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arXiv research

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.

168,695 papers · 148 categories

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0111 · Jan 201419922001200920172026
6 results for “n-widths”
Sharp Bounds on the Approximation Rates, Metric Entropy, and nn-widths of Shallow Neural Networksstat.ML

Sharp bounds on neural network approximation rates and widths.

problem Estimating approximation rates, metric entropy, and n-widths of shallow neural networks.
method Introducing smoothly parameterized dictionaries and providing upper and lower bounds.
result Sharp bounds on approximation rates, metric entropy, and n-widths for neural networks with various activation functions.
shallow neural networksmetric entropyn-widthsapproximation ratessmoothly parameterized dictionaries
2021-01-29abs ↗pdf ↗
Sharp Lower Bounds on the Approximation Rate of Shallow Neural Networksstat.ML

Sharp lower bounds on shallow neural networks' approximation rates are derived.

problem The efficiency of shallow neural networks in approximating functions.
method Lower bounding the L2L^2-metric entropy and Kolmogorov nn-widths of the convex hull of neural network basis functions.
result Sharp lower bounds on the approximation rates for shallow neural networks are provided.
shallow neural networksapproximation ratesmetric entropyKolmogorov n-widthsconvex hull
2021-06-28abs ↗pdf ↗
Pricing of basket options Iq-fin.CP

Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of Lévy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear system …

2014-01-08abs ↗pdf ↗
Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometrymath.NA

Enhanced autoencoders improve ROMs for PDEs by capturing essential properties.

problem Autoencoders struggle to capture essential properties for accurate ROMs.
method Introduced symmetric Convolutional AutoEncoders (CAEs) that preserve manifold properties.
result Symmetric CAEs yield more accurate latent trajectories and robust models.
AutoencodersReduced-Order ModelingConvolutional Neural NetworksPartial Differential EquationsManifold Parametrization
2026-07-01abs ↗pdf ↗
Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networkscs.LG

LPINNs solve complex PDEs by reformulating PINNs on Lagrangian frame, reducing training complexity.

problem Complexity in training PINNs, especially for convection-diffusion equations.
method Propose LPINNs, a Lagrangian reformulation of PINNs, with two branches solving state variables and characteristics curves.
result Loss landscapes of LPINNs are less sensitive to problem complexity compared to traditional PINNs.
Physics-informed neural networksPINNsLagrangian formulationConvection-diffusion equationsTraining complexity
2022-05-05abs ↗pdf ↗