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방금 기계 학습 및 신경망을 연구하기 시작 했으므로 backpropagation의 작동 방식을 이해하는 데 어려움을 겪고 있습니다. 간단한 매트릭스 기반 접근법을 사용하여 Java에서 간단한 NN을 개발하려고했습니다. 하나의 교육 예제 만 입력하면 네트워크가 완벽하게 작동하지만 더 많이 사용하려고하면 출력은 항상 원하는 교육 출력의 평균입니다. http://neuralnetworksanddeeplearning.com/images/tikz21.pngBackpropagation Neural Network가 작동하지 않습니다.
package neuralnetwork;
/**
* @author Paolo Pellizzoni
*/
public class NeuralNetwork {
static final int in_l = 2;
static final int h_l = 5;
static final int out_l = 1;
public static double[][] w2 = new double[h_l][in_l];
public static double[][] w3 = new double[out_l][h_l];
public static double[] b2 = new double[h_l];
public static double[] b3 = new double[out_l];
public static double[][] x = {{3,4},{2,3}};
public static double[][] y = {{0.3,0.7}};
public static double[][] test = {{3}, {2}};
// using x = {{3},{2}} and y = {{0.3}} it works
public static void main(String[] args) {
trainNN(0.2);
double[][] m = a_3(test);
for(int i=0; i<m.length; i++){
for(int j=0; j<m[0].length; j++){
System.out.print(m[i][j]+" ");
}
System.out.println();
}
}
// ---------- FUNCTIONS ----------
static void inizialize_weights(double[][] m){
for(int i=0; i<m.length; i++){
for(int j=0; j<m[0].length; j++){
m[i][j]= Math.random();
}
}
}
static void trainNN(double rate){
inizialize_weights(w2);
inizialize_weights(w3);
for(int c=0; c<500; c++){
double[][] dJ_w3 = dJ_w3(x, y);
double[][] dJ_w2 = dJ_w2(x, y);
double[] dJ_b3 = dJ_b3(x, y);
double[] dJ_b2 = dJ_b2(x, y);
w3 = matrix_sum(w3, dJ_w3, -rate);
w2 = matrix_sum(w2, dJ_w2, -rate);
b3 = vect_sum(b3, dJ_b3, -rate);
b2 = vect_sum(b2, dJ_b2, -rate);
}
}
static double[][] a_3(double[][] inputs){
return sigmoid(z_3(inputs));
}
static double[][] z_3(double[][] inputs){
return matrix_sum_vect(matrix_product(w3, a_2(inputs)), b3, 1);
}
static double[][] a_2(double[][] inputs){
return sigmoid(z_2(inputs));
}
static double[][] z_2(double[][] inputs){
return matrix_sum_vect(matrix_product(w2, inputs), b2, 1);
}
static double[][] delta3 (double[][] inputs, double[][] y){
return matrix_hadamard(
matrix_sum(a_3(inputs), y, -1),
sigmoid_prime(z_3(inputs))
);
}
static double[][] delta2 (double[][] inputs, double[][] y){
return matrix_hadamard(
matrix_product(
transpose_matrix(w3),
delta3(inputs, y)),
sigmoid_prime(z_2(inputs))
);
}
static double[][] dJ_w3 (double[][] inputs, double[][] y){
double[][] dJ_w3 = new double[out_l][h_l];
double[][] delta3 = delta3(inputs, y);
double[][] a2 = a_2(inputs);
for(int i=0; i<delta3.length; i++){
for(int j=0; j<a2.length; j++){
double tmp = 0;
for(int k=0; k<a2[0].length; k++){
tmp += a2[j][k]*delta3[i][k];
}
dJ_w3[i][j] = tmp/a2[0].length;
}
}
return dJ_w3;
}
static double[][] dJ_w2 (double[][] inputs, double[][] y){
double[][] dJ_w2 = new double[h_l][in_l];
double[][] delta2 = delta2(inputs, y);
double[][] a1 = inputs;
for(int i=0; i<delta2.length; i++){
for(int j=0; j<a1.length; j++){
double tmp = 0;
for(int k=0; k<a1[0].length; k++){
tmp += a1[j][k]*delta2[j][k];
}
dJ_w2[i][j] = tmp/a1[0].length;
}
}
return dJ_w2;
}
static double[] dJ_b3 (double[][] inputs, double[][] y){
double[] dJ_b3 = new double[out_l];
double[][] delta3 = delta3(inputs, y);
for(int i=0; i<delta3.length; i++){
double tmp = 0;
for(int k=0; k<delta3[0].length; k++){
tmp += delta3[i][k];
}
dJ_b3[i] = tmp/delta3[0].length;
}
return dJ_b3;
}
static double[] dJ_b2 (double[][] inputs, double[][] y){
double[] dJ_b2 = new double[h_l];
double[][] delta2 = delta2(inputs, y);
for(int i=0; i<delta2.length; i++){
double tmp = 0;
for(int k=0; k<delta2[0].length; k++){
tmp += delta2[i][k];
}
dJ_b2[i] = tmp/delta2[0].length;
}
return dJ_b2;
}
// ----- Math -----
static double[][] matrix_product(double[][] a, double[][] b){ // matrix multiplication
int m1ColLength = a[0].length;
int m2RowLength = b.length;
if(m1ColLength != m2RowLength) return null;
int mRRowLength = a.length;
int mRColLength = b[0].length;
double[][] mResult = new double[mRRowLength][mRColLength];
for(int i = 0; i < mRRowLength; i++) {
for(int j = 0; j < mRColLength; j++) {
for(int k = 0; k < m1ColLength; k++) {
mResult[i][j] += a[i][k] * b[k][j];
}
}
}
return mResult;
}
static double[][] matrix_sum(double[][] a, double[][] b, double is_sum){ //matrix sum
int m1ColLength = a[0].length;
int m2RowLength = b.length;
int m1RowLength = a.length;
int m2ColLength = b[0].length;
if(m1ColLength != m2ColLength || m1RowLength != m2RowLength) return null;
double[][] mResult = new double[m1RowLength][m1ColLength];
for(int i = 0; i < m1RowLength; i++) {
for(int j = 0; j < m1ColLength; j++) {
mResult[i][j]=a[i][j]+(b[i][j])*is_sum;
}
}
return mResult;
}
static double[] vect_sum(double[] a, double[] b, double is_sum){ // vector sum
int m2RowLength = b.length;
int m1RowLength = a.length;
if(m1RowLength != m2RowLength) return null;
double[] mResult = new double[m1RowLength];
for(int i = 0; i < m1RowLength; i++) {
mResult[i]=a[i]+(b[i])*is_sum;
}
return mResult;
}
static double[][] matrix_sum_vect(double[][] a, double[] b, double is_sum){ // adds a vector to each column
int m1ColLength = a[0].length;
int m2RowLength = b.length;
int m1RowLength = a.length;
if(m1RowLength != m2RowLength) return null;
double[][] mResult = new double[m1RowLength][m1ColLength];
for(int i = 0; i < m1RowLength; i++) {
for(int j = 0; j < m1ColLength; j++) {
mResult[i][j]=a[i][j]+(b[i])*is_sum;
}
}
return mResult;
}
static double[][] matrix_hadamard(double[][] a, double[][] b){ // hadamard product
int m1ColLength = a[0].length;
int m2RowLength = b.length;
int m1RowLength = a.length;
int m2ColLength = b[0].length;
if(m1ColLength != m2ColLength || m1RowLength != m2RowLength) return null;
double[][] mResult = new double[m1RowLength][m1ColLength];
for(int i = 0; i < m1RowLength; i++) {
for(int j = 0; j < m1ColLength; j++) {
mResult[i][j]=a[i][j]*b[i][j];
}
}
return mResult;
}
static double[][] matrix_x_scalar(double[][] a, double scalar){ // matrix times scalar
int m1ColLength = a[0].length;
int m1RowLength = a.length;
double[][] mResult = new double[m1RowLength][m1ColLength];
for(int i = 0; i < m1RowLength; i++) {
for(int j = 0; j < m1ColLength; j++) {
mResult[i][j]=a[i][j]*scalar;
}
}
return mResult;
}
static double[][] transpose_matrix(double [][] m){
double[][] mResult = new double[m[0].length][m.length];
for (int i = 0; i < m.length; i++)
for (int j = 0; j < m[0].length; j++)
mResult[j][i] = m[i][j];
return mResult;
}
static double sigmoid(double z) {
return 1.0/(1.0+Math.exp(-z));
}
static double[][] sigmoid(double[][] z) {
for(int i=0; i<z.length; i++){
for(int j=0; j<z[0].length; j++){
z[i][j]= sigmoid(z[i][j]);
}
}
return z;
}
static double sigmoid_prime(double z) {
return sigmoid(z)*(1-sigmoid(z));
}
static double[][] sigmoid_prime(double[][] z) {
for(int i=0; i<z.length; i++){
for(int j=0; j<z[0].length; j++){
z[i][j]= sigmoid_prime(z[i][j]);
}
}
return z;
}// ----- end math -----
}
나는 평균 모든 그라디언트,하지만 난 그냥 그것을 찾을 수 없다는 오류가 어쩌면 K 루프에서 dJ_w3, dJ_w2 기능을 숨 깁니다 것을 매우 확신합니다. 도와 주시겠습니까?