进一步梳理理解了一下正向和反向传播。Forward 是利用当前网络对一条数据进行预测的过程，BackPropagation 是根据误差进行网络权重调节的过程。

       完整的代码在72天，这里只粘贴Forward和BackPropagation两个方法。

	/*** ************************************************************ Forward prediction.* * @param paraInput   The input data of one instance.* @return   The data at the output end.* ************************************************************/public double[] forward(double[] paraInput) {// Initialize the input layer.for (int i = 0; i < layerNodeValues[0].length; i++) {layerNodeValues[0][i] = paraInput[i];}//of for i// Calculate the node values of each layer.double z;for (int l = 1; l < numLayers; l++) {for (int j = 0; j < layerNodeValues[l].length; j++) {// Initialize according to the offset, which is always +1//(l-1)层的第（该层节点个数）个节点（偏置）指向下一层[j]节点的值；z等于该边的权值。z = edgeWeights[l - 1][layerNodeValues[l - 1].length][j];//数组edgeWeights的第三维表示下一层节点的索引// Weighted sum on all edges for this node.for (int i = 0; i < layerNodeValues[l - 1].length; i++) {z += edgeWeights[l - 1][i][j] * layerNodeValues[l - 1][i];}//of for i (循环上一层的节点)// Sigmoid activation.// This line should be changed for other activation functions.layerNodeValues[l][j] = 1 / (1 + Math.exp(-z));}//of for j（循环要计算的节点的当前层节点）}//of for l（循环神经网络的层）return layerNodeValues[numLayers - 1];}//of forward/*** ******************************************************* Back propagation and change the edge weights.* * @param paraTarget  For 3-class data, it is [0, 0, 1], [0, 1, 0] or [1, 0, 0].* *******************************************************/public void backPropagation(double[] paraTarget) {// Step 1. Initialize the output layer error.int l = numLayers - 1;   //第l层，即输出层for (int j = 0; j < layerNodeErrors[l].length; j++) {layerNodeErrors[l][j] = layerNodeValues[l][j] * (1 - layerNodeValues[l][j]) * (paraTarget[j] - layerNodeValues[l][j]); //套用输出层误差公式。上游传过来的值（即误差）乘以激活函数的倒数，这里sigmod的倒数为y(1-y)。）}//of for j// Step 2. Back-propagation even for l == 0while (l > 0) {l--;// Layer l, for each node.for (int j = 0; j < layerNumNodes[l]; j++) {double z = 0.0;// For each node of the next layer.for (int i = 0; i < layerNumNodes[l + 1]; i++) {if (l > 0) {z += layerNodeErrors[l + 1][i] * edgeWeights[l][j][i];//(l+1)层的第i个节点，乘以l层第j个节点指向下一层第i个节点的边的权重。}//of if// Weight adjusting.edgeWeightsDelta[l][j][i] = mobp * edgeWeightsDelta[l][j][i] + learningRate * layerNodeErrors[l + 1][i] * layerNodeValues[l][j];edgeWeights[l][j][i] += edgeWeightsDelta[l][j][i];if (j == layerNumNodes[l] - 1) {// Weight adjusting for the offset part.//偏置节点没包含在每层节点个数里，所以要加1.edgeWeightsDelta[l][j + 1][i] = mobp * edgeWeightsDelta[l][j + 1][i]+ learningRate * layerNodeErrors[l + 1][i];edgeWeights[l][j + 1][i] += edgeWeightsDelta[l][j + 1][i];}//of if}//of for i// Record the error according to the differential of Sigmoid.// This line should be changed for other activation functions.layerNodeErrors[l][j] = layerNodeValues[l][j] * (1 - layerNodeValues[l][j]) * z;}//of for j}//of while}//of backPropagation

edgeWeights与edgeWeightsDelta两个三维数组，再声明的时候第二维大小就是“layerNumNodes[l] + 1”。所以，偏置节点没包含在layerNumNodes[l] 里。因此在偏置调整时第二维的下标是j+1。