Transfer Learning from Foundational Optimization Embeddings to Unsupervised SAT Representations
Summary: arXiv:2604.15448v1 Announce Type: cross
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).
Introduction
In the field of artificial intelligence and operations research, the development of efficient algorithms for solving combinatorial problems has been a significant challenge. Mixed-integer programming (MIP) has become a standard approach for addressing these challenges, leading to the creation of foundational optimization embeddings. These embeddings provide a robust framework for representing complex optimization problems, allowing for improved performance across various domains.
Research Focus
This research focuses on the potential of foundational optimization embeddings to be adapted for Boolean satisfiability (SAT) problems. SAT is a crucial decision problem in computer science and has wide-ranging applications, including verification, planning, and artificial intelligence. By mapping Conjunctive Normal Form (CNF) formulas into a bipartite constraint-variable graph representation used for MIPs, we aim to leverage the strengths of optimization embeddings in the SAT domain.
Methodology
- Mapping CNF Formulas: The first step involves representing SAT instances in a format compatible with foundational optimization embeddings.
- Reusing Pre-trained Models: By employing the existing pre-trained embedding model, we avoid the need for architectural changes or supervised fine-tuning.
- Unsupervised Tasks: Our approach focuses on unsupervised tasks, such as clustering SAT instances and identifying distributions.
Results
Our findings demonstrate that foundational optimization embeddings successfully capture structural regularities in SAT instances. This capability is essential for performing unsupervised tasks, as it allows for the identification of patterns and relationships within the data. The adaptability of these embeddings signifies their potential to transfer knowledge across different problem domains.
Conclusion
The results of our study indicate that foundational optimization embeddings can effectively transfer to constraint satisfaction domains, specifically in the context of SAT. This advancement marks a significant step toward a unified representational framework that encompasses both optimization and decision problems. By bridging the gap between these two areas, we pave the way for more efficient algorithms and methods in artificial intelligence.
Future Directions
- Exploring additional decision problems that may benefit from similar embeddings.
- Investigating the impact of different embedding architectures on performance.
- Examining the scalability of this approach in large-scale SAT instances.
As research in this area continues to evolve, the implications for both theory and practical applications are profound. The work presented here not only enhances our understanding of optimization and decision problems but also contributes to the ongoing development of intelligent systems capable of tackling complex challenges.