Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging

Pinaki Mohanty, Ruqi Zhang
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4600-4608, 2026.

Abstract

High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limitation makes it difficult for sampling methods to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose Hyperbolic Secant-squared Gibbs-Sampling (HiSS), a novel family of sampling algorithms that integrates a Metropolis-within-Gibbs framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design ensures that the auxiliary variable encapsulates the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-mohanty26a, title = { Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging }, author = {Mohanty, Pinaki and Zhang, Ruqi}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4600--4608}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/mohanty26a/mohanty26a.pdf}, url = {https://proceedings.mlr.press/v300/mohanty26a.html}, abstract = { High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limitation makes it difficult for sampling methods to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose Hyperbolic Secant-squared Gibbs-Sampling (HiSS), a novel family of sampling algorithms that integrates a Metropolis-within-Gibbs framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design ensures that the auxiliary variable encapsulates the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization. } }
Endnote
%0 Conference Paper %T Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging %A Pinaki Mohanty %A Ruqi Zhang %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-mohanty26a %I PMLR %P 4600--4608 %U https://proceedings.mlr.press/v300/mohanty26a.html %V 300 %X High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limitation makes it difficult for sampling methods to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose Hyperbolic Secant-squared Gibbs-Sampling (HiSS), a novel family of sampling algorithms that integrates a Metropolis-within-Gibbs framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design ensures that the auxiliary variable encapsulates the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization.
APA
Mohanty, P. & Zhang, R.. (2026). Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4600-4608 Available from https://proceedings.mlr.press/v300/mohanty26a.html.

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