arXiv research

Develops a hedging method for multi-asset derivatives with correlation risk.

We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…

Study variance-optimal hedging of forward curve derivatives under stochastic volatility.

The paper generalizes Cartan Geometry using Polacek and Siegel's approach.

The paper explores symmetries and conservation laws in Hamiltonian systems.

Alternative dynamic paired comparison model using Gaussian Processes.

Improves predictions by integrating forward-looking views into dynamic factor models.

Derives equations of motion for systems with angular momentum on Finsler geometries.

The paper calculates sensitivities for financial derivatives using path weighting methods.

Vanilla SGD learns SIM from anisotropic data without explicit covariance estimation.

Anisotropic data structure affects learning dynamics and generalization error in linear networks.

Develops a regression model for partially observed dynamic tensor data.

Paper introduces a novel method for dynamic covariance estimation with random forests.

Study on friction forces for nonholonomic systems using affine connections.

Method uses derivatives for dynamic index tracking and risk control.

In this paper we investigate the relations between semispray, nonlinear connection, dynamical covariant derivative and Jacobi endomorphism on Lie algebroids. Using these geometric structures, we study the symmetries of second order differential equations in the general framework of Lie algebroids.

Study of accelerated dynamics for convex function minimization with noisy gradients.

We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent $n$-vectors. In this framework, which is fully covariant, we geometrically derive pha…

Paper solves portfolio selection under uncertain covariance matrix using robust optimization.

Bayesian neural networks improve cancer dynamics prediction.

Enhanced EEG classification using augmented covariance matrix.

DARTS optimizes covariate selection in trials with limited data.

New kernels from ELU and GELU networks reveal non-trivial fixed points.

Invariant covariant derivatives on homogeneous spaces are characterized.

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.

HCLM framework uses entropy regularization for open learning systems.

The paper shows objective derivatives are covariant derivatives on Riemannian metrics.

Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.

Constructs covariant derivatives for Ehresmann connections.

Study shows how anisotropic data affects learning dynamics in phase retrieval.

Optimizes SGLD noise structure for better generalization bounds.

Dynamic treatment effects estimated over time using covariate balancing.

Evaluating AI investment strategies

Homotopy equivalence between formalities with different covariant derivatives.

Dynamic pricing algorithms can work with covariates without i.i.d. assumptions.

A new framework for efficient sequence maps using Bayesian filtering and covariance.

Proposes a new semi-parametric framework for batched bandits with covariates.

The paper develops methods to reduce deployment risk under dynamic covariate shifts.

We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of mult…

Derives a formula for the k-th covariant derivative of tensor fields.

A new Hawkes process model captures order book dynamics in high-frequency trading.

New study on guidance in masked diffusion models, showing how it shapes sampling dynamics.

Formulae for non-symmetric connections derived from covariant derivatives.

A new ranking model with dynamic covariates improves statistical analysis.

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following…

New analysis of Muon and SignSGD on matrix-valued least squares problems.

AniDS improves molecular force field modeling by learning anisotropic noise.

A dynamical system on the total space of the fibre bundle of second order accelerations, $T^2M$, is defined as a third order vector field $S$ on $T^2M$, called semispray, which is mapped by the second order tangent structure into one of the Liouville vector field. For a regular Lagrangian of second order we prove that …