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Inference-time sampling can elicit strong reasoning abilities from language models without additional training. Existing power-sampling methods do so by sharpening the distribution over full generated outputs, favoring completions that are…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…
A dramatic rise in the flow of manipulated image content on the Internet has led to an aggressive response from the media forensics research community. New efforts have incorporated increased usage of techniques from computer vision and…
Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
In this paper, among other results, there are described (complete) simple - simultaneously ideal- and congruence-simple - endomorphism semirings of (complete) idempotent commutative monoids; it is shown that the concepts of simpleness,…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
Provenance, or information about the sources, derivation, custody or history of data, has been studied recently in a number of contexts, including databases, scientific workflows and the Semantic Web. Many provenance mechanisms have been…
Large language models are increasingly customized through fine-tuning and other adaptations, creating challenges in enforcing licensing terms and managing downstream impacts. Tracking model origins is crucial both for protecting…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ideals of commutative rings. In order to establish a good…
Anytime inference is inference performed incrementally, with the accuracy of the inference being controlled by a tunable parameter, usually time. Such anytime inference algorithms are also usually interruptible, gradually converging to the…
We study the last fall degrees of {\em semi-local} polynomial systems, and the computational complexity of solving such systems for closed-point and rational-point solutions, where the systems are defined over a finite field. A semi-local…
It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a…
The main objective of explanations is to transmit knowledge to humans. This work proposes to construct informative explanations for predictions made from machine learning models. Motivated by the observations from social sciences, our…
Predicting compound-protein affinity is critical for accelerating drug discovery. Recent progress made by machine learning focuses on accuracy but leaves much to be desired for interpretability. Through molecular contacts underlying…
Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these,…
Explaining why an answer is (or is not) returned by a query is important for many applications including auditing, debugging data and queries, and answering hypothetical questions about data. In this work, we present the first practical…