High-probability guarantees for linear accessibility in feature superposition

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.

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Information Retrieval (cs.IR); Machine Learning (cs.LG); Probability (math.PR)

arXiv:2609.09556 [stat.ML]

(or arXiv:2609.09556v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.09556 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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