Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation
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| Format: | Preprint |
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2024
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| _version_ | 1866916261361876992 |
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| author | Park, Yeachan Kim, Minseok Kim, Yeoneung |
| author_facet | Park, Yeachan Kim, Minseok Kim, Yeoneung |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation Park, Yeachan Kim, Minseok Kim, Yeoneung Machine Learning Artificial Intelligence 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. |
| title | Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2405.16658 |