anthology-of-the-sota

LIT-525: Transformers Learn Low Sensitivity Functions: Investigations and Implications

2 min read

Properties4
StatusActive
Tagsanalysis-and-evaluation, model-architecture, model-stability
Cited as “paper” byNOTE-271 — One metric that separates transformers from every other architecture, and what it buys
Cited as “source” byTHEORY-064 — Transformers are biased toward low-sensitivity functions, and that bias is what their robustness is made of

Graph View

Vasudeva, Fu, Zhou, Kau, Huang and Sharan (2024) — ARXIV-2403.06925, ICLR 2025. Read as NOTE-271.

Key takeaways

  • One metric, and it separates architectures. Sensitivity — how likely the output is to change under random token-wise perturbation of the input — is lower for transformers than for MLPs, CNNs, ConvMixers and LSTMs, across both vision and language, at matched training accuracy.
  • It has a pedigree. On Boolean inputs, sensitivity relates to the degree of the representing multilinear polynomial and to decision-tree size, so low sensitivity is a form of simplicity bias. The paper proves the low-sensitivity bias of transformers in the NTK regime via spectral bias, and proves low sensitivity implies better robustness.
  • It is actionable. Regularizing for low sensitivity improves robustness further, on CIFAR-10-C.
  • It tracks flatness, connecting an inductive-bias statement to the loss-landscape literature.
  • It moves during a grokking plateau. On modular addition, sensitivity falls while the training loss does not, which makes it a progress measure.

Standing in the anthology

It answers a question the record poses and cannot currently answer. THEORY-041, SOTA-012 and THEORY-035 all circle what distinguishes transformer training from everything else, in terms of conditioning and sharpness. This offers a single scalar that is architecture-comparable, cheap, and defined on the function rather than on the weights.

Its grokking result belongs beside SOTA-200. That practice says to check whether an emergent capability is a metric artefact, and cites the reverse-engineering of one network to recover the continuous progress under its discontinuity. Sensitivity is a candidate progress measure that needs no reverse engineering and is defined for any architecture. The record does not fold it into the practice, because it is demonstrated on one synthetic task.

Filed for the metric, not the ranking. “Transformers beat CNNs on robustness” is a comparison the record has no use for. That a single computable quantity predicts robustness, tracks flatness and moves during a plateau is the reason this is here.

Backlinks