A phase transition between positional and semantic learning in a solvable model of dot-product attention

• URL: http://arxiv.org/abs/2402.03902v1
• Date: Tue, 6 Feb 2024 11:13:54 GMT
• Title: A phase transition between positional and semantic learning in a solvable model of dot-product attention
• Authors: Hugo Cui, Freya Behrens, Florent Krzakala, Lenka Zdeborov\'a
• Abstract summary: We show how a dot-product attention layer learns a positional attention matrix and a semantic attention matrix. For an algorithmic task, we experimentally show how the same simple architecture can learn using either the positional or semantic mechanism.
• Score: 20.83573496458023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate how a dot-product attention layer learns a positional attention matrix (with tokens attending to each other based on their respective positions) and a semantic attention matrix (with tokens attending to each other based on their meaning). For an algorithmic task, we experimentally show how the same simple architecture can learn to implement a solution using either the positional or semantic mechanism. On the theoretical side, we study the learning of a non-linear self-attention layer with trainable tied and low-rank query and key matrices. In the asymptotic limit of high-dimensional data and a comparably large number of training samples, we provide a closed-form characterization of the global minimum of the non-convex empirical loss landscape. We show that this minimum corresponds to either a positional or a semantic mechanism and evidence an emergent phase transition from the former to the latter with increasing sample complexity. Finally, we compare the dot-product attention layer to linear positional baseline, and show that it outperforms the latter using the semantic mechanism provided it has access to sufficient data.

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