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.
Equivalence shown between two mathematical concepts for hyperbolic surfaces.
The paper connects different convergence concepts in geometric analysis.
Study extends null distance concept to Lorentzian length spaces for spacetime analysis.
This work shows how transformers use multi-concept word semantics for efficient in-context learning.
We introduce a new concept, data irrecoverability, and show that the well-studied concept of data privacy is sufficient but not necessary for data irrecoverability. We show that there are several regularized loss minimization problems that can use perturbed data with theoretical guarantees of generalization, i.e., loss…
Study introduces fractional mass concept for surfaces, proving its convergence.
The paper proves stability of the positive mass theorem using intrinsic flat convergence.
New algorithm learns multiclass concepts with finite Littlestone dimension.
Study Gromov-Hausdorff convergence of metric pairs and tuples.
BC-LLM uses LLMs to find concepts without predefined sets, improving interpretability and performance.
Theory extends optimal learning rates without realizability assumption.
New method tackles concept shifts in nonparametric regression using robust and adaptive transfer learning.
Introduces generalized almost statistical convergence and its properties.
This paper analyzes saddle points and minimax points in non-convex smooth games.
New approach proves convergence of SA and SGD with weaker conditions.
The paper reconstructs Lorentzian spacetimes from causal sets.
New approach for testable learning using moment matching and Rademacher complexity.
New varifold solutions for mean curvature flow converge and are unique.
The article introduces a new convergence concept for Lorentzian spaces and applies it to generalized cones.
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. T…
A new algorithm for K-means clustering in evolving data streams.
Variational method for eigenvalues on manifolds.
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual mixing concepts may not be appropriate for measuring the dependence among these ob…
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. I…
Service robots benefit from encoding information in semantically meaningful ways to enable more robust task execution. Prior work has shown multi-relational embeddings can encode semantic knowledge graphs to promote generalizability and scalability, but only within a batched learning paradigm. We present Incremental Se…
One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample mean of graphs include: non-existence, non-uniqueness, statistical inconsistency,…
We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost su…
Researchers define quantiles on Riemannian manifolds using optimal transport.
Study homogenizes equations on parallelizable manifolds using tensor localization and periodicity.
The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…
This thesis investigates belief propagation's performance in graphical models with loops.
In this paper we introduce a Guan-Li type volume preserving mean curvature flow for free boundary hypersurfaces in a ball. We give a concept of star-shaped free boundary hypersurfaces in a ball and show that the Guan-Li type mean curvature flow has long time existence and converges to a free boundary spherical cap, pro…
New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.
New sampling and diffusion models methods introduced without density function assumptions.
Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we translate the property (NFLVR-S) in terms of so called structure conditions and we intr…
We derive scaling laws for optimizing neural networks in hardware.
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothn…
Paper proves Shapley value convergence in Bayesian learning games.
This study analyses, through cross-section estimation methods, the influence of spatial effects and human capital in the conditional productivity convergence (product per worker) in the economic sectors of NUTs III of mainland Portugal between 1995 and 2002. To analyse the data, Moran's I statistics is considered, and …
We extend the concept of renormalized volume for geometrically finite hyperbolic -manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic structures over an acylindrical 3-manifold with geometrically finite limit. This allows us to show that the renormalized volume attains its…
Deep learning models viewed through tame geometry for convergence guarantees.
Enhanced Markov chain sampler learns network statistics faster.
We study two important concepts in adversarial deep learning---adversarial training and generative adversarial network (GAN). Adversarial training is the technique used to improve the robustness of discriminator by combining adversarial attacker and discriminator in the training phase. GAN is commonly used for image ge…
New method shows how order of gradient updates impacts stability and convergence in deep learning.
Inspired by the work of Leung-Wan, we study the mean curvature flow in hyperkähler manifolds starting from hyper-Lagrangian submanifolds, a class of middle dimensional submanifolds, which contains the class of complex Lagrangian submanifolds. For each hyper-Lagrangian submanifold, we define a new energy concept called …
The paper studies invariant weighted Bergman metrics on domains.
Deep reinforcement learning enables algorithms to learn complex behavior, deal with continuous action spaces and find good strategies in environments with high dimensional state spaces. With deep reinforcement learning being an active area of research and many concurrent inventions, we decided to focus on a relatively …
We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…