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arXiv · 2409.16112

Self-attention as an attractor network: transient memories without backpropagation

Francesco D'Amico·Matteo Negri
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Abstract

Transformers are one of the most successful architectures of modern neural networks. At their core there is the so-called attention mechanism, which recently interested the physics community as it can be written as the derivative of an energy function in certain cases: while it is possible to write the cross-attention layer as a modern Hopfield network, the same is not possible for the self-attention, which is used in the GPT architectures and other autoregressive models. In this work we show that it is possible to obtain the self-attention layer as the derivative of local energy terms, which resemble a pseudo-likelihood. We leverage the analogy with pseudo-likelihood to design a recurrent model that can be trained without backpropagation: the dynamics shows transient states that are strongly correlated with both train and test examples. Overall we present a novel framework to interpret self-attention as an attractor network, potentially paving the way for new theoretical approaches inspired from physics to understand transformers.

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Francesco D'Amico, Matteo Negri. 2024-09-24. Self-attention as an attractor network: transient memories without backpropagation. https://arxiv.org/abs/2409.16112

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