High-probability guarantees for linear accessibility in feature superposition
Quick summary
arXiv:2609.09556v1 Announce Type: cross 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 approxim
Key takeaways
- arXiv:2609.09556v1 Announce Type: cross 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 approxim
Why it matters
This development shows AI moving deeper into everyday software. Productivity potential should be weighed against price, data permissions, exportability and the preservation of human control.
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