Clustering in Causal Attention Masking

• URL: http://arxiv.org/abs/2411.04990v2
• Date: Sun, 10 Nov 2024 17:07:45 GMT
• Title: Clustering in Causal Attention Masking
• Authors: Nikita Karagodin, Yury Polyanskiy, Philippe Rigollet,
• Abstract summary: This work presents a modification of the self-attention dynamics proposed by Geshkovski et al. (arXiv:2312.10794) to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modification into an interacting particle system cannot be interpreted as a mean-field gradient flow.
• Score: 24.786862288360076
• License:
• Abstract: This work presents a modification of the self-attention dynamics proposed by Geshkovski et al. (arXiv:2312.10794) to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modification translates into an interacting particle system that cannot be interpreted as a mean-field gradient flow. Despite this loss of structure, we significantly strengthen the results of Geshkovski et al. (arXiv:2312.10794) in this context: While previous rigorous results focused on cases where all three matrices (Key, Query, and Value) were scaled identities, we prove asymptotic convergence to a single cluster for arbitrary key-query matrices and a value matrix equal to the identity. Additionally, we establish a connection to the classical R\'enyi parking problem from combinatorial geometry to make initial theoretical steps towards demonstrating the existence of meta-stable states.

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