Related papers: Learning Functions on Multiple Sets using Multi-Se…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

In latest years, deep learning has gained a leading role in the pansharpening of multiresolution images. Given the lack of ground truth data, most deep learning-based methods carry out supervised training in a reduced-resolution domain.…

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand,…

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation…

Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification…

Transformers are crucial across many AI fields, such as large language models, computer vision, and reinforcement learning. This prominence stems from the architecture's perceived universality and scalability compared to alternatives. This…

In many real-world applications, modeling both the internal structure of sets and their temporal relationships is essential for capturing complex underlying patterns. Sequential multiple-instance learning aims to address this challenge by…

Many current approaches to machine learning in particle physics use generic architectures that require large numbers of parameters and disregard underlying physics principles, limiting their applicability as scientific modeling tools. In…

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better…

Recently, deep-learning-based approaches have been widely studied for deformable image registration task. However, most efforts directly map the composite image representation to spatial transformation through the convolutional neural…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Most uses of machine learning today involve training a model from scratch for a particular task, or sometimes starting with a model pretrained on a related task and then fine-tuning on a downstream task. Both approaches offer limited…

We present a generalization of Transformers to any-order permutation invariant data (sets, graphs, and hypergraphs). We begin by observing that Transformers generalize DeepSets, or first-order (set-input) permutation invariant MLPs. Then,…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…