Open Problem: Separating Geometric and Algorithmic Compression via Cayley-Table Completion
Modern statistical learning theory and deep learning characterize generalization primarily in terms of continuous capacity control (e.g., norm-based regularization, margin maximization, low-rank bias). While highly successful in continuous domains, deep learning consistently fails to extrapolate exact algorithmic or discrete algebraic rules, reflecting a missing inductive bias toward algorithmic complexity minimization. We propose the Cayley-table completion as the canonical testbed for this missing bias, serving as the discrete algebraic counterpart to matrix completion. Just as matrix factorization combined with weight decay yields an implicit geometric bias toward low linear rank, rece...
| Authors | Dongsung Huh |
|---|---|
| Primary category | cs.LG |
| Published | 28 May 2026 |
| Last updated at source | 28 May 2026 |
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