Counterdiabatic Hamiltonian Monte Carlo

2026-02-26 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

Counterdiabatic Hamiltonian Monte Carlo (CHMC) is a novel sampling method designed to accelerate convergence in Hamiltonian Monte Carlo (HMC) for distributions with differentiable densities, particularly challenging multimodal problems. HMC typically struggles with slow convergence when interpolating between an initial tractable distribution and a complex target distribution. CHMC addresses this by introducing a learned "counterdiabatic" term to the Hamiltonian, inspired by quantum state preparation techniques. This term allows for more efficient transport of particles through a series of time-varying distributions, reducing the "lag" or dissipation seen in standard HMC with rapidly changing parameters. The method integrates with Sequential Monte Carlo (SMC) samplers, using a weighting scheme derived from the non-equilibrium fluctuation theorem to maintain unbiased samples. Initial benchmarks on 1D Gaussian and double-well potentials demonstrate that CHMC significantly improves particle transport compared to standard HMC under fast schedules.

Key takeaway

For research scientists working on complex sampling problems with multimodal distributions, CHMC offers a promising approach to accelerate convergence. You should consider integrating a learned counterdiabatic term into your HMC-based Sequential Monte Carlo pipelines to improve particle transport efficiency, especially when dealing with rapidly changing target distributions. This method can reduce the computational burden associated with slow equilibration, allowing for faster exploration of challenging probability landscapes.

Key insights

CHMC accelerates HMC sampling by learning a counterdiabatic term to efficiently transport particles across time-varying distributions.

Principles

• Counterdiabatic terms compensate for lag in time-varying Hamiltonians.
• Learning an approximation of Aλ enables efficient sampling.
• Sequential Monte Carlo provides a framework for consistent weighting.

Method

CHMC involves defining a path of densities, learning a counterdiabatic gauge potential Aλ using a neural network or polynomial approximation, and applying it within a time-varying Hamiltonian HCλ. Weights are computed for particles after each step using the non-equilibrium fluctuation theorem.

In practice

• Parameterize Aλ with a neural network or sum of polynomials.
• Refresh momentum every n_l steps to ensure ergodicity.
• Use a splitting integrator for Hamiltonian dynamics.

Topics

• Hamiltonian Monte Carlo
• Counterdiabatic Driving
• Sequential Monte Carlo
• Multimodal Sampling
• Variational Learning

Code references

• reubenharry/counterdiabatic-hmc

Best for: Research Scientist, AI Researcher, AI Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.