arXiv:2606. 18525v2 Announce Type: replace Abstract: We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition.
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arXiv:2606. 18525v1 Announce Type: new Abstract: We propose a hierarchical attention mechanism based on two-level overlapping Schwarz domain decomposition.
arXiv:2605. 08475v3 Announce Type: replace-cross Abstract: In this paper, we study in-context kernel ridge regression (KRR) with Gaussian kernels and show, both theoretically and empirically, that a standard softmax-attention transformer can approximate the KRR predictor during its forward pass.
arXiv:2607. 20214v1 Announce Type: cross Abstract: The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths.
arXiv:2609.21523v1 Announce Type: new Abstract: A system may be compressed before its downstream task is fully known. We ask how much retained state is then necessary and how much can be saved by lim...
The paper investigates the training dynamics of attention mechanisms in high-dimensional settings, focusing on attention-indexed models that encompass multi-layer and multi-head architectures. It shows that while the loss landscape can be described by a finite set of trace order parameters, the online stochastic gradient descent dynamics involve an infinite hierarchy of matrix moments that can be accurately approximated by a finite truncated system. The study further reveals that the choice of attention parameterization acts as an implicit bias: untied attention can get trapped in uninformative states, whereas tied attention induces symmetry breaking and enables weak recovery with θ(d² log d) samples, and untied attention exhibits a fast-slow dynamic leading to weak recovery when symmetry is broken.
The paper introduces low‑rank orthogonalization, a technique that exploits the low‑rank nature of gradients in neural network training to perform matrix orthogonalization more efficiently. Building on this, the authors present low‑rank matrix‑signed gradient descent (MSGD) and a low‑rank variant of the Muon optimizer, showing through experiments that low‑rank Muon matches or surpasses vanilla Muon on GPT‑2 and LLaMA pretraining, especially for larger models. Theoretical analysis provides iteration‑complexity bounds for both low‑rank MSGD and low‑rank Muon under heavy‑tailed noise.