Related papers: Quantified Linear and Polynomial Arithmetic Satisf…
Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and…
Quantization is a practical technique for making large language models easier to deploy by reducing the precision used to store and operate on model weights. This can lower memory use and improve runtime feasibility on constrained hardware,…
We address the problem of \emph{quantification}, a supervised learning task whose goal is, given a class, to estimate the relative frequency (or \emph{prevalence}) of the class in a dataset of unlabelled items. Quantification has several…
Large language models (LLMs) have transformed natural language processing but pose significant challenges for real-world deployment. These models necessitate considerable computing resources, which can be costly and frequently unavailable.…
The identity testing of rational formulas (RIT) in the free skew field efficiently reduces to computing the rank of a matrix whose entries are linear polynomials in noncommuting variables\cite{HW15}. This rank computation problem has…
Satisfiability modulo nonlinear real arithmetic theory (SMT(NRA)) solving is essential to multiple applications, including program verification, program synthesis and software testing. In this context, recently model constructing…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…
This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
Modern Large Language Models (LLMs) often require external tools, such as machine learning classifiers or knowledge retrieval systems, to provide accurate answers in domains where their pre-trained knowledge is insufficient. This…
Quantized Large Language Models (LLMs) are used more often in qualitative analysis because they run fast and need fewer computing resources. This study examines how different lower bits quantization levels (8-bit, 4-bit, 3-bit, and 2-bit)…
Large Language Models (LLMs) excel in NLP, but their demands hinder their widespread deployment. While Quantization-Aware Training (QAT) offers a solution, its extensive training costs make Post-Training Quantization (PTQ) a more practical…
Motivated by the prevailing paradigm of using unsupervised learning for efficient exploration in reinforcement learning (RL) problems [tang2017exploration,bellemare2016unifying], we investigate when this paradigm is provably efficient. We…
Requirements over strings, commonly represented using natural language (NL), are particularly relevant for software systems due to their heavy reliance on string data manipulation. While individual requirements can usually be analyzed…
Being a fully automated technique for resource analysis, automatic amortized resource analysis (AARA) can fail in returning worst-case cost bounds of programs, fundamentally due to the undecidability of resource analysis. For programmers…
Increasing the number of parameters in large language models (LLMs) usually improves performance in downstream tasks but raises compute and memory costs, making deployment difficult in resource-limited settings. Quantization techniques,…
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves…
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…