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In recent years, there has been growing interest in the field of functional neural networks. They have been proposed and studied with the aim of approximating continuous functionals defined on sets of functions on Euclidean domains. In this…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…

Pre-trained on extensive text and image corpora, current Multi-Modal Large Language Models (MLLM) have shown strong capabilities in general visual reasoning tasks. However, their performance is still lacking in physical domains that require…

Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously…

Graph neural networks (GNNs), as the de-facto model class for representation learning on graphs, are built upon the multi-layer perceptrons (MLP) architecture with additional message passing layers to allow features to flow across nodes.…

MLP-based architectures, which consist of a sequence of consecutive multi-layer perceptron blocks, have recently been found to reach comparable results to convolutional and transformer-based methods. However, most adopt spatial MLPs which…

Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation. We introduce FUTON (Fourier Tensor…

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…

Vision-Language Models (VLMs) combine a vision encoder and a large language model (LLM) through alignment training, showing strong performance on multimodal tasks. A central component in this architecture is the projection layer, which maps…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead,…

Transformer-based language models exhibit complex and distributed behavior, yet their internal computations remain poorly understood. Existing mechanistic interpretability methods typically treat attention heads and multilayer perceptron…

Implicit neural representation (INR) models signals as continuous functions using neural networks, offering efficient and differentiable optimization for inverse problems across diverse disciplines. However, the representational capacity of…

When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…

Multimodal Large Language Models (MLLMs) have remarkably progressed in analyzing and understanding images. Despite these advancements, accurately regressing values in charts remains an underexplored area for MLLMs. For visualization, how do…

This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however…

Recent works have successfully applied Large Language Models (LLMs) to function modeling tasks. However, the reasons behind this success remain unclear. In this work, we propose a new evaluation framework to comprehensively assess LLMs'…

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…