arXiv research

Improved lower bound for first Dirichlet eigenvalue using variance refinement.

Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained. However, as a proposal…

UCB-V algorithm improves on UCB for MAB problems with variance estimates.

The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.

A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully exploits information about the potentially heterogeneous mean, variance, and ceiling of…

Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of categorical sequences a policy gradient estimator, which evaluates a set of corr…

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

The paper refines and generalizes worst-case law invariant convex risk measures.

A new method for online personalized learning reduces gradient variance by dynamically selecting peers.

This paper develops a new theory for ensemble learning beyond variance reduction.

New algorithms reduce regret in online MDPs by adapting to data and variance.

We refine the recent local rigidity result for the marked length spectrum obtained by the first and third author in \cite{Guillarmou-Lefeuvre-18} and give an alternative proof using the geodesic stretch between two Anosov flows and some uniform estimate on the variance appearing in the central limit theorem for Anosov …

The Data Clustering (DC) problem is of central importance for the area of Machine Learning (ML), given its usefulness to represent data structural similarities from input spaces. Differently from Supervised Machine Learning (SML), which relies on the theoretical frameworks of the Statistical Learning Theory (SLT) and t…

New RL algorithm GDPO improves DLM reasoning efficiency.

Introduces SMMV preferences to avoid inconsistency in portfolio selection.

The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some $ε\in (0,1]$. Surprisingly, moments of order 2 (i.e., finite variance) are suffi…

New inequality for refined knot invariants in a specific space.

A new methodology has been introduced to clean the correlation matrix of single stocks returns based on a constrained principal component analysis using financial data. Portfolios were introduced, namely "Fundamental Maximum Variance Portfolios", to capture in an optimal way the risks defined by financial criteria ("Bo…

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…

New statistical methods improve TD learning for policy evaluation.

Single model estimates ensemble uncertainty efficiently.

New algorithm improves online learning with reduced discretization.

Refines neural network predictions using background knowledge for improved accuracy.

New research shows label refinement and weak training have limitations for aligning LLMs.

Paper analyzes \FedAvg's convergence and introduces a new algorithm to reduce bias.

Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.

This paper removes the finite variance assumption for deep convolutional neural networks.

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.

In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …

New CRB derived for curved models using extrinsic geometry.

Paper improves TD learning algorithm bounds with linear approx.

Refined 3D index uses surgery and gradings to distinguish 3-manifolds.

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Fu…

Paper introduces geometry-aware normalizing flows for improved causal inference.

Refines deep generative models to improve data density precision.

Established a stable cohomotopy refinement for Pin(2) monopole invariants.

Enhances CEV model pricing with high-order scheme and adaptive time stepping.

Refined 1-cocycle for knots helps quantify isotopies.

The study provides a comprehensive error analysis for diffusion models.

Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …

We note that our stable homotopy refinements of Khovanov's arc algebras and tangle invariants induce refinements of Chen-Khovanov and Stroppel's platform algebras and tangle invariants, and discuss the topological Hochschild homology of these refinements.

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not explicitly measure the uncertainties. This is conceptually similar to heteroscedastic ne…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regressi…

EGR refines and assesses protein complex structures.

New method reduces distributed non-convex optimization rounds and bits.

A novel framework refines diffusion models iteratively for better downstream reward optimization.

We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the $Ω$-background. This form enables us to relate refined C…

Study uses AI to refine loan assessments, improving credit default predictions.