# Transfer Learning from Foundational Optimization Embeddings to Unsupervised SAT Representations

arXiv: https://arxiv.org/abs/2604.15448 · HTML: https://mlsanity.com/paper/2604.15448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Guiding High-Performance SAT Solvers with Unsat-Core Predictions](https://mlsanity.com/paper/1903.04671/) (2019)
- [VQGraph: Rethinking Graph Representation Space for Bridging GNNs and MLPs](https://mlsanity.com/paper/2308.02117/) (2023)
- [NLocalSAT: Boosting Local Search with Solution Prediction](https://mlsanity.com/paper/2001.09398/) (2020)
- [Augment with Care: Contrastive Learning for Combinatorial Problems](https://mlsanity.com/paper/2202.08396/) (2022)
- [NeuroBack: Improving CDCL SAT Solving using Graph Neural Networks](https://mlsanity.com/paper/2110.14053/) (2021)
- [G4SATBench: Benchmarking and Advancing SAT Solving with Graph Neural Networks](https://mlsanity.com/paper/2309.16941/) (2023)
- [Enhancing SAT solvers with glue variable predictions](https://mlsanity.com/paper/2007.02559/) (2020)
- [FORGE: Foundational Optimization Representations from Graph Embeddings](https://mlsanity.com/paper/2508.20330/) (2025)

## Abstract (arXiv)

Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on solver-generated labels. In this work, we investigate whether such representations generalize beyond optimization to decision problems, focusing on Boolean satisfiability (SAT). We adapt the foundational optimization architecture to SAT by mapping CNF formulas into the same bipartite constraint-variable graph representation used for MIPs. This allows direct reuse of the pre-trained embedding model without architectural changes or supervised fine-tuning. Our results show that these embeddings capture structural regularities in SAT instances and support unsupervised tasks such as instance clustering and distribution identification. We demonstrate, for the first time, that foundational optimization embeddings can transfer to constraint satisfaction domains. Our findings is a step toward a unified representational framework for both optimization and decision problems.