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arXiv · 2306.17844

The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks

Ziqian Zhong·Ziming Liu·Max Tegmark·Jacob Andreas
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Abstract

Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested that the answer is yes. Using modular addition as a prototypical problem, we show that algorithm discovery in neural networks is sometimes more complex. Small changes to model hyperparameters and initializations can induce the discovery of qualitatively different algorithms from a fixed training set, and even parallel implementations of multiple such algorithms. Some networks trained to perform modular addition implement a familiar Clock algorithm; others implement a previously undescribed, less intuitive, but comprehensible procedure which we term the Pizza algorithm, or a variety of even more complex procedures. Our results show that even simple learning problems can admit a surprising diversity of solutions, motivating the development of new tools for characterizing the behavior of neural networks across their algorithmic phase space.

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Ziqian Zhong, Ziming Liu, Max Tegmark, Jacob Andreas. 2023-11-21. The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks. https://arxiv.org/abs/2306.17844

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