A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method normalizes EBM training by introducing a learnable parameter.
Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.
Score-based methods fail with isolated components and incorrect mixing proportions.
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…
Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here we show that inferring the parameters of a unnormalised model on a space can …
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 …
Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.
We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983 under the assumption on the surface gravity and generalises previous results due to …
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…
New methods combine model predictions to avoid linear mixtures' limitations.
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…
We study the geometric properties of Darboux transforms of constant mean curvature (CMC) surfaces and use these transforms to obtain an algebro-geometric representation of constant mean curvature tori. We find that the space of all Darboux transforms of a CMC torus has a natural subset which is an algebraic curve (call…
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 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…
Develops a new Bayesian inference method for discrete data.
New tractable density models from squaring neural networks.
Batch normalisation doesn't affect variational inference but fails for larger batch sizes.
Proposes a method to apply conformal prediction to probabilistic time series forecasting models.
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 …
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte…
Paper uses referenced thermodynamic integration for Bayesian model selection in a complex COVID-19 transmission model.
Kernelised flows improve density estimation and generation with fewer parameters.
New method accelerates Parallel Tempering using neural samplers.
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…
A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the probabilities of each variable being zero, or Gaussian-distributed. Using the p…
Improved normalising flows using Student's t-distribution for robust training.
Method estimates bivariate causal models using normalising flows and variational Gaussian process regression.
Unified flow solves Christoffel-Minkowski problem for .
Adapts linearised Laplace method for deep learning models.
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 -bound for the time derivative of the solution. The result is s…
RotRNN uses rotations to simplify long sequence modelling.
Improved spectral convergence bounds for diffusion maps on tori.
In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence …
Bitcoin volatility shows multifractal structure, contradicting rough volatility models.
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 …
New algorithm STCV improves sparse model discovery from normalised data.
The paper derives inequalities for Riemannian submersions and their applications.
In recent years there has been a growing interest in image generation through deep learning. While an important part of the evaluation of the generated images usually involves visual inspection, the inclusion of human perception as a factor in the training process is often overlooked. In this paper we propose an altern…
New proof of Schwarzschild stability using geometric gauge.
We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A_8, is complete and non-singular on R^8. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S^4, and …
Gradient flow method solves isoperimetric inequality for maps.
Score matching method improves density estimation for truncated data on manifolds.
Combines neural networks with splitting-up method for filtering equations.
The paper studies CMC foliations and their conformal aspects on Riemannian manifolds.
Novel method recursively partitions sample space for density estimation.