Foundation Lab

Knowledge Distillation: Learning from Teachers

How you get small models from large ones—DistilBERT is 40% smaller, 60% faster, 97% of performance

Concept 62 of 100EfficiencyPhase 6

#62DistillationEfficiency

key equation\mathcal{L} = \alpha \mathcal{L}_{KL}(S(x), T(x)) + (1-\alpha) \mathcal{L}_{CE}(S(x), y)

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 62 of 100DistillationEfficiency / Phase 6: Modern efficiency & inference

Current question

Hard labels say "cat, not dog"; soft labels say "mostly cat, a bit dog, definitely not car"

\mathcal{L} = \alpha \mathcal{L}_{KL}(S(x), T(x)) + (1-\alpha) \mathcal{L}_{CE}(S(x), y)

PredictionCommit before the demo.

Ask what should change when the equation is manipulated, then let the visualization test that expectation.

EvidenceCompare local witness and source.

Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.

InvariantName what survives notation changes.

The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.

Next moveContinue in the newer notebook.

This atlas page keeps the working demo; the domain notebook carries the fuller Intuition -> Math -> Code -> Demo sequence.

How you get small models from large ones—DistilBERT is 40% smaller, 60% faster, 97% of performance
Soft targets contain "dark knowledge": teacher's uncertainty about similar classes
Modern LLM training uses distillation: smaller models trained on larger model outputs

What is still poorly explained in textbooks and papers:

Hard labels say "cat, not dog"; soft labels say "mostly cat, a bit dog, definitely not car"
Temperature τ controls how much dark knowledge transfers: τ→∞ means uniform (no info)
Distillation works even when student has different architecture than teacher

If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.

Key Equation

\mathcal{L} = \alpha \mathcal{L}_{KL}(S(x), T(x)) + (1-\alpha) \mathcal{L}_{CE}(S(x), y)

Train a student $S$ to match a teacher $T$ 's soft predictions:

\mathcal{L} = (1-\alpha) \mathcal{L}_{CE}(S(x), y) + \alpha \mathcal{L}_{KL}(S(x), T(x))

Use temperature $\tau$ to soften teacher outputs:

p_i^T = \frac{\exp(z_i^T / \tau)}{\sum_j \exp(z_j^T / \tau)}

Higher $\tau$ → more uniform → more information about relative similarities.

Hinton, Vinyals, Dean2015NIPS Workshop

Sanh et al.2019arXiv

Choose the next question to carry this object forward.