Towards a mathematical theory of superposition
We develop a mathematical theory of superposition in neural networks using tools from frame theory and compressed sensing. In our model, a sparse binary vector \(x\) of active features is encoded through an overcomplete dictionary \(W\), and feature recovery is performed by applying \(\operatorname{ReLU}(W^\top W x+b)\) with an appropriate bias vector \(b\). We prove several recovery theorems for this model. In the random-support setting, we establish high-probability support recovery for nearly tight, low-coherence dictionaries, with guarantees when the expected sparsity is up to order \(d/\log n\). In the worst-case support setting, we give a sharp and computable criterion for which spa...
| Authors | Michael I. Ivanitskiy, John Jasper, Emily J. King et al. |
|---|---|
| Primary category | stat.ML |
| Published | 27 August 2026 |
| Last updated at source | 27 August 2026 |
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