Related papers: Urgent problems at small x
The short-time and global behaviour are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition…
Automated question-answering (QA) systems increasingly rely on retrieval-augmented generation (RAG) to ground large language models (LLMs) in authoritative medical knowledge, ensuring clinical accuracy and patient safety in Artificial…
We start with an effective field theory containing classical vortex solutions and show that the fluctuations of these vortices are described by an effective string theory. Viewed as a model for long distance QCD, this theory provides a…
We examine critically the evidence for deviations from next-to-leading order perturbative DGLAP evolution in HERA data. We briefly review the status of perturbative small-x resummation and of global determinations of parton distributions.…
In this paper, we analyze and empirically show that the learned relevance for conventional information retrieval (IR) scenarios may be inconsistent in retrieval-augmented generation (RAG) scenarios. To bridge this gap, we introduce OpenRAG,…
Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…
Large language models (LLMs) inevitably exhibit hallucinations since the accuracy of generated texts cannot be secured solely by the parametric knowledge they encapsulate. Although retrieval-augmented generation (RAG) is a practicable…
Microbiome data are complex in nature, involving high dimensionality, compositionally, zero inflation, and taxonomic hierarchy. Compositional data reside in a simplex that does not admit the standard Euclidean geometry. Most existing…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
Closure seems to be something rheologists would prefer to avoid. Here, the story of closure is told in such a way that one should enduringly forget any improper undertone of "uncontrolled approximation" or "necessary evil" which might…
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are…
Retrieval-Augmented Generation (RAG) has emerged as a critical technique for enhancing large language model (LLM) capabilities. However, practitioners face significant challenges when making RAG deployment decisions. While existing research…
We present an effective action for the electroweak sector of the Standard Model valid for the calculation of scattering amplitudes in the high energy (Regge) limit. Gauge invariant Wilson lines are introduced to describe reggeized degrees…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
Neural networks have demonstrated significant potential in solving partial differential equations (PDEs). While global approaches such as Physics-Informed Neural Networks (PINNs) offer promising capabilities, they often lack inherent…
Retrieval Augmented Generation (RAG) provides the necessary informational grounding to LLMs in the form of chunks retrieved from a vector database or through web search. RAG could also use knowledge graph triples as a means of providing…
Exchange-driven growth (EDG) is a process in which pairs of clusters interact by exchanging single unit with a rate given by a kernel $K(j,k)$. Despite EDG model's common use in the applied sciences, its rigorous mathematical treatment is…
We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…
Retrieval-augmented generation (RAG) has emerged as an approach to augment large language models (LLMs) by reducing their reliance on static knowledge and improving answer factuality. RAG retrieves relevant context snippets and generates an…
Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or…