Related papers: Theoretical Properties of Projection Based Multila…

Deep functional maps have recently emerged as a successful paradigm for non-rigid 3D shape correspondence tasks. An essential step in this pipeline consists in learning feature functions that are used as constraints to solve for a…

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…

Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a…

To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional…

Multilayer perceptrons (MLPs) are an integral part of large language models, yet their dense representations render them difficult to understand, edit, and steer. Recent methods learn interpretable approximations via neuron-level sparsity,…

In this paper, a novel multi-head multi-layer perceptron (MLP) structure is presented for implicit neural representation (INR). Since conventional rectified linear unit (ReLU) networks are shown to exhibit spectral bias towards learning…

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Vision-Language Pre-Trained models, notably CLIP, that utilize contrastive learning have proven highly adept at extracting generalizable visual features. To inherit the well-learned knowledge of VLP models for downstream tasks, several…

The traditional Multilayer Perceptron (MLP) using McCulloch-Pitts neuron model is inherently limited to a set of neuronal activities, i.e., linear weighted sum followed by nonlinear thresholding step. Previously, Generalized Operational…

A multi-layer perceptron (MLP) is a type of neural networks which has a long history of research and has been studied actively recently in computer vision and graphics fields. One of the well-known problems of an MLP is the capability of…

Implicit neural fields, typically encoded by a multilayer perceptron (MLP) that maps from coordinates (e.g., xyz) to signals (e.g., signed distances), have shown remarkable promise as a high-fidelity and compact representation. However, the…

Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…

In this paper, we propose a probabilistic representation of MultiLayer Perceptrons (MLPs) to improve the information-theoretic interpretability. Above all, we demonstrate that the activations being i.i.d. is not valid for all the hidden…

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 Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…

Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations.…

A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing…

Inner products of neural network feature maps arise in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It…

Multivariate functional data has received considerable attention but testing for equality of mean surfaces and its profile has limited progress. The existing literature has tested equality of either mean curves of univariate functional…