Width-Independent Compressibility of Deep Neural Networks

Abstract: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 technique which is aware of the low-dimensional input, and a layer-wise reweighting that preserves the input-output mapping.

Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Information Theory (cs.IT)

arXiv:2608.21752 [cs.LG]

(or arXiv:2608.21752v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.21752 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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