# Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging

arXiv: https://arxiv.org/abs/2604.10821 · HTML: https://mlsanity.com/paper/2604.10821/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 86 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 30 of 30)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Dirichlet Diffusion Score Model for Biological Sequence Generation](https://mlsanity.com/paper/2305.10699/) (2023)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [A Contour Stochastic Gradient Langevin Dynamics Algorithm for Simulations of Multi-modal Distributions](https://mlsanity.com/paper/2010.09800/) (2020)
- [Discrete Langevin Sampler via Wasserstein Gradient Flow](https://mlsanity.com/paper/2206.14897/) (2022)
- [Post-training Quantization with Multiple Points: Mixed Precision without Mixed Precision](https://mlsanity.com/paper/2002.09049/) (2020)
- [A Framework for Adaptive MCMC Targeting Multimodal Distributions](https://mlsanity.com/paper/1812.02609/) (2018)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Enhanced gradient-based MCMC in discrete spaces](https://mlsanity.com/paper/2208.00040/) (2022)
- [Gradient-based Discrete Sampling with Automatic Cyclical Scheduling](https://mlsanity.com/paper/2402.17699/) (2024)
- [Efficient Informed Proposals for Discrete Distributions via Newton's Series Approximation](https://mlsanity.com/paper/2302.13929/) (2023)
- [A Practical Diffusion Path for Sampling](https://mlsanity.com/paper/2406.14040/) (2024)
- [Geometric Rates of Convergence for Kernel-based Sampling Algorithms](https://mlsanity.com/paper/1907.08410/) (2019)
- [Entropy-Guided Sampling of Flat Modes in Discrete Spaces](https://mlsanity.com/paper/2505.02296/) (2025)

## Built on by (most cited first, 1 of 1)

- [EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization](https://mlsanity.com/paper/2610.04953/) (2026)

## Abstract (arXiv)

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 limits their ability 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 allows the auxiliary variable to encapsulate 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.