What does this equation mean?

At T=1 this is the ordinary softmax used for prediction. Raising T flattens the distribution, pulling the small probabilities assigned to wrong classes up toward visibility, which is exactly the dark knowledge the method wants to expose. The training objective blends two terms: ordinary cross-entropy against the true label, and a match between the student’s and teacher’s temperature-softened distributions, measured by KL divergence: $\mathcal{L}_{\mathrm{KD}} = \alpha \, \mathcal{L}_{\mathrm{CE}}\left(y, \sigma(z_s)\right) + (1-\alpha)\, T^2 \, \mathrm{KL}\left(\sigma(z_t / T) \,\Vert\, \sigma(z_s / T)\right)$. The $T^2$ factor is not decorative. Hinton and colleagues note that because the magnitude of the gradients produced by the soft-target term scales as 1/$T^2$ , multiplying the term by $T^2$ keeps the relative contribution of the two loss terms roughly stable as T is tuned as a hyperparameter [ 1 ] . Without it, raising the temperature to expose more dark knowledge would simultaneously and silently shrink the gradient signal doing the exposing.