Trained MLPs and transformers solving modular addition can be unified under an approximate Chinese Remainder Theorem, and deep or embedding-based networks learn only O(log n) frequency features.
Levels of Analysis for Machine Learning
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abstract
Machine learning is currently involved in some of the most vigorous debates it has ever seen. Such debates often seem to go around in circles, reaching no conclusion or resolution. This is perhaps unsurprising given that researchers in machine learning come to these discussions with very different frames of reference, making it challenging for them to align perspectives and find common ground. As a remedy for this dilemma, we advocate for the adoption of a common conceptual framework which can be used to understand, analyze, and discuss research. We present one such framework which is popular in cognitive science and neuroscience and which we believe has great utility in machine learning as well: Marr's levels of analysis. Through a series of case studies, we demonstrate how the levels facilitate an understanding and dissection of several methods from machine learning. By adopting the levels of analysis in one's own work, we argue that researchers can be better equipped to engage in the debates necessary to drive forward progress in our field.
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Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks
Trained MLPs and transformers solving modular addition can be unified under an approximate Chinese Remainder Theorem, and deep or embedding-based networks learn only O(log n) frequency features.