arXiv research

Mirzakhani volumes of moduli spaces are polylogarithmic.

Study higher genus polylogarithms under Riemann surface degenerations.

Investigates webs related to cluster algebras and polylogarithms.

Paper solves no-swap regret minimization for combinatorial bandits with polylogarithmic dependence on N.

We prove optimal subspace embedding conjecture up to sub-polylogarithmic factors.

New algorithm reduces regret in online portfolio and quantum state learning.

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

QATS efficiently decodes HMMs with polylogarithmic complexity.

New method proves fast regret bounds for online RLHF with generalized preferences.

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have dimension-independent bounds for the underlying $\mathit{continuous}$ processes under s…

In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the case when the inner functions Ui's are real rational functions. First we prove that…

Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size $n$, the (inverse) target error $1/ε$, and the (inverse) fail…

Study shows sample complexity for multicalibration is Θ(ε^-3) with polylogarithmic factors.

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $ε^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy …

Improved GNN simulation of WL test with exponentially lower complexity.

Kähler information manifolds for signal filters in weighted Hardy spaces are explored.

New algorithms minimize regret in both adversarial and stochastic contexts.

The paper explores the geometry of the Spence-Kummer trilogarithm equation and its Galois analogue.

New method uses higher-order Langevin dynamics for efficient parallel sampling.

Machine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Eve…

Improved bounds for estimating discrete distributions in KL divergence.

This work proves that large models can be compressed significantly without losing performance.

Improved guarantees for misspecified kernelized bandit optimization.

Efficiently estimates binary product distributions with privacy.

New algorithm selects best distribution privately in nearly-linear time.

The paper analyzes GD for KANs, deriving bounds for training, generalization, and privacy.

New algorithms optimize without tuning, matching tuned SGD performance.

New method controls linear systems with adversarial disturbances.

Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine learning algorithms for supervised learning---for which statistical guarantees are …

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for con…

Study growth of systoles in arithmetic manifolds, focusing on $k$-dimensional cases.

New algorithms achieve optimal regret in sliding window model with limited memory.

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to com…

Neural networks can achieve optimal sample complexity for learning single-index models.

New algorithms for privately learning decision lists and halfspaces.

Quantum algorithm speeds up Lasso regression by quadratically faster per iteration.

New DP optimization methods for sparse gradients, improving on existing algorithms.

We consider minimizing a nonconvex, smooth function $f$ on a Riemannian manifold $\mathcal{M}$. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manifold). The rate of convergence depends as $1/ε^2$ o…

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexi…

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on "light-tail" noise assumptions or exhibit worse sample complexity. In this …

Constructs manifolds from quantum codes with novel geometric properties.

The paper solves robust learning of Gaussian mixtures with nearly optimal guarantees.

A new algorithm estimates mean adaptively to covariance, faster and more flexible than existing methods.

The Fock-Bargmann-Hartogs domain $D_{n,m}(μ)$ ($μ>0$) in $\mathbf{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-μ\|z\|^2},$ where $(z,w)\in \mathbf{C}^n\times \mathbf{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbf{C}^{n+m}$. Recently, Yamamori gave an explicit formula for the Bergman kernel of the…

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Paper presents a faster classical algorithm for principal component regression.

Protocol learns pure quantum states with minimal disturbance.