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 -metric manifolds. We characterize when such a connection is a…
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48 results for “adapted connections”
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-forms, which splits into various subspaces. We study the parts of the torsion tensor according to this splitting to complete…
In this paper, we study the well adapted connection attached to a -metric manifold, proving it exists for any of the four geometries and obtaining a explicit formula as a derivation law. Besides we characterize the coincidence of the well adapted connection with the Levi Civita and the Chern connections.
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 -connection on a graded bundle. In a natural sense weighted -connections are adapte…
Unified framework for adaptive connection sampling in GNNs improves performance and robustness.
problem Over-smoothing and over-fitting in deep GNNs.
method Adaptive connection sampling trained jointly with GNN model parameters.
result Adaptive connection sampling mathematically equivalent to Bayesian GNNs approximation.
Given a complex manifold equipped with a holomorphic action of a connected complex Lie group , and a holomorphic principal --bundle over equipped with a --connection , we investigate the connections on the principal --bundle that are (strongly) adapted to . Examples are provided by…
Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structuremath.DG
There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…
New connections defined for a specific geometric structure.
problem Characterizing manifolds with a paracontact structure.
method Introduced and studied a pair of associated Schouten-van Kampen affine connections.
result Curvature properties of the connections are obtained.
The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
problem Computing curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
method Sub-Riemannian limits of Gaussian curvature, Schouten-Van Kampen affine connections, and adapted connections.
result Gauss-Bonnet theorems associated with Schouten-Van Kampen affine connections in the Heisenberg group.
Study integrability of specific geometric structures on odd Courant algebroids.
problem Characterize integrability of B_n-generalized structures on odd exact Courant algebroids.
method Characterize integrability in terms of existence of adapted generalized connections.
result Describe affine spaces of adapted generalized connections for integrable structures.
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic and arbitrary frames is considered.
This paper presents a novel adaptively connected neural network (ACNet) to improve the traditional convolutional neural networks (CNNs) {in} two aspects. First, ACNet employs a flexible way to switch global and local inference in processing the internal feature representations by adaptively determining the connection s…
Holonomy groups of K-contact sub-Riemannian manifolds are isomorphic.
problem Holonomy groups of K-contact sub-Riemannian manifolds.
method Proved isomorphism of holonomy groups under specific conditions.
result Holonomy groups of K-contact sub-Riemannian manifolds are isomorphic.
Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptationq-bio.NC
Interneurons improve learning in neural networks by accelerating convergence.
problem Rapid adaptation to changing input statistics in neural networks.
method Two mathematically tractable recurrent linear neural networks were compared: one with direct recurrent connections and the other with interneurons that mediate recurrent communication.
result The network with interneurons converges more quickly than the network with direct recurrent connections, scaling logarithmically with initialization spectrum.
The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structuremath.DG
We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.
Dual-attention GCN improves text classification by adapting to textual complexity.
problem Challenges in learning discriminative features from texts due to graph variants.
method Proposes a dual-attention GCN with connection-attention and hop-attention mechanisms.
result Achieves state-of-the-art performance on text classification tasks.
This paper explores how effective sample size, dimensionality, and model performance are related in covariate shift adaptation.
problem Understanding the relationship between effective sample size, dimensionality, and generalization in covariate shift adaptation.
method Building a unified theory connecting effective sample size, data dimensionality, and generalization in the context of covariate shift adaptation.
result Dimensionality reduction or feature selection can increase effective sample size, supporting the practice of reducing dimensionality before covariate shift adaptation.
In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric space is of rank one.
Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this paper, we introduce a novel SICE approach using adaptive thresholding. Our method i…
Adaptive lateral connections improve visual action recognition.
problem Feedforward neural models lack feedback and lateral connections like the primate visual cortex.
method Dynamic weights in recurrent lateral connections, iteratively reintroduced input.
result Significant performance gains in visual action recognition without pretraining.
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-st…
The main purpose of present paper is to study the affine connection induced from the horizontal lift on the cross-section determined by a vector field in Mn with respect to the adapte frame of .
Accelerates policy optimization in RL with optimistic and adaptive updates.
problem Improving policy optimization methods in reinforcement learning.
method Integrates foresight into policy improvement step via optimistic and adaptive updates.
result Designs an optimistic policy gradient algorithm, adaptive via meta-gradient learning.
Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to study because there is no prefered connection when the submanifold is not totally geodesic. For the particular case of degenerate totally umbilical hypersurfaces, we show that there are "Weyl" connections adapted to the induced structure on t…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseud…
We study geometry on real gerbes in the spirit of Cheeger-Simons theory. The concepts of adaptations and holonomy forms are introduced for flat connections on real gerbes. Their relations to complex gerbes with connections are presented, as well as results in loop and map spaces.
A -metric manifold has an almost complex or almost product structure and a compatible metric . We show that there exists a canonical involution in the set of connections on such a manifold, which allows to define a projection over the set of connections adapted to . This projection sends the Le…
Defines Witt structures for pseudo-Riemannian manifolds.
problem No specific problem stated; focuses on new structure.
method Introduces a connection adapted to Witt structures.
result Revisits geodesics and symmetric spaces in new context.
Adaptive reduction scheme approximates optimal policy in regularized MDPs.
problem Finding near optimal policy in regularized MDPs with biased solutions.
method Adaptive reduction of regularization parameter λ to approximate optimal policy.
result Iteration complexity reduced for obtaining ε-optimal policy.
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which th…
Bayesian approach improves AdaLoRA's performance and efficiency.
problem Improving the efficiency and performance of adaptive low-rank adaptation.
method Utilized Bayesian metrics and the Improved Variational Online Newton (IVON) optimizer for adaptive parameter budget allocation.
result Bayesian counterpart outperforms sensitivity-based importance metric and is faster than AdaLoRA.
Study variational problem on manifold with special distributions.
problem Generalize Einstein metrics on manifold with multiple distributions.
method Define functional of pseudo-Riemannian metric and contorsion tensor, prove critical pairs make distributions totally umbilical.
result Metrics in critical pairs make all distributions totally umbilical.
Derives Levi-Civita connection formulas for specific geometries.
problem Determining geometric invariants of Lorentzian manifolds.
method Explicitly derives Christoffel symbols in terms of adapted frame fields.
result Formulas for geometric invariants of Lorentzian manifolds.
New approach tackles class imbalance in long-tailed datasets using domain adaptation techniques.
problem Class imbalance in long-tailed datasets leading to poor model performance.
method Proposes a meta-learning approach to estimate differences between class-conditioned distributions.
result Validated approach on six benchmark datasets and three loss functions.
New approach connects Finsler geometry's metric and connections.
problem Deriving Finsler geometry's metric and connections from compatibility axioms.
method Compatibility axioms between metric and Finsler connection.
result Metrical formulation of Finsler geometry for field theory.
New algorithm reduces TV-denoising to adaptive online learning.
problem Estimating TV-bounded functions from noisy samples.
method Deep connection to Strongly Adaptive online learning; time algorithm.
result Near minimax optimal rate of under squared error loss.
Paper presents a self-adaptive learning model for robust classification and regression.
problem Dealing with various datasets of different complexity.
method Combines DNDN and DSP, an end-to-end training approach with multiple randomly initialized softmax layers and adaptive soft pruning.
result The model demonstrates no performance loss compared with unpruned models and higher robustness over different data and feature distributions.
We introduce the notion of a nested open book, a submanifold equipped with an open book structure compatible with an ambient open book, and describe in detail the special case of a push-off of the binding of an open book. This enables us to explicitly describe a natural open book decomposition of a fibre connected sum …
This paper addresses the problem of unsupervised domain adaption from theoretical and algorithmic perspectives. Existing domain adaptation theories naturally imply minimax optimization algorithms, which connect well with the domain adaptation methods based on adversarial learning. However, several disconnections still …
Time Adaptive Gaussian Modelstat.ML
TAGM models time-varying connections between variables.
problem Inferring temporal relationships between covariates.
method Time Adaptive Gaussian Model (TAGM) using Hidden Markov Models and Gaussian Graphical Models.
result TAGM outperforms state-of-the-art methods for temporal network inference.
New adaptive first-order methods improve on quasi-Newton variants.
problem Designing efficient gradient methods for practical applications.
method Online scaled gradient methods (OSGM) with new adaptive methods OSGM-Best.
result OSGM-Best matches quasi-Newton variants but requires less memory and cheaper iterations.
The paper derives inequalities and formulas for generalized Ricci flow.
problem Understanding and characterizing generalized Ricci flow.
method Using Bochner formula and adapted Malliavin gradient, the paper derives inequalities and characterizes generalized Ricci flow.
result Characterizations of generalized Ricci flow via inequalities for the associated Malliavin gradient.
Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler spacemath.DG
On the slit tangent manifold of a Finsler space there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle…
LARGE adapts regularization for better graph estimation in high-dimensional data.
problem Challenges in selecting optimal regularization parameters for graph estimation.
method Locally Adaptive Regularization for Graph Estimation (LARGE) that adapts nodewise penalties.
result LARGE consistently outperforms benchmark methods in graph recovery and estimation accuracy.
LoRA enhances model adaptability without increasing parameters.
problem Theoretical understanding of LoRA's adaptability.
method Theoretical analysis of LoRA's expressive power.
result LoRA can adapt any model to a smaller target model with a specific rank.
Enhances financial time-series prediction by adapting pre-trained models to new data.
problem Adapting pre-trained financial models to new data sets efficiently.
method Augmented Bilinear Network that retains and adjusts pre-trained neural network knowledge.
result Improves prediction performance and reduces model complexity.
Study deforms Hermitian metrics with positive curvature.
problem Deforming Hermitian metrics with positive curvature.
method Adapted conformal perturbation method to Hermitian setting.
result Hermitian metrics with quasi-positive curvature can be deformed to positive curvature.
The famous Uniformization Theorem states that on closed Riemannian surfaces there always exists a metric of constant curvature for the Levi-Cevita connection. In this article we prove that an analogue of the uniformization theorem also holds for connections with metric torsion in the case of non-positive Euler characte…