Streamlining constraints (or streamliners, for short) narrow the search space, enhancing the speed and feasibility of solving complex constraint satisfaction problems. Traditionally, streamliners were crafted manually or generated through systematically combined atomic constraints with high-effort offline testing. Our approach utilizes the generative capabilities of Large Language Models (LLMs) to propose effective streamliners for problems specified in the MiniZinc constraint programming language and integrates feedback to the LLM with quick empirical tests for validation. Evaluated across seven diverse constraint satisfaction problems, our method achieves substantial runtime reductions. We compare the results to obfuscated and disguised variants of the problem to see whether the results depend on LLM memorization. We also analyze whether longer offline runs improve the quality of streamliners and whether the LLM can propose good combinations of streamliners.

Streamlining constraints (or streamliners, for short) narrow the search space, enhancing the speed and feasibility of solving complex constraint satisfaction problems. Traditionally, streamliners were crafted manually or generated through systematically combined atomic constraints with high-effort offline testing. Our approach utilizes the generative capabilities of Large Language Models (LLMs) to propose effective streamliners for problems specified in the MiniZinc constraint programming language and integrates feedback to the LLM with quick empirical tests for validation. Evaluated across seven diverse constraint satisfaction problems, our method achieves substantial runtime reductions. We compare the results to obfuscated and disguised variants of the problem to see whether the results depend on LLM memorization. We also analyze whether longer offline runs improve the quality of streamliners and whether the LLM can propose good combinations of streamliners.

We present a novel approach to learn the structure of large Bayesian Networks (BNs) of bounded treewidth. Our approach combines the complementary strengths of heuristic and MaxSAT-based methods. Both methods operate in parallel and cooperate in a mutually advantageous way to improve the quality of the learned BN structures. Our work utilizes an approach proposed by Peruvemba Ramaswamy and Szeider (AAAI'21, NeurIPS'21, UAI'22), which continually applies a MaxSAT-based algorithm to a BN obtained from heuristic search. We create a continuous and dynamic refinement process by allowing the heuristic and the MaxSAT-based technique to cooperate and repeatedly share their work. Our rigorous experiments show that the collaboration between the two methods is a powerful strategy for increasing the score of the learned BN structure. Moreover, the rate at which the score increases is significantly higher than that of the individual methods by themselves. Our results provide a strong argument for combining complementary approaches to learn treewidth-bounded BNs in a collaborative way.

Probabilistic generating circuits (PGCs) are economical representations of multivariate probability generating polynomials (PGPs). They unify and extend decomposable probabilistic circuits and determinantal point processes, admitting tractable computation of marginal probabilities. However, the need for addition and multiplication of high-degree polynomials incurs a significant additional factor in the complexity of inference. Here, we give a new inference algorithm that eliminates this extra factor. Specifically, we show that it suffices to keep track of the highest degree coefficients of the computed polynomials, rendering the algorithm linear in the circuit size. In addition, we show that determinant-based circuits need not be expanded to division-free circuits, but can be handled by division-based fast algorithms. While these advances enhance the appeal of PGCs, we also discover an obstacle to learning them from data: it is NP-hard to recognize whether a given PGC encodes a PGP. We discuss the implications of our ambivalent findings and sketch a method, in which learning is restricted to PGCs that are composed of moderate-size subcircuits.

We propose a new score-based algorithm for learning the structure of a Bayesian Network (BN). It is the first algorithm that simultaneously supports the requirements of (i) learning a BN of bounded treewidth, (ii) satisfying expert constraints, including positive and negative ancestry properties between nodes, and (iii) scaling up to BNs with several thousand nodes. The algorithm operates in two phases. In Phase 1, we utilize a modified version of an existing BN structure learning algorithm, modified to generate an initial Directed Acyclic Graph (DAG) that supports a portion of the given constraints. In Phase 2, we follow the BN-SLIM framework, introduced by Peruvemba Ramaswamy and Szeider (AAAI 2021). We improve the initial DAG by repeatedly running a MaxSAT solver on selected local parts. The MaxSAT encoding entails local versions of the expert constraints as hard constraints. We evaluate a prototype implementation of our algorithm on several standard benchmark sets. The encouraging results demonstrate the power and flexibility of the BN-SLIM framework. It boosts the score while increasing the number of satisfied expert constraints.

We present a new approach for learning the structure of a treewidth-bounded Bayesian Network (BN). The key to our approach is applying an exact method (based on MaxSAT) locally, to improve the score of a heuristically computed BN. This approach allows us to scale the power of exact methods—so far only applicable to BNs with several dozens of random variables—to large BNs with several thousands of random variables. Our experiments show that our method improves the score of BNs provided by state-of-the-art heuristic methods, often significantly.

We propose new methods for learning Bayesian networks (BNs) that reliably support fast inference. We utilize maximum state space size as a more fine-grained measure for the BN's reasoning complexity than the standard treewidth measure, thereby accommodating the possibility that variables range over domains of different sizes. Our methods combine heuristic BN structure learning algorithms with the recently introduced MaxSAT-powered local improvement method (Peruvemba Ramaswamy and Szeider, AAAI'21). Our experiments show that our new learning methods produce BNs that support significantly faster exact probabilistic inference than BNs learned with treewidth bounds.