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Implicit neural representations are a promising new avenue of representing general signals by learning a continuous function that, parameterized as a neural network, maps the domain of a signal to its codomain; the mapping from spatial…
Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…
Neural models learn data representations that lie on low-dimensional manifolds, yet modeling the relation between these representational spaces is an ongoing challenge. By integrating spectral geometry principles into neural modeling, we…
Many neural network architectures are known to be Turing Complete, and can thus, in principle implement arbitrary algorithms. However, Transformers are unique in that they can implement gradient-based learning algorithms under simple…
With the proliferation of mobile devices and the Internet of Things, deep learning models are increasingly deployed on devices with limited computing resources and memory, and are exposed to the threat of adversarial noise. Learning deep…
Compact neural network offers many benefits for real-world applications. However, it is usually challenging to train the compact neural networks with small parameter sizes and low computational costs to achieve the same or better model…
Implicit Neural Representations (INRs) are proving to be a powerful paradigm in unifying task modeling across diverse data domains, offering key advantages such as memory efficiency and resolution independence. Conventional deep learning…
We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…
In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning…
Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to…
Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…
We propose a novel method to train deep convolutional neural networks which learn from multiple data sets of varying input sizes through weight sharing. This is an advantage in chemometrics where individual measurements represent exact…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
In this paper, we develop novel techniques that can be used to alter the architecture of a neural network, while maintaining the function it represents. Such operations are known as function preserving transforms and have proven useful in…
Convolutional Neural Networks are very efficient at processing signals defined on a discrete Euclidean space (such as images). However, as they can not be used on signals defined on an arbitrary graph, other models have emerged, aiming to…
Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…
Inspired by the brain, deep neural networks (DNN) are thought to learn abstract representations through their hierarchical architecture. However, at present, how this happens is not well understood. Here, we demonstrate that DNN learn…
State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework…