Transfer Learning from Foundational Optimization Embeddings to Unsupervised SAT Representations

2026-04-16

AI Summary

This work investigates whether foundation embeddings trained for optimization problems can generalize to decision problems such as Boolean satisfiability (SAT), enabling cross-task transfer. By mapping conjunctive normal form (CNF) formulas onto the same bipartite constraint-variable graph structure used in mixed-integer programming, the authors directly transfer a pretrained embedding model without architectural modifications or supervised fine-tuning, achieving unsupervised representation learning. This study provides the first evidence that foundation optimization embeddings can be effectively transferred to constraint satisfaction problems, advancing a unified representational framework for optimization and decision tasks. Experiments demonstrate that the approach successfully captures structural regularities in SAT instances, supporting unsupervised clustering and distribution identification, thereby validating the feasibility and efficacy of cross-domain transfer.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Learning to Search
• Machine Learning: Other Foundations of Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Transfer Learning
• Foundational Embeddings
• Boolean Satisfiability
• Unsupervised Representation
• Constraint Satisfaction

Innovation

• transfer learning
• foundational embeddings
• Boolean satisfiability
• unsupervised representation
• constraint satisfaction