arXiv research

Improves parameter selection for denoising with elastic net.

Generalised regularisation equals robustness for exotic function classes.

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…

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.

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

This work uncovers algorithm-dependent regularisation in diffusion models.

Noise regularisation in deep nets makes them behave like Gaussian processes.

Theory for RLHF generalization under reward shift and clipped KL.

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

Critical initialisation strategies are identified for noisy ReLU networks.

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

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

ResNets can approximate input distances under certain conditions, but existing theory is flawed.

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

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…

We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.

New framework monitors neural network training and reveals regularisation mechanisms.

Two-dimensional Yang-Mills theory defects and orbifolds studied.

Representer theorem conditions extended to reflexive Banach spaces.

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

Denoising autoencoders (DAEs) have proven useful for unsupervised representation learning, but a thorough theoretical understanding is still lacking of how the input noise influences learning. Here we develop theory for how noise influences learning in DAEs. By focusing on linear DAEs, we are able to derive analytic ex…

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

Graph-dependent implicit regularisation improves Distributed SGD for convex problems.

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.

Investigates gradient descent dynamics and introduces new regularisation methods.

We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure.

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

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.

Unified theory for adaptive image convolutions using metric perspectives.

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

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.

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…

Global analysis of Dixmier traces and Wodzicki residues on compact Lie groups.

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

Regularising for invariance to data augmentation improves machine learning models.

The report analyzes infinite-dimensional output space regression.

Unified understanding of three continual learning regularisation methods.

New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.

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

SPReD uses uncertainty to decide imitation from demonstrations.

Novel method decorrelates neurons for better deep learning model generalization.

ICCNLS models complex relationships as convex and concave components.

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the…