arXiv research

GeoAdaLer enhances geometric understanding of Adam for stochastic optimization.

Geometric methods solve sampling, optimisation, inference, and adaptive decision-making.

Modeling bone microarchitecture adaptation using geometric flows.

New theory for clustering in geometric and adaptive settings.

New algorithm adapts to optimize non-convex problems efficiently.

Optimal transport aligns source and target distributions for linear regression in 2D.

Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter space, thus enabling chains to achieve a faster convergence rate when measured in n…

In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, and on Kodaira surfaces.

A new method evolves point clouds using B-splines for smooth surfaces.

Adapts Stein's method for geometric inequalities, addressing boundary terms.

GSAN learns adaptive node representations using geometric scattering and attention.

We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $ρ$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example supported on a $d$-dimensional Riemannian manifold. Geometric Multi-Resolution Analysis (GM…

Introduces GFC for learning complex dynamical systems with geometric constraints.

Paper describes integrable structure of Hitchin moduli spaces.

New proofs for complex Hopf manifolds using geometric structures.

A lightweight framework improves convergence and stability of PINNs for complex PDEs.

The paper constructs new supergravity backgrounds using specific geometric constraints.

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with theoreticians pursuing mathematical optimality at a cost of obtaining specialized…

In this technical note, we adapt an idea of Gabai to construct non-uniquely ergodic, non-geometric, arational trees.

Paper proposes a probabilistic alignment method for domain adaptation.

GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.

Geometric approach for unsupervised word embedding alignment.

New algorithm improves Bayesian neural networks using adaptive importance sampling.

Geometric Graph Alignment enhances IoT intrusion detection using NID data.

A new Riemannian framework optimizes LoRA for faster convergence and better performance.

Unified theory for adaptive image convolutions using metric perspectives.

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full linear frame bundle of the field configuration space, and it inherits a generaliz…

In this paper, we investigate a curvature-adapted and proper complex equifocal submanifold in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples. In future, the results in this paper will be used to give a submanifold geometri…

Locally adaptive federated learning improves convergence in distributed machine learning.

Study shows how steepest descent algorithms' geometric margin increases during training.

The Cheeger-Gromoll theorem is adapted for groups, revealing geometric properties of virtually abelian groups.

We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associated, via the so-called clutching map. To this end we adapt to our fra…

Adapts stereographic projection for ellipsoid and elliptic paraboloid.

Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.

New accelerators for EM improve convergence speed in complex mixture models.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

This paper develops a general method for constructing Poisson integrators.

We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of $(J^2=\pm1)$-metric manifolds. We characterize when such a connection is a…

We provide two examples of spectral analysis techniques of Schroedinger operators applied to geometric Laplacians. In particular we show how to adapt the method of analytic dilation to Laplacians on complete manifolds with corners of codimension 2 finding the absence of singular continuous spectrum for these operators,…

Adaptive sampling improves graph diffusion models by maintaining uniform information speed.

Every normal subgroup of Cantor tree's mapping class group is geometric.

Develops a new geometric framework for non-conservative field theories.

Unsupervised domain adaptation aims to transfer and adapt knowledge learned from a labeled source domain to an unlabeled target domain. Key components of unsupervised domain adaptation include: (a) maximizing performance on the target, and (b) aligning the source and target domains. Traditionally, these tasks have eith…

Domain adaptation is transfer learning which aims to generalize a learning model across training and testing data with different distributions. Most previous research tackle this problem in seeking a shared feature representation between source and target domains while reducing the mismatch of their data distributions.…

Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids we define the notion of a weighted $A$-connection on a graded bundle. In a natural sense weighted $A$-connections are adapte…

We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of Jang's equation. Substantial new geometric insights regarding the lower order properties of marginally outer trapped surfa…

We prove a general result about the short time existence and uniqueness of second order geometric flows transverse to a Riemannian foliation on a compact manifold. Our result includes some flows already existing in literature, as the transverse Ricci flow, the Sasaki-Ricci flow and the Sasaki J-flow and motivates the s…

Study optimal policy regret in partially observable Markov games with adaptive opponents.