算法之神经网络：从生物启发的计算革命到万物智能的数学载体

import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.factory.Nd4j;

public class NeuralNetwork {
    private INDArray W1, b1, W2, b2; // 参数矩阵
    private final double learningRate;

    public NeuralNetwork(double lr) {
        this.learningRate = lr;
        // 初始化参数：输入层2节点，隐藏层3节点，输出层1节点
        W1 = Nd4j.randn(2, 3).mul(0.01);
        b1 = Nd4j.zeros(1, 3);
        W2 = Nd4j.randn(3, 1).mul(0.01);
        b2 = Nd4j.zeros(1, 1);
    }

    // 前向传播
    public INDArray forward(INDArray X) {
        INDArray Z1 = X.mmul(W1).add(b1);
        INDArray A1 = sigmoid(Z1);
        INDArray Z2 = A1.mmul(W2).add(b2);
        return sigmoid(Z2);
    }

    // 反向传播
    public void backward(INDArray X, INDArray Y) {
        // 前向计算
        INDArray Z1 = X.mmul(W1).add(b1);
        INDArray A1 = sigmoid(Z1);
        INDArray Z2 = A1.mmul(W2).add(b2);
        INDArray A2 = sigmoid(Z2);

        // 计算梯度
        INDArray dZ2 = A2.sub(Y);
        INDArray dW2 = A1.transpose().mmul(dZ2);
        INDArray db2 = dZ2.sum(0);
        
        INDArray dZ1 = dZ2.mmul(W2.transpose()).mul(A1.sub(A1.mul(A1)));
        INDArray dW1 = X.transpose().mmul(dZ1);
        INDArray db1 = dZ1.sum(0);

        // 参数更新
        W1.subi(dW1.mul(learningRate));
        b1.subi(db1.mul(learningRate));
        W2.subi(dW2.mul(learningRate));
        b2.subi(db2.mul(learningRate));
    }

    private INDArray sigmoid(INDArray x) {
        return Nd4j.ones(x.shape()).div(Nd4j.exp(x.neg()).add(1.0));
    }

    public static void main(String[] args) {
        // XOR问题示例
        INDArray X = Nd4j.create(new double[][]{{0,0}, {0,1}, {1,0}, {1,1}});
        INDArray Y = Nd4j.create(new double[][]{{0}, {1}, {1}, {0}});
        
        NeuralNetwork nn = new NeuralNetwork(0.1);
        for(int i=0; i<10000; i++) {
            nn.backward(X, Y);
        }
        System.out.println(nn.forward(X)); // 应接近目标值
    }
}

// 使用Deeplearning4J构建CNN
MultiLayerConfiguration config = new NeuralNetConfiguration.Builder()
        .updater(new Adam(0.001))
        .list()
        .layer(new ConvolutionLayer.Builder(5,5).nIn(1).nOut(20).build())
        .layer(new SubsamplingLayer.Builder().poolingType(PoolingType.MAX).build())
        .layer(new DenseLayer.Builder().nOut(500).build())
        .layer(new OutputLayer.Builder(LossFunctions.LossFunction.NEGATIVELOGLIKELIHOOD).nOut(10).activation(Activation.SOFTMAX).build())
        .build();

// 自注意力机制核心计算
INDArray Q = input.mmul(WQ);
INDArray K = input.mmul(WK);
INDArray V = input.mmul(WV);
INDArray scores = Q.mmul(K.transpose()).div(Math.sqrt(d_k));
INDArray attention = Nd4j.getExecutioner().exec(new SoftMax(scores, 1));
INDArray output = attention.mmul(V);