Exact Scaling Laws for a Random-Features Bigram Model
Understanding neural scaling laws is increasingly important for theory and practice, yet first-principles explanations remain limited even in simple settings. In this work, we study capacity-limited scaling in a bottlenecked bigram model with power-law (Zipf) token statistics, viewed as an analytically tractable toy model of a large language model. Fixed random embeddings serve as a proxy for representational capacity and induce an explicit bottleneck of width, allowing us to derive scaling laws for prediction regret as a function of model width, vocabulary size, and the Zipf exponent. Our results complement recent theoretical accounts based on optimization dynamics by isolating scaling d...
| Authors | Julian Enoch, Elvis Dohmatob |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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