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

arXiv: https://arxiv.org/abs/2605.21722 · HTML: https://mlsanity.com/paper/2605.21722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 35 references that are in the map.
- First posted on arXiv 20 May 2026.

## Builds on (most cited first, 2 of 2)

- [Scaling Autoregressive Models for Lattice Thermodynamics](https://mlsanity.com/paper/2603.14695/) (2026)
- [Sampling from Energy distributions with Target Concrete Score Identity](https://mlsanity.com/paper/2510.23106/) (2025)

## Built on by (most cited first, 2 of 2)

- [FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions](https://mlsanity.com/paper/2609.02948/) (2026)
- [Fixed-point neural samplers on discrete spaces](https://mlsanity.com/paper/2610.01739/) (2026)

## Abstract (arXiv)

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.