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A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…

This paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted…

Continual learning (CL) is crucial for language models to dynamically adapt to the evolving real-world demands. To mitigate the catastrophic forgetting problem in CL, data replay has been proven a simple and effective strategy, and the…

Restarts are a widely-used class of techniques integral to the efficiency of Conflict-Driven Clause Learning (CDCL) Boolean SAT solvers. While the utility of such policies has been well-established empirically, a theoretical explanation of…

Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…

A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean literals. One of the popular, efficient ideas used to solve PB-problems (a set of PB-constraints) is to translate them to SAT instances (encodings) via, for…

Continual Learning (CL) in Automatic Speech Recognition (ASR) suffers from catastrophic forgetting when adapting to new tasks, domains, or speakers. A common strategy to mitigate this is to store a subset of past data in memory for…

Expanding the linguistic diversity of instruct large language models (LLMs) is crucial for global accessibility but is often hindered by the reliance on costly specialized target language labeled data and catastrophic forgetting during…

In this paper we introduce Clause Cuts: linear inequalities obtained from clauses that are logically implied by a CNF formula, resembling strengthened no-good cuts. With these cuts, we tighten mixed-integer linear programming (MILP)…

Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…

Although well-established in general reinforcement learning (RL), value-based methods are rarely explored in constrained RL (CRL) for their incapability of finding policies that can randomize among multiple actions. To apply value-based…

Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature for solving several counting problems efficiently. A canonical counting problem is #SAT, which asks to count the satisfying assignments…

In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem…

Continual learning (CL) seeks to mitigate catastrophic forgetting when models are trained with sequential tasks. A common approach, experience replay (ER), stores past exemplars but only sparsely approximates the data distribution, yielding…

Behavior Cloning (BC) on curated (or filtered) data is the predominant paradigm for supervised fine-tuning (SFT) of large language models; as well as for imitation learning of control policies. Here, we draw on a connection between this…

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…

More and more languages have a need for constraint solving capabilities for features like error detection or automatic code generation. Imagine a dependently typed language that can immediately implement a program as soon as its type is…

Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…

We present Self-Driven Strategy Learning ($\textit{sdsl}$), a lightweight online learning methodology for automated reasoning tasks that involve solving a set of related problems. $\textit{sdsl}$ does not require offline training, but…