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 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 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 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.
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.
arXiv Machine Learning
Aug 12
Off-Axis, On Purpose: Where a Transformer Computes Concepts and Why it Does So
arXiv:2608. 10251v1 Announce Type: cross Abstract: A transformer's answer lives on one axis: the direction its unembedding reads.
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.
Hugging Face Trending Papers
Jun 11
Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers
Grokking -- where a transformer on modular arithmetic suddenly transitions from near-chance to near-perfect validation accuracy -- is attributed to a Fourier circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior circuit knowledge.
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).
arXiv AI
Jul 23
An Isotropy-Preserving Spectral Cap for Muon: Theory and Three Case Studies
arXiv:2607. 19771v1 Announce Type: cross Abstract: Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood.