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Equation 10 · Part 11 · A History of Small and On-Device AI

Starting index or lower bound: j

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

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

j occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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 : 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…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.