相关论文: Contamination-Free Measures and Algebraic Operatio…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To…
With the present paper we conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instability from a random Gaussian field of density fluctuations. In paper I, we…
Large language models can exhibit emergent reasoning behaviors, often manifested as recurring lexical patterns (e.g., "wait," indicating verification). However, complex reasoning trajectories remain sparse in unconstrained sampling, and…
Networks can be highly complex systems with numerous interconnected components and interactions. Granular computing offers a framework to manage this complexity by decomposing networks into smaller, more manageable components, or granules.…
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…
The language models, especially the basic text classification models, have been shown to be susceptible to textual adversarial attacks such as synonym substitution and word insertion attacks. To defend against such attacks, a growing body…
Most of the existing information retrieval systems are based on bag of words model and are not equipped with common world knowledge. Work has been done towards improving the efficiency of such systems by using intelligent algorithms to…
The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of…
We use information geometry, in which the local distance between models measures their distinguishability from data, to quantify the flow of information under the renormalization group. We show that information about relevant parameters is…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We are faced with data comprised of entities interacting over time: this can be individuals meeting, customers buying products, machines exchanging packets on the IP network, among others. Capturing the dynamics as well as the structure of…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…
We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Chemical systems are traditionally described by lists of species, reactions, and externally imposed kinetic laws, a framework that lacks an intrinsic algebraic structure governing how transformations compose. We propose an axiomatic…
A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…