arXiv research

Second-order economic theory considers new variables to improve price volatility predictions.

Second-order optimizers retain residual information after data deletion, affecting machine unlearning.

Exact second-order optimization for deep learning reduces computational cost and improves performance.

SOLBP extends efficient inference to uncertain Bayesian networks.

Developed a theory of local convexity for second order differential equations on Lie algebroids.

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

Negative step sizes improve second-order methods for neural networks.

Simplified argument for second order estimate in quaternionic Calabi-Yau problem.

Paper studies second order tail probabilities in risk models.

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 …

Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.

Paper generalizes connections between Lie groups and affine connections.

In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the topology of fibers of the rank two prolongations. Moreover, by using properties of …

In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimizatio…

AdamQLR optimizes Adam with K-FAC heuristics, achieving comparable performance to tuned benchmarks.

The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a quantifiable reduction of risk concentration a challenging task. In the present pap…

We show that, for mechanical system with external forces, the equations of deviations of solution curves of the corresponding Lagrange equations,determine a nonlinear connection on the second order osculator (second order tangent) bundle. In particular, Jacobi equations in Finsler and Riemann spaces determine such a no…

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…

Second-order guarantees for federated learning algorithms.

New findings show second-order scoring rules can't accurately represent epistemic uncertainty.

The second order method as Newton Step is a suitable technique in Online Learning to guarantee regret bound. The large data is a challenge in Newton method to store second order matrices as hessian. In this paper, we have proposed an modified online Newton step that store first and second order matrices of dimension m …

New method explains predictive uncertainty by focusing on second-order effects.

We apply the Cartan equivalence method to the study of real analytic second order ODEs under the local real analytic diffeomorphism of $\C^2$ which are area-preserving. This enables us to give a characterization of the second order ODEs which are equivalent to $y^{\prime\prime}=0$ under such transformations. Moreover w…

This paper presents a geometric-variational approach to continuous and discrete {\it second-order} field theories following the methodology of \cite{MPS}. Staying entirely in the Lagrangian framework and letting $Y$ denote the configuration fiber bundle, we show that both the multisymplectic structure on $J^3Y$ as well…

Paper introduces FoMoH for optimization without backpropagation.

Second-order methods improve differential privacy in convex optimization.

In this paper we define $n$th order Hessian structures on manifolds and study them. In particular, when $n = 3$, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it certain class of connections} on the second-order tangent bundle of a manifold. Furt…

Using a model for the bundle $\hat{\mathcal F}^2M$ of semi-holonomic second order frames of a manifold $M$ as an extension of the bundle ${\mathcal F}^2M$ of holonomic second order frames of $M$, we introduce in $\hat{\mathcal F}^2M$ a principal bundle structure over ${\mathcal F}^2M$, the structure group being the add…

A new method for faster optimization of noisy functions.

New methods using natural gradient for structured optimization.

Study stabilizes second-order systems to first-order dynamics.

AdaSub optimizes with second-order info in low-dims subspace.

Paper proposes a second-order method for faster SVI convergence.

Paper uses second-order differential geometry to study stochastic mechanics.

Paper derives estimates for complex Hessian equations on Hermitian manifolds.

Study second order integrability of Einstein deformations on Riemannian and Kähler manifolds.

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we …

New superintegrable systems derived from Frobenius structures.

Minimal surfaces in third-order ODEs identified for linear second-order ODEs.

New geometric proof of convex function differentiability and approximation.

We develop a second-order model for limit order books in a single scaling regime.

A new method for faster optimization in high dimensions.

In the present paper we consider the problem of local equivalence of second order ODEs which are cubic in second derivative under the action of the pseudogroup of contact transformations. We show how it may be reduced to the equivalence problem of 2-webs in $\mathbb{R}^3$ under the action of finite-dimensional group, a…

Paper introduces STSL, a second-order Tweedie sampler for efficient posterior sampling in inverse problems.

Improved Local SGD convergence for general convex objectives with bounded second-order heterogeneity.

A new framework for measuring uncertainty in machine learning models.

We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also show that, modulo Cartan duality and point transformations, the Painlevé-I equati…

We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a non-uniform grid with more grid-points ar…