arXiv research

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

Develops unbiased averaging methods for second order optimization in distributed systems.

A method for inferring motility models and heterogeneity from particle trajectories.

The thesis clarifies when local updates outperform centralized methods in heterogeneous data environments.

Study finds risk sharing without convexity assumptions.

Second-order guarantees for federated learning algorithms.

The notion that economies should normally be in equilibrium is by now well-established; equally well-established is that economies are almost never precisely in equilibrium. Using a very general formulation, we show that under dynamics that are second-order in time a price system can remain away from equilibrium with p…

SLEDGE algorithm reduces gradient computation errors in optimization.

Study proposes BFEL framework for privacy-preserving FL in personalized healthcare.

New method speeds up deep learning optimization.

Study on evolving interfaces with complex curvature and density effects.

Efficient Bayesian FL method improves predictive accuracy and uncertainty estimates.

Study on dynamic curves with elastic energy and spontaneous curvature.

New algorithm improves understanding of decentralized SBO transient iteration complexity.

Network representation learning (NRL) has been widely used to help analyze large-scale networks through mapping original networks into a low-dimensional vector space. However, existing NRL methods ignore the impact of properties of relations on the object relevance in heterogeneous information networks (HINs). To tackl…

Method learns cell interaction rules from individual trajectories.

This work develops a learning theory for inferring interaction kernels in complex agent systems.

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…

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…

C-kNN-LSH identifies similar patient histories for causal inference in longitudinal data.

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.