Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
arXiv preprint arXiv:2303.06173 , year=
10 Pith papers cite this work, alongside 2 external citations. Polarity classification is still indexing.
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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.
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
Diffusion models show grokking on modular addition by composing periodic operand representations in simple data regimes or by separating arithmetic computation from visual denoising across timesteps in varied regimes.
Grokking delay follows T_grok - T_mem = Θ(γ_eff^{-1} log(‖θ_mem‖² / ‖θ_post‖²)), derived from norm separation in regularized optimization and validated with high correlations across 293 runs.
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.
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.
Experiments on modular arithmetic with heavy label noise show that over-parameterized networks form a distributed internal generalization structure that can be extracted via frequency methods to achieve high accuracy despite 80% noise.
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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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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Grokking of Diffusion Models: Case Study on Modular Addition
Diffusion models show grokking on modular addition by composing periodic operand representations in simple data regimes or by separating arithmetic computation from visual denoising across timesteps in varied regimes.
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The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization
Grokking delay follows T_grok - T_mem = Θ(γ_eff^{-1} log(‖θ_mem‖² / ‖θ_post‖²)), derived from norm separation in regularized optimization and validated with high correlations across 293 runs.
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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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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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Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise
Experiments on modular arithmetic with heavy label noise show that over-parameterized networks form a distributed internal generalization structure that can be extracted via frequency methods to achieve high accuracy despite 80% noise.
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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.