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Training neural network to approximate functions

I have absolutely no experience with neural networks, and now I just play with the FANN library to learn them. Thus, the goal is to train the network to approximate the sinusoidal function. For this, I use 3 layers of NN 1 input, 3 hidden and 1 output neurons. the code

const unsigned int num_input = 1;
const unsigned int num_output = 1;
const unsigned int num_layers = 3;
const unsigned int num_neurons_hidden = 3;

struct fann *ann;

ann = fann_create_standard(num_layers, num_input, num_neurons_hidden, num_output);

fann_set_activation_steepness_hidden(ann, 1);
fann_set_activation_steepness_output(ann, 1);

fann_set_activation_function_hidden(ann, FANN_SIGMOID_SYMMETRIC);
fann_set_activation_function_output(ann, FANN_SIGMOID_SYMMETRIC);

fann_set_train_stop_function(ann, FANN_STOPFUNC_BIT);
fann_set_bit_fail_limit(ann, 0.01f);

fann_set_training_algorithm(ann, FANN_TRAIN_RPROP);

fann_randomize_weights(ann, 0, 1);

for(int i=0; i<2; ++i) {
    for(float angle=0; angle<10; angle+=0.1) {
        float sin_anle = sinf(angle);
        fann_train(ann, &angle, &sin_anle);
    }
}

int k = 0;
for(float angle=0; angle<10; angle+=0.1) {
    float sin_anle = sinf(angle);
    float *o = fann_run(ann, &angle);
    printf("%d\t%f\t%f\t\n", k++, *o, sin_anle);
}

fann_destroy(ann);

However, I have results that have nothing to do with a real sinusoidal function. I believe that there is some fundamental error in my network design.

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1 answer

You select the Resilient Backpropagation (Rprop) optimization algorithm in this line:

fann_set_training_algorithm(ann, FANN_TRAIN_RPROP);

Rprop - . , . fann_train

- (. fann_train_enum), .

, FANN_TRAIN_INCREMENTAL. : fann_train_on_data, fann_train_on_file fann_train_epoch.

, , :

  • . (0.5).
  • . 20 000.
  • 3 . , . I, [0,3], .
  • .:) 0.02f.
  • Rprop - , - Levenberg-Marquardt, .

, , , :

0       0.060097        0.000000
1       0.119042        0.099833
2       0.188885        0.198669
3       0.269719        0.295520
4       0.360318        0.389418
5       0.457665        0.479426
6       0.556852        0.564642
7       0.651718        0.644218
8       0.736260        0.717356
9       0.806266        0.783327
10      0.860266        0.841471
11      0.899340        0.891207
12      0.926082        0.932039
...

:

#include <cstdio>
#include <cmath>
#include <fann.h>
#include <floatfann.h>

int main()
{
  const unsigned int num_input = 1;
  const unsigned int num_output = 1;
  const unsigned int num_layers = 3;
  const unsigned int num_neurons_hidden = 2;

  const float angleRange = 3.0f;
  const float angleStep = 0.1;
  int instances = (int)(angleRange/angleStep);

  struct fann *ann;

  ann = fann_create_standard(num_layers, num_input, num_neurons_hidden, num_output);

  fann_set_activation_function_hidden(ann, FANN_SIGMOID_SYMMETRIC);
  fann_set_activation_function_output(ann, FANN_SIGMOID_SYMMETRIC);

  fann_set_train_stop_function(ann, FANN_STOPFUNC_BIT);
  fann_set_bit_fail_limit(ann, 0.02f);

  fann_set_training_algorithm(ann, FANN_TRAIN_INCREMENTAL);

  fann_randomize_weights(ann, 0, 1);

  fann_train_data *trainingSet;
  trainingSet = fann_create_train(instances, 1, 1); // instances, input dimension, output dimension
  float angle=0;
  for(int instance=0; instance < instances; angle+=angleStep, instance++) {
      trainingSet->input[instance][0] = angle;
      trainingSet->output[instance][0] = sinf(angle);
  }

  fann_train_on_data(ann, trainingSet, 20000, 10, 1e-8f); // epochs, epochs between reports, desired error

  int k = 0;
  angle=0;
  for(int instance=0; instance < instances; angle+=angleStep, instance++) {
      float sin_angle = sinf(angle);
      float *o = fann_run(ann, &angle);
      printf("%d\t%f\t%f\t\n", k++, *o, sin_angle);
  }

  fann_destroy(ann);

  return 0;
}

, fann_create_train FAN 2.2.0.

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