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 neural network model uses polynomial chaos theory to improve neural signal processing.
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorith…
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain precise symmetry (Feigenbaum numbers) is even more surprising. As an illustration o…
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
Novel CMG framework improves financial sentiment forecasting.
Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum m…
This paper uses neural networks to predict stock prices more accurately.
The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.
Modeling financial chaos with market makers' risk appetite.
STS clarifies chaos and stochastic dynamics, linking algebraic topology and physics.
It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural networks, the foundation of this hypothesis on generic non-linear systems remain…
The study reveals chaos in geometric objects embedded in higher dimensions.
Study on neural networks with non-normal interactions reveals unique spectral properties.
The resilience of low-degree Rademacher chaos is studied, providing probabilistic lower bounds.
We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights. Our results reveal an order-to-chaos expressivity phase transition, with networks in the chaotic phase computing nonlinear functions whose g…
New theory shows EDMD works well in chaotic systems.
We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos theory, we adopt a pedagogical approach demonstrating how to adjust this paramet…
The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the enormous practical success of AI, these algorithms are only loosely inspired from the b…
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
This article is solicited by C.\ Adams for a special issue of {\it Chaos, Solitons and Fractals\/} devoted to knot theory and its applications. We present some recent results about Dehn surgeries on arborescent knots and links.
In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques fro…
New stock market index captures market chaos and volatility.
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tra…
New insights into neural network training efficiency.
Enhances polynomial chaos models with uncertainty intervals.
We give emphasis on the use of chaos-based rigorous nonlinear technique called Visibility Graph Analysis, to study one economic time series - gold price of USA. This method can offer reliable results with fiinite data. This paper reports the result of such an analysis on the times series depicting the fluctuation of go…
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
The paper introduces invariants to describe period-doubling routes to chaos in dynamical systems.
Dropout schedules can be optimized to significantly reduce model test loss.
Neural networks solve SPDEs using Wiener chaos expansion.
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets better than a homogeneous model. The components of a vector Ornstein-Uhlenbeck proc…
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
The Financial Chaos Index models stock market volatility across three regimes based on mutual price fluctuations.
Paper studies matching of samples from two distributions with a Gibbs probability weight.
In this letter, as a proof of concept, we propose a deep learning-based approach to attack the chaos-based image encryption algorithm in \cite{guan2005chaos}. The proposed method first projects the chaos-based encrypted images into the low-dimensional feature space, where essential information of plain images has been …
We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these random networks. Our main practical result is to show that random networks may be…
In this paper we study the price dynamics in a simple model of financial markets with heterogeneous agents. We concentrate on how increases in the total number of active traders influences fluctuations of asset prices. We find that a curious route to chaos is observed when the total number of [active traders] increases…
Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
The paper models ATM cash withdrawal chaos and forecasts using deep learning.
The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single…
Study of homogeneous spaces in Hartree-Fock-Bogoliubov theory.
This paper proposes a new method to optimize portfolio allocation with transaction costs using Wiener chaos expansion.
New theory explains contrastive learning via overlapping augmented views.
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural networks can efficiently model chaotic dynamics by becoming structurally chaotic t…
New model reveals balance crucial for robust neural coding.
In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of Euclidean space. Their motivation was to provide a characterization of quasi-disks, i.e. domains which are quasiconformally homeomorphic to the unit disk. As a gener…