Decomposed Learning and Grokking

ICLR 2025 Conference Submission10406 Authors

Keywords: grokking, optimisation, linear algebra, SVD, compression

TL;DR: Exploring a novel SVD based training regime that can mitigate and avoid the grokking phenomena.

Abstract: Grokking is a delayed transition from memorisation to generalisation in neural networks. It poses challenges for efficient learning, particularly in structured tasks and small-data regimes. This paper explores grokking in modular arithmetic, explicitly focusing on modular division with a modulus of 97. We introduce a novel learning method called Decomposed Learning, which leverages Singular Value Decomposition (SVD) to modify the weight matrices of neural networks. Decomposed learning reduces or avoids grokking by changing the representation of the weight matrix, $A$, into the product of three matrices $U$, $\Sigma$ and $V^T$, promoting the discovery of compact, generalisable representations early in the learning process. Through empirical evaluations on the modular division task, we show that Decomposed Learning significantly reduces the effect of grokking and, in some cases, eliminates it. Moreover, Decomposed Learning can reduce the parameters required for practical training, enhancing model efficiency and generalisation. These results suggest that our SVD-based method provides a practical and scalable solution for mitigating grokking, with implications for broader transformer-based learning tasks.

Primary Area: optimization

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Submission Number: 10406