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gnn_softmax.c

Go to the documentation of this file.

/***************************************************************************
 *  @file gnn_mse.h
 *  @brief Softmax Activation Function.
 *
 *  @date   : 03-09-03 20:41
 *  @author : Pedro Ortega C. <peortega@dcc.uchile.cl>
 *  Copyright  2003  Pedro Ortega C.
 ****************************************************************************/
/*
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Library General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */

/**
 * @defgroup gnn_softmax_doc gnn_softmax : Softmax Activation Function.
 * @ingroup gnn_atomic_doc
 *
 * The \ref gnn_softmax datatype implements a node that computes the function:
 * \f[ y_i = \frac{ \exp(x_i) }{ \sum_k^n \exp(x_k) } \f]
 * where \f$i = 1,\ldots,n\f$.
 *
 * The different outputs \f$y_i\f$ of the softmax function are normalized:
 * they sum all up to 1. Softmax outputs lie in the interval \f$[0;1]\f$, and
 * they can be interpreted as probabilities.
 *
 * @warning This node should be fed with small values.
 */



/******************************************/
/* Include Files                          */
/******************************************/

#include "gnn_softmax.h"
#include <math.h>



/******************************************/
/* Static Declaration                     */
/******************************************/

typedef struct _gnn_softmax
{
    gnn_node node;
    gsl_vector *e;
    gsl_vector *y;
} gnn_softmax;

static int
gnn_softmax_f (gnn_node *node,
               const gsl_vector *x,
               const gsl_vector *w,
               gsl_vector *y);

static int
gnn_softmax_dx (gnn_node *node,
                const gsl_vector *x,
                const gsl_vector *w,
                const gsl_vector *dy,
                gsl_vector *dx);



/******************************************/
/* Static Implementation                  */
/******************************************/

/**
 * @brief Computes the output.
 * @ingroup gnn_softmax_doc
 *
 * This functions evaluates the softmax function.
 *
 * @param node  A pointer to a \ref gnn_softmax node.
 * @param x The input vector \f$x\f$.
 * @param w The parameter vector \f$w\f$ (which is empty in this case).
 * @param y The output buffer vector \f$y\f$.
 * @return Returns 0 on success.
 */
static int
gnn_softmax_f (gnn_node *node,
               const gsl_vector *x,
               const gsl_vector *w,
               gsl_vector *y)
{
    size_t i;
    size_t size;
    double sum = 0.0;
    gnn_softmax *snode;

    /* get the size */
    size = gnn_node_input_get_size (node);

    /* get the view as a softmax node */
    snode = (gnn_softmax *) node;
    
    /* hold a pointer to the output vector */
    snode->y = y;

    /* evaluate */
    for (i=0; i<size; ++i)
    {
        double xi;
        double ei;

        xi = gsl_vector_get (x, i);
        ei = exp (xi);
        gsl_vector_set (snode->e, i, ei);
        sum += ei;
    }
    for (i=0; i<size; ++i)
    {
        double ei;
        double yi;

        ei = gsl_vector_get (snode->e, i);
        yi = ei / sum;
        gsl_vector_set (y, i, yi);
    }

    return 0;
}

/**
 * @brief Computes \f$ \frac{\partial E}{\partial X} \f$.
 * @ingroup gnn_softmax_doc
 *
 * This functions computes the gradient of the softmax function,
 * given \f$ \frac{\partial E}{\partial Y} \f$ (dy). The function is,
 * \f[ \frac{\partial E}{\partial x_i}
 *     = \sum_j y_j (\delta_{ji} - y_i) \frac{\partial E}{\partial y_j}
 * \f]
 *
 * @param node  A pointer to a \ref gnn_softmax node.
 * @param x  The input vector \f$x\f$.
 * @param w  The parameter vector \f$w\f$ (which is empty in this case).
 * @param dy The vector \f$\frac{\partial E}{\partial y}\f$.
 * @param dx The output buffer vector \f$\frac{\partial E}{\partial x}\f$.
 * @return Returns 0 on success.
 */
static int
gnn_softmax_dx (gnn_node *node,
                const gsl_vector *x,
                const gsl_vector *w,
                const gsl_vector *dy,
                gsl_vector *dx)
{
    size_t i;
    size_t j;
    size_t size;
    gnn_softmax *snode;

    /* get the size */
    size = gnn_node_input_get_size (node);

    /* get the view as a softmax node */
    snode = (gnn_softmax *) node;

    /* evaluate */
    for (i=0; i<size; ++i)
    {
        double yi;
        double dxi;

        dxi = 0.0;
        yi  = gsl_vector_get (snode->y, i);
        
        for (j=0; j<size; ++j)
        {
            double yj;
            double dyj;

            yj   = gsl_vector_get (snode->y, j);
            dyj  = gsl_vector_get (dy, j);
            
            dxi += (i==j)?    yj * (1.0 - yi) * dyj
                          : - yj * yi * dyj;
        }

        gsl_vector_set (dx, i, dxi);
    }
    
    return 0;
}

/**
 * @brief Destroys the \ref gnn_softmax specific data.
 * @ingroup gnn_softmax_doc
 *
 * This is the destructor for \ref gnn_softmax nodes.
 *
 * @param node A pointer to a \ref gnn_softmax node.
 */
static void
gnn_softmax_destroy (gnn_node *node)
{
    gnn_softmax *snode;
    
    assert (node != NULL);
    
    snode = (gnn_softmax *) node;
    if (snode->e != NULL)
        gsl_vector_free (snode->e);
        
    return;
}



/******************************************/
/* Public Interface                       */
/******************************************/

/**
 * @brief Creates a Softmax activation function node.
 * @ingroup gnn_softmax_doc
 *
 * This function creates a node of the \ref gnn_softmax type.
 *
 * @param input_size The input size \f$n\f$.
 * @param a The \f$a\f$ factor.
 * @param b The \f$b\f$ factor.
 * @return A pointer to a new \ref gnn_softmax node.
 */
gnn_node *
gnn_softmax_new (int input_size)
{
    int status;
    gnn_node *node;
    gnn_softmax *snode;

    /* check if sizes are positive */
    if (input_size < 1)
    {
        GSL_ERROR_VAL ("size should be strictly positive for gnn_softmax node",
                       GSL_ENOMEM, NULL);
        return NULL;
    }

    /* allocate the node */
    node = (gnn_node *) malloc (sizeof (gnn_softmax));
    if (node == NULL)
    {
        GSL_ERROR_VAL ("could not allocate memory for gnn_softmax node",
                       GSL_ENOMEM, NULL);
    }
    
    /* Initialize the node */
    status = gnn_node_init (node,
                            "gnn_softmax",
                            gnn_softmax_f,
                            gnn_softmax_dx,
                            NULL,
                            gnn_softmax_destroy);
    if (status)
    {
        GSL_ERROR_VAL ("could not initialize gnn_softmax node",
                       GSL_EFAILED, NULL);
    }
    
    status = gnn_node_set_sizes (node, input_size, input_size, 0);
    if (status)
    {
        GSL_ERROR_VAL ("could not set sizes for gnn_softmax node",
                       GSL_EFAILED, NULL);
    }
    
    /* build buffer */
    snode = (gnn_softmax *) node;
    snode->e = gsl_vector_alloc (input_size);
    if (snode->e == NULL)
    {
        gnn_node_destroy (node);
        GSL_ERROR_VAL ("could not allocate memory gnn_softmax buffer",
                       GSL_ENOMEM, NULL);
    }

    return node;
}

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