Related papers: Two Optimizations on the St\aa lmarck Procedure
The CDCL algorithm is the leading solution adopted by state-of-the-art solvers for SAT, SMT, ASP, and others. Experiments show that the performance of CDCL solvers can be significantly boosted by embedding domain-specific heuristics,…
We propose a new method based on sparse optimal discriminant clustering (SODC), incorporating a penalty term into the scoring matrix based on convex clustering. With the addition of this penalty term, it is expected to improve the accuracy…
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…
The primal-dual splitting algorithm (PDSA) by Chambolle and Pock is efficient for solving structured convex optimization problems. It adopts an extrapolation step and achieves convergence under certain step size condition. Chang and Yang…
Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) as it requires ensuring the correctness of each reasoning step. Researchers have been strengthening the mathematical reasoning abilities of LLMs…
Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…
The superposition calculus for reasoning in first-order logic with equality relies on simplification orderings on terms. Modern saturation provers use the Knuth-Bendix order (KBO) and the lexicographic path order (LPO) for discovering…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…
Direct Preference Optimization (DPO) is broadly utilized for aligning Large Language Models (LLMs) with human values because of its flexibility. Despite its effectiveness, it has been observed that the capability of DPO to generate…
This paper is concerned with the online bandit nonlinear control, which aims to learn the best stabilizing controller from a pool of stabilizing and destabilizing controllers of unknown types for a given nonlinear dynamical system. We…
Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over…
A recently introduced framework of semidiscretisations for hyperbolic conservation laws known as correction procedure via reconstruction (CPR, also known as flux reconstruction) is considered in the extended setting of summation-by-parts…
Mathematical reasoning is a fundamental capability for large language models (LLMs), yet achieving high performance in this domain remains a significant challenge. The auto-regressive generation process often makes LLMs susceptible to…
SAT solvers are indispensable in formal verification for hardware and software with many important applications. CDCL is the most widely used framework for modern SAT solvers, and restart is an essential technique of CDCL. When restarting,…
We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential…
We propose prioritized unit propagation with periodic resetting, which is a simple but surprisingly effective algorithm for solving random SAT instances that are meant to be hard. In particular, an evaluation on the Random Track of the 2017…
Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long…
Recent advancements in post-training methodologies for large language models (LLMs) have highlighted reinforcement learning (RL) as a critical component for enhancing reasoning. However, the substantial computational costs associated with…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…