我试图在Java中使用反向传播实现FFNN,但不知道哪里出了问题。当网络中只有一个神经元时,它能够正常工作,但是我编写了另一个处理更大网络的类,却发现什么都没有收敛。似乎这是数学问题 - 或者说是我的数学实现问题 - 但我已经检查了几次,找不到任何问题。这应该能够正常运行。
节点类:
package arr;
import util.ActivationFunction;
import util.Functions;
public class Node {
public ActivationFunction f;
public double output;
public double error;
private double sumInputs;
private double sumErrors;
public Node(){
sumInputs = 0;
sumErrors = 0;
f = Functions.SIG;
output = 0;
error = 0;
}
public Node(ActivationFunction func){
this();
this.f = func;
}
public void addIW(double iw){
sumInputs += iw;
}
public void addIW(double input, double weight){
sumInputs += (input*weight);
}
public double calculateOut(){
output = f.eval(sumInputs);
return output;
}
public void addEW(double ew){
sumErrors+=ew;
}
public void addEW(double error, double weight){
sumErrors+=(error*weight);
}
public double calculateError(){
error = sumErrors * f.deriv(sumInputs);
return error;
}
public void resetValues(){
sumErrors = 0;
sumInputs = 0;
}
}
LineNetwork类:
package arr;
import util.Functions;
public class LineNetwork {
public double[][][] weights; //layer of node to, # of node to, # of node from
public Node[][] nodes; //layer, #
public double lc;
public LineNetwork(){
weights = new double[2][][];
weights[0] = new double[2][1];
weights[1] = new double[1][3];
initializeWeights();
nodes = new Node[2][];
nodes[0] = new Node[2];
nodes[1] = new Node[1];
initializeNodes();
lc = 1;
}
private void initializeWeights(){
for(double[][] layer: weights)
for(double[] curNode: layer)
for(int i=0; i<curNode.length; i++)
curNode[i] = Math.random()/10;
}
private void initializeNodes(){
for(Node[] layer: nodes)
for(int i=0; i<layer.length; i++)
layer[i] = new Node();
nodes[nodes.length-1][0].f = Functions.HSF;
}
public double feedForward(double[] inputs) {
for(int j=0; j<nodes[0].length; j++)
nodes[0][j].addIW(inputs[j], weights[0][j][0]);
double[] outputs = new double[nodes[0].length];
for(int i=0; i<nodes[0].length; i++)
outputs[i] = nodes[0][i].calculateOut();
for(int l=1; l<nodes.length; l++){
for(int i=0; i<nodes[l].length; i++){
for(int j=0; j<nodes[l-1].length; j++)
nodes[l][i].addIW(
outputs[j],
weights[l][i][j]);
nodes[l][i].addIW(weights[l][i][weights[l][i].length-1]);
}
outputs = new double[nodes[l].length];
for(int i=0; i<nodes[l].length; i++)
outputs[i] = nodes[l][i].calculateOut();
}
return outputs[0];
}
public void backpropagate(double[] inputs, double expected) {
nodes[nodes.length-1][0].addEW(expected-nodes[nodes.length-1][0].output);
for(int l=nodes.length-2; l>=0; l--){
for(Node n: nodes[l+1])
n.calculateError();
for(int i=0; i<nodes[l].length; i++)
for(int j=0; j<nodes[l+1].length; j++)
nodes[l][i].addEW(nodes[l+1][j].error, weights[l+1][j][i]);
for(int j=0; j<nodes[l+1].length; j++){
for(int i=0; i<nodes[l].length; i++)
weights[l+1][j][i] += nodes[l][i].output*lc*nodes[l+1][j].error;
weights[l+1][j][nodes[l].length] += lc*nodes[l+1][j].error;
}
}
for(int i=0; i<nodes[0].length; i++){
weights[0][i][0] += inputs[i]*lc*nodes[0][i].calculateError();
}
}
public double train(double[] inputs, double expected) {
double r = feedForward(inputs);
backpropagate(inputs, expected);
return r;
}
public void resetValues() {
for(Node[] layer: nodes)
for(Node n: layer)
n.resetValues();
}
public static void main(String[] args) {
LineNetwork ln = new LineNetwork();
System.out.println(str2d(ln.weights[0]));
for(int i=0; i<10000; i++){
double[] in = {Math.round(Math.random()),Math.round(Math.random())};
int out = 0;
if(in[1]==1 ^ in[0] ==1) out = 1;
ln.resetValues();
System.out.print(i+": {"+in[0]+", "+in[1]+"}: "+out+" ");
System.out.println((int)ln.train(in, out));
}
System.out.println(str2d(ln.weights[0]));
}
private static String str2d(double[][] a){
String str = "[";
for(double[] arr: a)
str = str + str1d(arr) + ",\n";
str = str.substring(0, str.length()-2)+"]";
return str;
}
private static String str1d(double[] a){
String str = "[";
for(double d: a)
str = str+d+", ";
str = str.substring(0, str.length()-2)+"]";
return str;
}
}
快速解释结构:每个节点都有一个激活函数f;
f.eval
评估函数,f.deriv
评估其导数。 Functions.SIG
是标准的S型函数,Functions.HSF
是Heaviside阶跃函数。为了设置函数的输入,您需要使用包含前一个输出权重的值调用addIW
。在反向传播中,使用addEW
完成类似操作。节点按照2D数组组织,权重以描述的3D数组单独组织。我知道这可能有点困难 - 我当然知道这段代码违反了多少Java约定 - 但我感激任何人可以提供的帮助。
编辑:由于这个问题和我的代码都是巨大的文本墙,如果有一个涉及到许多复杂表达式的行你不想弄清楚,请添加注释或其他要求我并尽快回答它。
编辑2:这里的具体问题是这个网络没有收敛XOR。以下是一些输出来说明这一点:
9995:{1.0,0.0}:1 1 9996:{0.0,1.0}:1 1 9997:{0.0,0.0}:0 1 9998:{0.0,1.0}:1 0 9999:{0.0,1.0}:1 1 每行的格式为
TEST NUMBER:{INPUTS}:EXPECTED ACTUAL
。网络对每个测试调用train
,因此该网络进行了10000次反向传播。如果有人想运行它,这里是两个额外的类:
package util;
public class Functions {
public static final ActivationFunction LIN = new ActivationFunction(){
public double eval(double x) {
return x;
}
public double deriv(double x) {
return 1;
}
};
public static final ActivationFunction SIG = new ActivationFunction(){
public double eval(double x) {
return 1/(1+Math.exp(-x));
}
public double deriv(double x) {
double ev = eval(x);
return ev * (1-ev);
}
};
public static final ActivationFunction HSF = new ActivationFunction(){
public double eval(double x) {
if(x>0) return 1;
return 0;
}
public double deriv(double x) {
return (1);
}
};
}
package util;
public interface ActivationFunction {
public double eval(double x);
public double deriv(double x);
}
现在这段话变得更长了。该死。