My neural network is trained (from scratch) to get further away from the goal

Question content

This is my first time creating a neural network and I decided to create it in golang which is usually not the language used for this purpose , but I want to get a good understanding of how they work from scratch with only the basic libraries.

The goal of this program is to train a neural network to be able to add two numbers (1-10). To do this, I created a neural network class called rawai (the best name I could think of) and gave it a 1 input layer (array of size 2), 1 hidden layer (array of size 2 array) and 1 output layer (array of size 1).

The weight has two 2d arrays, one is ih (hidden input) [2,2], and the other is ho, [2,1].

The following is the code to start ai, train and test ai. You will see several debugging statements that I have used and any other functions that are not golang or its packages will be shown in the following code of my rawai class. This is called by my main function:

func additionneuralnetworktest() {
    nn := newrawai(2, 2, 1, 1/math.pow(10, 15))
    fmt.printf("weights ih before: %v\n\nweights ho after: %v\n", nn.weightsih, nn.weightsho)
    //train neural network
    //
    for epoch := 0; epoch < 10000000; epoch++ {
        for i := 0; i <= 10; i++ {
            for j := 0; j <= 10; j++ {
                inputs := make([]float64, 2)
                targets := make([]float64, 1)
                inputs[0] = float64(i)
                inputs[1] = float64(j)
                targets[0] = float64(i) + float64(j)
                nn.train(inputs, targets)
                if epoch%20000 == 0 && i == 5 && j == 5 {
                    fmt.printf("[training] [epoch %d] %f + %f = %f targets[%f]\n", epoch, inputs[0], inputs[1], nn.outputlayer[0], targets[0])
                }

            }

        }
    }
    // test neural network
    a := rand.intn(10) + 1
    b := rand.intn(10) + 1
    inputs := make([]float64, 2)
    inputs[0] = float64(a)
    inputs[1] = float64(b)
    prediction := nn.feedforward(inputs)[0]
    fmt.printf("%d + %d = %f\n", a, b, prediction)
    fmt.printf("weights ih: %v\n\nweights ho: %v\n", nn.weightsih, nn.weightsho)

}

The following is all the code in the rawai file:

type RawAI struct {
    InputLayer   []float64   `json:"input_layer"`
    HiddenLayer  []float64   `json:"hidden_layer"`
    OutputLayer  []float64   `json:"output_layer"`
    WeightsIH    [][]float64 `json:"weights_ih"`
    WeightsHO    [][]float64 `json:"weights_ho"`
    LearningRate float64     `json:"learning_rate"`
}

func NewRawAI(inputSize, hiddenSize, outputSize int, learningRate float64) *RawAI {
    nn := RawAI{
        InputLayer:   make([]float64, inputSize),
        HiddenLayer:  make([]float64, hiddenSize),
        OutputLayer:  make([]float64, outputSize),
        WeightsIH:    randomMatrix(inputSize, hiddenSize),
        WeightsHO:    randomMatrix(hiddenSize, outputSize),
        LearningRate: learningRate,
    }
    return &nn
}
func (nn *RawAI) FeedForward(inputs []float64) []float64 {
    // Set input layer
    for i := 0; i < len(inputs); i++ {
        nn.InputLayer[i] = inputs[i]
    }

    // Compute hidden layer
    for i := 0; i < len(nn.HiddenLayer); i++ {
        sum := 0.0
        for j := 0; j < len(nn.InputLayer); j++ {
            sum += nn.InputLayer[j] * nn.WeightsIH[j][i]
        }
        nn.HiddenLayer[i] = sum
        if math.IsNaN(sum) {
            panic(fmt.Sprintf("Sum is NaN on Hidden Layer:\nInput Layer: %v\nHidden Layer: %v\nWeights IH: %v\n", nn.InputLayer, nn.HiddenLayer, nn.WeightsIH))
        }

    }

    // Compute output layer
    for k := 0; k < len(nn.OutputLayer); k++ {
        sum := 0.0
        for j := 0; j < len(nn.HiddenLayer); j++ {
            sum += nn.HiddenLayer[j] * nn.WeightsHO[j][k]
        }
        nn.OutputLayer[k] = sum
        if math.IsNaN(sum) {
            panic(fmt.Sprintf("Sum is NaN on Output Layer:\n Model: %v\n", nn))
        }

    }

    return nn.OutputLayer
}
func (nn *RawAI) Train(inputs []float64, targets []float64) {
    nn.FeedForward(inputs)

    // Compute output layer error
    outputErrors := make([]float64, len(targets))
    for k := 0; k < len(targets); k++ {
        outputErrors[k] = targets[k] - nn.OutputLayer[k]
    }

    // Compute hidden layer error
    hiddenErrors := make([]float64, len(nn.HiddenLayer))
    for j := 0; j < len(nn.HiddenLayer); j++ {
        errorSum := 0.0
        for k := 0; k < len(nn.OutputLayer); k++ {
            errorSum += outputErrors[k] * nn.WeightsHO[j][k]
        }
        hiddenErrors[j] = errorSum * sigmoidDerivative(nn.HiddenLayer[j])
        if math.IsInf(math.Abs(hiddenErrors[j]), 1) {
            //Find out why
            fmt.Printf("Hidden Error is Infinite:\nTargets:%v\nOutputLayer:%v\n\n", targets, nn.OutputLayer)
        }
    }

    // Update weights
    for j := 0; j < len(nn.HiddenLayer); j++ {
        for k := 0; k < len(nn.OutputLayer); k++ {
            delta := nn.LearningRate * outputErrors[k] * nn.HiddenLayer[j]
            nn.WeightsHO[j][k] += delta
        }
    }
    for i := 0; i < len(nn.InputLayer); i++ {
        for j := 0; j < len(nn.HiddenLayer); j++ {
            delta := nn.LearningRate * hiddenErrors[j] * nn.InputLayer[i]
            nn.WeightsIH[i][j] += delta
            if math.IsNaN(delta) {
                fmt.Print(fmt.Sprintf("Delta is NaN.\n Learning Rate: %f\nHidden Errors: %f\nInput: %f\n", nn.LearningRate, hiddenErrors[j], nn.InputLayer[i]))
            }
            if math.IsNaN(nn.WeightsIH[i][j]) {
                fmt.Print(fmt.Sprintf("Delta is NaN.\n Learning Rate: %f\nHidden Errors: %f\nInput: %f\n", nn.LearningRate, hiddenErrors[j], nn.InputLayer[i]))
            }
        }
    }

}
func (nn *RawAI) ExportWeights(filename string) error {
    weightsJson, err := json.Marshal(nn)
    if err != nil {
        return err
    }
    err = ioutil.WriteFile(filename, weightsJson, 0644)
    if err != nil {
        return err
    }
    return nil
}
func (nn *RawAI) ImportWeights(filename string) error {
    weightsJson, err := ioutil.ReadFile(filename)
    if err != nil {
        return err
    }
    err = json.Unmarshal(weightsJson, nn)
    if err != nil {
        return err
    }
    return nil
}

//RawAI Tools:
func randomMatrix(rows, cols int) [][]float64 {
    matrix := make([][]float64, rows)
    for i := 0; i < rows; i++ {
        matrix[i] = make([]float64, cols)
        for j := 0; j < cols; j++ {
            matrix[i][j] = 1.0
        }
    }
    return matrix
}
func sigmoid(x float64) float64 {
    return 1.0 / (1.0 + exp(-x))
}
func sigmoidDerivative(x float64) float64 {
    return x * (1.0 - x)
}

func exp(x float64) float64 {
    return 1.0 + x + (x*x)/2.0 + (x*x*x)/6.0 + (x*x*x*x)/24.0
}

The output example is as follows: As you can see, it slowly moves away from the target and continues to do so. After asking, googling and searching this site I couldn't find where my error was so I decided to ask this question.

Correct answer

I think you are using the mean squared error and forgetting the - after differentiating.

So change:

outputerrors[k] =  (targets[k] - nn.outputlayer[k])

To:

outputErrors[k] = -(targets[k] - nn.OutputLayer[k])

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