arXiv research

Proves finite step termination of Kähler-Einstein metric singularity formation.

Finite 2-step nilpotent groups studied by Kim and Manturov.

In this article we use the "escape from subvarieties lemma" introduced by Eskin--Mozes--Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a sim…

Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…

New framework guarantees convergence of multi-step MAML.

New RL method learns K-step lookahead Q-functions for fixed-horizon MDPs.

The paper analyzes convergence properties of NGA and PAMe for $L_1$-norm PCA.

Paper adapts ACI for online multi-step time-series forecasting with coverage guarantees.

We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an associated ordinary differential equation (ODE). We obtain finite-time bounds on t…

Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential geometry of N using representation theory of the complexified complex semisimple Lie …

The paper examines special Q-nets that terminate after a finite number of Laplace steps.

Policy gradient methods achieve linear convergence in simple MDPs.

We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.

MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.

The paper calculates prices for multi-step barrier options under the Black-Scholes model.

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our main focus is to characterize the finite-time complexity of this method under time-…

New TD method stabilizes average-reward learning.

In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total $Q$-curvature. This is a higher dimensional analogue of Li and Tam's result \cite{L-T} on surfaces with finite total Gaussian curvature. The main step in the proof is based on the construction of a quasiconformal map wh…

This study reveals efficient finite-difference computation for gradient regularization in deep learning.

Improved solver maintains positivity and accuracy across all time steps.

This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Suc…

Unified framework for finite-sample RL algorithms using Lyapunov theory.

Two complete knot invariants from diagrams, finite or infinite.

Many 2D Artin groups are residually finite.

In its simplest form, the traffic flow prediction problem is restricted to predicting a single time-step into the future. Multi-step traffic flow prediction extends this set-up to the case where predicting multiple time-steps into the future based on some finite history is of interest. This problem is significantly mor…

Transformers solve parity problems efficiently with step-by-step reasoning.

Avare improves optimization and sampling with adaptive importance sampling.

Proves finitely generated graded rings for klt singularities.

This paper characterizes semigenerated Carnot groups and applies it to rectifiability of perimeter sets.

Study on Nesterov's method in stochastic settings, revealing divergence under certain conditions.

New embedding method in function spaces improves expressiveness.

We study the class of holomorphic and isometric submersions between finite-type Teichmüller spaces. We prove that, with potential exceptions coming from low-genus phenomena, any such map is a forgetful map $\mathcal{T}_{g,n} \rightarrow \mathcal{T}_{g,m}$ obtained by filling in punctures. This generalizes a classical r…

We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…

We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, such a two-step procedure does not necessarily work well because the first step is performed without …

New method identifies parameters of wider shallow neural networks with biases.

Path integral method calculates barrier option prices.

In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When th…

Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.

Paper analyzes convergence rates for multi-agent learning in games.

Fewer data weight updates lead to faster convergence in machine learning models.

Paper solves convertible bond valuation using finite elements with penalty method.

Distributed statistical inference has recently attracted enormous attention. Many existing work focuses on the averaging estimator. We propose a one-step approach to enhance a simple-averaging based distributed estimator. We derive the corresponding asymptotic properties of the newly proposed estimator. We find that th…

The abstract proves a global splitting theorem for Poisson manifolds.

A multibranched surface is a 2-dimensional polyhedron without vertices. We introduce moves for multibranched surfaces embedded in a 3-manifold, which connect any two multibranched surfaces with the same regular neighborhoods in finitely many steps.

Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.

FHBI enhances generalization in Bayesian inference with iterative steps in functional spaces.

We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of finite coverings of surfaces for which we need to develop a relative …