相关论文: Functional Multi-Layer Perceptron: a Nonlinear Too…

While Large Language Models (LLMs) are fundamentally next-token prediction systems, their practical applications extend far beyond this basic function. From natural language processing and text generation to conversational assistants and…

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…

Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…

Recent progress on Transformers and multi-layer perceptron (MLP) models provide new network architectural designs for computer vision tasks. Although these models proved to be effective in many vision tasks such as image recognition, there…

In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between…

We present a model of Continuous Variable Quantum Perceptron (CVQP) whose architecture implements a classical perceptron. The necessary non-linearity is obtained via measuring the output qubit and using the measurement outcome as input to…

The wide variety of brain imaging technologies allows us to exploit information inherent to different data modalities. The richness of multimodal datasets may increase predictive power and reveal latent variables that otherwise would have…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…

We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…

In this study, we focus on a generalized nonparametric scalar-on-function regression model for heterogeneously distributed and strongly mixing data. We provide almost complete convergence rates for the local linear estimator of the…

The classical functional linear regression model (FLM) and its extensions, which are based on the assumption that all individuals are mutually independent, have been well studied and are used by many researchers. This independence…

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…

Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an interpretation for their classification results. Machine learning models that are interpretable are…

Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…

Multi-Task Learning (MTL) aims at boosting the overall performance of each individual task by leveraging useful information contained in multiple related tasks. It has shown great success in natural language processing (NLP). Currently, a…

Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily…

We argue that many properties of fully-connected feedforward neural networks (FCNNs), also called multi-layer perceptrons (MLPs), are explainable from the analysis of a single pair of operations, namely a random projection into a…

The performance of multilingual pretrained models is highly dependent on the availability of monolingual or parallel text present in a target language. Thus, the majority of the world's languages cannot benefit from recent progress in NLP…