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.
There is a large body of work, built on tools developed in mathematics and physics, demonstrating that financial market prices exhibit self-similarity at different scales. In this paper, we explore the use of analytical topology to characterize financial price series. While wavelet and Fourier transforms decompose a si…
We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction…
Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.
problem Theoretical properties of quantum machine learning models, particularly their expressive power.
method Investigated how data encoding affects the expressive power of parametrized quantum circuits.
result Quantum models can access increasingly rich frequency spectra by repeating data encoding gates, potentially making them universal function approximators.
A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph …
The classical inverse problem of recovering a simply connected smooth planar domain from the Steklov spectrum \cite{E} is equivalent to the problem of recovering, up to a conformal equivalence, a positive function a∈C∞(S) on the unit circle S={eiθ} from the eigenvalue spectrum of t…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…
Study explores how neural networks and Transformers learn modular arithmetic with multiple inputs.
problem Understanding how neural networks and Transformers learn modular arithmetic with multiple inputs.
method Analytical characterization of features learned by neural networks and Transformers, focusing on margin maximization and Fourier spectra.
result Neural networks and Transformers require a minimum neuron count of \( m \geq 2^{2k-2} \cdot (p-1) \) to solve modular addition problems with \( k \) inputs and modulus \( p \).
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …
We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an a…
We study the transversal wave equation on a compact Riemannian foliated manifold. As applications, we get an Egorov's type theorem for transversally elliptic operators, state a relationship between the singularities of the Fourier transform of the spectrum distribution function of a transversally elliptic operator and …
Bayesian time series forecasting improves by dynamically adapting to recent information.
problem Lack of forgetting mechanism in signature kernel for time series forecasting.
method Introducing a novel forgetting mechanism for signature features using Random Fourier Decayed Signature Features (RFDSF) with Gaussian processes (GPs).
result Demonstrates superior performance compared to other GP-based alternatives and state-of-the-art probabilistic time series forecasting algorithms.
We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…