Neural Network Lab Neural Network Activation Functions in C James McCaffrey explains what neural network activation functions are and why they’re necessary, and explores three common activation functions. This article describes what neural network activation functions are, explains why activation functions are necessary, describes three common activation functions, gives guidance on when to use a particular activation function, and presents C implementation details of common activation functions. The best way to see where this article is headed is to take a look at the screenshot of a demo program in Figure visual studio 2013 activator. The demo program creates a visual studio 2013 activator connected, two-input, two-hidden, two-output node neural network. After setting the inputs to 1.
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Neural Network Lab Neural Network Activation Functions in C James McCaffrey explains what neural network activation functions are and why they’re necessary, and explores three common activation functions. This article describes what neural network activation functions are, explains why activation functions are necessary, describes three common activation functions, gives guidance on when to use a particular activation function, and presents C implementation details of common activation functions.
The best way to see where this article is headed is to take a look at the screenshot of a demo program in Figure 1. The demo program creates a fully connected, two-input, two-hidden, two-output node neural network. After setting the inputs to 1. The activation function demo. The demo program illustrates three common neural network activation functions: Using the logistic sigmoid activation function for both the input-hidden and hidden-output layers, the output values are 0.
The same inputs, weights and bias values yield outputs of 0. And the outputs when using the softmax activation function are 0. This article assumes you have at least intermediate-level programming skills and a basic knowledge of the neural network feed-forward mechanism. The demo program is coded in C , but you shouldn’t have too much trouble refactoring the code to another language if you wish. To keep the main ideas clear, all normal error checking has been removed. The Demo Program The entire demo program, with a few minor edits, is presented in Listing 1.
To create the demo, I launched Visual Studio any recent version will work and created a new C console application program named ActivationFunctions. After the template code loaded, I removed all using statements except the one that references the System namespace.
In the Solution Explorer window I renamed the file Program. Listing 1. Activation demo program structure. WriteLine “Begin neural network activation function demo” ; Console.
WriteLine “Setting inputs to 1. SetInputs inputs ; Console. WriteLine “Setting input-hidden weights to 0. WriteLine “Setting input-hidden biases to 0. WriteLine “Setting hidden-output weights to 0. WriteLine “Setting hidden-output biases to 0. SetWeights weights ; Console. WriteLine “Computing outputs using Log-Sigmoid activation” ; dnn.
ComputeOutputs “logsigmoid” ; Console. Write dnn. WriteLine dnn. ToString “F4” ; Console. WriteLine “Computing outputs using Hyperbolic Tangent activation” ; dnn. ComputeOutputs “hyperbolictangent” ; Console. WriteLine “Computing outputs using Softmax activation” ; dnn. ComputeOutputs “softmax” ; Console. WriteLine “Softmax NN outputs are: WriteLine “End demo” ; Console.
WriteLine ex. Message ; Console. CopyTo this. Exp hoSum1 – max ; return Math. You should be able to determine the meaning of the weight and bias class members. For example, class member ihWeights01 holds the weight value for input node 0 to hidden node 1. Member hoWeights10 holds the weight for hidden node 1 to output node 0.
Member ihSum0 is the sum of the products of inputs and weights, plus the bias value, for hidden node 0, before an activation function has been applied. Member ihResult0 is the value emitted from hidden node 0 after an activation function has been applied to ihSum0. The computations for the outputs when using the logistic sigmoid activation function are shown in Figure 2.
For hidden node 0, the top-most hidden node in the figure, the sum is 1. Notice that I use separate bias values rather than the annoying to me, anyway technique of treating bias values as special weights associated with a dummy 1. The activation function is indicated by F in the figure. After applying the logistic sigmoid function to 0. This value is used as input to the output-layer nodes. Logistic sigmoid activation output computations.
The Logistic Sigmoid Activation Function In neural network literature, the most common activation function discussed is the logistic sigmoid function. The function is also called log-sigmoid, or just plain sigmoid. The function is defined as: The log-sigmoid function accepts any x value and returns a value between 0 and 1. Values of x smaller than about return a value very, very close to 0.
Values of x greater than about 10 return a value very, very close to 1. The logistic sigmoid function. Because the log-sigmoid function constrains results to the range 0,1 , the function is sometimes said to be a squashing function in neural network literature. It is the non-linear characteristics of the log-sigmoid function and other similar activation functions that allow neural networks to model complex data. The demo program implements the log-sigmoid function as: Although compilers are now much more robust, it’s somewhat traditional to include such boundary checks in neural network activation functions.
The Hyperbolic Tangent Activation Function The hyperbolic tangent function is a close cousin to the log-sigmoid function. The hyperbolic tangent function is defined as: When graphed, the hyperbolic tangent function looks very similar to the log-sigmoid function. Most modern programming languages, including C , have a built-in hyperbolic tangent function defined.
The demo program implements the hyperbolic tangent activation function as: For example, the demo program output values when using the softmax activation function are 0. The idea is that output values can then be loosely interpreted as probability values, which is extremely useful when dealing with categorical data. The softmax activation function is best explained by example. Consider the demo shown in Figure 1 and Figure 2.
The pre-activation sums for the hidden layer nodes are 0. First, a scaling factor is computed: A naive implementation of the softmax activation function could be: Exp hoSum1 ; else throw new Exception “Unknown layer” ; return Math. Listing 2. Implementation relying on properties of the exponential function. There are a few guidelines for choosing neural network activation functions.
If all input and output data is numeric, and none of the values are negative, the log-sigmoid function is a good option. For numeric input and output where values can be either positive or negative, the hyperbolic tangent function is often a good choice.
In situations where input is numeric and the output is categorical, such as a stock recommendation to sell, buy or hold, using softmax activation for the output layer and the tanh function for the hidden layer often works well.
Data analysis with neural networks often involves quite a bit of trial and error, including experimenting with different combinations of activation functions. There are many other activation functions in addition to the ones described in this article. The Heaviside step function can be defined as: In my experience, the step function rarely performs well except in some rare cases with 0,1 -encoded binary data.
Another activation function you might come across is the Gaussian function. The function is also called the “normal distribution. Small and large values of x return 0.
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