Temperature Scaling

Getting a classifier to be accurate is only half the story. When it says “90% confident,” you also want that to mean “it’s right about 9 times out of 10.” Temperature scaling is a simple way to fix overconfident or underconfident probability outputs without changing the model’s predicted class.

What it is (and what it changes)

Temperature scaling is a post-hoc calibration method for multi-class classifiers that output logits (the raw scores before softmax), such as neural networks. It introduces one learned scalar parameter T and rescales logits before converting them to probabilities:

p(y=k | x) = softmax(z_k / T)

If T > 1, the logits shrink and the predicted probabilities become less extreme (reducing overconfidence). If T < 1, probabilities become sharper (addressing underconfidence). Importantly, dividing all logits by the same T does not change which class has the largest probability, so accuracy stays the same; only the probability values change.

How it’s fit in practice

You fit T on a held-out validation set by minimizing negative log-likelihood (cross-entropy) using the model’s logits and true labels. This makes it lightweight and stable compared with more flexible calibrators. In PyTorch, it’s commonly implemented as a tiny wrapper module with one parameter optimized via LBFGS/Adam; conceptually it plays a similar role to scikit-learn’s probability calibration tools, but tailored to softmax logits.

Why it matters (real-world examples)

• Medical diagnosis: a “95%” cancer risk should correspond to real observed frequencies for safe triage decisions.
• Fraud detection: calibrated probabilities let you set thresholds based on expected cost, not gut feel.
• Churn prediction: reliable probabilities improve ranking, budgeting, and intervention planning.

Without calibration, a model can look great on accuracy yet produce probabilities that mislead downstream decisions, risk estimates, and threshold tuning.