arXiv research

Investigates gradient descent dynamics and introduces new regularisation methods.

We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is the core of kernel methods in machine learning as it makes th…

SPReD uses uncertainty to decide imitation from demonstrations.

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logari…

Graph poly-Laplacian method improves regression accuracy.

DAEs can generate images without additional loss terms, inheriting VAE properties.

Paper advances sparse regularisation theory for measures with new kernel insights.

This paper improves inverse problem solving with weakly convex regularisers and proves convergence.

GNIs induce a regulariser that penalizes high-frequency components in neural network activations.

We introduce and study a notion of singular hermitian metrics on holomorphic vector bundles, following Berndtsson and P{ă}un. We define what it means for such a metric to be curved in the sense of Griffiths and investigate the assumptions needed in order to locally define the cuvature $Θ^h$ as a matrix of currents. We …

Generalised regularisation equals robustness for exotic function classes.

A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.

A Python package solves source duplication in single channel LVMs using spectral regularisation.

We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regulari…

New framework monitors neural network training and reveals regularisation mechanisms.

Improved control approach for correlated bandits with better performance.

This work uncovers algorithm-dependent regularisation in diffusion models.

Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov regularisation parameter from noisy data. In this work, we improve their results and ext…

New method prevents deep learning forgetting past by remembering key examples.

Novel approach finds implicit regularisation in two-player games using BEA.

Regularization preserves topological data structure in autoencoders.

Regularisation improves ML classifier stability against poisoning attacks.

Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.

Paper proves uniqueness of Ricci flows from nonatomic measures on surfaces.

Study on GD and SGD over diagonal networks, focusing on stepsizes and regularisation.

This work shows how penalising bias terms in norm regularisation leads to sparse solutions.

Regularizes ML algorithms for robust multivariate analysis against distribution shifts.

Study on how noise and variation-norm regularisation help shallow ReLU networks use fewer neurons.

Convolutional neural networks have had a great success in numerous tasks, including image classification, object detection, sequence modelling, and many more. It is generally assumed that such neural networks are translation invariant, meaning that they can detect a given feature independent of its location in the inpu…

This work optimizes RL algorithms using entropy regularisation for continuous-time LQ problems.

Paper studies particle method for LSV model calibration, proving convergence and error bounds.

Diffusion models adapt to data geometry through log-domain smoothing.

Effective regularisation of neural networks is essential to combat overfitting due to the large number of parameters involved. We present an empirical analogue to the Lipschitz constant of a feed-forward neural network, which we refer to as the maximum gain. We hypothesise that constraining the gain of a network will h…

New insights into how neural networks learn features, especially when they are very wide.

Matrix factorisation methods decompose multivariate observations as linear combinations of latent feature vectors. The Indian Buffet Process (IBP) provides a way to model the number of latent features required for a good approximation in terms of regularised reconstruction error. Previous work has focussed on latent fe…

Study on neural networks with regularisation and its impact on training dynamics.

Recent work has established the equivalence between deep neural networks and Gaussian processes (GPs), resulting in so-called neural network Gaussian processes (NNGPs). The behaviour of these models depends on the initialisation of the corresponding network. In this work, we consider the impact of noise regularisation …

We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to $C^{1,1}$. Our approach is based on regularisations of the metric adapted to the causal structure.

Regularising for invariance to data augmentation improves machine learning models.

Proves Hawking's theorem for less smooth spacetime metrics.

Local mass perspective on Bayesian inference

Unified understanding of three continual learning regularisation methods.

This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.

New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.

The paper studies $m$-positive currents and line bundles on complex manifolds.

We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an arbitrary subset of activations conditioned on the remainder. This is a generalisati…

Novel method decorrelates neurons for better deep learning model generalization.

ICCNLS models complex relationships as convex and concave components.