's required to give explanation for inaccuracy
+		// in the formula
 
-		//Multiplying of activations matrix for layer l-1 and δ[l] is imposible
-		//because view of matrices are following:
+		// Multiplying of activations matrix for layer l-1 and δ[l] is imposible
+		// because view of matrices are following:
 		//          A[l-1]       δ[l]
 		//         ⎡A[0]  ⎤     ⎡δ[0] ⎤
 		//         ⎢A[1]  ⎥     ⎢δ[1] ⎥
@@ -246,16 +246,16 @@ func (nn *NeuralNetwork) backward(aIn, aOut mat.Matrix) {
 		//         ⎢A[i]  ⎥  X  ⎢δ[i] ⎥
 		//         ⎢ ...  ⎥     ⎢ ... ⎥
 		//         ⎣A[s'] ⎦     ⎣δ[s] ⎦
-		//So we need to modify these matrices to apply mutiplications and got Weights matrix
-		//of following view:
+		// So we need to modify these matrices to apply mutiplications and got
+		// Weights matrix of following view:
 		//         ⎡w[0,0] ... w[0,j] ... w[0,s']⎤
 		//         ⎢w[1,0] ... w[1,j] ... w[1,s']⎥
 		//         ⎢              ...            ⎥
 		//         ⎢w[i,0] ... w[i,j] ... w[i,s']⎥
 		//         ⎢              ...            ⎥
 		//         ⎣w[s,0] ... w[s,j] ... w[s,s']⎦
-		//So we substitude matrices and transposes A[l-1] to get valid multiplication
-		//if following view:
+		// So we swap matrices and transpose A[l-1] to get valid multiplication
+		// of following view:
 		//           δ[l]               A[l-1]
 		//         ⎡δ[0] ⎤ x [A[0] A[1] ... A[i] ... A[s']]
 		//         ⎢δ[1] ⎥
@@ -266,10 +266,9 @@ func (nn *NeuralNetwork) backward(aIn, aOut mat.Matrix) {
 		weights := &mat.Dense{}
 		weights.Mul(delta, nn.A[l-1].T())
 
-		//!Prepend! new Biases and Weights
-		// Scale down
-		newBiases = append([]*mat.Dense{makeBackGradien(biases, nn.Biases[l], nn.alpha)}, newBiases...)
-		newWeights = append([]*mat.Dense{makeBackGradien(weights, nn.Weights[l], nn.alpha)}, newWeights...)
+		// !Prepend! new Biases and Weights
+		newBiases = append([]*mat.Dense{makeBackGradient(biases, nn.Biases[l], nn.alpha)}, newBiases...)
+		newWeights = append([]*mat.Dense{makeBackGradient(weights, nn.Weights[l], nn.alpha)}, newWeights...)
 	}
 
 	newBiases = append([]*mat.Dense{&mat.Dense{}}, newBiases...)