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Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
Non-local operations play a crucial role in computer vision enabling the capture of long-range dependencies through weighted sums of features across the input, surpassing the constraints of traditional convolution operations that focus…
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…
Quantum Neural Networks (QNNs) with random structures have poor trainability due to the exponentially vanishing gradient as the circuit depth and the qubit number increase. This result leads to a general belief that a deep QNN will not be…
A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural…
We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node…
Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems. We study a model problem with such structure -- a binary classification task that uses a deep fully-connected neural network to classify…
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…
Quantum data learning (QDL) provides a framework for extracting physical insights directly from quantum states, bypassing the need for any identification of the classical observable of the theory. A central challenge in many-body physics is…
Ensuring proper generalization is a critical challenge in applying data-driven methods for solving inverse problems in imaging, as neural networks reconstructing an image must perform well across varied datasets and acquisition geometries.…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often…
Quantum neural networks combine quantum computing with advanced data-driven methods, offering promising applications in quantum machine learning. However, the optimal paradigm for balancing trainability and expressivity in QNNs remains an…
Achieving a practical quantum speedup for deep neural networks (DNNs) remains a central yet elusive goal, hindered by the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement. We…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…