arXiv:2601.19791v3 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay. Specifically, we prove that the following stages occur: (i) the model overfits the training data early during training; (ii) poor generalization persists long after overfitting has manifested; and (iii) the generalization error eventually becomes arbitrarily small. Moreover, we show, both theoretica
The paper provides a theoretical understanding of 'grokking,' a critical phenomenon in AI where models generalize long after overfitting, advancing foundational AI research.
Understanding grokking can lead to more efficient and robust AI model training, potentially reducing computational waste and improving generalization in real-world applications.
This theoretical work provides provable insights into a previously empirical observation in AI, deepening our understanding of learning dynamics and potentially guiding future algorithm design.
- · AI researchers
- · Machine learning framework developers
- · Sectors reliant on robust AI generalization
- · None
Improved understanding of deep learning generalization phenomena for researchers.
Development of new algorithms or training methodologies that explicitly leverage or avoid grokking.
More computationally efficient and reliable AI systems across various applications due to optimized training.
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