Ask what should change when the equation is manipulated, then use the linked notebook demo to test that expectation.
Foundation Lab
Knowledge Distillation: Learning from Teachers
How you get small models from large ones—DistilBERT is 40% smaller, 60% faster, 97% of performance
#62DistillationEfficiency
key equation
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"
Use the linked notebook demo, this key equation, and canonical papers as separate witnesses for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
This atlas page has no local demo; the domain notebook carries the interactive witness and the fuller Intuition -> Math -> Code -> Demo sequence.
Why It Matters for Modern Models
- 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 Tutorials Skip
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
Visualization Status
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation here and the linked notebook demo. Come back here for the full walkthrough.
Key Equation
Train a student to match a teacher 's soft predictions:
Use temperature to soften teacher outputs:
Higher → more uniform → more information about relative similarities.