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Equation 10 · Part 2 · A History of Small and On-Device AI

Symbol z_i

qi=exp⁡(zi/T)∑jexp⁡(zj/T)q_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)}
ziz_i

What this part means

the teacher’s pre-softmax logits.

Its job in the formula

ziz_i occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

where ziz_i are the teacher’s pre-softmax logits.

The passage around this formula

…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 : qi=exp⁡(zi/T)∑jexp⁡(zj/T)q_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)}. where ziz_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 precisely that softness — the relative probabilities the teacher assigns to the wrong answers, not only the single correct label — that carries…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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