Related papers: Aberration in qualitative multilevel designs
We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…
Cosine similarity of contextual embeddings is used in many NLP tasks (e.g., QA, IR, MT) and metrics (e.g., BERTScore). Here, we uncover systematic ways in which word similarities estimated by cosine over BERT embeddings are understated and…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
Pruning has recently been widely adopted to reduce the parameter scale and improve the inference efficiency of Large Language Models (LLMs). Mainstream pruning techniques often rely on uniform layerwise pruning strategies, which can lead to…
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…
Assessing the quality of LLM-generated text remains a fundamental challenge in natural language processing. Current evaluation approaches often rely on isolated metrics or simplistic aggregations that fail to capture the nuanced trade-offs…
Language models (LMs) estimate a probability distribution over strings in a natural language; these distributions are crucial for computing perplexity and surprisal in linguistics research. While we are usually concerned with measuring…
The Gaussian process latent variable model (GPLVM) is a popular probabilistic method used for nonlinear dimension reduction, matrix factorization, and state-space modeling. Inference for GPLVMs is computationally tractable only when the…
This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide…
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…
The Weisfeiler-Leman algorithm ($1$-WL) is a well-studied heuristic for the graph isomorphism problem. Recently, the algorithm has played a prominent role in understanding the expressive power of message-passing graph neural networks…
This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example…
This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
Fine-grained domain generalization (FGDG) is a more challenging task than traditional DG tasks due to its small inter-class variations and relatively large intra-class disparities. When domain distribution changes, the vulnerability of…
Two-level factorial designs are widely used in industrial experiments. For processes involving \(n\) factors, the construction of designs comprising \(2^n\) and \(2^{n-p}\) factorials, arranged in blocks of size \(2^q\) is investigated. The…
Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which…
This paper discusses the estimation of the generalization gap, the difference between generalization performance and training performance, for overparameterized models including neural networks. We first show that a functional variance, a…
Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…