C# 中的激活函数列表
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【中文标题】C# 中的激活函数列表【英文标题】：List of activation functions in C# 【发布时间】：2016-07-22 21:47:58 【问题描述】：我可以在数学中找到激活函数列表，但在代码中找不到。 所以我想这将是代码中这样一个列表的正确位置，如果应该有的话。 从这两个链接中的算法翻译开始： https://en.wikipedia.org/wiki/Activation_function https://stats.stackexchange.com/questions/115258/comprehensive-list-of-activation-functions-in-neural-networks-with-pros-cons
目标是通过 UI 轻松访问 Activation 类（包含函数及其派生类）。
编辑： 我的尝试
using UnityEngine;
using System.Collections;
using System;
///<summary>
///Activation Functions from:
///https://en.wikipedia.org/wiki/Activation_function
///https://stats.stackexchange.com/questions/115258/comprehensive-list-of-activation-functions-in-neural-networks-with-pros-cons
///D infront means the Deravitive of the function
///x is the input of one perceptron. a is the alpha value sometimes needed.
///</summary>
[System.Serializable]
public class Activation
public ActivationType activationType;
public Activation(ActivationType type)
activationType = type;
public double AFunction(double x)
switch(activationType)
case ActivationType.Identity:
return Identity(x);
case ActivationType.BinaryStep:
return BinaryStep(x);
case ActivationType.Logistic:
return Logistic(x);
case ActivationType.Tanh:
return Tanh(x);
case ActivationType.ArcTan:
return ArcTan(x);
case ActivationType.ReLU:
return ReLU(x);
case ActivationType.SoftPlus:
return SoftPlus(x);
case ActivationType.BentIdentity:
return BentIdentity(x);
case ActivationType.Sinusoid:
return Sinusoid(x);
case ActivationType.Sinc:
return Sinc(x);
case ActivationType.Gaussian:
return Gaussian(x);
case ActivationType.Bipolar:
return Bipolar(x);
case ActivationType.BipolarSigmoid:
return BipolarSigmoid(x);
return 0;
public double ActivationDerivative(double x)
switch(activationType)
case ActivationType.Logistic:
return DLogistic(x);
case ActivationType.Tanh:
return DTanh(x);
case ActivationType.ArcTan:
return DArcTan(x);
case ActivationType.ReLU:
return DReLU(x);
case ActivationType.SoftPlus:
return DSoftPlus(x);
case ActivationType.BentIdentity:
return DBentIdentity(x);
case ActivationType.Sinusoid:
return DSinusoid(x);
case ActivationType.Sinc:
return DSinc(x);
case ActivationType.Gaussian:
return DGaussian(x);
case ActivationType.BipolarSigmoid:
return DBipolarSigmoid(x);
return 0;
public double AFunction(double x, double a)
switch(activationType)
case ActivationType.PReLU:
return PReLU(x,a);
case ActivationType.ELU:
return ELU(x,a);
return 0;
public double ActivationDerivative(double x, double a)
switch(activationType)
case ActivationType.PReLU:
return DPReLU(x,a);
case ActivationType.ELU:
return DELU(x,a);
return 0;
public double Identity(double x)
return x;
public double BinaryStep(double x)
return x < 0 ? 0 : 1;
public double Logistic(double x)
return 1/(1+Math.Pow(Math.E,-x));
public double DLogistic(double x)
return Logistic(x)*(1-Logistic(x));
public double Tanh(double x)
return 2/(1+Math.Pow(Math.E, -(2*x)))-1;
public double DTanh(double x)
return 1-Math.Pow(Tanh(x),2);
public double ArcTan(double x)
return Math.Atan(x);
public double DArcTan(double x)
return 1/Math.Pow(x,2)+1;
//Rectified Linear Unit
public double ReLU(double x)
return Math.Max(0,x);// x < 0 ? 0 : x;
public double DReLU(double x)
return Math.Max(0,1);// x < 0 ? 0 : x;
//Parameteric Rectified Linear Unit
public double PReLU(double x, double a)
return x < 0 ? a*x : x;
public double DPReLU(double x, double a)
return x < 0 ? a : 1;
//Exponential Linear Unit
public double ELU(double x, double a)
return x < 0 ? a*(Math.Pow(Math.E, x) - 1) : x;
public double DELU(double x, double a)
return x < 0 ? ELU(x, a)+a: 1;
public double SoftPlus(double x)
return Math.Log(Math.Exp(x)+1);
public double DSoftPlus(double x)
return Logistic(x);
public double BentIdentity(double x)
return (((Math.Sqrt(Math.Pow(x,2)+1))-1)/2)+x;
public double DBentIdentity(double x)
return (x/(2*Math.Sqrt(Math.Pow(x,2)+1)))+1;
// public float SoftExponential(float x)
//
//
//
public double Sinusoid(double x)
return Math.Sin(x);
public double DSinusoid(double x)
return Math.Cos(x);
public double Sinc(double x)
return x == 0 ? 1 : Math.Sin(x)/x;
public double DSinc(double x)
return x == 0 ? 0 : (Math.Cos(x)/x)-(Math.Sin(x)/Math.Pow(x,2));
public double Gaussian(double x)
return Math.Pow(Math.E, Math.Pow(-x, 2));
public double DGaussian(double x)
return -2*x*Math.Pow(Math.E, Math.Pow(-x,2));
public double Bipolar(double x)
return x < 0 ? -1:1;
public double BipolarSigmoid(double x)
return (1-Math.Exp(-x))/(1+Math.Exp(-x));
public double DBipolarSigmoid(double x)
return 0.5 * (1 + BipolarSigmoid(x)) * (1 - BipolarSigmoid(x));
public double Scaler(double x, double min, double max)
return (x - min) / (max - min);
public enum ActivationType
Identity,
BinaryStep,
Logistic,
Tanh,
ArcTan,
ReLU,
PReLU,
ELU,
SoftPlus,
BentIdentity,
Sinusoid,
Sinc,
Gaussian,
Bipolar,
BipolarSigmoid
不确定我的数学是否正确，所以我没有将其发布为答案。 如果有人愿意进行错误检查，我可以将其作为答案。
【问题讨论】：
我尝试过这个，但不确定我是否正确翻译了所有数学...我现在应该将其作为答案发布吗？ 如果它有效，它就是一个答案。如果这只是一次尝试，但您不知道它是否有效，则可以编辑“展示您的努力”类别中的问题。 DReLU 应该是x < 0 ? 0 : 1;
【参考方案1】：
我发现了这个：Soft Exponential activation function
C# 转换：
public double SoftExponential(double x, double alpha = 0.0, double max_value = 0.0)
// """Soft Exponential activation function by Godfrey and Gashler
// See: https://arxiv.org/pdf/1602.01321.pdf
// α == 0: f(α, x) = x
// α > 0: f(α, x) = (exp(αx)-1) / α + α
// α< 0: f(α, x) = -ln(1 - α(x + α)) / α
// """
if (alpha == 0)
return x;
else if (alpha > 0)
return alpha + (Math.Exp(alpha * x) - 1.0) / alpha;
else
return -Math.Log(1 - alpha * (x + alpha)) / alpha;
【讨论】：
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