Contextual Counting: A Mechanistic Study of Transformers on a Quantitative Task

• URL: http://arxiv.org/abs/2406.02585v1
• Date: Thu, 30 May 2024 20:52:23 GMT
• Title: Contextual Counting: A Mechanistic Study of Transformers on a Quantitative Task
• Authors: Siavash Golkar, Alberto Bietti, Mariel Pettee, Michael Eickenberg, Miles Cranmer, Keiya Hirashima, Geraud Krawezik, Nicholas Lourie, Michael McCabe, Rudy Morel, Ruben Ohana, Liam Holden Parker, Bruno Régaldo-Saint Blancard, Kyunghyun Cho, Shirley Ho,
• Abstract summary: This paper introduces the contextual counting task, a novel toy problem aimed at enhancing our understanding of Transformers. We present theoretical and empirical analysis using both causal and non-causal Transformer architectures.
• Score: 40.85615657802704
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformers have revolutionized machine learning across diverse domains, yet understanding their behavior remains crucial, particularly in high-stakes applications. This paper introduces the contextual counting task, a novel toy problem aimed at enhancing our understanding of Transformers in quantitative and scientific contexts. This task requires precise localization and computation within datasets, akin to object detection or region-based scientific analysis. We present theoretical and empirical analysis using both causal and non-causal Transformer architectures, investigating the influence of various positional encodings on performance and interpretability. In particular, we find that causal attention is much better suited for the task, and that no positional embeddings lead to the best accuracy, though rotary embeddings are competitive and easier to train. We also show that out of distribution performance is tightly linked to which tokens it uses as a bias term.

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