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. 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.
By Yoshiyuki Ootani
arXiv:2606. 08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles.
By Hu Tan, Kuo Gai, Shihua Zhang
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.
By Gunner Levi Howe
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
By Houston Haynes
arXiv:2604. 13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood.
By Laura Gomezjurado Gonzalez
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
By Joshua S. Schiffman
arXiv:2607. 22757v1 Announce Type: cross Abstract: We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted scalar action through embeddings, self-attention, and the training objective.
By T. Shaska
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
arXiv:2607. 14144v2 Announce Type: replace Abstract: The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality.
By Wenhui Chen, Jianlin Chen, Ziyao Lin, Chi Man Vong
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.
By Hu Tan, Kuo Gai, Shihua Zhang
arXiv:2607. 14144v1 Announce Type: new Abstract: The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality.
By Wenhui Chen, Jianlin Chen, Ziyao Lin, Chi Man Vong