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.
This work proposes a curvature-conditioned multiscale momentum method with sphere constraints, which significantly accelerates Muon across diverse architectures (dense, MoE) and model sizes (0.12B--2.3B parameters).
Shuchen Zhu, Yu-Xin Fang, Mingze Wang et al.· 0 citations
This work presents a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure, and proposes three lightweight and complementary improvements to scale vectors: branch-specific heterogeneity, improved placement around linear mappings, and magnitude-direction reparameterization.
This work proposes Mixture of Activations (MoA), a token-adaptive FFN design that mixes a dictionary of activation functions using lightweight input-dependent gates while sharing the same linear projections, suggesting that token-adaptive activation mixing is a simple and effective mechanism for improving FFN expressivity in LLMs.
