#ifndef _NEURAL_NETWORK1_H_ #define _NEURAL_NETWORK1_H_ #pragma interface #include #define SLOPE 1.0 #define S(x) (1.0 / (1.0 + exp (0.0 - SLOPE*(x)))) #define WRONG 0 #define GOOD 1 #define CORRECT 2 //**************************************************************************** // // Neural_network1 class: // // This class performs all the necessary functions needed to train // a Neural Network. The network has an input layer, one hidden // layer, 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_network2 // 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_network1 // 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 // //**************************************************************************** class Neural_network1 { private: // We need // // Matrix for hidden layer 1 activation [num_hidden1] // 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 output layer weights [hidden2] [outputs] // 2 Matrices for sum of all the deltas in an epoch - Back propagation // 1 Matrix for sum of deltas * weight for each neuron in hidden layers // 1 and 2 for backpropagation - Back propagation // // 2 Matrices for each weight's learning rate - delta-bar-delta rule // 2 Matrices for each weight's learning delta - delta-bar-delta rule // 2 Matrices for each weight's learning delta_bar - delta-bar-delta rule // 2 Matrices for each weight's momentum - hybrid delta-bar-delta rule // 2 Matrices for each weight's gaussian offset - Mod. Random Optimization // 2 Matrices for each weight's bias - Modified Random Optimization int num_inputs; int num_hidden1; 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 *output_act; double *input_weights; double *hidden1_weights; double *input_weights_sum_delta; double *hidden1_weights_sum_delta; double *hidden1_sum_delta_weight; double *input_learning_rate; double *hidden1_learning_rate; double *input_learning_delta; double *hidden1_learning_delta; double *input_learning_delta_bar; double *hidden1_learning_delta_bar; double *input_momentum; double *hidden1_momentum; double *input_weights_g_offset; double *hidden1_weights_g_offset; double *input_weights_bias; double *hidden1_weights_bias; void allocate_weight_matrices (); void allocate_bp_matrices (); void allocate_rand_opt_matrices (); void allocate_all_matrices () { allocate_weight_matrices (); allocate_bp_matrices (); allocate_rand_opt_matrices (); }; void initialize_learning_matrices (); void initialize_weight_matrices (double range); void initialize_all_matrices (double range) { initialize_learning_matrices (); initialize_weight_matrices (range); }; void deallocate_bp_matrices (); void deallocate_rand_opt_matrices (); void deallocate_all_matrices (); public: //*********************************************************************** // Constructors : * // Full size specifications and learning parameters. * // Learning parameters are provided defaults which are set to * // just use the BP algorithm with no modifications. * // Set the backpropagation flag and/or the * // random_optimization_flag if you are going to train using * // these methods. If a flag is set to 0, then the matrices * // needed by that algorithm will not be allocated to save * // memory. * // To test only, set both flags to 0 to save memory. * // * // Read constructor which reads in the size and all the weights from * // a file. The network is resized to match the size specified * // by the file. Learning parameters may be specified * // as arguments. * //*********************************************************************** Neural_network1 (int number_inputs = 1, int number_hidden1 = 1, int number_outputs = 1, int backpropagation_flag = 1, int random_optimization_flag = 0, double range = 1.0, double variance = 0.01, double alpha = 0.0, double beta = 1.0, double epsilon = 0.1, double skip_epsilon = 0.0, double learning_rate = 0.1, double theta = 1.0, double phi = 0.0, double K = 0.0, double hdec = 0.0); Neural_network1 (String& filename, int& file_error, int backpropagation_flag = 1, int random_optimization_flag = 0, double variance = 0.01, double alpha = 0.0, double beta = 1.0, double epsilon = 0.1, double skip_epsilon = 0.0, double learning_rate = 0.1, double theta = 1.0, double phi = 0.0, double K = 0.0, double hdec = 0.0); ~Neural_network1 () { deallocate_all_matrices ();}; //************************************************************************** // 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 re_initialize_net (double range = 1.0, double learning_rate = 0.1, double variance = 0.01) { _learning_rate = learning_rate; _variance = variance; initialize_all_matrices (range); }; int save_weights (String& filename); int read_weights (String& filename); double get_hidden1_activation (int node) { return (hidden1_act [node]); }; double get_output_activation (int node) { return (output_act [node]); }; double get_input_weight (int input_node, int hidden1_node) { return (input_weights [hidden1_node * num_inputs + input_node]);}; double get_hidden1_weight (int hidden1_node, int output_node) { return (hidden1_weights [output_node * num_hidden1 + hidden1_node]);}; //******************************************************************* // 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). * //******************************************************************* int get_number_of_inputs () { return (num_inputs); }; int get_number_of_hidden1 () { return (num_hidden1); }; int get_number_of_outputs () { return (num_outputs); }; void set_size_parameters (int number_inputs, int number_hidden1, int number_outputs, double range = 3.0); //******************************************************************* // 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 backpropagation_flag () { return (bp_flag); }; int backpropagation_flag (int flag); int random_optimization_flag () { return (rand_opt_flag); }; int random_optimization_flag (int flag); double learning_rate () { return (_learning_rate); }; double learning_rate (double learning_rate); double alpha () { return _alpha;}; double alpha (double alpha) {double old_alpha = _alpha; _alpha = alpha; return old_alpha;}; double beta () { return _beta;}; double beta (double beta) {double old_beta = _beta; _beta = beta; return old_beta;}; double epsilon () { return _epsilon;}; double epsilon (double epsilon) {double old_epsilon = _epsilon; _epsilon = epsilon; return old_epsilon;}; double skip_epsilon () { return _skip_epsilon; }; double skip_epsilon (double skip_epsilon) {double old_skip = _skip_epsilon; _skip_epsilon = skip_epsilon; return old_skip;}; double theta () { return _theta;}; double theta (double theta) {double old_theta = _theta; _theta = theta; return old_theta;}; double phi () { return _phi;}; double phi (double phi) {double old_phi = _phi; _phi = phi; return old_phi;}; double K () { return _K;}; double K (double K) {double old_K = _K; _K = K; return old_K;}; double hdec () { return _hdec;}; double hdec (double hdec) {double old_hdec = _hdec; _hdec = hdec; return old_hdec;}; double variance () { return _variance;}; double variance (double variance) {double old_variance = _variance; _variance = variance; return old_variance;}; // I use this because I can never remember what the standard delta-bar-delta // parameter settings are that I use. void set_standard_dbd_parameters (); long get_iterations () { return (training_examples); }; //************************************************************************** // 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. * // * // backpropagation : 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 backpropagation * // 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 backpropagation. 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 backpropagation (double input [], double desired_output [], int& done); double calc_forward (double input [], double desired_output [], int& num_wrong, int& skip, int print_it, int& actual_printed); int calc_forward_test (double input [], double desired_output [], int print_it, double correct_eps, double good_eps); void update_weights (); double calc_forward_rand_opt (double input [], double desired_output [], int& num_wrong, int direction); int generate_gaussian_offsets (); void update_weights_with_offset (int direction); void kick_weights (double range); }; #endif