Related papers: Multivariate growth and cogrowth
Two major areas of interest in the era of Large Language Models regard questions of what do LLMs know, and if and how they may be able to reason (or rather, approximately reason). Since to date these lines of work progressed largely in…
Large Language Models (LLMs) have achieved remarkable capabilities, yet their improvement methods remain fundamentally constrained by human design. We present Self-Developing, a framework that enables LLMs to autonomously discover,…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
We review one of the most fruitful areas in cosmology today that bridge theory and data - the temporal growth of large-scale structure. We go over the growth's physical foundations, and derive its behavior in simple cosmological models.…
We study the cosmology of Galileon modified gravity models in the linear perturbation regime. We derive the fully covariant and gauge invariant perturbed field equations using two different methods, which give consistent results, and solve…
In this manuscript, we studied the accelerated expansion history of the universe and the formations of large-scale structures using $f(Q)$ gravity model. The expansion rate of the universe within distance modulus and redshift has been…
In the literature, it was proposed that the growth index $\gamma$ is useful to distinguish the scenarios of dark energy and modified gravity. In the present work, we consider the constraints on the growth index $\gamma$ by using the latest…
We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the…
Large Language Models (LLMs) showcase remarkable abilities, yet they struggle with limitations such as hallucinations, outdated knowledge, opacity, and inexplicable reasoning. To address these challenges, Retrieval-Augmented Generation…
This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it…
Large language models (LLMs) are powerful tools that have found applications beyond human-machine interfaces and chatbots. In particular, their ability to generate reasoning traces motivated their use in many prediction tasks like math…
Generating feasible Pareto fronts for constrained bi-objective continuous optimization is central to multi-criteria decision-making. Existing methods usually rely on iterative scalarization, evolutionary search, or problem-specific solvers,…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…
It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d,C), SU(d)) and Hermitian matrices. We here…
In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (\alpha ,\beta…
The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. It is of interest to differentiate between them, by using both the expansion history and the growth history. In the…
Multi-objective optimization is a common problem in practical applications, and multi-objective evolutionary algorithm (MOEA) is considered as one of the effective methods to solve these problems. However, their randomness sometimes…
This paper investigates Large Language Models (LLMs) ability to assess the economic soundness and theoretical consistency of empirical findings in spatial econometrics. We created original and deliberately altered "counterfactual" summaries…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
The sharp growth and distortion theorems are established for slice monogenic extensions of univalent functions on the unit disc $\mathbb D\subset \mathbb C$ in the setting of Clifford algebras, based on a new convex combination identity.…