Notes by Lex Toumbourou

The Softmax Activation Function converts a vector of numbers into a vector of probabilities that sum to 1. It's applied to a model's outputs (or Logits) in Multi-class Classification.

It is the multi-class extension of the Sigmoid Activation Function.

The equation is:

$\sigma(\vec{z})_{i} = \frac{e^{z_i}}{\sum\limits_{j=1}^{K}e^{z_j}}$

The intuition for it is that $e^{x_i}$ is always positive and increases fast, amplifying more significant numbers. Therefore, it tends to find a single result and is less useful for problems where you are unsure if inputs will always contain a label. For that, use multiple binary columns with the Sigmoid Activation Function.

Howard et al. (2020) (pg. 223-227)

Code example:

import numpy as np, pandas as pd

def softmax(x):
    return np.exp(x) / np.exp(x).sum()

logits =  np.array([-3.5, -2.37, 1.54, 5.23]) # some arbitrary numbers I made up that could have come out of a neural network
probs = softmax(logits)

pd.DataFrame({'logit': logits, 'prob': probs}, index=['woman', 'man', 'camera', 'tv'])

Softmax is part of the Categorical Cross-Entropy Loss, applied before passing results to Negative Log-Likelihood function.

Backlinks

• Categorical Cross-Entropy Loss
• Negative Log-Likelihood