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.
This work investigates how multi-round reasoning improves LLM performance.
problem Improving problem-solving abilities in complex tasks with LLMs.
method Investigates approximation, learnability, and generalization properties of multi-round auto-regressive models.
result Transformers with finite context windows are universal approximators for Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning.
In machine learning the best performance on a certain task is achieved by fully supervised methods when perfect ground truth labels are available. However, labels are often noisy, especially in remote sensing where manually curated public datasets are rare. We study the multi-modal cadaster map alignment problem for wh…
The AdaBoost algorithm was designed to combine many "weak" hypotheses that perform slightly better than random guessing into a "strong" hypothesis that has very low error. We study the rate at which AdaBoost iteratively converges to the minimum of the "exponential loss." Unlike previous work, our proofs do not require …
We address the M-best-arm identification problem in multi-armed bandits. A player has a limited budget to explore K arms (M<K), and once pulled, each arm yields a reward drawn (independently) from a fixed, unknown distribution. The goal is to find the top M arms in the sense of expected reward. We develop an algorithm …
In this paper, we present a scalable distributed implementation of the Sampled Limited-memory Symmetric Rank-1 (S-LSR1) algorithm. First, we show that a naive distributed implementation of S-LSR1 requires multiple rounds of expensive communications at every iteration and thus is inefficient. We then propose DS-LSR1, a …
Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus…
We consider the problem of strongly-convex online optimization in presence of adversarial delays; in a T-iteration online game, the feedback of the player's query at time t is arbitrarily delayed by an adversary for d_t rounds and delivered before the game ends, at iteration t+d_t-1. Specifically for \algo{online-gradi…
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has…
Paper proposes AggITD for efficient federated hypergradient computation.
problem Computing hypergradient in federated settings is challenging due to distributed and nonlinear construction of global Hessian matrices.
method AggITD: a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation.
result AggITD achieves the same sample complexity as AID-based approaches but with fewer communication rounds, especially in heterogeneous data environments.
Around 2007, A. Chang, J. Qing, and P. Yang proved a conformal gap theorem for Bach-flat metrics with round sphere as the model case. In this article, we extend this result to prove conformally invariant gap theorems for Bach-flat 4-manifolds with (CP2,gFS) and $(\mathbb{S}^2\times\mathbb{S}^2,g_{prod…
We study distributed algorithms for expected loss minimization where the datasets are large and have to be stored on different machines. Often we deal with minimizing the average of a set of convex functions where each function is the empirical risk of the corresponding part of the data. In the distributed setting wher…
Federated learning opens a number of research opportunities due to its high communication efficiency in distributed training problems within a star network. In this paper, we focus on improving the communication efficiency for fully decentralized federated learning over a graph, where the algorithm performs local updat…
In recent years, content recommendation systems in large websites (or \emph{content providers}) capture an increased focus. While the type of content varies, e.g.\ movies, articles, music, advertisements, etc., the high level problem remains the same. Based on knowledge obtained so far on the user, recommend the most d…
We consider the best-arm identification problem in multi-armed bandits, which focuses purely on exploration. A player is given a fixed budget to explore a finite set of arms, and the rewards of each arm are drawn independently from a fixed, unknown distribution. The player aims to identify the arm with the largest expe…
Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7-sphere by a freely-act…
In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that …
The paper develops efficient estimators for semi-parametric binary models in distributed computing.
problem Estimation and inference challenges in large-scale data under non-smooth objective functions.
method Proposes one-shot and multi-round divide-and-conquer estimators with adaptive kernel smoothing to relax constraints and achieve superlinear optimization error.
result Establishes quadratic convergence up to optimal statistical error rate and handles dataset heterogeneity and high-dimensional sparse parameters.
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.