arXiv research

Proposes a method to apply conformal prediction to probabilistic time series forecasting models.

We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically noninvertible in order to approximate the target closely. This result has implications for all flow-based models, and espec…

Kernelised flows improve density estimation and generation with fewer parameters.

Improved normalising flows using Student's t-distribution for robust training.

We show uniqueness of classical solutions of the normalised two-dimensional Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time $L^2$-bound for the time derivative of the solution. The result is s…

Method estimates bivariate causal models using normalising flows and variational Gaussian process regression.

Gradient flow method solves isoperimetric inequality for maps.

In 2004, Manning showed that the topological entropy of the geodesic flow for a surface of negative curvature decreases as the metric evolves under the normalised Ricci flow. It is an interesting open problem, also due to Manning, to determine to what extent such behaviour persists for higher dimensional manifolds. In …

NSFs learn SDE transition laws for efficient sampling.

AMF-VI uses adaptive mixtures of flows for robust VI across diverse distributions.

In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised fl…

We analyse Ricci flow (normalised/un-normalised) of product manifolds --unwarped as well as warped, through a study of generic examples. First, we investigate such flows for the unwarped scenario with manifolds of the type $\mathbb S^n\times \mathbb S^m$, $\mathbb S^n\times \mathbb H^m$, $\mathbb H^m\times \mathbb H^n$…

MixerFlow combines MLP-Mixer with normalizing flows for efficient image modeling.

Proposes a probabilistic approach to semi-supervised learning using normalizing flows.

In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the C^infty-topology to a simple circle. Our results yield a characterisation of …

A new method for discrete data normalizing flows using latent transformations.

JAPAN uses flow-based models to create adaptive prediction areas with better coverage guarantees.

We consider a shrinking flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_n^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_n is the n-th symmetric polynomial of the principle curvature r…

Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and …

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution equations. Several novelties appear in the context of scale factor evolution, fix…

Study shows superdiffusive behavior in geodesic flows on curved surfaces.

Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "g…

Proposes a method to model financial returns with extreme shocks using flexible tail transformations.

Geodesic concavity and hypersymplectic structures in $G2$-structures space.

We compute the Yamabe invariants for a new infinite class of closed $4$-dimensional manifolds by using a "twisted" version of the Seiberg-Witten equations, the $\mathrm{Pin}^-(2)$-monopole equations. The same technique also provides a new obstruction to the existence of Einstein metrics or long-time solutions of the no…

Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex d…

A new method normalizes EBM training by introducing a learnable parameter.

We study the space of Sasaki metrics on a compact manifold $M$ by introducing an odd-dimensional analogue of the $J$-flow. That leads to the notion of critical metric in the Sasakian context. In analogy to the Kähler case, on a polarised Sasakian manifold there exists at most one normalised critical metric. The flow is…

Batch normalisation doesn't affect variational inference but fails for larger batch sizes.

Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their fl…

Unified flow solves $L^p$ Christoffel-Minkowski problem for $p>1$.

New method for modeling densities on Riemannian manifolds with symmetries.

Study on flows of G2-structures on contact Calabi-Yau 7-manifolds.

A comparison theorem for the isoperimetric profile on the universal cover of surfaces evolving by normalised Ricci flow is proven. For any initial metric, a model comparison is constructed that initially lies below the profile of the initial metric and which converges to the profile of the constant curvature metric. Th…

Study of superintegrable systems linked to affine hypersurfaces.

Study of Coxeter diagrams and Artin-Tits groups, focusing on normalisers and wall intersections.

Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to improve the generalisation capacity of a DNN model. Considering a weight matrix W …

CFMI improves missing data imputation across various data types and dimensions.

New method accelerates Parallel Tempering using neural samplers.

Frugal Flows learn complex data and infer marginal causal effects.

In the present paper, we develop a picture formalism which gives rise to an invariant that dominates several known invariants of classical and virtual knots: the Jones polynomial, the Kuperberg bracket, and the normalised arrow polynomial.

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular he…

On a K-unstable toric variety we show the existence of an optimal destabilising convex function. We show that if this is piecewise linear then it gives rise to a decomposition into semistable pieces analogous to the Harder-Narasimhan filtration of an unstable vector bundle. We also show that if the Calabi flow exists f…

New gradient estimator improves training for normalizing flows.

In this paper we consider the steepest descent $H^{-1}$-gradient flow of the length functional for immersed plane curves, known as the curve diffusion flow. It is known that under this flow there exist both initially immersed curves which develop at least one singularity in finite time and initially embedded curves whi…

We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_k is the k-th symmetric polynomial of the principle curvature …

In this paper we study a contracting flow of closed, convex hypersurfaces in the Euclidean space $\mathbb R^{n+1}$ with speed $f r^α K$, where $K$ is the Gauss curvature, $r$ is the distance from the hypersurface to the origin, and $f$ is a positive and smooth function. If $α\ge n+1$, we prove that the flow exists for …

Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.