用java写bp神经网络（一）

根据前篇博文《神经网络之后向传播算法》，现在用java实现一个bp神经网络。矩阵运算采用jblas库，然后逐渐增加功能，支持并行计算，然后支持输入向量调整，最后支持L-BFGS学习算法。

上帝说，要有神经网络，于是，便有了一个神经网络。上帝还说，神经网络要有节点，权重，激活函数，输出函数，目标函数，然后也许还要有一个准确率函数，于是，神经网络完成了：

public class Net {
	List<DoubleMatrix> weights = new ArrayList<DoubleMatrix>();
	List<DoubleMatrix> bs = new ArrayList<>();
	List<ScalarDifferentiableFunction> activations = new ArrayList<>();
	CostFunctionFactory costFunc;
	CostFunctionFactory accuracyFunc;
	int[] nodesNum;
	int layersNum;
	public Net(int[] nodesNum, ScalarDifferentiableFunction[] activations,CostFunctionFactory costFunc) {
		super();
		this.initNet(nodesNum, activations);
		this.costFunc=costFunc;
		this.layersNum=nodesNum.length-1;
	}

	public Net(int[] nodesNum, ScalarDifferentiableFunction[] activations,CostFunctionFactory costFunc,CostFunctionFactory accuracyFunc) {
		this(nodesNum,activations,costFunc);
		this.accuracyFunc=accuracyFunc;
	}
	public void resetNet() {
		this.initNet(nodesNum, (ScalarDifferentiableFunction[]) activations.toArray());
	}

	private void initNet(int[] nodesNum, ScalarDifferentiableFunction[] activations) {
		assert (nodesNum != null && activations != null
				&& nodesNum.length == activations.length + 1 && nodesNum.length > 1);
		this.nodesNum = nodesNum;
		this.weights.clear();
		this.bs.clear();
		this.activations.clear();
		for (int i = 0; i < nodesNum.length - 1; i++) {
			// 列数==输入；行数==输出。
			int columns = nodesNum[i];
			int rows = nodesNum[i + 1];
			double r1 = Math.sqrt(6) / Math.sqrt(rows + columns + 1);
			//r1=0.001;
			// W
			DoubleMatrix weight = DoubleMatrix.rand(rows, columns).muli(2*r1).subi(r1);
			//weight=DoubleMatrix.ones(rows, columns);
			weights.add(weight);

			// b
			DoubleMatrix b = DoubleMatrix.zeros(rows, 1);
			bs.add(b);

			// activations
			this.activations.add(activations[i]);
		}
	}
}

 上帝造完了神经网络，去休息了。人说，我要使用神经网络，我要利用正向传播计算各层的结果，然后利用反向传播调整网络的状态，最后，我要让它能告诉我猎物在什么方向，花儿为什么这样香。

public class Propagation {
	Net net;

	public Propagation(Net net) {
		super();
		this.net = net;
	}


	// 多个样本。
	public ForwardResult forward(DoubleMatrix input) {
		
		ForwardResult result = new ForwardResult();
		result.input = input;
		DoubleMatrix currentResult = input;
		int index = -1;
		for (DoubleMatrix weight : net.weights) {
			index++;
			DoubleMatrix b = net.bs.get(index);
			final ScalarDifferentiableFunction activation = net.activations
					.get(index);
			currentResult = weight.mmul(currentResult).addColumnVector(b);
			result.netResult.add(currentResult);

			// 乘以导数
			DoubleMatrix derivative = MatrixUtil.applyNewElements(
					new ScalarFunction() {
						@Override
						public double valueAt(double x) {
							return activation.derivativeAt(x);
						}

					}, currentResult);

			currentResult = MatrixUtil.applyNewElements(activation,
					currentResult);
			result.finalResult.add(currentResult);

			result.derivativeResult.add(derivative);
		}

		result.netResult=null;// 不再需要。
		
		return result;
	}

	

    // 多个样本梯度平均值。
	public BackwardResult backward(DoubleMatrix target,
			ForwardResult forwardResult) {
		BackwardResult result = new BackwardResult();
		DoubleMatrix cost = DoubleMatrix.zeros(1,target.columns);
		DoubleMatrix output = forwardResult.finalResult
				.get(forwardResult.finalResult.size() - 1);
		DoubleMatrix outputDelta = DoubleMatrix.zeros(output.rows,
				output.columns);
		DoubleMatrix outputDerivative = forwardResult.derivativeResult
				.get(forwardResult.derivativeResult.size() - 1);

		DoubleMatrix accuracy = null;
		if (net.accuracyFunc != null) {
			accuracy = DoubleMatrix.zeros(1,target.columns);
		}

		for (int i = 0; i < target.columns; i++) {
			CostFunction costFunc = net.costFunc.create(target.getColumn(i)
					.toArray());
			cost.put(i, costFunc.valueAt(output.getColumn(i).toArray()));
			// System.out.println(i);
			DoubleMatrix column1 = new DoubleMatrix(
					costFunc.derivativeAt(output.getColumn(i).toArray()));
			DoubleMatrix column2 = outputDerivative.getColumn(i);
			outputDelta.putColumn(i, column1.muli(column2));

			if (net.accuracyFunc != null) {
				CostFunction accuracyFunc = net.accuracyFunc.create(target
						.getColumn(i).toArray());
				accuracy.put(i,
						accuracyFunc.valueAt(output.getColumn(i).toArray()));
			}
		}
		result.deltas.add(outputDelta);
		result.cost = cost;
		result.accuracy = accuracy;
		for (int i = net.layersNum - 1; i >= 0; i--) {
			DoubleMatrix pdelta = result.deltas.get(result.deltas.size() - 1);

			// 梯度计算，取所有样本平均
			DoubleMatrix layerInput = i == 0 ? forwardResult.input
					: forwardResult.finalResult.get(i - 1);
			DoubleMatrix gradient = pdelta.mmul(layerInput.transpose()).div(
					target.columns);
			result.gradients.add(gradient);
			// 偏置梯度
			result.biasGradients.add(pdelta.rowMeans());

			// 计算前一层delta，若i=0，delta为输入层误差，即input调整梯度，不作平均处理。
			DoubleMatrix delta = net.weights.get(i).transpose().mmul(pdelta);
			if (i > 0)
				delta = delta.muli(forwardResult.derivativeResult.get(i - 1));
			result.deltas.add(delta);
		}
		Collections.reverse(result.gradients);
		Collections.reverse(result.biasGradients);
		
		//其它的delta都不需要。
		DoubleMatrix inputDeltas=result.deltas.get(result.deltas.size()-1);
		result.deltas.clear();
		result.deltas.add(inputDeltas);
		
		return result;
	}

	public Net getNet() {
		return net;
	}

}

 上面是一次正向/反向传播的具体代码。训练方式为批量训练，即所有样本一起训练。然而我们可以传入只有一列的input/target样本实现adapt方式的串行训练，也可以把样本分成很多批传入实现mini-batch方式的训练，这，不是Propagation要考虑的事情，它只是忠实的把传入的数据正向过一遍，反向过一遍，然后把过后的数据原封不动的返回给你。至于传入什么，以及结果怎么运用，是Trainer和Learner要做的事情。下回分解。