Scores, softmax and confidence AI

Why a high displayed probability is not the same as demonstrated reliability.

A classifier first produces scores, also called logits. Softmax converts them into positive values that sum to one:

$$p_k=\frac{\exp(s_k)}{\sum_j\exp(s_j)}.$$

For two scores $[2,1]$, the probabilities are approximately $[0.731,0.269]$. Adding the same constant to both scores leaves these probabilities unchanged. The PyTorch softmax definition describes this normalization.

In these reports, the largest probability determines the displayed prediction. The true-class curve instead tracks the probability assigned to the recorded label, which may not be the predicted class. It is a window- or image-specific value, while the dashed accuracy curve aggregates the validation set.

A value of 90% is a model output, not a measured guarantee of being correct 90% of the time. Neither pilot calibrates probabilities. Scores can change substantially while the winning class stays the same, so probability and accuracy curves need not have the same shape.

Explore the neural-network demo.