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.
RNNs solve modular addition tasks using low rank and sparse Fourier structures.
NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.
We construct a certain cross product of two copies of the braided dual of a quasitriangular Hopf algebra , which we call the elliptic double , and which we use to construct representations of the punctured elliptic braid group extending the well-known representations of the planar braid group attache…
Derives representations invariant under crystallographic groups for functions.
Equivariant neural networks use symmetry to interpret complex data.
We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including Lévy and affine proc…
Neural networks learn spectral representations for group composition.
Every torus knot can be represented as a Fourier-(1,1,2) knot which is the simplest possible Fourier representation for such a knot. This answers a question of Kauffman and confirms the conjecture made by Boocher, Daigle, Hoste and Zheng. In particular, the torus knot T(p,q) can be parameterized as x(t)=cos(pt), y(t)=c…
A new method for nonstationary Gaussian processes using Fourier features.
Fourier representation improves KSD for infinite-dimensional data.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
Efficiently scales continuous kernels with sparse Fourier domain learning.
Scalable kernel methods for large datasets using Fourier representations and NUFFT.
Localized signal representation on graph bundles using Fourier analysis.
This paper analyzes SHAP values using Fourier expansions for model interpretability.
Ordering examples in modular arithmetic training affects model performance.
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…
IGT learns graph representations without supervision.
We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution, the density distribution of each class is smoothed by a low-pass filter separate…
The article provides representations of exchange option prices under SVJD dynamics.
Unified approach for interpretable regression with flexible modeling.
Extend classical theory of affine processes to path-dependent setting
We revisit Rahimi and Recht (2007)'s kernel random Fourier features (RFF) method through the lens of the PAC-Bayesian theory. While the primary goal of RFF is to approximate a kernel, we look at the Fourier transform as a prior distribution over trigonometric hypotheses. It naturally suggests learning a posterior on th…
RP-GFRFT unifies fractional order and rotation control for graph signals.
New Fourier features improve high-precision approximation in large-scale problems.
New spectral mixture representation for isotropic kernels simplifies random Fourier features.
Many theories of deep learning have shown that a deep network can require dramatically fewer resources to represent a given function compared to a shallow network. But a question remains: can these efficient representations be learned using current deep learning techniques? In this work, we test whether standard deep l…
Enhances GPLVM for multi-view data with scalable latent representation learning.
Quantum methods improve option pricing accuracy.
Local norms of Fourier multipliers bounded on discrete subgroups of Lie groups.
New neural operators learn structured patterns efficiently.
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier feat…
Quantum-assisted Gaussian process speeds up data regression.
These notes are an extended version of a talk given by the author in the seminar "Theorie Spectrale et Geometrie" at the Institut Fourier in No- vember 2016. We present here some aspects of a work in collaboration with B. Collier and N. Tholozan (arXiv:1702.08799). We describe how Higgs bundle theory and pseudo-hyperbo…
We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the …
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenien…
Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated with the cyclic group Z/3Z. This operator appears as a natural extension of the La…
In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy, we use a Fourier approach in a general multidime…
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power…
Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.
We consider the representation space of a compact surface, that is the space of morphisms from the fundamental group to SU(2) up to conjugation. We show that the trace functions associated to multicurves on the surface are linearly independent as functions on the representation space. The proof relies on the Fourier de…
Three RFF-based methods for nonlinear causal discovery in mixed data.
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to …
New model captures patient-level EHR data efficiently.
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…
We establish various results on the large level limit of projective quantum representations of surface mapping class groups obtained by quantizing moduli spaces of flat SU(n)-bundle. Working with the metaplectic correction, we proved that these projective representations lift to asymptotic representations. We show that…