# Softmax It is often used as the last activation function of a neural network to normalize the output of a network to a probability distribution over predicted output classes. Softmax is an activation function that scales numbers/logits into probabilities. The output of a Softmax is a vector (say `v`) with probabilities of each possible outcome. The probabilities in vector `v` sums to one for all possible outcomes or classes. Mathematically, Softmax is defined as, $$ S(y)*i = \frac{exp(y\_i)}{\sum*{j=1}^n exp(y\_j)} $$ ### **Example** Consider a CNN model which aims at classifying an image as either a dog, cat, horse or cheetah (4 possible outcomes/classes). The last (fully-connected) layer of the CNN outputs a vector of logits, L, that is passed through a Softmax layer that transforms the logits into probabilities, P. These probabilities are the model predictions for each of the 4 classes. ![Image for post](https://miro.medium.com/max/781/1*KvygqiInUpBzpknb-KVKJw.jpeg) Let us calculate the probability generated by the first logit after Softmax is applied, $$ exp(3.2)=24.5325, exp(1.3) = 3.6693, exp(0.2)=1.2214, exp(0.8)=2.2255 $$ Therefore, $$ S(3.2) = \frac{exp(3.2)}{exp(3.2)+exp(1.3)+exp(0.2)+exp(0.8)} = 0.775 $$ And similar for softmax of 1.3, 0.2, and 0.8 {% embed url="" %} --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://ai.nuhil.net/deep-learning/softmax.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.