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.
Examines how first-order differential operators can be equivalently transformed.
Extends first-order flexes of surfaces to second-order flexes.
Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for algorithms using noise in the first-order information is quite involved and hides the es…
New vector fields integrate first-order ODEs.
Study first-order locally convex Lie algebroids in Bastiani calculus.
Study stabilizes second-order systems to first-order dynamics.
A new method solves complex constrained minimax problems.
A guide for solving first-order elliptic boundary value problems.
Optimal first-order methods are shown to be fundamental limits in functional estimation.
First-order ODEs linked to flat surfaces, leading to integrability.
We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function and the corresponding penalized estimator , we construct a quantity ,…
A new first-order sampler improves diffusion probabilistic model sampling quality.
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support learning higher…
Extends a theorem for first-order elliptic operators on manifolds.
The aim of this paper is fourfold. Firstly, we introduce and study the f-ultra-harmonic maps. Secondly, we recall the geometric dynamics generated by a first order normal PDE system and we give original results regarding the geometric dynamics generated by other first order PDE systems. Thirdly, we determine the Gauss …
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularit…
In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g.~the volume standing at the top of the book). We study the fluctuations of the …
Second-order optimizers retain residual information after data deletion, affecting machine unlearning.
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
CEFOL uses deep learning for dynamic programming with recursive utility.
Efficient algorithm for contextual bandits with first-order guarantees.
First-order method solves stochastic bilevel optimization with linear constraints.
We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical s…
New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.
The properties of the Riemann extensions of nonriemannian spaces defined by the first order systems of differential equations are considered.
Graph Convolution Network (GCN) has been recognized as one of the most effective graph models for semi-supervised learning, but it extracts merely the first-order or few-order neighborhood information through information propagation, which suffers performance drop-off for deeper structure. Existing approaches that deal…
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them,…
New algorithm reduces online decision-making regret with efficient LP re-solving and parallel first-order method.
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic formulation of first-order field theories. The Lagrange-d'Alembert formalism is also d…
New lower bounds for bilevel optimization with first-order oracles.
We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.
We develop a second-order model for limit order books in a single scaling regime.
New methods boost first-order optimization with faster rates.
Unified bounds for iterative algorithms with Gaussian data matrices.
DEO uses gradient information to escape saddle points in neural networks.
This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in t…
Solves second-order PDEs using quotients and differential invariants.
A new method solves a complex optimization problem efficiently.
A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them a…
We study first order local invariants of Vassiliev type for Lagrangian immersions with generic planar caustics. For this we produce some examples of 2-parameter families of Lagrangian maps and study their bifurcation diagrams.
Second-order economic theory considers new variables to improve price volatility predictions.
Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex optimization it is often crucial to find a second-order stationary…
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…
Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.
We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.
A first-order Lagrangian variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by is proved to be regular and its H…
New sampling method guarantees approximate first-order stationary points for non-convex functions.