Scalable Physics-Inspired Transformers for Spin Glasses
For researchers in statistical mechanics and combinatorial optimization, this work provides a scalable and efficient method for sampling frustrated spin glasses, overcoming limitations of existing machine-learning approaches.
The paper develops a physics-inspired transformer with sparse attention and spin-tailored embeddings that achieves up to 100x speedup over variational autoregressive networks, enabling neural-network simulations of spin glasses to unprecedented sizes on a single GPU.
Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address these challenges. By further leveraging FlashAttention for parallel ancestral sampling, it achieves up to two orders of magnitude speedup over vanilla variational autoregressive networks, enabling neural-network simulations of spin-glass systems to unprecedented sizes on a single GPU. It can resolve full probability distributions, free energies, and overlap statistics across temperatures, for Sherrington-Kirkpatrick and 2D or 3D Edwards-Anderson models, where existing machine-learning methods encounter limitations at certain temperatures. This framework thus establishes a scalable paradigm for frustrated spin-glass systems.