相关论文: Lifted Unit Propagation for Effective Grounding

Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…

In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit…

We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…

The determinant and higher loop terms, usually treated with the Pauli-Villars and higher covariant derivatives methods, in the background field method in 4 dimensions can hardly be regularized simultaneously. At the same time we observe…

The rise of foundation models has shifted focus from resource-intensive fine-tuning to prompt engineering, a paradigm that steers model behavior through input design rather than weight updates. While manual prompt engineering faces…

Reasoning on large and complex real-world models is a computationally difficult task, yet one that is required for effective use of many AI applications. A plethora of inference algorithms have been developed that work well on specific…

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…

Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between…

Foundation models are rapidly transforming Earth Observation data mining by enabling generalizable and scalable solutions for key tasks such as scene classification and semantic segmentation. While most efforts in the geospatial domain have…

It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…

Post-training has demonstrated its importance in enhancing the reasoning capabilities of large language models (LLMs). The primary post-training methods can be categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning…

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of…

Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…

Repeated executions of reasoning tasks for varying inputs are necessary in many applicative settings, such as stream reasoning. In this context, we propose an incremental grounding approach for the answer set semantics. We focus on the…

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling…

Binary Decision Diagram (BDD) based set bounds propagation is a powerful approach to solving set-constraint satisfaction problems. However, prior BDD based techniques in- cur the significant overhead of constructing and manipulating graphs…

Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…

This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…

Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…

Augmenting large language models (LLM) to use external tools enhances their performance across a variety of tasks. However, prior works over-rely on task-specific demonstration of tool use that limits their generalizability and…