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.
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.
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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.
arXiv AI
Jul 7
Grokking Is Conditional and Fragile: A Fully-Tractable, Multi-Seed Study at 12K Parameters
arXiv:2607. 05104v1 Announce Type: cross Abstract: Grokking -- the delayed onset of generalization long after a network has fit its training set - -is usually studied in models too large to read completely and reported from single training runs.
arXiv Machine Learning
Aug 27
Spectral Allocation: Why Muon Outperforms Adam, and How to Improve Muon
The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.
arXiv Machine Learning
Sep 22
Muon Can Outperform Dedicated Continual Learning Methods
arXiv:2609.24678v1 Announce Type: new Abstract: Continual learning with Low-Rank Adapters (LoRA) typically mitigates forgetting by penalizing the overlap between a new update and the accumulated past...
arXiv AI
Jul 9
At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics
arXiv:2607. 06639v1 Announce Type: cross Abstract: On modular arithmetic, a network's embedding keeps compressing for tens of thousands of steps after it has already generalized.
arXiv AI
Jul 20
Kolmogorov--Arnold Networks for Small Language Models
arXiv:2607. 15525v1 Announce Type: cross Abstract: Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks.
arXiv AI
Sep 10
Equivariance Breaks the Learning Rate
arXiv:2609.08381v1 Announce Type: cross Abstract: Equivariant networks are commonly trained with Adam, yet recent work reports that matrix-structured optimizers such as Muon can perform better on the...
arXiv Machine Learning
Jun 3
MuLoCo: Muon is a practical inner optimizer for DiLoCo
arXiv:2505. 23725v3 Announce Type: replace Abstract: DiLoCo is a powerful framework for training large language models (LLMs), enabling larger optimal batch sizes and increased accelerator utilization under networking constraints.
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.
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.
arXiv Machine Learning
Jul 16
Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations
arXiv:2607. 13749v1 Announce Type: new Abstract: Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately.