Width-Independent Compressibility of Deep Neural Networks
It has long been known that well-trained neural networks can be compressed very strongly without affecting their performance, an important phenomenon that remains poorly understood. We prove a uniform compressibility theorem for deep multilayer perceptrons with analytic activations. For a deep, wide fixed teacher network, there exists a narrow (same depth) network that approximately represents the same function as the original. The reachable compressed width is strikingly independent of the original width, but is $O((\log(1/\varepsilon))^{d_{in}})$, where $\varepsilon$ is the error budget and $d_{in}$ is the effective input dimension. Our construction involves a novel derivative-matching ...
| Authors | Hong-Yi Wang, Mingze Wang, Liu Ziyin |
|---|---|
| Primary category | cs.LG |
| Published | 22 August 2026 |
| Last updated at source | 22 August 2026 |
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