Related papers: From Reachability to Learnability: Geometric Desig…

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of…

Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of…

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds…

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are…

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the…

A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Deep learning optimization exhibits structure that is not captured by worst-case gradient bounds. Empirically, gradients along training trajectories are often temporally predictable and evolve within a low-dimensional subspace. In this work…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…

Deep Neural Networks (DNNs) have shown unparalleled achievements in numerous applications, reflecting their proficiency in managing vast data sets. Yet, their static structure limits their adaptability in ever-changing environments. This…

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…

The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process…

The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…

Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…