Related papers: Generalization analysis of quantum neural networks…
Neural ordinary differential equations (neural ODEs) are a popular family of continuous-depth deep learning models. In this work, we consider a large family of parameterized ODEs with continuous-in-time parameters, which include…
Hybrid classical-quantum models aim to harness the strengths of both quantum computing and classical machine learning, but their practical potential remains poorly understood. In this work, we develop a unified mathematical framework for…
Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing…
Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms.…
Quantization lowers memory usage, computational requirements, and latency by utilizing fewer bits to represent model weights and activations. In this work, we investigate the generalization properties of quantized neural networks, a…
Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning, analogous to classical neural networks in deep learning. Ensuring consistent performance across diverse datasets is crucial for…
The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep…
Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network…
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their…
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…
Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate \emph{scaled} ResNet in the limit of infinitely deep and wide…
Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…
We derive a new Rademacher complexity bound for deep neural networks using Koopman operators, group representations, and reproducing kernel Hilbert spaces (RKHSs). The proposed bound describes why the models with high-rank weight matrices…
We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the…
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core…
Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…
We derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out…
We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear…