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Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a…
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.…
Attention heads are one of the building blocks of large language models (LLMs). Prior work on investigating their operation mostly focused on analyzing their behavior during inference for specific circuits or tasks. In this work, we seek a…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…
Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we…
Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in…
This study identifies that visual-related functional decoding is distributed across different decoder layers in Multimodal Large Language Models (MLLMs). Typically, each function, such as counting, grounding, or OCR recognition, narrows…
Due to their weak inductive bias, Multi-Layer Perceptrons (MLPs) have subpar performance at low-compute levels compared to standard architectures such as convolution-based networks (CNN). Recent work, however, has shown that the performance…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way. For networks, previously proposed systems are developed. Perceptron networks in disjunctive…
Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities.…
This paper gives the definition of Transparent Neural Network "TNN" for the simulation of the globallocal vision and its application to the segmentation of administrative document image. We have developed and have adapted a recognition…
Click-through rate (CTR) prediction is one of the fundamental tasks for online advertising and recommendation. While multi-layer perceptron (MLP) serves as a core component in many deep CTR prediction models, it has been widely recognized…
Compared to convolutional layers, fully-connected (FC) layers are better at modeling the long-range dependencies but worse at capturing the local patterns, hence usually less favored for image recognition. In this paper, we propose a…
Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…
Multi-layer perceptrons (MLP) have proven to be effective scene encoders when combined with higher-dimensional projections of the input, commonly referred to as \textit{positional encoding}. However, scenes with a wide frequency spectrum…
Many real-world phenomena can be modeled as a graph, making them extremely valuable due to their ubiquitous presence. GNNs excel at capturing those relationships and patterns within these graphs, enabling effective learning and prediction…