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.
DREAM model improves computational efficiency for non-linear effects in relational event models.
We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations between the cotangent bundles specified by generating functions depending on positio…
SSL framework identifies non-linear systems without labeled data.
Develops deep learning methods for non-linear PDEs in credit risk.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
New neural network models for complex functional data analysis.
New deep learning model for image reconstruction using Fourier space relations.
This study develops a multi-factor framework where not only market risk is considered but also potential changes in the investment opportunity set. Although previous studies find no clear evidence about a positive and significant relation between return and risk, favourable evidence can be obtained if a non-linear rela…
Defines simplicity of non-linear mappings using information geometry.
New recursion found for hyperbolic sphere volumes.
Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility reductions of PDEs.
PEA improves PCA and k-means for non-linear data and complex clusters.
Develops goodness-of-fit tests for noisy submanifold samples.
In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of -Snell enveloppe. Then, in a second step, we re…
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this pa…
A fast deep learning method for parallel MRI without calibration.
Variational auto-encoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single non-linear embedding. In this work, we illustrate how this non-linear latent embedding can be used as a collective variable for enhanced sampling, and present a simple modification th…
New method for learning causal relationships in PNL models.
This paper proposes a new method to learn integration schemes for complex ODEs.
New models learn stable latent clusters without side info.
New algorithm tames non-linear growth in stochastic optimization.
Proposes using DII to identify non-linear causal relationships in EU Allowances returns.
Unified framework for multi-user bandits using Laplacian kernels.
BAVART model combines VAR and BART for non-linear forecasting.
Enhances xVA valuation with initial margin and CSA discounting.
We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected…
SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, …
Financial markets are complex adaptive systems, and are commonly studied as complex networks. Most of such studies fall short in two respects: they do not account for non-linearity of the studied relationships, and they create one network for the whole studied time series, providing an average picture of a very long, e…
We show how the relation between -manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations on sections of a Lie algebroid. When the base is a point, we obtain a generalizat…
Estimates causal effects using neural autoregressive density estimators.
We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of …
The paper investigates non-linear and heavy-tailed predictability in transition-energy financial markets.
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical Society. I dedicate the lecture to the memory of my teacher S.S. Chern who had …
This work proposes a mathematical framework for loss landscapes and optimization in deep neural networks.
We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…
In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely res…
This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean curvature surfaces. This differential geometric interpretation provides an impor…
Study modular surfaces in Lorentz-Minkowski 3-space, classifying and analyzing their curvature and applications.
On any space-like W-surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as …
MinShap improves feature selection accuracy and stability in complex models.
The purpose of this note is two give a mathematical treatment to the low energy effective theory of the two-dimensional sigma model. Perhaps surprisingly, our low energy effective theory encodes much of the topology and geometry of the target manifold. In particular, we relate the -function of our theory to the Ricc…
Quantile Temporal-Difference learning proved convergent with proof.
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential…
A new GRNN tackles multi-relational data learning.
DANCE optimizes neural network and accelerator design for faster, more efficient DNN execution.