Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective
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Computer Science > Machine Learning
Title:Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective
Abstract:We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (this https URL).
| Comments: | Accepted to ICML 2026 (Regular) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.27476 [cs.LG] |
| (or arXiv:2605.27476v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.27476
arXiv-issued DOI via DataCite (pending registration)
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