arXiv Machine Learning
Efficient Support Recovery of Mixtures of Sparse Linear Classifiers with Fewer Measurements
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Learning Positive Linear Combinations of ReLUs in Fully Polynomial Time
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Separating Oblivious and Adaptive Models of Variable Selection
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The Price of Sparsity: Sufficient Conditions for Sparse Recovery using Sparse and Sparsified Measurements
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Towards a mathematical theory of superposition
The paper develops a mathematical theory of superposition in neural networks using frame theory and compressed sensing. It shows that a sparse binary vector of active features can be encoded by an overcomplete dictionary and recovered via a ReLU operation with a suitable bias. The authors prove recovery theorems for both random-support and worst-case support settings, providing high-probability guarantees for low-coherence dictionaries and a sharp criterion for sparsity levels, with explicit results for Gaussian random matrices and equiangular tight frames.