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

• URL: http://arxiv.org/abs/2306.17844v2
• Date: Tue, 21 Nov 2023 17:08:34 GMT
• Title: The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks
• Authors: Ziqian Zhong, Ziming Liu, Max Tegmark, Jacob Andreas
• Abstract summary: We show that algorithm discovery in neural networks is sometimes more complex. We show that even simple learning problems can admit a surprising diversity of solutions.
• Score: 59.26515696183751
• License: http://creativecommons.org/licenses/by/4.0/
• 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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