MetaDNS: Enhancing Exploration in Discrete Neural Samplers via Well-Tempered Metadynamics

2026-05-20

AI Summary

Sampling from discrete multimodal distributions is often hindered by mode collapse and an inability to surmount high energy barriers, limiting accurate free energy estimation and phase transition studies. This work introduces tempered metadynamics—a technique previously unexplored in discrete settings—into discrete diffusion and autoregressive neural samplers. By applying an adaptive, history-dependent bias potential along low-dimensional reaction coordinates, the method actively promotes exploration of high-energy barrier regions. It substantially enhances sampling efficiency for high-energy states that are typically inaccessible to conventional approaches. On benchmark low-temperature tasks—including Ising and Potts models as well as Cu-Au alloys—the proposed framework accurately reproduces thermodynamic distributions with fewer bias deposition steps and enables high-fidelity reconstruction of free energy landscapes.

Abstract

Sampling from discrete distributions with multiple modes and energy barriers is fundamental to machine learning and computational physics. Recent discrete neural samplers like MDNS suffer from mode collapse and fail to sample high-energy barrier regions between modes, which is critical for free energy estimation and understanding phase transitions. We propose Metadynamics Discrete Neural Sampler (MetaDNS), a general framework integrating well-tempered metadynamics into discrete diffusion or autoregressive samplers. By maintaining an adaptive, history-dependent bias potential along selected low-dimensional coordinates, MetaDNS forces exploration of previously inaccessible regions, enabling free energy reconstruction infeasible with standard neural samplers due to a lack of high-energy samples. On challenging low-temperature benchmarks including Ising, Potts, and the copper-gold binary alloy, MetaDNS reproduces the thermodynamic distribution. Compared to MCMC-based metadynamics, MetaDNS also achieves comparable exploration requiring fewer bias deposition steps.

Problem

• discrete sampling
• mode collapse
• energy barriers
• free energy estimation
• phase transitions

Innovation

• metadynamics
• discrete neural sampling
• free energy estimation
• mode exploration
• bias potential