Geometric Limits of Knowledge Distillation: A Minimum-Width Theorem via Superposition Theory
Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width $d_S$ can encode at most $d_S \cdot g(α)$ features, where $g(α) = 1/((1-α)\ln\frac{1}{1-α})$ is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure $F \approx 28{,}700$ features at $α\...
| Authors | Nilesh Sarkar, Dawar Jyoti Deka |
|---|---|
| Primary category | cs.LG |
| Published | 5 April 2026 |
| Last updated at source | 7 April 2026 |
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