How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding

• URL: http://arxiv.org/abs/2303.04245v2
• Date: Mon, 24 Jul 2023 17:29:04 GMT
• Title: How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding
• Authors: Yuchen Li, Yuanzhi Li, Andrej Risteski
• Abstract summary: We provide mechanistic understanding of how transformers learn "semantic structure" We show, through a combination of mathematical analysis and experiments on Wikipedia data, that the embedding layer and the self-attention layer encode the topical structure.
• Score: 56.222097640468306
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of mathematical analysis and experiments on Wikipedia data and synthetic data modeled by Latent Dirichlet Allocation (LDA), that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

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