A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
AdaSDBO solves decentralized bilevel optimization without problem parameters, achieving competitive performance.
problem Decentralized bilevel optimization problems without known parameters.
method AdaSDBO, a fully problem-parameter-free algorithm with adaptive stepsizes.
result AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}
ight)$, matching state-of-the-art methods up to polylogarithmic factors.
We consider minimizing a nonconvex, smooth function f on a Riemannian manifold 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/ε2 o…
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 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…
We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondl…
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…
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 …
The paper explores the geometry of the Spence-Kummer trilogarithm equation and its Galois analogue.
problem Investigating the geometry and functional equation of the Spence-Kummer trilogarithm.
method Using algebraic relations between polylogarithm generating series and path systems, along with tensor and homotopy criteria for functional equations.
result Derives a precise form of the Spence-Kummer equation and its Galois analogue.
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…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order d (i.e., a d-fold multiway array) in Rn1×n2×⋯×nd. It focuses on the task of estimatin…
This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.
problem Score estimation and sampling guarantees for heavy-tailed targets in diffusion models.
method Kernel density estimation and minimax rates analysis for score estimation and sampling guarantees.
result Sharp minimax rates for score estimation and sampling guarantees for heavy-tailed targets, revealing qualitative differences between exponential and polynomial tails.
We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label nois…
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…
The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in recovering communities in the SBM from statistical and computational points of view, there are still gaps in understanding the fundamental information theoretic and computational l…