The Competition for Deeper Architectures at Test Time
stochasticchasm · x · 2026-07-18
The post praises a cleverly designed problem setting using modular arithmetic: framing the task as recursive modular exponentiation, similar to the highly serial dependency problems found in cryptography courses.
The quoted section introduces an optimizer × architecture competition called "One Layer Deeper." The goal is to test whether models can run "deeper" during inference than during training, and whether training requires better optimizers to maintain stability when depth becomes a recurrent structure. The core example is $y=x^{2^T} \bmod N$, where each squaring step depends on the previous one. A standard Transformer, having a fixed depth, will fail when $T$ exceeds its serial computation capacity in a single forward pass, emphasizing the critical role of architectural inductive bias.
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