Related papers: QRAT Polynomially Simulates Merge Resolution

This paper presents the reduced biquaternion mixed least squares and total least squares (RBMTLS) method for solving an overdetermined system $AX \approx B$ in the reduced biquaternion algebra. The RBMTLS method is suitable when matrix $B$…

Retrieval-Augmented Generation (RAG) systems leverage Large Language Models (LLMs) to generate accurate and reliable responses that are grounded in retrieved context. However, LLMs often generate inconsistent outputs for semantically…

Requirements engineering (RE) is critical to software success, yet automating it remains challenging because multiple, often conflicting quality attributes must be balanced while preserving stakeholder intent. Existing Large-Language-Model…

We make progress in a long-standing problem of batch reinforcement learning (RL): learning $Q^\star$ from an exploratory and polynomial-sized dataset, using a realizable and otherwise arbitrary function class. In fact, all existing…

With the growing interest in quantum programs, ensuring their correctness is a fundamental challenge. Although constraint-solving techniques can overcome some limitations of traditional testing and verification, they have not yet been…

We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such…

We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path…

Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…

Fair representation learning (FRL) is a popular class of methods aiming to produce fair classifiers via data preprocessing. Recent regulatory directives stress the need for FRL methods that provide practical certificates, i.e., provable…

Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation…

Popular centroid-based clustering methods are typically optimized for global objectives, and may fail to adequately represent large groups of datapoints. Thus, one needs proportionality notions suited for metric settings. Ideally, such…

Quality estimation (QE) is the task of automatically evaluating the quality of translations without human-translated references. Calculating BLEU between the input sentence and round-trip translation (RTT) was once considered as a metric…

Training large reasoning models (LRMs) with reinforcement learning in STEM domains is hindered by the scarcity of high-quality, diverse, and verifiable problem sets. Existing synthesis methods, such as Chain-of-Thought prompting, often…

One approach to reducing the massive costs of large language models (LLMs) is the use of quantized or sparse representations for training or deployment. While post-training compression methods are very popular, the question of obtaining…

This paper considers solving convex quadratic programs (QPs) in a real-time setting using a regularized and smoothed Fischer-Burmeister method (FBRS). The Fischer-Burmeister function is used to map the optimality conditions of the quadratic…

Quadratization for partial differential equations (PDEs) is a process that transforms a nonquadratic PDE into a quadratic form by introducing auxiliary variables. This symbolic transformation has been used in diverse fields to simplify the…

Defining and measuring the error of a measurement is one of the most fundamental activities in experimental science. However, quantum theory shows a peculiar difficulty in extending the classical notion of root-mean-square (rms) error to…

The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…

This paper presents a formally verified quantifier elimination (QE) algorithm for first-order real arithmetic by linear and quadratic virtual substitution (VS) in Isabelle/HOL. The Tarski-Seidenberg theorem established that the first-order…

Reinforcement learning (RL) is a classical tool to solve network control or policy optimization problems in unknown environments. The original Q-learning suffers from performance and complexity challenges across very large networks. Herein,…