# A Boltzmann-machine-enhanced Transformer For DNA Sequence Classification

arXiv: https://arxiv.org/abs/2603.26465 · HTML: https://mlsanity.com/paper/2603.26465/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [cosFormer: Rethinking Softmax in Attention](https://mlsanity.com/paper/2202.08791/) (2022)
- [DNABERT-2: Efficient Foundation Model and Benchmark For Multi-Species Genome](https://mlsanity.com/paper/2306.15006/) (2023)
- [Are Transformers with One Layer Self-Attention Using Low-Rank Weight Matrices Universal Approximators?](https://mlsanity.com/paper/2307.14023/) (2023)
- [Replacing softmax with ReLU in Vision Transformers](https://mlsanity.com/paper/2309.08586/) (2023)
- [Attention in a family of Boltzmann machines emerging from modern Hopfield networks](https://mlsanity.com/paper/2212.04692/) (2022)
- [Boltzmann Attention Sampling for Image Analysis with Small Objects](https://mlsanity.com/paper/2503.02841/) (2025)
- [Quantum-Boosted High-Fidelity Deep Learning](https://mlsanity.com/paper/2508.11190/) (2025)

## Abstract (arXiv)

DNA sequence classification requires not only high predictive accuracy but also the ability to uncover latent site interactions, combinatorial regulation, and epistasis-like higher-order dependencies. Although the standard Transformer provides strong global modeling capacity, its softmax attention is continuous, dense, and weakly constrained, making it better suited for information routing than explicit structure discovery. In this paper, we propose a Boltzmann-machine-enhanced Transformer for DNA sequence classification. Built on multi-head attention, the model introduces structured binary gating variables to represent latent query-key connections and constrains them with a Boltzmann-style energy function. Query-key similarity defines local bias terms, learnable pairwise interactions capture synergy and competition between edges, and latent hidden units model higher-order combinatorial dependencies. Since exact posterior inference over discrete gating graphs is intractable, we use mean-field variational inference to estimate edge activation probabilities and combine it with Gumbel-Softmax to progressively compress continuous probabilities into near-discrete gates while preserving end-to-end differentiability. During training, we jointly optimize classification and energy losses, encouraging the model to achieve accurate prediction while favoring low-energy, stable, and interpretable structures. We further derive the framework from the energy function and variational free energy to the mean-field fixed-point equations, Gumbel-Softmax relaxation, and the final joint objective. The proposed framework provides a unified view of integrating Boltzmann machines, differentiable discrete optimization, and Transformers for structured learning on biological sequences.