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Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
As deep learning gains popularity in modelling dynamical systems, we expose an underappreciated misunderstanding relevant to modelling dynamics on networks. Strongly influenced by graph neural networks, latent vertex embeddings are…
Deep neural networks (DNNs) have recently achieved impressive success across a wide range of real-world vision and language processing tasks, spanning from image classification to many other downstream vision tasks, such as object…
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…
Real-world networks are composed of diverse interacting and evolving entities, while most of existing researches simply characterize them as particular static networks, without consideration of the evolution trend in dynamic networks.…
Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered…
Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large…
Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
Conventional computer vision models rely on very deep, feedforward networks processing whole images and trained offline with extensive labeled data. In contrast, biological vision relies on comparatively shallow, recurrent networks that…
Zooplankton images, like many other real world data types, have intrinsic properties that make the design of effective classification systems difficult. For instance, the number of classes encountered in practical settings is potentially…
Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…