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activation_function.h
/*
Copyright (c) 2013, Taiga Nomi
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of the <organization> nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#pragma once
#include "tiny_dnn/util/util.h"
#include <algorithm>
namespace tiny_dnn {
namespace activation {
class function {
public:
function() = default;
function(const function &) = default;
#ifndef CNN_DEFAULT_MOVE_CONSTRUCTOR_UNAVAILABLE
function(function &&) = default;
#endif
function &operator =(const function &) = default;
#ifndef CNN_DEFAULT_ASSIGNMENT_OPERATOR_UNAVAILABLE
function &operator =(function &&) = default;
#endif
virtual ~function() = default;
virtual float_t f(const vec_t& v, size_t index) const = 0;
void itef(vec_t& out, const vec_t& in, size_t cnt) const {
for (size_t i = 0; i < cnt; i++) {
out[i] = f(in, i);
}
}
// dfi/dyi
virtual float_t df(float_t y) const = 0;
// dfi/dyk (k=0,1,..n)
virtual vec_t df(const vec_t& y, size_t i) const { vec_t v(y.size(), 0); v[i] = df(y[i]); return v; }
// return if dfi/dyk is one-hot vector
virtual bool one_hot() const { return true; }
// target value range for learning
virtual std::pair<float_t, float_t> scale() const = 0;
};
class identity : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override { return v[i]; }
float_t df(float_t /*y*/) const override { return float_t(1); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
class sigmoid : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override { return float_t(1) / (float_t(1) + std::exp(-v[i])); }
float_t df(float_t y) const override { return y * (float_t(1) - y); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
class relu : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override { return std::max(float_t(0), v[i]); }
float_t df(float_t y) const override { return y > float_t(0) ? float_t(1) : float_t(0); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
typedef relu rectified_linear; // for compatibility
class leaky_relu : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override { return (v[i] > float_t(0)) ? v[i] : float_t(0.01) * v[i]; }
float_t df(float_t y) const override { return y > float_t(0) ? float_t(1) : float_t(0.01); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
class elu : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override { return (v[i]<float_t(0) ? (exp(v[i])- float_t(1)) : v[i]); }
float_t df(float_t y) const override { return (y > float_t(0) ? float_t(1) : (float_t(1)+y)); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
class softmax : public function {
public:
float_t f(const vec_t& v, size_t i) const override {
float_t alpha = *std::max_element(v.begin(), v.end());
float_t numer = std::exp(v[i] - alpha);
float_t denom = float_t(0);
for (auto x : v)
denom += std::exp(x - alpha);
return numer / denom;
}
float_t df(float_t y) const override {
return y * (float_t(1) - y);
}
virtual vec_t df(const vec_t& y, size_t index) const override {
vec_t v(y.size(), 0);
for (size_t i = 0; i < y.size(); i++)
v[i] = (i == index) ? df(y[index]) : -y[i] * y[index];
return v;
}
virtual bool one_hot() const override { return false; }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0), float_t(1)); }
};
class tan_h : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override {
return std::tanh(v[i]);
}
void itef(vec_t& out, const vec_t& in, size_t cnt) const {
for (size_t i = 0; i < cnt; i++) {
out[i] = std::tanh(in[i]);
}
}
// fast approximation of tanh (improve 2-3% speed in LeNet-5)
/*float_t f(float_t x) const {
const float_t x2 = x * x;
x *= 1.0 + x2 * (0.1653 + x2 * 0.0097);
return x / std::sqrt(1.0 + x * x);// invsqrt(static_cast<float>(1.0 + x * x));
}*/
float_t df(float_t y) const override { return float_t(1) - sqr(y); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(-0.8), float_t(0.8)); }
private:
/*float invsqrt(float x) const {
float x2 = x * 0.5f;
long i = *reinterpret_cast<long*>(&x);
i = 0x5f3759df - (i >> 1);
x = *reinterpret_cast<float*>(&i);
x = x * (1.5f - (x2 * x * x));
return x;
}*/
};
// s tan_h, but scaled to match the other functions
class tan_hp1m2 : public function {
public:
using function::df;
float_t f(const vec_t& v, size_t i) const override {
const float_t ep = std::exp(v[i]);
return ep / (ep + std::exp(-v[i]));
}
float_t df(float_t y) const override { return 2 * y *(float_t(1) - y); }
std::pair<float_t, float_t> scale() const override { return std::make_pair(float_t(0.1), float_t(0.9)); }
};
} // namespace activation
} // namespace tiny_dnn
tiny_dnn::activation::elu
Definition activation_function.h:101
tiny_dnn::activation::function
Definition activation_function.h:34
tiny_dnn::activation::identity
Definition activation_function.h:67
tiny_dnn::activation::leaky_relu
Definition activation_function.h:93
tiny_dnn::activation::relu
Definition activation_function.h:83
tiny_dnn::activation::sigmoid
Definition activation_function.h:75
tiny_dnn::activation::softmax
Definition activation_function.h:109
tiny_dnn::activation::tan_h
Definition activation_function.h:137
tiny_dnn::activation::tan_hp1m2
Definition activation_function.h:174
tiny_dnn::image
Simple image utility class.
Definition image.h:94