C#中的激活函数列表

Question

我可以在数学中找到激活函数的列表，但无法在代码中找到。 如果有必要的话，我想这将是一个正确的地方来放置代码中的此类列表。 从这两个链接中开始翻译算法： https://en.wikipedia.org/wiki/Activation_function https://stats.stackexchange.com/questions/115258/comprehensive-list-of-activation-functions-in-neural-networks-with-pros-cons

目标是创建一个激活类（包括函数及其导数），通过用户界面轻松访问。

编辑：

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
}

我不确定自己的计算是否正确，因此没有将其发布为答案。 如果有人愿意检查错误，我可以将其作为答案。

- Rottjung

---

我做了一个尝试，但不确定我是否正确地翻译了所有的数学术语...现在我应该把它发布为答案吗？ - Rottjung

如果它能正常工作，那就是一个答案。如果只是尝试但不确定是否有效，那就是对问题的编辑，属于“展示你的努力”类别。 - Visual Vincent

DReLU 应该是 x < 0 ? 0 : 1;。 - The_Black_Smurf

Answer 1

I found this: 软指数激活函数 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;
}

- Rusty Nail