Related papers: Multivariate growth and cogrowth
Retrieval-augmented generation (RAG) frameworks enable large language models (LLMs) to retrieve relevant information from a knowledge base and incorporate it into the context for generating responses. This mitigates hallucinations and…
A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular,…
Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on…
Multilingual retrieval-augmented generation (MRAG) requires models to effectively acquire and integrate beneficial external knowledge from multilingual collections. However, most existing studies employ a unitive process where queries of…
We construct an increasing, submultiplicative, arbitrarily rapid function which is not equivalent to the growth function of any finitely generated algebra, demonstrating the difficulty in characterizing growth functions in an asymptotic…
Accurate assessment of cognitive decline from spontaneous speech remains challenging due to limited dataset size and class imbalance. In this work, we propose a large language model (LLM)-driven data augmentation framework to improve the…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Two currently debated problems in galaxy evolution, the fundamentally local or global nature of the main sequence of star formation and the evolution of the mass-size relation of star forming galaxies (SFGs), are shown to be intimately…
In this paper we study logarithmic double phase problems with variable exponents involving nonlinearities that have generalized critical growth. We first prove new continuous and compact embedding results in order to guarantee the…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
Advancements in natural language generation (NLG) and large language models (LLMs) have led to proficient text generation in various tasks. However, integrating intricate constraints into neural text generation, due to LLMs' opacity,…
We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…
We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both, their growths tend to the upper bound and their cogrowths tend to the lower bound. The condition is represented by planarity…
We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…
Convolutional Low-Density-Parity-Check (LDPC) ensembles have excellent performance. Their iterative threshold increases with their average degree, or with the size of the coupling window in randomized constructions. In the later case, as…
Let $G$ be a toral relatively hyperbolic group, and let $\varphi\in\mathrm{Aut}(G)$. We prove that, under iteration of $\varphi$, the conjugacy length $||\varphi^n(g)||$ of every element $g\in G$ grows like $n^d\lambda^n$ for some…
Post-training compression of large language models (LLMs) often relies on low-rank weight approximations that represent each column of the weight matrix in a shared low-dimensional subspace. This strategy is computationally efficient but…
We show that there exists a finitely generated group of growth ~f for all functions f:\mathbb{R}\rightarrow\mathbb{R} satisfying f(2R) \leq f(R)^{2} \leq f(\eta R) for all R large enough and \eta\approx2.4675 the positive root of…
We analyze the Fourier growth, i.e. the $L_1$ Fourier weight at level $k$ (denoted $L_{1,k}$), of various well-studied classes of "structured" $\mathbb{F}_2$-polynomials. This study is motivated by applications in pseudorandomness, in…
We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for…