High-probability guarantees for linear accessibility in feature superposition — Paper

Abstract

Neural networks can leverage feature superposition to encode more concepts than dimensions, but cross-feature interference constrains the linear accessibility of simultaneously active features. By framing linear accessibility as a compressed sensing problem, we derive high-probability bounds for fixed supports under subgaussian noise, proving the sufficient dimension scales linearly ($d=O_{\varepsilon}(k \log m)$) rather than prior worst-case quadratic limits. We then validate these bounds across system parameters through Gaussian-tail approximations. These results quantify the geometric constraints of the linear representation hypothesis, providing a framework for evaluating sparse autoencoders, compositional generalization, and neural interpretability.

Authors 1

Enrico Vompa

Specification

Official page: arxiv.org/abs/2609.09556
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
arXiv id: 2609.09556
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Categories: stat.ML, cs.AI, cs.IR, cs.LG, math.PR
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
PDF: arxiv.org/pdf/2609.09556
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Primary category: stat.ML
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh

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9

Source tiers

T19

Freshest observation

2 h ago

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None

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Authors: Enrico Vompa

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Claim history · Abstract

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Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
Neural networks can leverage feature superposition to encode more concepts than dimensions, but cross-feature interference constrains the linear accessibility of simultaneously active features. By framing linear accessibility as a compressed sensing problem, we derive high-probability bounds for fixed supports under subgaussian noise, proving the sufficient dimension scales linearly ($d=O_{\varepsilon}(k \log m)$) rather than prior worst-case quadratic limits. We then validate these bounds across system parameters through Gaussian-tail approximations. These results quantify the geometric constraints of the linear representation hypothesis, providing a framework for evaluating sparse autoencoders, compositional generalization, and neural interpretability.	11 Sept 2026 21:03 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperHigh-probability guarantees for linear accessibility in feature superposition
New paper: High-probability guarantees for linear accessibility in feature superposition
arxiv
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.AI	feed	T1· Official	2 h ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.