arXiv research

Study shows how heavy-tailed Hawkes processes can model rough volatility in financial markets.

New convergence bounds for shuffling-based SGD methods in distributed learning.

The paper improves the empirical bootstrap method for non-normal estimators.

This paper improves convergence guarantees for gradient clipping in deep learning.

Paper tightens lower bounds on decentralized training complexity.

A new contrastive MI estimator improves efficiency and tightness.

We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $τ$ rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…

This paper analyzes OGDA and EG methods for nonconvex minimax problems.

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally,…

We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient method (OG) and consensus optimization (CO), which enjoy linear convergence in cas…

Unified complexity bound for sampling logconcave distributions

Paper analyzes convergence of DDPM for general distributions.

PAGE is a simple gradient estimator for nonconvex optimization problems.

Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.

Sampling without replacement speeds up optimization in minimax problems.

This paper analyzes convergence of RMSProp and Adam in non-convex optimization with tight complexity bounds.

In this paper, we quantitative convergence in $W_2$ for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a…

Study improves distributed linear estimation under adversarial conditions.

Unified framework for analyzing graph neural operators converging to graph limits.

Paper studies identifiability and stability of drifting fields in generative modeling.

The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.

We establish a tight characterization of the worst-case rates for the excess risk of agnostic learning with sample compression schemes and for uniform convergence for agnostic sample compression schemes. In particular, we find that the optimal rates of convergence for size-$k$ agnostic sample compression schemes are of…

Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise to a piecewise linear (PL) approximant. This is extended to isotopic convergenc…

This work improves the Euler method for masked diffusion models, providing tighter convergence guarantees.

Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known tight triangulated manifolds are stacked. It is known that locally stacked tight t…

New bounds on SGD's final iterate convergence rate in constant dimension.

In theoretical analysis of deep learning, discovering which features of deep learning lead to good performance is an important task. In this paper, using the framework for analyzing the generalization error developed in Suzuki (2018), we derive a fast learning rate for deep neural networks with more general activation …

Tight geodesics were introduced by Masur-Minsky in [17]. They and their hierarchies have been a powerful tool in the study of the curve complex, mapping class groups, Teichmüller spaces, and hyperbolic 3-manifolds. In the same paper, they showed that there are at least one and at most finitely many tight geodesics betw…

We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetr…

Improved SEG method converges to Nash equilibrium in bilinear games.

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear conve…

Value aggregation is a general framework for solving imitation learning problems. Based on the idea of data aggregation, it generates a policy sequence by iteratively interleaving policy optimization and evaluation in an online learning setting. While the existence of a good policy in the policy sequence can be guarant…

The study identifies conditions for algorithms to have tight generalization bounds.

Surgery on knots always admits a tight contact structure.

Tight maps was introduced along tight homomorphisms by Burger, Iozzi and Wienhard with aims towards maximal representations. In this paper we classify tight maps into classical Hermitian symmetric spaces and give a partial result for the exceptional spaces.

3-manifold triangulations are Golod and tight, proven through a topological characterization.

Simply connected spaces of tight frames identified.

The study finds many tight contact structures on hyperbolic 3-spheres.

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

This research analyzes the error convergence rate of GAN models.

Study tight contact structures on specific 3-manifolds.

Classifies tight contact structures on surgeries of the Whitehead link.

Step decay schedules improve convergence in non-convex optimization.

Hogwild! adapts to distributed data by varying mini-batch sizes.

In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that any lens space admits only finitely many tight contact structures.

In \cite{confol} Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation $ξ$ on $T^3$ violating the Thurston-Bennequin inequalities. This answers a question from \cite{confol} negatively. Although the tightness of a confoliation does not imply the Thurston-Benn…

The DANE algorithm is an approximate Newton method popularly used for communication-efficient distributed machine learning. Reasons for the interest in DANE include scalability and versatility. Convergence of DANE, however, can be tricky; its appealing convergence rate is only rigorous for quadratic objective, and for …

Classifies real tight contact structures on lens spaces and solid tori.