Equation 4 · Comparing the Main Approaches to Training Data and Synthetic Data
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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 and for teacher and student logits, for the softmax, y for the hard label, and T for a softening temperature, the canonical…
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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 and for teacher and student logits, for the softmax, y for the hard label, and T for a softening temperature, the canonical objective blends the two signals:
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