Temperature scaling ($q_k=\exp (z_k/T)/{\sum }_j\exp (z_j/T)$)

Temperature scaling is a method of probability calibration that divides a model's neural network logits by one fitted positive scalar before applying the softmax function. The temperature is selected after model training, using labels in a held-out validation set to minimize the negative log-likelihood. It adjusts reported probabilities without retraining all model weights.^[ref]

For class scores $z_1,\dots ,z_K$ and $T>0$,For the synthetic two-class scores $(2,0)$, the first-class probability isThe selected class remains the first while its reported confidence decreases.

The preservation of the selected class follows directly: dividing by positive $T$ preserves every score ordering and equality, and exponentiation is strictly increasing. Thus the set of classes attaining the largest score is unchanged. This concerns ordering between classes within one example; it does not assert preservation of confidence ordering between different examples.

A motivating measurement in the original study compares reliability diagrams for a 110-layer image-classification network. Its reported expected calibration error changes from $12.67\%$ before calibration to $0.96\%$ after temperature scaling. This is a result for that experimental setup and binned metric, not a guarantee for every classifier or input distribution.^[ref]

Use separate data for fitting the temperature and for final evaluation. One scalar can improve an overall confidence mismatch but cannot represent every class-specific or input-dependent error. The name refers to this probability transformation; no physical temperature is being measured.