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.
New algorithm learns nonlinear phenomena from noisy local measurements without data exchange.
This article demonstrates the possibility of constructing indicators of critical and crisis phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems such as recurrent analysis of dynamic systems and the calculation of permutation entropy are used. It is shown th…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynam…
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet electromagnetic Yang-Mills energies, starting from some given nonlinear evolution OD…
Manifold methods improve amino acid classification in LIBS spectra.
Exact asymptotic solutions found for nonlinear Hawkes processes.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
Study shows scaling up models doesn't always improve downstream tasks.
Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case o…
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this…
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as operators on probability distributions for observed data, we show that the distribu…
Noise balance theory explains SGD's behavior in neural networks.
A novel model uses ODE-based random features to model nonlinear dynamical systems.
Paper studies rigidity phenomena for elliptic systems on Riemannian manifolds.
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometri…
Flexible nonlinear Hawkes processes for time-varying systems.
New method classifies nonlinear time series using deep CNNs and bispectra.
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems model…
Optimal execution strategy for merger & acquisition contracts with price impact.
This paper extends RMT for deep learning models beyond eigenvalues.
This paper explores non-periodic folding of Spidron units, revealing nonlinear dynamics.
Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical approaches that do consider both phenomena simulta…
Letter analyzes training dynamics of a nonlinear contrastive learning model in high dimensions.
Training task diversity improves ICL with linear attention.
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number …
The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stoc…
Study uses DMD to analyze oceanic features in Strait of Gibraltar.
GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
Survey on stability of Minkowski spacetime in relativity.
New techniques identify shifts in financial market sectors.
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …
Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencie…
A new method infers parameters from PDEs using Gaussian processes.
Study explores Liouville's theorem and SLP for harmonic functions on cones and surfaces.
Proves a theorem for Assouad dimension with applications to distance sets and radial projections.
Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces [Physica A 370, pp91-97, 2006]. By analyzing high-frequency financial time series of …
The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate local symmetries. The whole package provides a functional analytic framework to de…
Develops a machine learning framework for computing most probable paths in stochastic systems.
New method integrates sparse parametric and nonparametric techniques for complex system modeling.
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate nonlinear second order differential equations on Euclidean space. One naturally wond…
The paper argues against the inefficiency of explaining deep learning phenomena.
In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative -Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary concen…
New scalable variational Bayes methods for Hawkes processes.
Predicting unobserved bifurcations in time series with unsupervised parameter extraction.
An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, or…
Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a BN layer, and a nonlinear activation function. This basic network helps us unde…
Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing "related" objects/phenomena. The first o…
FNOs improve spatio-temporal forecasting without needing PDE details.