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arXiv Machine Learning

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.

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arXiv Machine Learning
Sep 18

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.

By Rub\'en Dar\'io Guerrero
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arXiv Machine Learning
1d ago

Directions That Don't Drift: Stiefel Manifold Routing for Transformer Attention

The paper proposes constraining the query and key projection matrices in Transformer attention to the Stiefel manifold and optimizing them with a Riemannian Adam optimizer. It demonstrates that this geometric constraint yields significant performance gains on a CIFAR‑10 patch benchmark, with the constrained model outperforming standard AdamW by up to +6.79 percentage points. The authors also show that weight decay has no effect on the constrained frames and that the improvement is driven by a scale‑free step size rather than the manifold projection or equivariance properties.

By Rub\'en Dar\'io Guerrero
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arXiv Machine Learning
Sep 11

Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking

The study investigates the delayed transition from memorization to generalization—known as grokking—in two‑hidden‑layer MLPs trained on modular arithmetic. By exploring 384 hyperparameter configurations, the authors derive a power‑law scaling relation for the onset time of generalization, showing that data complexity dominates over model capacity. A clear phase boundary at weight decay around 1.0 separates grokking from non‑grokking regimes, and weight norm trajectories indicate implicit regularization during the transition.

By Anish Kataria
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arXiv AI
Jun 30

A Stochastic--Geometric Theory of Scaling Laws in Grokking

arXiv:2606. 30388v1 Announce Type: cross Abstract: Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged delay, often through an abrupt transition.

By R\'ois\'in Luo, Christian Gagn\'e, Jonas Ngnaw\'e, Ihsan Ullah, Karyn Morrissey
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arXiv Machine Learning
Jun 15

Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It

arXiv:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.

By Dhruv Sarkar, Vaneet Aggarwal
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