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Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation…

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…

The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self--gravitating flows in which the dynamics is described in…

Retrieval-augmented generation (RAG) systems face significant challenges in multi-hop question answering (MHQA), where complex queries require synthesizing information across multiple document chunks. Existing approaches typically rely on…

Question Generation (QG), as a challenging Natural Language Processing task, aims at generating questions based on given answers and context. Existing QG methods mainly focus on building or training models for specific QG datasets. These…

Retrieval-augmented generation (RAG) has demonstrated strong performance in single-hop question answering (QA) by integrating external knowledge into large language models (LLMs). However, its effectiveness remains limited in multi-hop QA,…

Retrieval-Augmented Generation (RAG) mitigates hallucination in Large Language Models (LLMs) by incorporating external data, with Knowledge Graphs (KGs) offering crucial information for question answering. Traditional Knowledge Graph…

The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared…

Representing systems using the SAPPhIRE causality model is found useful in supporting design-by-analogy. However, creating a SAPPhIRE model of artificial or biological systems is an effort-intensive process that requires human experts to…

Recursive loops in a logic program present a challenging problem to the PLP framework. On the one hand, they loop forever so that the PLP backward-chaining inferences would never stop. On the other hand, they generate cyclic influences,…

One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to process long contexts, yet a notable gap remains in generating long, aligned outputs. This limitation stems from a training gap where…

Hypothesis generation is a fundamental step in scientific discovery, yet it is increasingly challenged by information overload and disciplinary fragmentation. Recent advances in Large Language Models (LLMs) have sparked growing interest in…

Transforming unstructured text into structured data is a complex task, requiring semantic understanding, reasoning, and structural comprehension. While Large Language Models (LLMs) offer potential, they often struggle with handling…

This paper studies the Lagrange stabilization of a class of nonlinear systems whose linear part has a singular system matrix and which have multiple periodic (in state) nonlinearities. Both state and output feedback Lagrange stabilization…

Despite the crucial importance of accelerating text generation in large language models (LLMs) for efficiently producing content, the sequential nature of this process often leads to high inference latency, posing challenges for real-time…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

Large language models (LLMs) exhibit strong semantic understanding, yet struggle when user instructions involve ambiguous or conceptually misaligned terms. We propose the Language Graph Model (LGM) to enhance conceptual clarity by…

In this paper we extend the study initiated in arXiv:2302.04709v2 [hep-th] to the computation of one-loop elastic amplitudes. We consider 1+1 dimensional massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic…