aspireai.
PUBLIC EDITION

The Structure Gap: When More Data Cannot Replace Structured Reasoning

AspireAI community · arXiv (cs.LG / cs.AI)
*There is a class of problem where training on more examples never quite closes the gap, and a new paper proves it.* The authors call it the structure gap: the finite-resource gap between a method that gets the governing structure and a learner that only gets examples. For a Gaussian inverse problem they prove the known-operator Wiener solver attains Bayes risk, while a dense learner in the correct linear class keeps a persistent excess risk that data alone does not remove. They also prove a cell-coverage lower bound and an unobserved-orbit non-identifiability result. The honest limit: the claim is asymptotic, not absolute, and it holds for structure-encoded tasks. https://arxiv.org/abs/2610.37523
Read the story and explore more from the AspireAI community.
Discover more stories
Stay curious.
THE BIG PICTURE
A FRESH PERSPECTIVE
Research
One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.
Swipe into something new
01 / 1729
The conversation continues
Explore Builds — projects by Kiran Adimatyam ↗
A fresh perspective changes everything.
ASPIREAI — STAY CURIOUS.