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[2602.16967] Early-Warning Signals of Grokking via Loss-Landscape Geometry
Summary
The paper explores early-warning signals of 'grokking' in machine learning, focusing on the commutator defect as a precursor to generalization in sequence-learning tasks.
Why It Matters
Understanding grokking and its early-warning signals is crucial for improving machine learning models, particularly in their ability to generalize from training data. This research provides insights into the mechanisms that influence model performance, which can inform future developments in AI and machine learning.
Key Takeaways
- Grokking involves a shift from memorization to generalization during training.
- The commutator defect serves as a reliable early-warning signal for delayed generalization.
- Causal interventions can significantly impact the grokking process.
- Different tasks exhibit varying levels of sensitivity to causal manipulations.
- Findings are architecture-agnostic, applicable across various machine learning models.
Computer Science > Machine Learning arXiv:2602.16967 (cs) [Submitted on 19 Feb 2026] Title:Early-Warning Signals of Grokking via Loss-Landscape Geometry Authors:Yongzhong Xu View a PDF of the paper titled Early-Warning Signals of Grokking via Loss-Landscape Geometry, by Yongzhong Xu View PDF HTML (experimental) Abstract:Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular arithmetic. Whether this mechanism extends beyond arithmetic remains open. We study two sequence-learning benchmarks: SCAN compositional generalization and Dyck-1 depth prediction. Across both tasks and a wide range of learning rates, the commutator defect -- a curvature measure derived from non-commuting gradient updates -- rises well before generalization, with lead times following a superlinear power law (alpha approximately 1.18 for SCAN, approximately 1.13 for Dyck), consistent with prior results on modular arithmetic. Weight-space PCA reveals that spectral concentration is not a universal precursor; the commutator defect is. Causal interventions demonstrate a mechanistic role: amplifying non-commutativity accelerates grokking (roughly 32% on SCAN, roughly 50% on Dyck), while suppressing orthogonal gradient flow delays or prevents it. The three task families form a spectrum of causal sensitivity -- modular arithmetic is rigid, Dyck is responsive, SCAN is intermediate -- yet su...
