Related papers: Two Optimizations on the St\aa lmarck Procedure

In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…

Modern CDCL SAT solvers learn clauses rapidly, and an important heuristic is the clause deletion scheme. Most current solvers have two (or more) stores of clauses. One has ``valuable'' clauses which are never deleted. Most learned clauses…

The decision variable selection policy used by the most competitive CDCL (Conflict-Driven Clause Learning) SAT solvers is either VSIDS (Variable State Independent Decaying Sum) or its variants such as exponential version EVSIDS. The common…

Aligning large language models (LLMs) with human intent is critical for enhancing their performance across a variety of tasks. Standard alignment techniques, such as Direct Preference Optimization (DPO), often rely on the binary…

Direct preference optimization (\texttt{DPO}) has emerged as a promising approach for solving the alignment problem in AI. In this paper, we make two counter-intuitive observations about \texttt{DPO}. First, we show that \texttt{DPO} loss…

Existing reinforcement learning approaches for Large Language Models typically perform policy optimization at the granularity of individual tokens or entire response sequences. However, such formulations often misalign with the natural…

3-SAT problem is of great importance to many technical and scientific applications. This paper presents a new hybrid evolutionary algorithm for solving this satisfiability problem. 3-SAT problem has the huge search space and hence it is…

Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…

Ignoring uncertainty in combinatorial optimization leads to suboptimal decisions in practice. Nevertheless, the focus is often on deterministic combinatorial optimization problems, mainly because they are already challenging enough without…

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address…

We propose Dual Approximation Policy Optimization (DAPO), a framework that incorporates general function approximation into policy mirror descent methods. In contrast to the popular approach of using the $L_2$-norm to measure function…

Large Language Models (LLMs) are increasingly embedded in enterprise workflows, yet their performance remains highly sensitive to prompt design. Automatic Prompt Optimization (APO) seeks to mitigate this instability, but existing approaches…

Recent Large Reasoning Models (LRMs) have achieved remarkable performance in solving complex problems via supervised fine-tuning (SFT) and reinforcement learning (RL). Although existing RL algorithms significantly enhance model accuracy,…

The widespread application of large language models (LLMs) raises increasing demands on ensuring safety or imposing constraints, such as reducing harmful content and adhering to predefined rules. While there have been several works studying…

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…

The alignment of Large Language Models (LLMs) is crucial for ensuring their safety and reliability in practical applications. Direct Preference Optimization (DPO) has emerged as an efficient method that directly optimizes models using…

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…

We previously designed Partial Order Conflict Driven Clause Learning (PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a partial order on decision levels, and showed that it can speed up the solving on problems with a…

We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric…

Our work presents a novel reinforcement learning (RL) based framework to optimize heuristic selection within the conflict-driven clause learning (CDCL) process, improving the efficiency of Boolean satisfiability (SAT) solving. The proposed…