Numerator: exp(z_i / T)

The passage around this formula

Hinton, Vinyals and Dean’s 2015 paper, “Distilling the Knowledge in a Neural Network,” is the one the field actually cites, and it earned that position by generalizing the 2006 idea and giving it a mechanism simple enough to fit into any neural network’s training pipeline. Instead of training a small model against a large model’s hard output labels, distillation trains it against the large “teacher” model’s full, softened probability distribution over classes — the softmax output computed at a raised temperature T : $q_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)}$. where $z_i$ are the teacher’s pre-softmax logits. “Using a higher value for T produces a softer probability distribution over classes” [ 4 ] , and it is…

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