简介
RNN（recurrent neural network ）循环（递归）神经网络主要用来处理序列数据。因为传统的神经网络从输入－隐含层－输出是全连接的，层中的神经元是没有连接的，所以对于输入数据本身具有时序性（例如输入的文本数据，每个单词之间有一定联系）的处理表现并不理想。而RNN每一个输出与前面的输出建立起关联，这样就能够很好的处理序列化的数据。
单纯循环神经网络也面临一些问题，如无法处理随着递归，权重指数级爆炸或消失的问题，难以捕捉长期时间关联。这些可以结合不同的LSTM很好的解决这个问题。
本文主要介绍简单的RNN用OC的实现，并通过训练MNIST数据来检测模型。后面有时间再介绍LSTM的实现。
公式
简单的RNN就三层，输入－隐含层－输出，如下：
将其展开的模型如下：
其中，A这个隐含层的操作就是将当前输入与前面的输出相结合，然后激活就得到当前状态信号。如下：
计算公式如下：
其中Xt是输入数据序列，St是的状态序列，V＊St就是图中Ot输出，softmax运算并没有画出来。
由于RNN结构简单，反向传播的公式结合一点数理知识就可以求得，这里就不列出，详见代码实现。
数据处理
由于没找到比较好的训练数据，这里用的是前面《OC实现Softmax识别手写数字》文章里面的MNIST数据源。输入数据处理、softmax实现也都是复用的。
图片数据本质上并非是序列化的，我这里将图片的每行的的像素数据当作一个信号输入，如果一共N行，序列长度就是N。训练数据是28＊28维的图片，那么就是每个信号是28＊1，一共时间长度是28。
RNN实现
简单的RNN实现流程并不复杂，需要训练的参数就5个：输入的权值、神经元间转移的权值、输出的权值、以及两个转移和输出的偏置量。直接看代码：
//
// MLRnn.m
// LSTM
//
// Created by Jiao Liu on 11/9/16.
// Copyright © 2016 ChangHong. All rights reserved.
//
#import "MLRnn.h"
@implementation MLRnn
#pragma mark - Inner Method
+ (double)truncated_normal:(double)mean dev:(double)stddev
{
double outP = 0.0;
do {
static int hasSpare = 0;
static double spare;
if (hasSpare) {
hasSpare = 0;
outP = mean + stddev * spare;
continue;
}
hasSpare = 1;
static double u,v,s;
do {
u = (rand() / ((double) RAND_MAX)) * 2.0 - 1.0;
v = (rand() / ((double) RAND_MAX)) * 2.0 - 1.0;
s = u * u + v * v;
} while ((s >= 1.0) || (s == 0.0));
s = sqrt(-2.0 * log(s) / s);
spare = v * s;
outP = mean + stddev * u * s;
} while (fabsl(outP) > 2*stddev);
return outP;
}
+ (double *)fillVector:(double)num size:(int)size
{
double *outP = malloc(sizeof(double) * size);
vDSP_vfillD(&num, outP, 1, size);
return outP;
}
+ (double *)weight_init:(int)size
{
double *outP = malloc(sizeof(double) * size);
for (int i = 0; i < size; i++) {
outP[i] = [MLRnn truncated_normal:0 dev:0.1];
}
return outP;
}
+ (double *)bias_init:(int)size
{
return [MLRnn fillVector:0.1f size:size];
}
+ (double *)tanh:(double *)input size:(int)size
{
for (int i = 0; i < size; i++) {
double num = input[i];
if (num > 20) {
input[i] = 1;
}
else if (num < -20)
{
input[i] = -1;
}
else
{
input[i] = (exp(num) - exp(-num)) / (exp(num) + exp(-num));
}
}
return input;
}
#pragma mark - Init
- (id)initWithNodeNum:(int)num layerSize:(int)size dataDim:(int)dim
{
self = [super init];
if (self) {
_nodeNum = num;
_layerSize = size;
_dataDim = dim;
[self setupNet];
}
return self;
}
- (id)init
{
self = [super init];
if (self) {
[self setupNet];
}
return self;
}
- (void)setupNet
{
_inWeight = [MLRnn weight_init:_nodeNum * _dataDim];
_outWeight = [MLRnn weight_init:_nodeNum * _dataDim];
_flowWeight = [MLRnn weight_init:_nodeNum * _nodeNum];
_outBias = calloc(_dataDim, sizeof(double));
_flowBias = calloc(_nodeNum, sizeof(double));
_output = calloc(_layerSize * _dataDim, sizeof(double));
_state = calloc(_layerSize * _nodeNum, sizeof(double));
}
#pragma mark - Main Method
- (double *)forwardPropagation:(double *)input
{
_input = input;
// clean data
double zero = 0;
vDSP_vfillD(&zero, _output, 1, _layerSize * _dataDim);
vDSP_vfillD(&zero, _state, 1, _layerSize * _nodeNum);
for (int i = 0; i < _layerSize; i++) {
double *temp1 = calloc(_nodeNum, sizeof(double));
double *temp2 = calloc(_nodeNum, sizeof(double));
if (i == 0) {
vDSP_mmulD(_inWeight, 1, (input + i * _dataDim), 1, temp1, 1, _nodeNum, 1, _dataDim);
vDSP_vaddD(temp1, 1,_flowBias, 1, temp1, 1, _nodeNum);
}
else
{
vDSP_mmulD(_inWeight, 1, (input + i * _dataDim), 1, temp1, 1, _nodeNum, 1, _dataDim);
vDSP_mmulD(_flowWeight, 1, (_state + (i-1) * _nodeNum), 1, temp2, 1, _nodeNum, 1, _nodeNum);
vDSP_vaddD(temp1, 1, temp2, 1, temp1, 1, _nodeNum);
vDSP_vaddD(temp1, 1,_flowBias, 1, temp1, 1, _nodeNum);
}
[MLRnn tanh:temp1 size:_nodeNum];
vDSP_vaddD((_state + i * _nodeNum), 1, temp1, 1, (_state + i * _nodeNum), 1, _nodeNum);
vDSP_mmulD(_outWeight, 1, temp1, 1, (_output + i * _dataDim), 1, _dataDim, 1, _nodeNum);
vDSP_vaddD((_output + i * _dataDim), 1, _outBias, 1, (_output + i * _dataDim), 1, _dataDim);
free(temp1);
free(temp2);
}
return _output;
}
- (void)backPropagation:(double *)loss
{
double *flowLoss = calloc(_nodeNum, sizeof(double));
for (int i = _layerSize - 1; i >= 0 ; i--) {
vDSP_vaddD(_outBias, 1, (loss + i * _dataDim), 1, _outBias, 1, _dataDim);
double *transWeight = calloc(_nodeNum * _dataDim, sizeof(double));
vDSP_mtransD(_outWeight, 1, transWeight, 1, _nodeNum, _dataDim);
double *tanhLoss = calloc(_nodeNum, sizeof(double));
vDSP_mmulD(transWeight, 1, (loss + i * _dataDim), 1, tanhLoss, 1, _nodeNum, 1, _dataDim);
double *outWeightLoss = calloc(_nodeNum * _dataDim, sizeof(double));
vDSP_mmulD((loss + i * _dataDim), 1, (_state + i * _nodeNum), 1, outWeightLoss, 1, _dataDim, _nodeNum, 1);
vDSP_vaddD(_outWeight, 1, outWeightLoss, 1, _outWeight, 1, _nodeNum * _dataDim);
double *tanhIn = calloc(_nodeNum, sizeof(double));
vDSP_vsqD((_state + i * _nodeNum), 1, tanhIn, 1, _nodeNum);
double *one = [MLRnn fillVector:1 size:_nodeNum];
vDSP_vsubD(tanhIn, 1, one, 1, tanhIn, 1, _nodeNum);
if (i != _layerSize - 1) {
vDSP_vaddD(tanhLoss, 1, flowLoss, 1, tanhLoss, 1, _nodeNum);
}
vDSP_vmulD(tanhLoss, 1, tanhIn, 1, tanhLoss, 1, _nodeNum);
vDSP_vaddD(_flowBias, 1, tanhLoss, 1, _flowBias, 1, _nodeNum);
if (i != 0) {
double *transFlow = calloc(_nodeNum * _nodeNum, sizeof(double));
vDSP_mtransD(_flowWeight, 1, transFlow, 1, _nodeNum, _nodeNum);
vDSP_mmulD(transFlow, 1, tanhLoss, 1, flowLoss, 1, _nodeNum, 1, _nodeNum);
free(transFlow);
double *flowWeightLoss = calloc(_nodeNum * _nodeNum, sizeof(double));
vDSP_mmulD(tanhLoss, 1, (_state + (i-1) * _nodeNum), 1, flowWeightLoss, 1, _nodeNum, _nodeNum, 1);
vDSP_vaddD(_flowWeight, 1, flowWeightLoss, 1, _flowWeight, 1, _nodeNum * _nodeNum);
free(flowWeightLoss);
}
double *inWeightLoss = calloc(_nodeNum * _dataDim, sizeof(double));
vDSP_mmulD(tanhLoss, 1, (_input + i * _dataDim), 1, inWeightLoss, 1, _nodeNum, _dataDim, 1);
vDSP_vaddD(_inWeight, 1, inWeightLoss, 1, _inWeight, 1, _nodeNum * _dataDim);
free(transWeight);
free(tanhLoss);
free(outWeightLoss);
free(tanhIn);
free(one);
free(inWeightLoss);
}
free(flowLoss);
free(loss);
}
@end
很多初始化方法以及内部函数直接是复用《OC实现(CNN)卷积神经网络》中相关的方法。
结语
我这里使用RNN，迭代2500次，每次训练100张图片，单个神经元节点个数选择50，得到的正确率94%左右。
有兴趣的朋友可以点这里看完整代码。
本文参考：
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