Transformer sampler matches MCMC on the 2D XY model up to 96x96
Original title: Sampling the XY model with an attention-based neural network
A locality-informed autoregressive network reproduces energy, magnetization and helicity modulus without missing configuration modes.
Researchers present a transformer-based variational autoregressive network for sampling continuous lattice systems, applied to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. Locality-informed attention and approximate probabilities are built in. Trained on lattices up to 96x96, the sampler outperforms existing neural samplers and matches Markov Chain Monte Carlo energy, magnetization and helicity modulus. A mode-dropping estimator finds no missed regions of configuration space.
- The model is trained on lattices up to 96 by 96.
- Physics-informed ingredients include locality-informed attention and approximate probabilities.
- A mode-dropping estimator checks that no configuration-space regions are missed.
From the original article
1 min read at arxiv.orgWe present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities.
By Piotr Białas · arxiv.org
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