Related papers: Generalization analysis of quantum neural networks…
Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the…
Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
Machine learning models trained by different optimization algorithms under different data distributions can exhibit distinct generalization behaviors. In this paper, we analyze the generalization of models trained by noisy iterative…
Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal…
There has been considerable effort to better understand the generalization capabilities of deep neural networks both as a means to unlock a theoretical understanding of their success as well as providing directions for further improvements.…
We investigate approaches to regularisation during fine-tuning of deep neural networks. First we provide a neural network generalisation bound based on Rademacher complexity that uses the distance the weights have moved from their initial…
Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns…
Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide…
We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based…
Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of…
In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…
Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform…
We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that…
This paper presents novel generalization bounds for the multi-kernel learning problem. Motivated by applications in sensor networks and spatial-temporal models, we assume that the dataset is mixed where each sample is taken from a finite…
Algorithmic stability is among the most potent techniques in generalization analysis. However, its derivation usually requires a stepsize $\eta_t = \mathcal{O}(1/t)$ under non-convex training regimes, where $t$ denotes iterations. This…
Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when…
This paper aims at studying the sample complexity of graph convolutional networks (GCNs), by providing tight upper bounds of Rademacher complexity for GCN models with a single hidden layer. Under regularity conditions, theses derived…