Softmax activation function is used as an activation function for models using neural networks in applied ML-machine learning. What it does is that in N values network configurations classification tasks having N classes as the output,  the softmax function normalizes outputs by assigning probabilities to the sum of weighted values such that the sum of probabilities is equal to1. Thus each class has its own probability distribution in the class membership. The Softmax function can then be described as the mathematical function converting the output into probability vector numbers from the input vector numbers with each vector value’s probabilities proportional to its relative value vector scale.

  1. Predicting Probabilities in Neural Networks
  2. Softmax Activation Functions

1. Predicting Probabilities in Neural Networks

Problems in predictive modelling use models of neural networks to classify the model where the given input is to be assigned a class-label by predicting the class membership probability. The binomial probability distribution is used for binary classification problems using a single node network output layer where the output probability is expected to be class 1. Multinomial probability is used for multi-class classification problem using every class represented by a node in the output layer, and the sum of predicted probabilities is equal to one.

All neural networks/softmax neural networks thus need activation functions for making predictions. The different activation functions are:

  • Linear Activation Function: This method uses node linear activation or node weighted values input and is called the “no activation function” due to the lack of transformation. Its likelihood or probability lies between 1 and 0. And it can output numeric values since no transformation occurs. This leads it to fail when used with multinomial or binomial probability cases.

Sigmoid Activation Function: This activation function is used to predict class membership probabilities and is also known as the logistic function because of its S-shaped characteristic output curve between values of 1 and 0 with the mid or vertical value of 0.5. Thus mapping is easy as the input’s weighted sum is approximated to 1.0, and negative input values mapped to the 0-values. It is widely used for outputs where the binary classification problem activation functions output is always a non-mutually exclusive Binomial probability distribution. Hence the function is called a multi-label and not a multi-class activation function. It fails with the multinomial probability distribution of mutually-exclusive classes in multi-class classification problems where the Softmax activation function is used as an alternate activation function.

Softmax, Argmax and Max functions: 

  • Max Function: This is so-called as it is the maximum mathematical function or max function in python for a list of numeric values that outputs the largest numeric value. It is implemented in Python using the max in list python /max() Python function for Softmax activation function.
  • Argmax Function: This function is also called “arg max,” or argmax mathematical function outputs the list’s index having the largest numeric value and is a Max function meta version that points out the value and position in the index list. It is implemented in Python using the argmax() NumPy function for the Softmax activation function.
  • Softmax Function: The Softmax function is the softer or more probabilistic version of the Max Function. Here the largest input value produces an output of the softmax function with value 1 while all other values of the input units have an output value of zero using the weighted model. To represent the probability of the argmax function with likelihoods, the values are scaled and transformed into probabilities. The sum of all values in the returned being equal to one and using the exponential values model. It can also be implemented in Python using the softmax() NumPy function for the Softmax activation function.

2. Softmax Activation Functions

Neural network models predicting data from a probability distribution that is multinomial over an n values discrete variable, use the Softmax activation function for the output layer activation function. Softmax is typically used as the activation function when 2 or more class labels are present in the class membership in the classification of multi-class problems.

It is also a general case of the sigmoid function when it represents the binary variable probability distribution. It works well where the model must internally weigh or choose multiple inputs in the concatenation softmax layers of a bottleneck and can be used as the activation function of the neural networks hidden layers. Another uncommon use of the softmax classifier is that it can be used for switching and the 3-class classification in the Keras deep-learning library.

The Softmax activation function working on the output layer node will output 1value per node, which are the probabilities with sum value-adding to 1. When using classification problems with multi-classes, the target variable with class labels is encoded from the first label, and data must be prepared for modelling. One-hot encoded means that the softmax activation output is a class label probabilistic representation of the integer/label encoded target variables.

Vectors are assigned for the position of the class label with values of zero for impossible events and 1 for certain ones. This example shows the supervised learning and correction of the probability distribution in the softmax activation function formula model containing multinomial values, using estimated values. The cross-entropy loss function is the error between the predicted and expected probability distributions. When reconverting these distributions to the class label with integer-codes, one uses the argmax() function.


Discussed above are some of the neural networks’ softmax activation functions, and what is softmax? Since Sigmoid and Linear activation functions do not cope well with tasks requiring multi-class classification, Softmax is used. It is a variant of the argmax function and outputs the largest value index in any list. It is implemented in Python and converts into a class label using the neural network model’s output.

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