#ifndef _NEURAL_NET2_H_ #define _NEURAL_NET2_H_ /* This is the "C" version of the Neural Network code */ #define SLOPE 1.0 #define S(x) (1.0 / (1.0 + exp (0.0 - SLOPE*(x)))) #define private #define public #define class typedef struct #define WRONG 0 #define GOOD 1 #define CORRECT 2 /***************************************************************************** // // Neural_net2 class: // // This class performs all the necessary functions needed to train // a Neural Network. The network has an input layer, two hidden // layers, and an output layer. The size of each layer is specified // a run time so there is no restriction on size except memory. // This is a feed-forward network with full connctions from one // layer to the next. // // The network can perform straight back-propagation with no // modifications (Rumelhart, Hinton, and Williams, 1985) which // will find a solution but not very quickly. The network can also // perform back-propagation with the delta-bar-delta and the // hybrid rule developed // by Robert A. Jacobs, University of Massachusetts // // "Increased Rates of Convergence Through Learning Rate Adaptation" // by Robert A. Jacobs. // Neural Networks, Vol 1. pp.295-307, 1988. // // The basic idea of this rule is that every weight has its own // learning rate and momentum. Each learning rate should be continously // changed according to the following rules - // - If the weight changes in the same direction as the previous update, // then the learning rate for that weight should increase by a constant. // - If the weight changes in the opposite direction as the previous // update, then the learning rate for that weight should decrease // exponentially. // // learning rate = e(t) for each individual weight // The exact formula for the change in learning rate (DELTA e(t)) is // // // | K if DELTA_BAR(t-1)*DELTA(t) > 0 // DELTA e(t) = | -PHI*e(t) if DELTA_BAR(t-1)*DELTA(t) < 0 // | 0 otherwise // // where DELTA(t) = dJ(t) / dw(t) ---> Partial derivative // // and DELTA_BAR(t) = (1 - THETA)*DELTA(t) + THETA*DELTA_BAR(t-1). // // The rule in the paper was: // delta weight (t) = (1 - ALPHA) * learning rate * dJ(t)/dw(t) + // ALPHA * delta weight (t - 1) // // I modified it slightly so that there is a separate parameter for // (1 - alpha) called BETA which can be set to any value. // Also added is the parameter HDEC which is the decay factor which is // supposed to only allow weight to survive that do useful work. // delta weight (t) = BETA * learning rate * dJ(t)/dw(t) + // ALPHA * delta weight (t - 1) - HDEC * weight (t-1) // // For full details of the algorithm, read the article in // Neural Networks. // // The parameter HDEC is from // "Learning translation invariant recognition in a massivelly parallel // network" // by G.E. Hinton // PARLE: Parallel Architectures and Languages Europe 1987 // Referenced from "Multilayer Perceptron, Fuzzy Sets, and // Classification" Neural Networks, Vol 1, NO. 5, Sept. 1992. // // Range of values // ALPHA [0,1.0] // BETA [0,1.0] // THETA [0,1.0] // PHI [0,1.0] // K [0,infinity) --> recommended range [0,1.0] // HDEC [0,infinity) --> recommended range [0,0.01) // // I know very little about the HDEC parameter. I read about it in // the "Multilayer..." paper and the paper did not go into // detail about it. // // To perform straight back-propagation, just construct a Neural_net2work2 // with no learning parameters specified (they default to straight // back-propagation) or set them to // ALPHA = 0.0, BETA = 1.0, THETA = 1.0, PHI = 0.0, K = 0.0, HDEC = 0.0 // // For momentum only with fixed learning rate // ALPHA = ?, BETA = 1.0, THETA = 1.0, PHI = 0.0, K = 0.0, HDEC = 0.0 // // However, using the delta-bar-delta rule should increase your rate of // convergence by a factor of 1 to 30 generally. The parameters for // the delta-bar-delta rule I use are // ALPHA = 0.0, BETA = 1.0, THETA = 0.8, PHI = 0.2, K = 0.025, HDEC = 0.0 // // The hybrid rule uses the delta-bar-delta learning update rule plus // sets ALPHA so that there is momentum. // ALPHA = 0.4 plus previous delta-bar-delta settings should generally // improve the rate of convergence even more. // // One more heuristic method has been employed in this Neural net class- // the skip heuristic. This is something I thought of and I am sure // other people have also. If the output activation is within // skip_epsilon of its desired for each output, then the calc_forward // routine returns the skip_flag = 1. This allows you to not waste // time trying to push already very close examples to the exact value. // If the skip_flag comes back '1', then don't bother calculating forward // or back-propagating the example for X number of epochs. You must // write the routine to skip the example yourself, but the Neural_net2work2 // will tell you when to skip the example. This heuristic also has the // advantage of reducing memorization and increases generalization. // Typical values I use for this heuristic - // skip_epsilon = 0.01 - 0.05 // number skipped = 2-10. // // As with all heuristics, some work well in some situations and // poorly in others. The delta-bar-delta and hybrid rule seem // somewhat succeptible to starting location so that training from // scratch may take 200 epochs one time and 10000 epochs another. // Experiment with all the values to see which work best for your // application. // // // Another training method has been implemented, the Random Optimization // Method by Solis & Wets, 1981. The reference is // // "A New Approach for Finding the Global Minimum of Error Function // of Neural Networks" by Norio Baba. // Neural Networks, Vol. 2, pp. 367-373, 1989. // // I implemented this algorithm because it claimed to be quite good. // However, it makes exaggerated generalized claims based upon on // three very limited tests. // // The basic algorithm is to generate a gaussian random offset for each // weight, see if adding (or subtracting) all of the offsets to the // weights will reduce the error. If the error is reduced, move to that // new location by adding (or subtracting) the offsets to the weights. // The claim is that this algorithm will find the Global Minimum with // probability 1, which is true. The example test cases used to show // that it converges faster than standard backpropagation are fudged // because they solve 10 input patterns with over 100 weights which // is ridiculously easy to do without learning anything because the // solution space is so large. However, when the solution space is // small (i.e. there are barely enough nodes to hold all the information) // then random optimization has a hard time finding the solution. // I tried to have it solve // the XOR problem with 2 inputs, 2 hidden1, 2 hidden2 and 1 output. // Delta-bar-delta solved it about half the time but this algorithm // solved it about 20% of the time. If I had let the algorithm go // forever, it would have eventually solved the problem, but not // for a long time. // // Basically if it does not solve the problem quickly, it won't for a // very long time. // // Now the answer to the question - If Random Optimization doesn't seem // to work in general, why include it? // The reason - for completeness. Someone may come across the paper // and want to try it so here it is. Also I have seen it work very // well for some applications. // // Comments and suggestions are welcome and can be emailed to me // anstey@sun.soe.clarkson.edu // / ****************************************************************************/ /* This 'class' (struct) is private. You should not modify it directly */ /* or corrupted data may occur. Only modify it through the 'class' */ /* functions listed below. */ class Neural_net2 { private /* // We need // // Matrix for hidden layer 1 activation [num_hidden1] // Matrix for hidden layer 2 activation [num_hidden2] // Matrix for output layer activation [num_outputs] // // Matrix for input to first hidden layer weights [num_inputs] [num_hidden1] // Matrix for hidden layer 1 to hidden layer 2 weights [hidden1] [hidden2] // Matrix for hidden layer 2 to output layer weights [hidden2] [outputs] // 3 Matrices for sum of all the deltas in an epoch - Back propagation // 2 Matrices for sum of deltas * weight for each neuron in hidden layers // 1 and 2 for backpropagation - Back propagation // // 3 Matrices for each weight's learning rate - delta-bar-delta rule // 3 Matrices for each weight's learning delta - delta-bar-delta rule // 3 Matrices for each weight's learning delta_bar - delta-bar-delta rule // 3 Matrices for each weight's momentum - hybrid delta-bar-delta rule // 3 Matrices for each weight's gaussian offset - Random Optimization // 3 Matrices for each weight's bias - Random Optimization */ int num_inputs; int num_hidden1; int num_hidden2; int num_outputs; int bp_flag; int rand_opt_flag; double _epsilon; double _skip_epsilon; double _learning_rate; double _alpha; double _beta; double _theta; double _phi; double _K; double _hdec; double _variance; long training_examples; long examples_since_update; double *hidden1_act; double *hidden2_act; double *output_act; double *input_weights; double *hidden1_weights; double *hidden2_weights; double *input_weights_sum_delta; double *hidden1_weights_sum_delta; double *hidden2_weights_sum_delta; double *hidden1_sum_delta_weight; double *hidden2_sum_delta_weight; double *input_learning_rate; double *hidden1_learning_rate; double *hidden2_learning_rate; double *input_learning_delta; double *hidden1_learning_delta; double *hidden2_learning_delta; double *input_learning_delta_bar; double *hidden1_learning_delta_bar; double *hidden2_learning_delta_bar; double *input_momentum; double *hidden1_momentum; double *hidden2_momentum; double *input_weights_g_offset; double *hidden1_weights_g_offset; double *hidden2_weights_g_offset; double *input_weights_bias; double *hidden1_weights_bias; double *hidden2_weights_bias; } Neural_net2; public /* These are the functions that operate on a struct Neural_net2 */ /* The first parameter to any Neural_net2 function (except constructors) is a pointer to an initialized Neural_net2 */ /************************************************************************ // Constructors : Each constructor returns a pointer to a * // Neural_net2 which has been initialized. * // * // Neural_net2_constr : Constructs (initializes) a Neural_net2 struct. * // Full size specifications and learning parameters need to be * // specified. * // * // Neural_net2_default_constr : Constructs (initializes) a Neural_net2 * // structure of the given size with the default learning * // parameters for BP and weights between +-1.0. * // * // Neural_net2_read_constr : Constructs (initializes) a Neural_net2 * // structure by reading the weights from a file. The size of * // the Neural_net2 is determined by the file. Learning * // parameters need to be specified. * // * // Neural_net2_default_read_constr : Constructs (initializes) a * // Neural_net2 structure by reading the weights from a file. * // The size of the Neural_net2 is determined by the file. * // Learning parameters are given default BP values. * // * // Destructor : The destructor destroys (frees) all matrices in a * // Neural_net2 structure * // * // Neural_net2_destr : YOU MUST CALL THIS ROUTINE TO DESTROY THE * // Neural_net2. The destructor frees all matrices in the * // Neural_net2. * / **********************************************************************/ Neural_net2 *Neural_net2_constr (int number_inputs, int number_hidden1, int number_hidden2, int number_outputs, int backpropagation_flag, int random_optimization_flag, double range, double variance, double alpha, double beta, double epsilon, double skip_epsilon, double learning_rate, double theta, double phi, double K, double hdec); Neural_net2 *Neural_net2_read_constr (char *filename, int *file_error, int backpropagationflag, int random_optimization_flag, double variance, double alpha, double beta, double epsilon, double skip_epsilon, double learning_rate, double theta, double phi, double K, double hdec); void Neural_net2_destr (Neural_net2 *nn); /* Inline functions if compiler supports inlining */ #ifdef __INLINE__ inline Neural_net2 *Neural_net2_default_constr (int number_inputs, int number_hidden1, int number_hidden2, int number_outputs, int backpropagation_flag, int random_optimization_flag, double range) { return (Neural_net2_constr (number_inputs,number_hidden1, number_hidden2,number_outputs, backpropagation_flag, random_optimization_flag,range,0.01,0.0,1.0, 0.1,0.0,0.1,1.0,0.0,0.0,0.0); } inline Neural_net2 *Neural_net2_default_read_constr (char *filename, int *file_error, int backpropagation_flag, int random_optimization_flag) { return (Neural_net2_read_constr (filename,file_error,backpropagation_flag, random_optimization_flag,0.01,0.0,1.0,0.1, 0.0,0.1,1.0,0.0,0.0,0.0); } #else Neural_net2 *Neural_net2_default_constr (int number_inputs, int number_hidden1, int number_hidden2, int number_outputs,int backpropagation_flag, int random_optimization_flag, double range); Neural_net2 *Neural_net2_default_read_constr (char *filename, int *file_error, int backpropagation_flag, int random_optimization_flag); #endif /*************************************************************************** // Weight parameter routines: * // save_weights : This routine saves the weights of the network * // to the file . * // * // read_weights : This routine reads the weight values from the file * // . The network is automatically resized to the * // size specified by the file. * // * // Activation routines return the node activation after a calc_forward * // has been performed. * // * // get_weight routines return the weight between node1 and node2. * // * / *************************************************************************/ void Neural_net2_re_initialize_net (Neural_net2 *nn, double range, double learning_rate, double variance); int Neural_net2_save_weights (Neural_net2 *nn, char *filename); int Neural_net2_read_weights (Neural_net2 *nn, char *filename); #ifdef __INLINE__ inline double Neural_net2_get_hidden1_activation (Neural_net2 *nn, int node) { return (nn->hidden1_act [node]); }; inline double Neural_net2_get_hidden2_activation (Neural_net2 *nn, int node) { return (nn->hidden2_act [node]); }; inline double Neural_net2_get_output_activation (Neural_net2 *nn, int node) { return (nn->output_act [node]); }; inline double Neural_net2_get_input_weight (Neural_net2 *nn, int input_node, int hidden1_node) { return (nn->input_weights [hidden1_node * nn->num_inputs + input_node]);}; inline double Neural_net2_get_hidden1_weight (Neural_net2 *nn, int hidden1_node, int hidden2_node) { return (nn->hidden1_weights [hidden2_node * nn->num_hidden1 + hidden1_node]);}; inline double Neural_net2_get_hidden2_weight (Neural_net2 *nn, int hidden2_node, int output_node) { return (nn->hidden2_weights [output_node*nn->num_hidden2+hidden2_node]);}; #else double Neural_net2_get_hidden1_activation (Neural_net2 *nn, int node); double Neural_net2_get_hidden2_activation (Neural_net2 *nn, int node); double Neural_net2_get_output_activation (Neural_net2 *nn, int node); double Neural_net2_get_input_weight (Neural_net2 *nn, int input_node, int hidden1_node); double Neural_net2_get_hidden1_weight (Neural_net2 *nn, int hidden1_node, int hidden2_node); double Neural_net2_get_hidden2_weight (Neural_net2 *nn, int hidden2_node, int output_node); #endif /******************************************************************** // Size parameters of network. * // The size of the network may be changed at any time. The weights * // will be copied from the old size to the new size. If the new * // size is larger, then the extra weights will be randomly set * // between +-range. The matrices used to hold learning updates * // and activations will be re-initialized (cleared). * / ******************************************************************/ #ifdef __INLINE__ inline int Neural_net2_get_number_inputs (Neural_net2 *nn) { return (nn->num_inputs); }; inline int Neural_net2_get_number_hidden1 (Neural_net2 *nn) { return (nn->num_hidden1); }; inline int Neural_net2_get_number_hidden2 (Neural_net2 *nn) { return (nn->num_hidden2); }; inline int Neural_net2_get_number_outputs (Neural_net2 *nn) { return (nn->num_outputs); }; #else int Neural_net2_get_number_inputs (Neural_net2 *nn); int Neural_net2_get_number_hidden1 (Neural_net2 *nn); int Neural_net2_get_number_hidden2 (Neural_net2 *nn); int Neural_net2_get_number_outputs (Neural_net2 *nn); #endif void Neural_net2_set_size_parameters (Neural_net2 *nn, int number_inputs, int number_hidden1, int number_hidden2, int number_outputs, double range); /******************************************************************** // Learning parameters functions. These parameters may be changed * // on the fly. The learning rate and K may have to be reduced as * // more and more training is done to prevent oscillations. * / ******************************************************************/ int Neural_net2_get_backpropagation_flag (Neural_net2 *nn); int Neural_net2_set_backpropagation_flag (Neural_net2 *nn, int flag); int Neural_net2_get_random_optimization_flag (Neural_net2 *nn); int Neural_net2_set_random_optimization_flag (Neural_net2 *nn, int flag); double Neural_net2_get_learning_rate (Neural_net2 *nn); double Neural_net2_set_learning_rate (Neural_net2 *nn, double learning_rate); /* I use this because I can never remember what the standard delta-bar-delta parameter settings are that I use. */ void Neural_net2_set_standard_dbd_parameters (Neural_net2 *nn); #ifdef __INLINE__ inline double Neural_net2_set_alpha (Neural_net2 *nn, double alpha) {double old_alpha = nn->_alpha; nn->_alpha = alpha; return old_alpha; } inline double Neural_net2_set_beta (Neural_net2 *nn, double beta) {double old_beta = nn->_beta; nn->_beta = beta; return old_beta; } inline double Neural_net2_set_epsilon (Neural_net2 *nn, double epsilon) {double old_eps = nn->_epsilon; nn->_epsilon = epsilon; return old_eps; } inline double Neural_net2_set_skip_epsilon (Neural_net2 *nn, double skip_eps) {double old_skip_eps = nn->_skip_epsilon; nn->_skip_epsilon = skip_eps; return old_skip_eps; } inline double Neural_net2_set_theta (Neural_net2 *nn, double theta) {double old_theta = nn->_theta; nn->_theta = theta; return old_theta; } inline double Neural_net2_set_phi (Neural_net2 *nn, double phi) {double old_phi = nn->_phi; nn->_phi = phi; return old_phi; } inline double Neural_net2_set_K (Neural_net2 *nn, double K) {double old_K = nn->_K; nn->_K = K; return old_K; } inline double Neural_net2_set_hdec (Neural_net2 *nn, double hdec) {double old_hdec = nn->_hdec; nn->_hdec = hdec; return old_hdec; } inline double Neural_net2_set_variance (Neural_net2 *nn, double variance) {double old_variance = nn->_variance; nn->_variance = variance; return old_variance; } inline double Neural_net2_get_alpha (Neural_net2 *nn) { return (nn->_alpha); } inline double Neural_net2_get_beta (Neural_net2 *nn) { return (nn->_beta); } inline double Neural_net2_get_epsilon (Neural_net2 *nn) { return (nn->_epsilon); }; inline double Neural_net2_get_skip_epsilon (Neural_net2 *nn) { return (nn->_skip_epsilon); }; inline double Neural_net2_get_theta (Neural_net2 *nn) { return (nn->_theta); }; inline double Neural_net2_get_phi (Neural_net2 *nn) { return (nn->_phi); }; inline double Neural_net2_get_K (Neural_net2 *nn) { return (nn->_K); }; inline double Neural_net2_get_hdec (Neural_net2 *nn) { return (nn->_hdec); } inline double Neural_net2_get_variance (Neural_net2 *nn) { return (nn->_variance); } inline long Neural_net2_get_iterations (Neural_net2 *nn) { return (nn->training_examples); } #else double Neural_net2_set_alpha (Neural_net2 *nn, double alpha); double Neural_net2_set_beta (Neural_net2 *nn, double beta); double Neural_net2_set_epsilon (Neural_net2 *nn, double epsilon); double Neural_net2_set_skip_epsilon (Neural_net2 *nn, double skip_eps); double Neural_net2_set_theta (Neural_net2 *nn, double theta); double Neural_net2_set_phi (Neural_net2 *nn, double phi); double Neural_net2_set_K (Neural_net2 *nn, double K); double Neural_net2_set_hdec (Neural_net2 *nn, double hdec); double Neural_net2_set_variance (Neural_net2 *nn, double variance); double Neural_net2_get_alpha (Neural_net2 *nn); double Neural_net2_get_beta (Neural_net2 *nn); double Neural_net2_get_epsilon (Neural_net2 *nn); double Neural_net2_get_skip_epsilon (Neural_net2 *nn); double Neural_net2_get_theta (Neural_net2 *nn); double Neural_net2_get_phi (Neural_net2 *nn); double Neural_net2_get_K (Neural_net2 *nn); double Neural_net2_get_hdec (Neural_net2 *nn); double Neural_net2_get_variance (Neural_net2 *nn); long Neural_net2_get_iterations (Neural_net2 *nn); #endif /************************************************************************** // The main neural network routines: * // * // The network input is an array of doubles which has a size of * // number_inputs. * // The network desired output is an array of doubles which has a size * // of number_outputs. * // * // back_propagation : Calculates how each weight should be changed. * // Assumes that calc_forward has been called just prior to * // this routine to calculate all of the node activations. * // * // calc_forward_rand_opt : Calculates the error for the input * // by adding (or subtracting) the gaussian offsets to the * // weights. First call generate_gaussian_offsets to create * // the offsets, call this routine for each example to find the * // global error. If the new global error is less than the * // current error, call update_weights_with_offsets. * // * // calc_forward : Calculates the output for a given input. Finds * // all node activations which are needed for back_propagation * // to calculate weight adjustment. Returns abs (error). * // The parameter skip is for use with the skip_epsilon * // parameter. What it means is if the output is within * // skip_epsilon of the desired, then it is so close that it * // should be skipped from being calculated the next X times. * // Careful use of this parameter can significantly increase * // the rate of convergence and also help prevent over-learning. * // * // calc_forward_test : Calculates the output for a given input. This * // routine is used for testing rather than training. It returns * // whether the test was CORRECT, GOOD or WRONG which is * // determined by the parameters correct_epsilon and * // good_epsilon. CORRECT > GOOD > WRONG. * // * // update_weights : Actually adjusts all the weights according to * // the calculations of back_propagation. This routine should * // be called at the end of every training epoch. The weights * // can be updated by the straight BP algorithm, or by the * // delta-bar-delta algorithm developed by Robert A. Jacobs * // which increases the rate of convergence generally by at * // least a factor of 10. The parameters THETA, PHI, and K * // determine which algorithm is used. The default settings * // for these parameters cause update_weights to use the straight * // BP algorithm. * // * // kick_weights : This routine changes all weights by a random amount * // within +-range. It is useful in case the network gets * // 'stuck' and is having trouble converging to a solution. I * // use it when the number wrong has not changed for the last 200 * // epochs. Getting the range right will take some trial and * // error as it depends on the application and the weights' * // actual values. * // * / *************************************************************************/ void Neural_net2_back_propagation (Neural_net2 *nn, double input [], double desired_output [], int *done); double Neural_net2_calc_forward (Neural_net2 *nn, double input [], double desired_output [], int *num_wrong, int* skip, int print_it, int *actual_printed); int Neural_net2_calc_forward_test (Neural_net2 *nn, double input [], double desired_output [], int print_it, double correct_eps, double good_eps); void Neural_net2_update_weights (Neural_net2 *nn); double Neural_net2_calc_forward_rand_opt (Neural_net2 *nn, double input [], double desired_output [], int *num_wrong, int direction); int Neural_net2_generate_gaussian_offsets (Neural_net2 *nn); void Neural_net2_update_weights_with_offset (Neural_net2 *nn, int direction); void Neural_net2_kick_weights (Neural_net2 *nn, double range); #endif