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Equation 6 · Part 2 · Comparing the Main Approaches to Training Data and Synthetic Data

Symbol λ

Ldistill=(1−λ) LCE(y, σ(zs))+λ T2 DKL(σ(zt/T) ∥ σ(zs/T))\mathcal{L}_{\mathrm{distill}} = (1-\lambda)\,\mathcal{L}_{\mathrm{CE}}(y,\, \sigma(z_s)) + \lambda\, T^2 \, D_{\mathrm{KL}}\big(\sigma(z_t/T) \,\|\, \sigma(z_s/T)\big)
λ\lambda

What this part means

λ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

λ is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Distillation is the oldest of the five and the easiest to state precisely. A student model is trained not on hard labels but on a teacher’s softened output distribution, on the reasoning that the relative probabilities the teacher assigns to wrong answers carry information a one-hot label discards entirely [ 1 ] . Where logits are unavailable — the ordinary case when the teacher is a closed API — the same idea is applied at one remove: the teacher’s sampled text stands in for its distribution, and the student is trained on that text directly. Writing ztz_t and zsz_s for teacher and student logits, σ\sigma for the softmax, y for the hard label, and T for a softening temperature, the canonical…

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