🤖 AI Summary
该研究通过压缩感知方法解决了神经网络中特征叠加导致的线性可访问性受限问题，证明了在次高斯噪声下所需维度线性增长。
📝 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.