相关论文: From Reachability to Learnability: Geometric Desig…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…

The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging…

The geometric structure of an optimization landscape is argued to be fundamentally important to support the success of deep neural network learning. A direct computation of the landscape beyond two layers is hard. Therefore, to capture the…

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…

Graph Neural Networks (GNNs) have emerged as a powerful, data-driven approach for Quantum Error Correction (QEC) decoding, capable of learning complex noise characteristics directly from syndrome data. However, the robustness of these…

Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial…

Scaling quantum computers requires tight integration of cryogenic control electronics with quantum processors, where Digital-to-Analog Converters (DACs) face severe power and area constraints. We investigate quantum neural network (QNN)…

We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme, which remains largely unknown due to the non-convex optimization landscape, the measurement error, and the…

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics…

Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. Current QNN models primarily employ variational circuits on an ansatz or a quantum feature map, often requiring multiple…

Deep neural network classifiers partition input space into high confidence regions for each class. The geometry of these class manifolds (CMs) is widely studied and intimately related to model performance; for example, the margin depends on…

Monocular depth estimation (MDE) has witnessed remarkable progress driven by Convolutional Neural Networks and transformer-based architectures. However, these approaches typically treat the problem as a generic image-to-image regression on…

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new…

Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of "Neural Collapse", where…

Given the success of the deep convolutional neural networks (DCNNs) in applications of visual recognition and classification, it would be tantalizing to test if DCNNs can also learn spatial concepts, such as straightness, convexity,…