logits

Logits are the raw, unnormalized scores produced by a classifier before a normalization step such as softmax. In binary classification, a single logit z corresponds to the log-odds of the positive class: p = sigmoid(z) = 1/(1+exp(-z)); equivalently z = log(p/(1-p)). In multi-class classification with K classes, the model outputs a vector z in R^K of logits. The predicted class probability is obtained by applying the softmax function: p_i = exp(z_i) / sum_j exp(z_j). The logits therefore encode relative evidence for each class; only their relative values matter for the final decision, while probabilities are obtained after normalization.

From a training perspective, using logits directly with cross-entropy loss is common: the loss computes the negative log-likelihood of the true class given the softmax of the logits. Numerically stable implementations often combine softmax and cross-entropy, or apply log_softmax to produce log-probabilities. Negative or positive values are both common, and the scale of logits can affect training dynamics, but only their relative differences influence outcomes. In neural networks, logits are typically the output of the final linear layer before a softmax (or sigmoid) activation.

Important distinctions include that logits are not probabilities themselves; they are real-valued scores. They can be interpreted as log-odds in the binary case and as unnormalized log-probabilities in the multiclass case.