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Equation 6 · Part 5 · Comparing the Main Approaches to Training Data and Synthetic Data

Symbol σ

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)
σ\sigma

What this part means

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

Its job in the formula

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

The passage around this formula

…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 objective blends the two signals: 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). The point of writing it out is the structure it exposes, not the arithmetic: the teacher term is fixed throughout training, so nothing the student…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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