arXiv research

New method for handling multi-dimensional singular controls with jump costs in mean-field problems.

In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative de…

Develops parametrised Poincaré duality for equivariant fixed points.

In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of gen…

New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.

Combines ML and DA to infer unresolved scale parametrisation from noisy data.

A new approach to unsupervised learning using recognition-parametrised models.

The paper shows how label noise in training can lead to solutions that solve a Lasso program.

We show that, for certain families $φ_{\mathbf{s}}$ of diffeomorphisms of high-dimensional spheres, the commutator of the Dehn twist along the zero-section of $T^*S^n$ with the family of pullbacks $φ^*_{\mathbf{s}}$ gives a noncontractible family of compactly-supported symplectomorphisms. In particular, we find example…

The abstract proves every knot type can be parametrized by smooth functions and studies limit knot types.

Neural networks outperform kernel methods in classifying high-dimensional Gaussian mixtures.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

Gradient descent with logistic loss can make two-layer networks interpolate binary classification data.

Two-layer neural networks can approximate functions with fractal singularities.

In this paper we are dealing with mean curvature flow with surgeries of two-convex hypersurfaces. The main focus is to expand on the discussion in Section $3$ of Mean Curvature Flow with Surgeries of Two-Convex Hypersurfaces by Huisken and Sinestrari. Firstly we wish to establish how the neck detection lemma allows us …

We introduce a new parameter to measure the inhomogeneity of training datasets.

We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the plane is known to admit a great variety of geometric properties which are also pres…

Researchers extend parametrization of Margulis spacetimes using strip deformations.

The study characterizes quasiperiodic surfaces in pseudo-hyperbolic spaces with curvature conditions.

Analytical method finds deeper optima in two-layer ReLU networks.

Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, …

Three-layer networks learn more complex features than two-layer networks.

We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with…

Proposes a new Gaussian factor for probabilistic inference with degenerate settings.

Study on deformations of Einstein and nearly G2 structures in 3-Sasaki manifolds.

Two-layer neural networks learn efficiently using kernel methods in mean-field analysis.

The paper proves rigidity for mapping class group actions on metrics of positive scalar curvature.

Two-layer networks trained on low-dimensional subspaces are vulnerable to adversarial examples.

Two-layer neural networks must be robust, even with arbitrary weights.

This work shows linear convergence for two-layer neural networks in mean-field regime.

In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincaré disc into a non-compact symmetric space, where the equivariance is with respect to representations of the fundamental group of a compact Riemann surface of genus at least two. We then study this moduli space…

We focus on estimating \emph{a priori} generalization error of two-layer ReLU neural networks (NNs) trained by mean squared error, which only depends on initial parameters and the target function, through the following research line. We first estimate \emph{a priori} generalization error of finite-width two-layer ReLU …

For a given bundle $ξ\colon E \to M$ over a manifold, configuration-section spaces on $ξ$ parametrise finite subsets $z \subseteq M$ equipped with a section of $ξ$ defined on $M \smallsetminus z$, with prescribed "charge" in a neighbourhood of the points $z$. These spaces may be interpreted physically as spaces of fiel…

We study the limits and methods of training two-layer autoencoders.

Study on SGD for overparameterized neural networks, focusing on convergence rates.

Study shows infoGAN's generalization error bound for two-layer networks.

Generalizes neural tangent kernel analysis for two-layer networks with noise and regularization.

This paper presents a phase diagram for two-layer neural networks under different initialization scales.

PHP connects to ReLU neural networks for scalable Bayesian inference.

Two-layer CNNs can overfit well if initialized correctly.

This paper explains double descent in linear neural networks, identifying new factors.

Two-layer networks learn hard GLMs with SGD in high dimensions.

Study of two-layer NNs under Gaussian mixtures data, proving polynomial models equivalent to neural networks.

Study computability of real numbers from group properties.

By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere we encounter the notion of a folded hyperkaehler 4-manifold and conjecture the existence of a family of such metrics parametrised by an infinite-dimensional analogue of Teichmueller space.

We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular …

It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing works, we investigate the gradient descent method for training two-layer neural ne…