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.
Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.
Paper presents a new policy gradient theorem using weak derivatives for reinforcement learning.
Paper investigates conditions for independence of weak gradients on metric spaces.
Weak correlations explain linear dynamics in deep learning models.
Studied SGD convergence under weak conditions.
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
Study shows how weak inverse anisotropic mean curvature flow behaves at infinity.
Study on test risk dynamics in learning theory with stochastic gradient flow.
Optimizes shapes on non-standard manifolds.
Self-test loss functions improve data-driven modeling of weak-form operators and gradient flows.
We prove the weak stability of expanding gradient Ricci solitons with positive curvature operator and quadratic curvature decay at infinity.
Proposes a constrained labeling method for weakly supervised learning.
Paper analyzes weak-to-strong generalization in CNNs, identifying data-scarce and data-abundant regimes.
Gradient descent benefits from tangent kernel advantages under specific conditions.
Paper proves uniqueness of weak solutions for Plateau flow.
New methods validate a hypothesis explaining how neural nets generalize well.
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexit…
The paper classifies special hypersurfaces in space forms.
A new parametric method studies Willmore flows and energy quantization.
Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.
Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.
We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in very simple learning settings. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradie…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner p…
The paper examines partial regularity of Lipschitz solutions to minimal surface system.
Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm, wh…
In this paper, we will establish an elliptic local Li-Yau gradient estimate for weak solutions of the heat equation on metric measure spaces with generalized Ricci curvature bounded from below. One of its main applications is a sharp gradient estimate for the logarithm of heat kernels. These results seem new even for s…
In dimension , there is a complete theory of weak solutions of Ricci flow - the singular Ricci flows introduced by Kleiner and Lott - which are unique across singularities, as was proved by Bamler and Kleiner. We show that uniqueness should not be expected to hold for Ricci flow weak solutions in dimensions $n\geq…
Study weak -K-contact manifolds, finding Einstein-type metrics and solitons.
This article analyzes the weak error of SGD optimization schemes.
The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudo gradient flows. W…
Large learning rates cause oscillations in NN weights that improve generalization.
Paper proposes a weak approximation of reflection coupling for non-convex optimization.
Lipschitz regularity proved for harmonic map heat flows into CAT(0) spaces.
In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove a sharp Yau's gradient gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition $RCD^*(…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment po…
Gradient Boosting Machine (GBM) is an extremely powerful supervised learning algorithm that is widely used in practice. GBM routinely features as a leading algorithm in machine learning competitions such as Kaggle and the KDDCup. In this work, we propose Accelerated Gradient Boosting Machine (AGBM) by incorporating Nes…
Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation…
In this paper we show how techniques coming from stochastic analysis, such as stochastic completeness (in the form of the weak maximum principle at infinity), parabolicity and -Liouville type results for the weighted Laplacian associated to the potential may be used to obtain triviality, rigidity results, and scal…
Paper develops methods for statistical inference in SGD with infinite variance.
Improved sampling method using regularized Stein Variational Gradient Flow.
New algorithm improves convergence of gradient boosting trees.
The goal of policy gradient approaches is to find a policy in a given class of policies which maximizes the expected return. Given a differentiable model of the policy, we want to apply a gradient-ascent technique to reach a local optimum. We mainly use gradient ascent, because it is theoretically well researched. The …
Improves data labeling efficiency in machine learning.
Natural images are virtually surrounded by low-density misclassified regions that can be efficiently discovered by gradient-guided search --- enabling the generation of adversarial images. While many techniques for detecting these attacks have been proposed, they are easily bypassed when the adversary has full knowledg…
A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the…
No expanding breathers found in noncompact Ricci flows with certain curvature conditions.
In this paper, we study the moduli spaces of noncollapsed Ricci flow solutions with bounded energy and scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study isoperimetric constant control, Kähler Ricci flow and moduli space of gradient shrinking solitons.