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[2602.21272] Counterdiabatic Hamiltonian Monte Carlo
Summary
The paper introduces Counterdiabatic Hamiltonian Monte Carlo (CHMC), an advanced sampling method that improves the efficiency of Hamiltonian Monte Carlo by incorporating a learned counterdiabatic term to address multimodal distribution challenges.
Why It Matters
This research is significant as it proposes a novel approach to enhance sampling efficiency in machine learning, particularly for complex multimodal distributions. By integrating counterdiabatic principles, CHMC could lead to faster convergence in various applications, making it a valuable contribution to the field of statistical sampling methods.
Key Takeaways
- CHMC enhances Hamiltonian Monte Carlo by using a learned counterdiabatic term.
- The method addresses slow convergence in multimodal sampling problems.
- CHMC can be viewed as a more efficient Sequential Monte Carlo sampler.
- The approach has potential applications in quantum state preparation.
- Benchmark tests demonstrate the effectiveness of CHMC on simple problems.
Statistics > Machine Learning arXiv:2602.21272 (stat) [Submitted on 24 Feb 2026] Title:Counterdiabatic Hamiltonian Monte Carlo Authors:Reuben Cohn-Gordon, Uroš Seljak, Dries Sels View a PDF of the paper titled Counterdiabatic Hamiltonian Monte Carlo, by Reuben Cohn-Gordon and 2 other authors View PDF HTML (experimental) Abstract:Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Computati...