arXiv research

Develops local curvature estimates for mean curvature flow.

Sharp curvature estimates for curvature flows help characterise ancient solutions.

Sharp curvature pinching for mean curvature flow in spheres proved.

Localizes curvature estimates for evolving hypersurfaces under various flows.

Proves Weinstein conjecture for specific contact manifolds.

Paper analyzes iterates in high-dimensional linear models and proposes estimators for their generalization error.

Paper analyzes iterative learning for concept classes and learns half-spaces.

WaveFit uses fixed-point iteration to create high-quality neural vocoders.

Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.

We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated torus knot type supports the standard contact structure. We also show that all iterated torus knots that fail the UTP support cabling knot …

Sharp analysis of power iteration for tensor PCA, improving convergence and stopping criteria.

Paper proves exponential lower bounds for policy iteration in MDPs.

We deduce from the work of Chen, that the restriction morphism from closed free iterated integrals to closed iterated integrals on loops is onto. We use this to show that the module of higher order invariants of smooth functions is generated by free closed iterated integrals.

Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is analyzed in solving the problem. The convergence of the iterations and the optim…

An iterative SE(3)-Transformer model is developed for graph data.

Study Ricci iteration on spheres and projective spaces, proving existence and convergence.

Stability of Einstein metrics under Ricci iteration studied.

Proposes a faster second-order method for MDPs.

New method confirms Ricci iteration converges to Kähler-Einstein metrics.

Iterative method learns unknown constraints for MPC control.

OMWU shows last iterate convergence in convex-concave games.

Paper introduces Ricci iteration for studying Kähler-Einstein metrics.

Iterates towards Kähler metrics with constant scalar curvature.

Iterated Amplification uses subproblem solutions to build training signals for complex tasks.

Algorithm recovers causal graphs from data with fewer tests.

Gradient descent with compressed iterates reduces model size for federated learning.

Spherical T-duality for iterated sphere bundles

In this paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \cite{CMO}, \cite{KM} and \cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bo…

Improved generalization with iterate averaging and adaptive algorithms.

DSPI connects natural policy gradient to policy iteration, proving global convergence.

Strong stability of ergodic iterations proven without ergodic driving sequence.

Enhances single-step adversarial training to defend against iterative adversarial examples.

New convergence rates for shuffling gradient methods without strong convexity.

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

Helix speeds up iterative ML development by optimizing workflow execution.

We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix repres…

We bound the index of a subgroup in iterated Kodaira fibrations.

The Ricci iteration is a discrete analogue of the Ricci flow. We give the first study of the Ricci iteration on a class of Riemannian manifolds that are not Kähler. The Ricci iteration in the non-Kähler setting exhibits new phenomena. Among them is the existence of so-called ancient Ricci iterations. As we show, these …

This study analyzes adversarial training on linearly separable data and finds that gradient updates can achieve large margins in polynomial iterations.

Last SGD iterate bounds for overparameterized linear regression.

We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), a natural adaptation of the Policy Search by Dynamic Programming a…

LocalKMeans parallelizes Lloyd's algorithm for distributed data.

Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.

New method improves subspace iteration for eigenvectors in machine learning.

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated inte…

We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the membrane case.

OptEx accelerates first-order optimization with parallelized iterations.