Fundamental limits of learning in sequence multi-index models and deep attention networks: High-dimensional asymptotics and sharp thresholds

• URL: http://arxiv.org/abs/2502.00901v1
• Date: Sun, 02 Feb 2025 20:27:11 GMT
• Title: Fundamental limits of learning in sequence multi-index models and deep attention networks: High-dimensional asymptotics and sharp thresholds
• Authors: Emanuele Troiani, Hugo Cui, Yatin Dandi, Florent Krzakala, Lenka Zdeborová,
• Abstract summary: We study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. Our analysis uncovers, in particular, how the different layers are learned sequentially.
• Score: 27.57989152496108
• License:
• Abstract: In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first establish a mapping of such models to sequence multi-index models, a generalization of the widely studied multi-index model to sequential covariates, for which we establish a number of general results. In the context of Bayesian-optimal learning, in the limit of large dimension $D$ and commensurably large number of samples $N$, we derive a sharp asymptotic characterization of the optimal performance as well as the performance of the best-known polynomial-time algorithm for this setting --namely approximate message-passing--, and characterize sharp thresholds on the minimal sample complexity required for better-than-random prediction performance. Our analysis uncovers, in particular, how the different layers are learned sequentially. Finally, we discuss how this sequential learning can also be observed in a realistic setup.

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