Related papers: Learning and generalization theories of large comm…
Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this…
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…
Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…
The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy…
PAC-Bayes learning is an established framework to both assess the generalisation ability of learning algorithms, and design new learning algorithm by exploiting generalisation bounds as training objectives. Most of the exisiting bounds…
The performance of large neural networks can be judged not only by their storage capacity but also by the time required for learning. A polynomial learning algorithm with learning time $\sim N^2$ in a network with $N$ units might be…
Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…
Machine Learning Interatomic Potentials play a fundamental role in computational chemistry and materials science, enabling applications from molecular dynamics simulations to drug design and materials discovery. While recent approaches can…
We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…
Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC)…
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…
Bounding the generalization error of a supervised learning algorithm is one of the most important problems in learning theory, and various approaches have been developed. However, existing bounds are often loose and lack of guarantees. As a…
Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…
We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…
We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions:…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
This paper provides theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, responding to an open question in the…
In this paper we show that the expected generalisation performance of a learning machine is determined by the distribution of risks or equivalently its logarithm -- a quantity we term the risk entropy -- and the fluctuations in a quantity…