Related papers: Quantified Linear and Polynomial Arithmetic Satisf…

Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common…

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to…

Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in…

Post-training quantization (PTQ) is an effective approach for deploying large language models (LLMs) under memory and latency constraints. Most existing PTQ methods determine quantization parameters by minimizing a layer-wise reconstruction…

Quantization is a promising approach for reducing memory overhead and accelerating inference, especially in large pre-trained language model (PLM) scenarios. While having no access to original training data due to security and privacy…

Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…

Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains…

Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying…

The growing scale of large language models (LLMs) not only demands extensive computational resources but also raises environmental concerns due to their increasing carbon footprint. Model quantization emerges as an effective approach that…

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…

Students benefit from math problems contextualized to their interests. Large language models (LLMs) offer promise for efficient personalization at scale. However, LLM-generated personalized problems may often have problems such as…

Partial penalized tests provide flexible approaches to testing linear hypotheses in high dimensional generalized linear models. However, because the estimators used in these tests are local minimizers of potentially non-convex…

Post-training Quantization (PTQ) has become a widely used technique for improving inference efficiency of large language models (LLMs). However, existing PTQ methods generally suffer from crucial limitations such as heavy calibration data…

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…

Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…

Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic formula (whose atoms are polynomial constraints) with…

We present a novel approach to the automatic synthesis of recursive programs from mixed-quantifier first-order logic properties. Our approach uses Skolemization to reduce the mixed-quantifier synthesis problem to a $\forall^*$-synthesis…

Network quantization has gained increasing attention with the rapid growth of large pre-trained language models~(PLMs). However, most existing quantization methods for PLMs follow quantization-aware training~(QAT) that requires end-to-end…

We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…