I have started to explore the implementation of back-propagation neural nets to allow a Arduino program to learn specific events based on windows of sensor data. I will start posting documentation of my progress in the near future. But for now, neural nets don't seem to be discussed in the forum yet. I'm sure that there must be some people here using them, or interested in using them with Arduino or other software. So I will start a topic here so there is at least space to share knowledge and discoveries on this subject.
Oh wow. Thats awesome. 
very interesting. please let me encourage you to describe your stratgy and approach ?
I for one will help test.
I would also be willing to help out. Just let me know.
This is very cool! 2 years ago i've tried to put a simple BPN in an ATMega8 on this little board
http://www.active-robots.com/products/controllr/mr8-details.shtml
This is not simple because it takes a lot of ram in pointers to the neurons and layers... :-[My code was similar to: http://www.neural-networks-at-your-fingertips.com/bpn.html
It was just shy try at BPN inside a microcontroller.... but I'll try to find the code and post it...
But maybe with the 328P and a lot of care or the arduino MEGA this can be done 
If you need something count me in! 
I use LumiNet for neural nets, but learning is not the main topic yet. And the topology has some restrictions.
In a LumiNet neural net, every hardware node is a neuron. What are the neurons in your net? Or did you implement a pure software (simulated) neural net that runs on a single Arduino hardware board?
I am very interested in your implementation.
It was simulated. The nodes where sigmoid activated...
The problem was that a simple XOR learning network consumed most of the ram and it was not practical....
but at that time I didn't spent any time trying to optimize de code... It was more like a "port" of a BPN with 2 input neurons 3 in the hidden layer and 1 output to the uC...
I think one can experiment with lots of variations. for example the activation function can an lookup table or be outside of the uC with discrete components.
But the main problem with the 8, 168 and the 328 is available RAM... the ideal is to make an implementation from scratch...
I think i would be VERY cool to have a Neural Network running inside an arduino board or just a standalone chip!
I'am making a small robot for me and my son but after that i will definitely look into this!!!
H File nnType.h
typedef int BOOL;
typedef double VAL;
#define FALSE 0
#define TRUE 1
#define NOT !
#define AND &&
#define OR ||
#define MIN(x,y) ((x)<(y) ? (x) : (y))
#define MAX(x,y) ((x)>(y) ? (x) : (y))
#define LO 0.1
#define HI 0.9
#define BIAS 1
#define sqr(x) ((x)*(x))
typedef struct { /* A LAYER OF A NET: */
int Units; /* - number of units in this layer */
VAL* Output; /* - output of ith unit */
VAL* Error; /* - error term of ith unit */
VAL** Weight; /* - connection weights to ith unit */
VAL** WeightSave; /* - saved weights for stopped training */
VAL** dWeight; /* - last weight deltas for momentum */
} LAYER;
typedef struct { /* A NET: */
LAYER** Layer; /* - layers of this net */
LAYER* InputLayer; /* - input layer */
LAYER* OutputLayer; /* - output layer */
double Alpha; /* - momentum factor */
double Eta; /* - learning rate */
double Gain; /* - gain of sigmoid function */
double Error; /* - total net error */
} NET;
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "nnTypes.h"
void InitializeRandoms() {
srand(4711);
}
int RandomEqualINT(int Low, int High) {
return rand() % (High-Low+1) + Low;
}
double RandomEqualDouble(double Low, double High) {
return ((double) rand() / RAND_MAX) * (High-Low) + Low;
}
//just for testing alternative ways of soring the values... (for now is the same: DOUBLE)
VAL DoubleToVal(double dValue) {
return (VAL) dValue;
}
double ValToDouble(VAL val) {
return (double) val;
}
void DEBUG(char *s) {
Serial.println(s);
}
#define NUM_LAYERS 3
#define N 2
#define M 1
int Units[NUM_LAYERS] = {N, 3, M};
double XOR_Outputs[4] = { 1.0, 0.0, 0.0, 1.0 };
double XOR_Inputs [4][2] = {
{0, 0},
{0, 1},
{1, 0},
{1, 1}
};
double TrainError;
double TestError;
void InitializeApplication(NET* Net) {
Net->Alpha = 0.5;
Net->Eta = 0.05;
Net->Gain = 1.0;
}
void FinalizeApplication(NET* Net) { }
/******************************************************************************
I N I T I A L I Z A T I O N
******************************************************************************/
void GenerateNetwork(NET* Net)
{
int l,i;
Net->Layer = (LAYER**) calloc(NUM_LAYERS, sizeof(LAYER*));
for (l=0; l<NUM_LAYERS; l++) {
Net->Layer[l] = (LAYER*) malloc(sizeof(LAYER));
if (Net->Layer[l] == NULL) DEBUG("NULL1");
Net->Layer[l]->Units = Units[l];
Net->Layer[l]->Output = (VAL*) calloc(Units[l]+1, sizeof(VAL));
Net->Layer[l]->Error = (VAL*) calloc(Units[l]+1, sizeof(VAL));
Net->Layer[l]->Weight = (VAL**) calloc(Units[l]+1, sizeof(VAL*));
Net->Layer[l]->WeightSave = (VAL**) calloc(Units[l]+1, sizeof(VAL*));
Net->Layer[l]->dWeight = (VAL**) calloc(Units[l]+1, sizeof(VAL*));
Net->Layer[l]->Output[0] = DoubleToVal(BIAS);
if (Net->Layer[l]->Output == NULL) DEBUG("NULL2");
if (Net->Layer[l]->Error == NULL) DEBUG("NULL3");
if (Net->Layer[l]->Weight == NULL) DEBUG("NULL4");
if (Net->Layer[l]->WeightSave == NULL) DEBUG("NULL5");
if (Net->Layer[l]->dWeight == NULL) DEBUG("NULL6");
if (l != 0) {
for (i=1; i<=Units[l]; i++) {
Net->Layer[l]->Weight[i] = (VAL*) calloc(Units[l-1]+1, sizeof(VAL));
Net->Layer[l]->WeightSave[i] = (VAL*) calloc(Units[l-1]+1, sizeof(VAL));
Net->Layer[l]->dWeight[i] = (VAL*) calloc(Units[l-1]+1, sizeof(VAL));
if (Net->Layer[l]->Weight[i] == NULL) DEBUG("NULL7");
if (Net->Layer[l]->WeightSave[i] == NULL) DEBUG("NULL8");
if (Net->Layer[l]->dWeight[i] == NULL) DEBUG("NULL9");
}
}
}
Net->InputLayer = Net->Layer[0];
Net->OutputLayer = Net->Layer[NUM_LAYERS - 1];
Net->Alpha = 0.9;
Net->Eta = 0.25;
Net->Gain = 1.0;
}
void RandomWeights(NET* Net)
{
int l,i,j;
for (l=1; l<NUM_LAYERS; l++) {
for (i=1; i<=Net->Layer[l]->Units; i++) {
for (j=0; j<=Net->Layer[l-1]->Units; j++) {
Net->Layer[l]->Weight[i][j] = DoubleToVal(RandomEqualDouble(-0.5, 0.5));
}
}
}
}
void SetInput(NET* Net, double* Input)
{
int i;
for (i=1; i<=Net->InputLayer->Units; i++) {
Net->InputLayer->Output[i] = DoubleToVal(Input[i-1]);
}
}
void GetOutput(NET* Net, double* Output)
{
int i;
for (i=1; i<=Net->OutputLayer->Units; i++) {
Output[i-1] = ValToDouble(Net->OutputLayer->Output[i]);
}
}
void SaveWeights(NET* Net)
{
int l,i,j;
for (l=1; l<NUM_LAYERS; l++) {
for (i=1; i<=Net->Layer[l]->Units; i++) {
for (j=0; j<=Net->Layer[l-1]->Units; j++) {
Net->Layer[l]->WeightSave[i][j] = Net->Layer[l]->Weight[i][j];
}
}
}
}
void RestoreWeights(NET* Net)
{
int l,i,j;
for (l=1; l<NUM_LAYERS; l++) {
for (i=1; i<=Net->Layer[l]->Units; i++) {
for (j=0; j<=Net->Layer[l-1]->Units; j++) {
Net->Layer[l]->Weight[i][j] = Net->Layer[l]->WeightSave[i][j];
}
}
}
}
void PropagateLayer(NET* Net, LAYER* Lower, LAYER* Upper)
{
int i,j;
double Sum;
for (i = 1; i <= Upper->Units; i++) {
Sum = 0;
for (j=0; j<=Lower->Units; j++) {
Sum += ValToDouble(Upper->Weight[i][j]) * ValToDouble(Lower->Output[j]);
}
Upper->Output[i] = DoubleToVal(1 / (1 + exp(-Net->Gain * Sum)));
}
}
void PropagateNet(NET* Net)
{
int l;
for (l=0; l<NUM_LAYERS-1; l++) {
PropagateLayer(Net, Net->Layer[l], Net->Layer[l+1]);
}
}
void ComputeOutputError(NET* Net, double* Target)
{
int i;
double Out, Err;
Net->Error = 0;
for (i = 1; i <= Net->OutputLayer->Units; i++) {
Out = ValToDouble(Net->OutputLayer->Output[i]);
Err = Target[i-1] - Out;
Net->OutputLayer->Error[i] = DoubleToVal(Net->Gain * Out * (1 - Out) * Err);
Net->Error += 0.5 * sqr(Err);
}
}
void BackpropagateLayer(NET* Net, LAYER* Upper, LAYER* Lower)
{
int i,j;
double Out, Err;
for (i = 1; i <= Lower->Units; i++) {
Out = ValToDouble(Lower->Output[i]);
Err = 0;
for (j = 1; j <= Upper->Units; j++) {
Err += ValToDouble(Upper->Weight[j][i]) * ValToDouble(Upper->Error[j]);
}
Lower->Error[i] = DoubleToVal(Net->Gain * Out * (1-Out) * Err);
}
}
void BackpropagateNet(NET* Net)
{
int l;
for (l=NUM_LAYERS-1; l>1; l--) {
BackpropagateLayer(Net, Net->Layer[l], Net->Layer[l-1]);
}
}
void AdjustWeights(NET* Net)
{
int l,i,j;
double Out, Err, dWeight;
for (l = 1; l < NUM_LAYERS; l++) {
for (i = 1; i <= Net->Layer[l]->Units; i++) {
for (j = 0; j <= Net->Layer[l-1]->Units; j++) {
Out = ValToDouble(Net->Layer[l-1]->Output[j]);
Err = ValToDouble(Net->Layer[l]->Error[i]);
dWeight = ValToDouble(Net->Layer[l]->dWeight[i][j]);
Net->Layer[l]->Weight[i][j] += DoubleToVal(Net->Eta * Err * Out + Net->Alpha * dWeight);
Net->Layer[l]->dWeight[i][j] = DoubleToVal(Net->Eta * Err * Out);
}
}
}
}
void SimulateNet(NET* Net, double* Input, double* Output, double* Target, BOOL Training)
{
SetInput(Net, Input);
PropagateNet(Net);
GetOutput(Net, Output);
ComputeOutputError(Net, Target);
if (Training) {
BackpropagateNet(Net);
AdjustWeights(Net);
}
}
void TrainNet(NET* Net, int Epochs)
{
int n, i;
double Output[M];
for (i = 0; i < Epochs; i++) {
for (n = 0; n < 4; n++) {
SimulateNet(Net, XOR_Inputs[n], Output, &XOR_Outputs[n], TRUE);
}
}
}
void TestNet(NET* Net)
{
int n;
double Output[M];
TrainError = 0;
for (n = 0; n < 4; n++) {
SimulateNet(Net, XOR_Inputs[n], Output, &XOR_Outputs[n], FALSE);
TrainError += Net->Error;
}
TestError = 0;
for (n = 0; n < 4; n++) {
SimulateNet(Net, XOR_Inputs[n], Output, &XOR_Outputs[n], FALSE);
TestError += Net->Error;
}
}
void EvaluateNet(NET* Net)
{
int n;
double Output [M];
DEBUG("--");
for (n = 0; n < 4; n++) {
SimulateNet(Net, XOR_Inputs[n], Output, &XOR_Outputs[n], FALSE);
DEBUG(Output [0]);
}
}
void setup()
{
Serial.begin(9600);
randomSeed(analogRead(0));
NET Net;
BOOL Stop;
double MinTestError;
InitializeRandoms();
GenerateNetwork(&Net);
RandomWeights(&Net);
InitializeApplication(&Net);
DEBUG("START");
Stop = FALSE;
MinTestError = 5000000;
do {
TrainNet(&Net, 10);
TestNet(&Net);
if (TestError < MinTestError) {
//DEBUG("Save");
//DEBUG(TrainError);
//DEBUG(TestError);
MinTestError = TestError;
SaveWeights(&Net);
}
else if (TestError < 0.2) {
DEBUG("END");
Stop = TRUE;
RestoreWeights(&Net);
}
} while (NOT Stop);
TestNet(&Net);
EvaluateNet(&Net);
TestNet(&Net);
EvaluateNet(&Net);
FinalizeApplication(&Net);
}
void loop() {
//This was not originaly for the arduino
for(;;);
}
I didn't found the code... (it was 2 years ago)
But I've ported it again...
Its learning well when compiled in visual studio but its taking a lot in the arduino... i think because of the precision in Math...
Its working but i didn't debug it and tried do change the learning rate, etc...
I will look into it again when i have time.