arXiv research

This work improves generalisation bounds using chaining and information theory.

Study shows bounds on volumes of weakly generalised alternating knots.

New PAC-Bayes bounds use Wasserstein distances to improve generalization.

New method optimises learning via surrogate PAC-Bayes bounds.

Paper simplifies link classification in 3-sphere using braids and templates.

Novel strategy for federated learning with privacy-preserving predictors and nonvacuous generalization bounds.

The paper improves generalization bounds using interpolation between various divergences.

PAC-Bayes bound requires prior to place mass on high-performing predictors.

Develops PAC-Bayesian framework for physics-informed machine learning.

Study generalization of voting classifiers using margin-based bounds.

New algorithm reduces regret in delayed feedback generalised linear bandits.

New bounds for shallow neural networks with deterministic parameters.

New bounds link flat minima to good generalisation in overparameterized models.

The purpose of this paper is to study the behaviour of sequences of generalised monopoles with a uniform bound on a certain L2-norm. We focus on the case that the target hyperKahler manifolds are Swann bundles. In 3-dimensional case, suppose that there exists an open submanifold Y' such that the hyperKahler potential a…

Quantum reservoirs risk bounds are analyzed using Rademacher complexity.

New stability bounds for GD in overparameterised shallow nets without NTK assumptions.

This work uncovers algorithm-dependent regularisation in diffusion models.

Contrastive unsupervised representation learning (CURL) is the state-of-the-art technique to learn representations (as a set of features) from unlabelled data. While CURL has collected several empirical successes recently, theoretical understanding of its performance was still missing. In a recent work, Arora et al. (2…

Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definit…

New PAC-Bayes bounds for unbounded loss functions.

We provide bounds on control learning error in stochastic systems.

Investigates Lipschitz continuity in neural networks across various settings.

In this paper, we establish a generalised Blaschke-Santalò inequality for convex bodies in $\mathbb R^{n+1}$. This inequality gives an upper bound estimate for the product of dual quermassintegrals of convex body and its polar set. Our argument is based on induction on dimensions.

New bounds improve generalization in machine learning with high probability.

Graph neural networks generalize well under certain conditions, explained by learning theory.

Improved PAC-Bayesian bounds by considering example difficulty.

PAC-Bayes bound for stable RNNs in time-series data.

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 values. This bound has no direct dependence on the number of weights and compares…

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating links of Menasco. We use this to prove various facts about the hyperbolic geometr…

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 for good generalisation is information about many similar learning tasks. Similar …

New examples show no upper bounds on link volumes on incompressible surfaces.

Improved similarity search in embeddings using InfoNCE loss.

New method reveals why GNNs perform well on certain datasets.

New bounds for model generalization under deterministic gradient descent.

OGD proves robustness to Catastrophic Forgetting in Continual Learning.

We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional …

Investigates tight PAC-Bayes bounds for small datasets.

The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of $L^q$ stability, and the strong use of moment inequalities. $L^q$ stability e…

The paper improves transformer generalization bounds using rank-dependent covering number bounds.

Paper uses SLT to improve model selection for SHM.

Sharp lower bound found for integral varifolds' mean curvature.

We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting result follows from an area comparison theorem for hypersurfaces with non-positi…

In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem…

Study introduces indecomposability for varifolds, leading to geometric consequences.

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map. This is an exposition of a special case of th…

Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.

Study on approximability and generalization in machine learning.