What does this equation mean?

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 $z_t$ and $z_s$ for teacher and student logits, $\sigma$ for the softmax, y for the hard label, and T for a softening temperature, the canonical objective blends the two signals: $\mathcal{L}_{\mathrm{distill}} = (1-\lambda)\,\mathcal{L}_{\mathrm{CE}}(y,\, \sigma(z_s)) + \lambda\, T^2 \, D_{\mathrm{KL}}\big(\sigma(z_t/T) \,\|\, \sigma(z_s/T)\big)$. 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 produces ever feeds back into it. There is no loop to compound and no possibility of the drift that shows up when a model is fitted repeatedly to its own unfiltered output.