Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
A tale of two circuits: Grokking as competition of sparse and dense subnetworks.arXiv preprint arXiv:2303.11873
11 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure of networks undergoing grokking on the sparse parity task, and find that the grokking phase transition corresponds to the emergence of a sparse subnetwork that dominates model predictions. On an optimization level, we find that this subnetwork arises when a small subset of neurons undergoes rapid norm growth, whereas the other neurons in the network decay slowly in norm. Thus, we suggest that the grokking phase transition can be understood to emerge from competition of two largely distinct subnetworks: a dense one that dominates before the transition and generalizes poorly, and a sparse one that dominates afterwards.
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FSD, a permutation-tested metric of Fourier circuit synchronization, precedes grokking by a mean of 1722 steps across nine modular addition setups and causally controls grokking timing when weight decay is varied at the FSD ceiling.
Multi-task grokking in Transformers produces staggered generalization, low-dimensional manifolds, weight-decay phase structure, holographic solutions, and transverse redundancy.
EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
Overparameterized two-qubit SU(4) QNNs exhibit grokking and epoch-wise double descent; depth raises generalization success, and weak L2 regularization anchors the post-grokking state against weight-norm drift.
A norm penalty constraining activations to a sqrt(d)-radius hypersphere accelerates grokking by up to 6x on modular arithmetic via radial suppression in activation dynamics.
Spectral analysis of activations and gradients provides new diagnostics that link batch size to representation geometry, early covariance tails to token efficiency, and spectral shifts to learning dynamics in decoder-only LLMs, backed by a mechanistic model.
Spectral entropy collapse in learned representations precedes and predicts grokking, with interventions showing it is not explained by parameter norm alone.
SingGuard introduces a policy-adaptive multimodal LLM guardrail with dynamic reasoning regimes and SingGuard-Bench, reporting SOTA F1 scores across 35 datasets and improved policy-following accuracy under runtime shifts.
Controlled experiments on Qwen-2.5-1.5B identify strategy selection (enabled by diverse SFT data) and strategy improvement (enabled by harder RL data) as the core mechanisms through which RL post-training enhances reasoning.
Grokking emerges near the model size where memorization timescale T_mem(P) intersects generalization timescale T_gen(P) on modular arithmetic.
citing papers explorer
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Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking
Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
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Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking
FSD, a permutation-tested metric of Fourier circuit synchronization, precedes grokking by a mean of 1722 steps across nine modular addition setups and causally controls grokking timing when weight decay is varied at the FSD ceiling.
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The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure
Multi-task grokking in Transformers produces staggered generalization, low-dimensional manifolds, weight-decay phase structure, holographic solutions, and transverse redundancy.
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Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking
EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
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Grokking and epoch-wise double descent in quantum neural networks
Overparameterized two-qubit SU(4) QNNs exhibit grokking and epoch-wise double descent; depth raises generalization success, and weak L2 regularization anchors the post-grokking state against weight-norm drift.
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Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization
A norm penalty constraining activations to a sqrt(d)-radius hypersphere accelerates grokking by up to 6x on modular arithmetic via radial suppression in activation dynamics.
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Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization
Spectral analysis of activations and gradients provides new diagnostics that link batch size to representation geometry, early covariance tails to token efficiency, and spectral shifts to learning dynamics in decoder-only LLMs, backed by a mechanistic model.
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Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin
Spectral entropy collapse in learned representations precedes and predicts grokking, with interventions showing it is not explained by parameter norm alone.
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SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning
SingGuard introduces a policy-adaptive multimodal LLM guardrail with dynamic reasoning regimes and SingGuard-Bench, reporting SOTA F1 scores across 35 datasets and improved policy-following accuracy under runtime shifts.
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Select and Improve: Understanding the Mechanics of Post-Training for Reasoning
Controlled experiments on Qwen-2.5-1.5B identify strategy selection (enabled by diverse SFT data) and strategy improvement (enabled by harder RL data) as the core mechanisms through which RL post-training enhances reasoning.
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Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds
Grokking emerges near the model size where memorization timescale T_mem(P) intersects generalization timescale T_gen(P) on modular arithmetic.