Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective
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| Authors | Hyunmin Cho et al. |
| Year | 2026 |
| HF Upvotes | 16 |
| arXiv | 2605.27476 |
| Download | |
| HF Page | View on Hugging Face |
Abstract
We characterize the pre-softmax attention matrix 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).
Engineering Breakdown
The Problem
We characterize the pre-softmax attention matrix QK^top in transformers as an associative memory matrix encoding pairwise associations between input features.
The Approach
Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics.
Key Results
Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).
Research Areas
This paper contributes to the following areas of AI/ML engineering:
- Machine learning
- Deep learning
- Neural networks
- Model optimization
- AI systems
- Balancing
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