Clustering in pure-attention hardmax transformers and its role in sentiment analysis

• URL: http://arxiv.org/abs/2407.01602v1
• Date: Wed, 26 Jun 2024 16:13:35 GMT
• Title: Clustering in pure-attention hardmax transformers and its role in sentiment analysis
• Authors: Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua,
• Abstract summary: We rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as the number of layers tends to infinity. We show that the transformer inputsally converge to a clustered equilibrium determined by special points called leaders. We then leverage this theoretical understanding to solve sentiment analysis problems from language processing using a fully interpretable transformer model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as the number of layers tends to infinity. By viewing such transformers as discrete-time dynamical systems describing the evolution of points in a Euclidean space, and thanks to a geometric interpretation of the self-attention mechanism based on hyperplane separation, we show that the transformer inputs asymptotically converge to a clustered equilibrium determined by special points called leaders. We then leverage this theoretical understanding to solve sentiment analysis problems from language processing using a fully interpretable transformer model, which effectively captures `context' by clustering meaningless words around leader words carrying the most meaning. Finally, we outline remaining challenges to bridge the gap between the mathematical analysis of transformers and their real-life implementation.

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