Related papers: Large deviation properties for pattern statistics …

We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…

Large language models (LLMs) are widely applied across diverse domains, raising concerns about their limitations and potential risks. In this study, we investigate two types of bias that LLMs may display: stereotype bias and deviation bias.…

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…

We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through two parameters only,…

We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

Recent large language models have been trained on vast datasets, but also often on repeated data, either intentionally for the purpose of upweighting higher quality data, or unintentionally because data deduplication is not perfect and the…

Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…

We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we…

Assessing personality traits using large language models (LLMs) has emerged as an interesting and challenging area of research. While previous methods employ explicit questionnaires, often derived from the Big Five model of personality, we…

Infants, adults, non-human primates and non-primates all learn patterns implicitly, and they do so across modalities. The biological evidence supports the hypothesis that the mechanism for this learning is general but computationally local.…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometric space, with the probability of a connection a (scaled)…

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…

Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…

We present a large-deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large-deviation rate function for the probability that the giant component occupies a fixed…

Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…