arXiv Machine Learning

Stiefel Attention: When the Geometry of Transformer Projection Matrices Dominates Optimizer Choice---and When It Does Not

The paper introduces Stiefel Attention, which constrains the query and key projection matrices of transformers to the Stiefel manifold and optimizes them with a Riemannian Adam variant. It demonstrates that this approach yields steepest‑descent updates, is well‑conditioned, and preserves learned attention geometry during weight decay. Empirical results show significant accuracy gains on modular arithmetic grokking and CIFAR‑10 patches, with the improvement attributed to a step‑scale‑free update rule rather than equivariance or projector changes.

Hugging Face Trending Papers

Jun 28

Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks

A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable.

llms computer-vision

arXiv Machine Learning

Jun 30

Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks

arXiv:2606. 29176v1 Announce Type: new Abstract: A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation.

By Tejas Pradeep Shirodkar

llms computer-vision

arXiv AI

Aug 10

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers

arXiv:2608. 07436v1 Announce Type: new Abstract: Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head.

By Ali Janati, Kaoutar El Maghraoui, Andrei Kanavalau, Anass Belfatmi

llms rag safety

arXiv Machine Learning

Jul 7

Directional Curvature from Armijo Backtracking: A Low-Cost Sharpness Probe and a Calibration-Free Learning-Rate Safeguard for Adam

arXiv:2607. 03998v1 Announce Type: new Abstract: The local sharpness of the loss, the top Hessian eigenvalue $\lambda_1$, determines the largest stable gradient step, but measuring it normally requires Lanczos or Hessian-vector iterations.

By Ashmitha R, J\"org Frochte

benchmarks safety

arXiv AI

Jun 3

Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group

arXiv:2606. 03003v1 Announce Type: cross Abstract: A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\v{u} y\=i f\v{a}n s\=an).

By Hongbo Wang (Stony Brook University)

arXiv Machine Learning

Aug 18

Is Grokking a Loss of Normal Hyperbolicity of the Interpolation Manifold?

arXiv:2608. 14803v1 Announce Type: new Abstract: A recent line of work recasts the post-memorization phase of grokking as constrained optimization: once a network interpolates the training set, weight decay drives a slow drift along the zero-loss manifold toward lower norm.

By Suvinava Basak

arXiv Machine Learning

Aug 6

The Loss Does Not See the Basis, but Adam Does

arXiv:2608. 05136v1 Announce Type: new Abstract: Gradient descent on a factored model $W = UV^\top$ is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not.

By Devender Singh

llms safety

arXiv Machine Learning

Sep 4

Activation-Keyed Momentum: An Anisotropic Momentum Update via the Delta Rule

The paper introduces Activation-Keyed Momentum (AK‑Momentum), a momentum update that uses the input activation of a linear layer as a key to apply a delta‑rule update, allowing each direction to decay at a rate proportional to its frequency of appearance. AK‑Momentum is proven to be a valid momentum, incorporates input‑side curvature correction without matrix inversion, and clears stale directions faster than traditional exponential moving average (EMA) under both fixed and drifting optima. It can replace the momentum buffer of any optimizer, scales with width under μP, adds only 22–25% extra compute, and demonstrates significant step‑count reductions in FineWeb‑Edu pretraining and other benchmarks. whyItMatters":"AK‑Momentum offers a principled, efficient way to adapt momentum decay to anisotropic training dynamics, improving convergence speed and stability across a range of models and datasets."

By Euijin Hong, Guannan Qu

arXiv AI

Jul 24

The Active Ingredient in Muon's Grokking

arXiv:2607. 20512v1 Announce Type: cross Abstract: The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW.

By Yufeng Wang

rag benchmarks

arXiv Machine Learning

Aug 21

DeltaMomentum: A Key-Value based Anisotropic Momentum Update via Delta Rule

arXiv:2608. 19491v1 Announce Type: new Abstract: Most modern optimizers form their momentum as an exponential moving average (EMA) of past gradients, forgetting every direction at one fixed rate.

By Euijin Hong, Guannan Qu

arXiv Machine Learning

6d ago

Temperon: Full-Time SAM Quality at a Third Less Wall-Clock

The paper introduces Temperon, a training strategy that uses plain SGD for the first 43% of the epoch budget and then hands off to a SAM‑wrapped Muon refiner for the remaining training. On datasets such as CIFAR‑10/100, SVHN, and Tiny ImageNet, Temperon achieves the same or better accuracy as full‑time SAM while reaching key performance targets faster and at lower cost. Ablation studies show that the Muon refiner contributes the majority of the performance gain, while the initial SGD explorer and its restarts add negligible benefit.

By Stamatis Mastromichalakis

llms fine-tuning

arXiv Computer Vision

Aug 24

When does fusing hand-crafted knowledge with learned representations pay? A cost-normalized benchmark of stacking, substitution, and interference

arXiv:2608.21098v1 Announce Type: new Abstract: Fusing prior knowledge with data-driven learning is attractive where data is scarce, yet no controlled account says when it helps, is redundant, or har...

By Ahmad AlMughrabi, Albert Clop, Benjamin Busam, Ricardo Marques, Petia Radeva

computer-vision benchmarks

Related stories