Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation

• URL: http://arxiv.org/abs/2405.16658v1
• Date: Sun, 26 May 2024 18:29:24 GMT
• Title: Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation
• Authors: Yeachan Park, Minseok Kim, Yeoneung Kim,
• Abstract summary: We focus on the grokking phenomenon that arises in learning arithmetic binary operations via the transformer model. We suggest various transfer learning mechanisms that expedite grokking.
• Score: 3.7812707887425048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\cite{power2022grokking}. Focusing on the grokking phenomenon that arises in learning arithmetic binary operations via the transformer model, we begin with a discussion on data augmentation in the case of commutative binary operations. To further accelerate, we elucidate arithmetic operations through the lens of the Kolmogorov-Arnold (KA) representation theorem, revealing its correspondence to the transformer architecture: embedding, decoder block, and classifier. Observing the shared structure between KA representations associated with binary operations, we suggest various transfer learning mechanisms that expedite grokking. This interpretation is substantiated through a series of rigorous experiments. In addition, our approach is successful in learning two nonstandard arithmetic tasks: composition of operations and a system of equations. Furthermore, we reveal that the model is capable of learning arithmetic operations using a limited number of tokens under embedding transfer, which is supported by a set of experiments as well.

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