arXiv:2606. 13276v1 Announce Type: cross Abstract: Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices.
Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices. In this work, we ask whether different transformer modules prefer different manifold geometries.
arXiv:2606. 27449v1 Announce Type: new Abstract: Multi-head attention conventionally partitions the hidden dimension equally across all heads at every layer, enforcing an identical representational subspace dimension (dh = dmodel/h) throughout the models depth.
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.
arXiv:2602. 18948v2 Announce Type: replace Abstract: Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively.
arXiv:2608. 02064v1 Announce Type: new Abstract: Feed-forward networks (FFNs) account for a large fraction of Transformer parameters, yet their hidden width is usually constant across depth.
arXiv:2609.15975v1 Announce Type: cross Abstract: Transformer representations evolve through learned additive transformations that either preserve their current direction or redirect it. We study thi...
arXiv:2602.15239v3 Announce Type: replace Abstract: Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for...
arXiv:2607. 18130v1 Announce Type: new Abstract: Most parameter-efficient finetuning (PEFT) methods adapt weights or activations, thus leaving one of the key Transformer components unchanged: residual connections.
arXiv:2608. 01283v1 Announce Type: new Abstract: All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al.
The paper investigates why adaptive optimizers like Adam outperform SGD when fine‑tuning Transformers. It introduces gradient heterogeneity—the variation in gradient norms across parameter blocks—and shows, both theoretically and experimentally, that this heterogeneity, together with Hessian heterogeneity, hampers SGD convergence while sign‑based methods such as SignSGD are less affected. The study links the source of gradient heterogeneity to layer‑normalization placement, finding that Post‑LN architectures exhibit the strongest effect, and uses SignSGD as a tractable proxy to analyze Adam‑like behavior and learning‑rate scaling.
arXiv:2609.07086v1 Announce Type: new Abstract: Transformers are a dominant architecture in modern machine learning, powering applications across vision, language, and beyond. At the core of their su...
arXiv:2606. 17830v1 Announce Type: cross Abstract: Neural network parameter spaces are inherently non-injective, as distinct parameter configurations can realize identical functions through functional equivalence.