Related papers: An Instantiation-Based Approach for Solving Quanti…
A natural and intuitive idea in model quantization is to approximate each component's quantized output to match its original. Motivated by this idea, most layer-wise post-training quantization (PTQ) methods focus on weight approximation at…
We present a comprehensive computational study of a class of linear system solvers, called {\it Triangle Algorithm} (TA) and {\it Centering Triangle Algorithm} (CTA), developed by Kalantari \cite{kalantari23}. The algorithms compute an…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
State-of-the-art performance in QA tasks is currently achieved by systems employing Large Language Models (LLMs), however these models tend to hallucinate information in their responses. One approach focuses on enhancing the generation…
The rapid development of parameter-efficient fine-tuning methods has noticeably improved the efficiency of adapting large language models. Among these, LoRA has gained widespread popularity due to its strong balance of effectiveness and…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either…
We address the problem of Conjunctive Query Answering (CQA) for the description logic $\dlssx$ ($\shdlssx$, for short) which extends the logic $\dlss$ with Boolean operations on concrete roles and with the product of concepts. The result is…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice,…
The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for…
This work investigates the relation between model-based quantifier instantiation (MBQI) and enumerative instantiation (EI) in Satisfiability Modulo Theories (SMT). MBQI operates at the semantic level and guarantees to find a counterexample…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Quantization is an indispensable technique for serving Large Language Models (LLMs) and has recently found its way into LoRA fine-tuning. In this work we focus on the scenario where quantization and LoRA fine-tuning are applied together on…