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:2607. 20552v1 Announce Type: new Abstract: Grokking -- the delayed generalization of neural networks long after they have memorized their training data -- wastes thousands of training epochs and is notoriously unpredictable.
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:2608. 07436v1 Announce Type: new Abstract: Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head.
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:2607. 04333v1 Announce Type: new Abstract: Grokking -- generalization arriving long after training-set interpolation -- can be accelerated by structure-agnostic interventions: gradient filtering, weight-norm clamping, geometric penalties on hidden representations.
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.
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. What happens at the extreme of this spectrum, when the architecture's expressible function class collapses to a finite-dimensional algebraic variety?
arXiv:2607. 16821v1 Announce Type: cross Abstract: Task arithmetic, sequential fine-tuning, activation steering, and first-order random search all operate through relatively small perturbations around an already trained checkpoint, and they rely on different local approximations: individual perturbations should be first-order predictable, task updates should compose with controlled interference, useful tangent structure should be stable and possible to estimate, and weight edits should have counterparts in representation space.
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
arXiv:2607. 20512v1 Announce Type: cross Abstract: The Muon optimizer reaches the grokking threshold on modular arithmetic faster than AdamW.
arXiv:2607. 12640v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards, and Group Relative Policy Optimization (GRPO) in particular, is now run routinely on a supervised checkpoint in the hope of producing a stronger agent.
arXiv:2606. 03938v1 Announce Type: cross Abstract: Multi-epoch training is becoming the standard now that compute is growing faster than the supply of high-quality text.