Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910263399153664 |
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| author | Cho, Hyunmin Han, Woo Kyoung Jin, Kyong Hwan |
| author_facet | Cho, Hyunmin Han, Woo Kyoung Jin, Kyong Hwan |
| contents | 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 (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27476 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective Cho, Hyunmin Han, Woo Kyoung Jin, Kyong Hwan Machine Learning Artificial Intelligence 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 (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition). |
| title | Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.27476 |