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Multimodal problems are omnipresent in the real world: autonomous driving, robotic grasping, scene understanding, etc... We draw from the well-developed analysis of similarity to provide an example of a problem where neural networks are…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
Textural and structural features can be regraded as "two-view" feature sets. Inspired by the recent progress in multi-view learning, we propose a novel two-view classification method that models each feature set and optimizes the process of…
Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently…
We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their…
In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…
The main objective of this paper is to investigate the spectral properties, maximum principles, and shape optimization problems for a broad class of nonlinear ``superposition operators" defined as continuous superpositions of operators of…
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that…
Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…
Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A…
Integrating task-relevant information into neural representations is a fundamental ability of both biological and artificial intelligence systems. Recent theories have categorized learning into two regimes: the rich regime, where neural…
Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered…
For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…
Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…
Deep learning models extract, before a final classification layer, features or patterns which are key for their unprecedented advantageous performance. However, the process of complex nonlinear feature extraction is not well understood, a…
Fully Connected Neural Networks (FCNNs) are often regarded as simple and intuitive architectures, yet they serve as the foundation for more complex models. Nonetheless, the lack of consensus on their interpretability continues to pose…
Multispectral and hyperspectral images are increasingly popular in different research fields, such as remote sensing, astronomical imaging, or precision agriculture. However, the amount of free data available to perform machine learning…
Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine…
It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…
We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a graph signal can be incorporated. It merges several…