arXiv:2610.17588v1 Announce Type: cross Abstract: Muon controls weight updates through the RMS movement of a linear layer's output. This implicitly treats the linear output as a proxy for the full mo...
The paper proposes a new update geometry for the language‑model head by treating the head and softmax as a single module and using Hilbert’s projective distance to measure functional change. It replaces the spectral norm with the Euclidean row diameter, derives a tractable RowNorm update rule, and demonstrates that RowNorm substantially reduces step diameters and Hilbert perturbations while only slightly increasing validation loss.
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
arXiv:2610.02705v1 Announce Type: cross Abstract: The Muon optimizer derives its update rule for hidden linear layers by solving a local linearization of the loss penalized by the spectral norm, moti...
The paper introduces a data‑driven criterion that dynamically selects optimal Linear Minimization Oracle (LMO) geometries for each layer of a deep neural network, bridging the gap between SGD and Muon updates. By deriving the criterion from gradient and activation statistics via a single‑step random feature regression surrogate, the authors enable a design space that interpolates between existing optimizers, including SGD, Muon, Adam, and MuAdam. The adaptive approach incurs only about a 3% runtime overhead and demonstrates competitive or superior performance compared to the best static optimizer across three training scenarios.
arXiv:2507. 07814v2 Announce Type: replace Abstract: We introduce a novel upper bound on the local Lipschitz constant of the dot-product self-attention block showing its dependence on the attention map distributions.
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
The paper introduces MuonGS, a variant of the Muon optimizer that employs Gram–Schmidt projection to remove the radial component of updates, thereby controlling weight norm growth without fixing it. By ensuring the weight norm grows at most proportionally to √{t}, MuonGS achieves a cumulative effective learning rate of ≥√{T} and an O(T^{-1/2}) stationarity guarantee for smooth scale‑invariant objectives. Experiments on 160M‑ and 400M‑parameter dense models and a 135M‑active/1B‑total MoE model show MuonGS attains lower validation perplexity than MuonH and an estimated token‑equivalent speedup of up to ~15% at matched validation loss.
arXiv:2512. 11784v2 Announce Type: replace Abstract: Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis.
Full attention exposes every token pair, whereas kernel attention compresses a sequence into a fixed-dimensional sketch. We show that this distinction becomes exponential at the first context length containing two competing candidates.
The paper introduces two novel attention operators derived from generalized statistical entropies. The Kaniadakis entropy yields a full-support normalization with algebraically decaying weights, while the Abe entropy produces an implicit reciprocal-symmetric operator. The authors analyze these operators through a Fisher-metric Lagrangian framework, compare them to Softmax and entmax, and provide a tangent-gradient test to distinguish changes in attention profiles from mere scaling effects.
arXiv:2607. 23050v1 Announce Type: new Abstract: Neural scaling laws describe how loss decreases as models, data, and compute grow, but they do not answer a prior question: for a fixed task, what is the minimum model capacity required to solve it?