Related papers: Partial Redundancy in Saturation
A classic result in algorithmic information theory is that every infinite binary sequence is computable from a Martin-Loef random infinite binary sequence. Proved independently by Kucera and Gacs, this result answered a question by Charles…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topological data analysis where matrix reduction is the major…
Computational efficiency has remained a critical consideration in scaling high-capacity language models, with inference latency and resource consumption presenting significant constraints on real-time applications. The study has introduced…
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
Summarizing legal decisions requires the expertise of law practitioners, which is both time- and cost-intensive. This paper presents techniques for extractive summarization of legal decisions in a low-resource setting using limited expert…
Redundancy is a fundamental characteristic of many biological processes such as those in the genetic, visual, muscular and nervous system; yet its function has not been fully understood. The conventional interpretation of redundancy is that…
A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…
Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming…
High-resolution Multimodal Large Language Models (MLLMs) face prohibitive computational costs during inference due to the explosion of visual tokens. Existing acceleration strategies, such as token pruning or layer sparsity, suffer from…
We present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over…
We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
Recent advancements in Large Language Models (LLMs) have demonstrated impressive capabilities across a range of natural language processing tasks, especially in reasoning, a cornerstone for achieving Artificial General Intelligence (AGI).…
The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations…
We study preprocessing techniques for clause normal forms of LTL formulas. Applying the mechanism of labelled clauses enables us to reinterpret LTL satisfiability as a set of purely propositional problems and thus to transfer simplification…
We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program…
Reasoning tasks are crucial in many domains, especially in science and engineering. Although large language models (LLMs) have made progress in reasoning tasks using techniques such as chain-of-thought and least-to-most prompting, these…
Visual Language Models require substantial computational resources for inference due to the additional input tokens needed to represent visual information. However, these visual tokens often contain redundant and unimportant information,…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…