Stochastic Attention via Langevin Dynamics on the Modern Hopfield Energy
Attention heads retrieve: given a query, they return a weighted average of stored values. We showed that this computation is one step of gradient descent on the modern Hopfield energy, and that Langevin sampling from the corresponding Boltzmann distribution yielded stochastic attention, a training-free sampler controlled by a single temperature parameter. Lowering the temperature gave exact retrieval; raising it gave open-ended generation. Because the energy gradient equals the attention map, no score network, training loop, or learned model was required, making the approach particularly suited to the low-data regime where learned generative models are starved of training signal. We deriv...
| Authors | Abdulrahman Alswaidan, Jeffrey D. Varner |
|---|---|
| Primary category | cs.LG |
| Published | 6 March 2026 |
| Last updated at source | 14 May 2026 |
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