Related papers: Generalization Bounds and Statistical Guarantees f…
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…
Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…
Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the…
We describe an approach for estimating the statistical risk of deep networks that contain a mix of learned and known operators. Building on the maximal training error bounds previously established for known operator learning, we derive a…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
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.…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
In this work, we study out-of-distribution (OOD) generalization in meta-reinforcement learning from an information-theoretic perspective. We begin by establishing OOD generalization bounds for meta-supervised learning under two distinct…
Length generalization remains a persistent challenge for neural networks: recurrent models tend to suffer from positional biases, while transformers are constrained by fixed computational depth. Regular languages provide a frequently used…
Group Relative Policy Optimization (GRPO) has emerged as the de facto Reinforcement Learning (RL) objective driving recent advancements in Multimodal Large Language Models. However, extending this success to open-source multimodal…
Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…
Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including…
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…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…
In this work we study generalization guarantees for the metric learning problem, where the metric is induced by a neural network type embedding of the data. Specifically, we provide uniform generalization bounds for two regimes -- the…
In this work, we propose a notion of practical learnability grounded in finite sample settings, and develop a conjugate learning theoretical framework based on convex conjugate duality to characterize this learnability property. Building on…
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…
This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…