The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.
By Ruoxi Yu, Haotian Jiang, Jingpu Cheng, Penghao Yu, Qianxiao Li, Zhong Li
arXiv:2608.30720v1 Announce Type: new
Abstract: Representational similarity is foundational to analyses of deep networks, yet distances between point-valued representations are not intrinsically tied...
By Kieran Murphy
arXiv:2609.16537v1 Announce Type: cross
Abstract: Transformers and state-space models (SSMs) are the two dominant families of sequence models, and a central open question is how far the analytical kn...
By Istabrak Abbes, Nizar Islah, Irina Rish, Sarath Chandar
The paper discusses how backpropagation enables deep learning but does not inherently organize parameters for reusable functional components, leading to weight entanglement where overlapping parameter sets hinder independent modification. It introduces weight operators—parameterized modules that can be composed at inference—to address this, proposing a two-stage learning process that first infers operator composition and then updates only the selected operators. Vector Networks (VNs) are presented as an implementation that couples operator selection to local error-driven updates, demonstrating that learned operators can be recombined in unseen ways while keeping updates confined to the relevant parameter sets.
By Giuseppe Chindemi, Benjamin F. Grewe
arXiv:2607. 13047v1 Announce Type: new Abstract: Parameter decomposition (PD) decomposes neural networks into interpretable computational components that faithfully reflect the original network's operations.
By Antoine Vigouroux, Lee Sharkey
arXiv:2606. 29256v1 Announce Type: cross Abstract: In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning.
By Peilin Liu, Ding-Xuan Zhou