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.
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…
First-order ODEs linked to flat surfaces, leading to integrability.
problem Integrating first-order ODEs.
method Defined Riemannian metrics on variable spaces, studied surface properties, and established connections between Jacobi fields and Lie point symmetries.
result Flat associated surfaces lead to integrable first-order ODEs.
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 h and the corresponding penalized estimator β^, we construct a quantity η,…
A new first-order sampler improves diffusion probabilistic model sampling quality.
problem The belief that first-order methods are inherently slower for diffusion probabilistic model sampling.
method A novel training-free, first-order sampler that approximates the forward-value evaluation via a one-step lookahead predictor.
result The proposed sampler provably approximates the ideal forward-value trajectory while retaining first-order convergence and can improve sample quality under the same NFE budget.
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…
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.
problem Analyzing generalization error for first order discretizations of Langevin diffusion.
method Providing a sufficient smoothness condition to show that first order methods can achieve arbitrarily runtime complexity for a given expected generalization error.
result First order methods can achieve arbitrarily runtime complexity 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 …
A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.
problem Learning representative node embeddings for signed directed networks considering both first-order and high-order topologies.
method Proposes a decoupled variational embedding (DVE) method that leverages a specially designed auto-encoder structure to capture both first-order and high-order topologies.
result Extensive experiments on real-world datasets show the effectiveness of DVE in link sign prediction and node recommendation tasks.
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…
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,…
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…
Paper explores second-order optimization in first-order methods, proving and disproving the necessity of square root.
problem Understanding and optimizing first-order optimization methods using second-order information.
method Rigorously proves Nesterov Accelerated Gradient uses past and current gradients to approximate Hessian. Relates adaptive methods to Natural Gradient Descent. Introduces AdaSqrt algorithm to remove square root in denominator.
result New algorithm AdaSqrt comparable to first-order methods on MNIST and beats Adam on CIFAR-10, casting doubt on the necessity of square root.
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.
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…
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.
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…
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.