Sigmoid Function#
Maps any real value to (0, 1), used for probabilities and gating.
Important
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What it is#
The sigmoid function \(\sigma\) maps any real number to the open interval (0, 1), tracing an S-shaped curve:
At \(z=0\) it returns 0.5; large positive \(z\) → near 1, large negative \(z\) → near 0.
Its role#
It is the inverse of the logit — it turns a log-odds score back into a probability — which makes it the output activation of logistic regression and of binary-classification output layers, and the basis of binary cross-entropy loss. Each output is an independent probability, so sigmoid also serves multi-label problems.
Watch out#
In the hidden layers of deep networks the sigmoid causes vanishing gradients (its slope flattens for large \(|z|\)), so ReLU-family activations are preferred there; sigmoid is kept for the output.
Theme: Model Training & Optimization · All terminology
Hint
Mind map — connected ideas
Log-Odds · Softmax Function · Squashing Function · Logistic Regression · Binary Classification · Classification Probability
Hint
More in Model Training & Optimization
Active Learning · Binary Cross-Entropy (BCE) · Deep Ensembles · Early Stopping · Ensemble · Epochs · FLOPs · Full Annotation · Hyperparameter · Label Noise · Log-Odds · Logit Space · Logits · Loss Functions
See also
Source article Adapted (context, re-expressed) in our own words from: Sigmoid Function (insightful-data-lab.com).