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The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…

We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…

Retrieval-Augmented Generation (RAG) has become a foundational paradigm for equipping large language models (LLMs) with external knowledge, playing a critical role in information retrieval and knowledge-intensive applications. However,…

Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequence. In this…

Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…

A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…

In comparison to the interpretation of classification models, the explanation of sequence generation models is also an important problem, however it has seen little attention. In this work, we study model-agnostic explanations of a…

Recent advances in Large Language Models (LLMs) have significantly improved complex reasoning capabilities. Retrieval-Augmented Generation (RAG) has further extended these capabilities by grounding generation in dynamically retrieved…

In their study of cyclic pattern containment, Domagalski et al. conjecture differential equations for the generating functions of circular permutations avoiding consecutive patterns of length 3. In this note, we prove and significantly…

Table Question Answering (TQA) aims to answer natural language questions over structured tables. Large Language Models (LLMs) enable promising solutions to this problem, with operator-centric solutions that generate table manipulation…

The generation of questions and answers (QA) from knowledge graphs (KG) plays a crucial role in the development and testing of educational platforms, dissemination tools, and large language models (LLM). However, existing approaches often…

In this paper we present the state of the art about the quarks: group SU(3), Lie algebra, the electric charge and mass. The quarks masses are generated in the same way as the lepton masses. It is constructed a term in the Lagrangian that…

Retrieval-Augmented Generation (RAG) grounds Large Language Models (LLMs) in external knowledge but often suffers from flat context representations and stateless retrieval, leading to unstable performance. We propose Stateful…

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…

I propose a paradigm for scientific progress in NLP centered around developing scalable, data-driven theories of linguistic structure. The idea is to collect data in tightly scoped, carefully defined ways which allow for exhaustive…

Retrieval-augmented generation (RAG) has become a fundamental paradigm for addressing the challenges faced by large language models in handling real-time information and domain-specific problems. Traditional RAG systems primarily rely on…

Within the evolving landscape of deep learning, the dilemma of data quantity and quality has been a long-standing problem. The recent advent of Large Language Models (LLMs) offers a data-centric solution to alleviate the limitations of…

For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…

Although the rise of large language models (LLMs) has introduced new opportunities for time series forecasting, existing LLM-based solutions require excessive training and exhibit limited transferability. In view of these challenges, we…