Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
In this article, we initiate a geometric measure theoretic approach to symplectic Hodge theory. In particular, we apply one of the central results in geometric measure theory, the Federer-Fleming deformation theorem, together with the cohomology theory of normal cur- rents on a differential manifold, to establish a fun…
By Federer and Fleming there exist at least one mass-minimizing normal current in every real-valued homology class of a Riemannian manifold. However the regularity of the mass-minimizing currents and their distributions may generally be quite complicated. In this paper we shall study how to construct nice metrics so th…
Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a film of oil stretched on a wire frame, and the problem came to be called Plateau's…
Inspired by the Gromov-Hausdorff distance, we define the intrinsic flat distance between oriented m dimensional Riemannian manifolds with boundary by isometrically embedding the manifolds into a common metric space, measuring the flat distance between them and taking an infimum over all isometric embeddings and all c…
The paper proves stability of a quasi-local positive mass theorem for graphical hypersurfaces.
problem Stability of a quasi-local positive mass theorem for graphical hypersurfaces.
method Worked with the Brown--York quasi-local mass, considering compact n-manifolds with boundary as graphs in R^(n+1).
result If the Brown--York mass of the boundary of a compact manifold is small, then the manifold is close to a Euclidean hyperplane.
We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where p>1 and n≥1. We give a complete classification of stable and finite Morse index solutions (whether positive or sign changing), in the full exponent range. We also compute an…
The paper solves a partial Plateau problem using H-mass.
problem Finding a surface of least area with a partially specified boundary.
method Minimizing H-mass over scans with boundary. result Existence of a rectifiable minimizer for the H-mass problem. pFedGame uses game theory for decentralized federated learning in dynamic networks.
problem Performance bottlenecks, data bias, model convergence issues, and model poisoning attacks in federated learning.
method pFedGame employs game theory to decentralize federated learning, avoiding a central aggregation server and addressing dynamic network challenges.
result pFedGame achieves higher accuracy (over 70%) in heterogeneous data compared to existing methods.
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
We propose and analyze a new type of stochastic first order method: gradient descent with compressed iterates (GDCI). GDCI in each iteration first compresses the current iterate using a lossy randomized compression technique, and subsequently takes a gradient step. This method is a distillation of a key ingredient in t…
Once one knows that singularities occur, one naturally wonders what the singularities are like. For minimal varieties the first answer, already known to Federer-Fleming in 1959, is that they weakly resemble cones. For mean curvature flow, by the combined work of Huisken, Ilmanen, and White, singularities weakly resembl…
New findings on metric spaces with finite Nagata dimension.
problem Understanding isoperimetric properties in subsets of metric spaces.
method Analyzing quasiconvex subsets with finite Nagata dimension and applying isoperimetric inequalities.
result Quasiconvex subsets of metric spaces with finite Nagata dimension are isoperimetrically undistorted up to a certain dimension.
In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions, one can restrict to simplicial spheres of particular shapes, called "round" and "u…
In this paper we present a new approach to Morse theory based on the de Rham-Federer theory of currents. The full classical theory is derived in a transparent way. The methods carry over uniformly to the equivariant and the holomorphic settings. Moreover, the methods are substantially stronger than the classical ones a…
We present a new approach to Morse and Novikov theories, based on the deRham Federer theory of currents, using the finite volume flow technique of Harvey and Lawson. In the Morse case, we construct a noncompact analogue of the Morse complex, relating a Morse function to the cohomology with compact forward supports of t…
We prove certain optimal systolic inequalities for a closed Riemannian manifold (X,g), depending on a pair of parameters, n and b. Here n is the dimension of X, while b is its first Betti number. The proof of the inequalities involves constructing Abel-Jacobi maps from X to its Jacobi torus T^b, which are area-decreasi…
This paper develops a federated EM algorithm for unsupervised learning of mixture models.
problem Theoretical foundations of unsupervised federated learning are lacking.
method Introduces a federated gradient EM algorithm (FedGrEM) for unsupervised learning of mixture models.
result Theoretical analysis shows FedGrEM outperforms local single-task learning.
A canonically defined mod 2 linear dependency current is associated to each collection of m sections of a real rank n vector bundle. This current is supported on the linear dependency set of the collection of sections. It is defined whenever the collection satisfies a weak measure theoretic condition called "atomicity"…
Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the ne…
Federated learning linked to mean-field games for large-scale learning.
problem Large-scale distributed and privacy-preserving learning algorithms.
method Established a connection between federated learning and mean-field games, presenting federated learning as a differential game.
result Properties of the equilibrium of the federated learning game were discussed.
We use Kirk's invariant of link maps S2⊔S2→S4 and its variations due to Koschorke and Kirk-Livingston to deduce results about classical links. Namely, we give a new proof of the Nakanishi-Ohyama classification of two-component links in S3 up to Δ-link homotopy. We also prove its version for string li…
In federated learning, a central server coordinates the training of a single model on a massively distributed network of devices. This setting can be naturally extended to a multi-task learning framework, to handle real-world federated datasets that typically show strong statistical heterogeneity among devices. Despite…
Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neumann eigenvalues of the submanifolds when they converge in the flat sense without losing volume. With an additional condition on the boundaries…
A d-bar-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O*-gerbes …
Federated learning technique improves convergence speed with communication delays.
problem Communication delays between edge nodes and aggregator in federated learning.
method Developed FedDelAvg, a technique that generalizes federated averaging to incorporate a weighting between current local model and delayed global model.
result FedDelAvg achieves a significant improvement in convergence speed, especially when optimizing the weighting scheme to account for delays.
Flexible device participation improves federated learning convergence.
problem Strict device participation limits federated learning reach.
method Analytical results and new aggregation scheme for flexible participation.
result Convergence improved with flexible device participation.
This paper examines federated learning from an information-theoretic perspective.
problem Understanding the conditions under which averaging model parameters in federated learning is beneficial.
method Measuring mutual information between representations and inputs/labels in local models and comparing it to the averaged model.
result Empirical results confirm the practical usefulness of averaging for neural networks, even with varying local dataset distributions.
FedVision uses federated learning to improve object detection without transmitting data.
problem Challenges in building object detection models on large training datasets due to privacy and cost issues.
method Federated learning (FL) platform for easy integration by non-experts.
result Significant efficiency improvement and cost reduction in smart city applications.
A new federated learning method reduces communication costs and improves adaptivity.
problem Large communication overhead and lack of adaptivity in federated learning.
method FedCAMS: A novel communication-efficient adaptive federated learning method with theoretical guarantees.
result FedCAMS achieves the same convergence rate as non-compressed federated learning methods.
Research improves federated text models for next word prediction.
problem Training models on distributed devices efficiently and effectively.
method Employ transfer learning in federated learning for next word prediction.
result Enhancements to current baselines with pretrained embeddings and whole model pretraining.
The paper analyzes privacy leakage in federated learning using linear algebra and optimization theory.
problem Privacy leakage in federated learning despite its promise for data privacy.
method Theoretical analysis from linear algebra and optimization theory perspectives.
result Derives sufficient conditions to prevent data reconstruction attacks and establishes an upper bound on privacy leakage.
A privacy-preserving framework detects faults in circular economy processes.
problem Lack of shared data across company borders due to privacy concerns.
method Federated Principal Component Analysis (PCA) and Secure Multiparty Computation.
result The proposed FedMSPC framework outperforms standard PCA in fault detection.
New federated conformal prediction method addresses label shift for uncertainty quantification.
problem Label shift in federated learning and its impact on uncertainty quantification.
method Quantile regression-based federated conformal prediction method with privacy constraints.
result Method provides valid coverage of prediction sets and differential privacy guarantees.
FLBench automates federated learning benchmarking.
problem Manual dataset partitioning fails to simulate real-world isolated data islands.
method Develops a federated learning benchmark suite with three domains.
result Automates evaluation of federated learning systems and algorithms.
Federated learning involves training statistical models over remote devices or siloed data centers, such as mobile phones or hospitals, while keeping data localized. Training in heterogeneous and potentially massive networks introduces novel challenges that require a fundamental departure from standard approaches for l…
New federated learning methods improve model performance on non-IID data.
problem Improving model performance on non-IID decentralized data.
method Proposed Federated AGMs using adaptive gradient methods with first-order and second-order momenta.
result The proposed Federated AGMs converge to a first-order stationary point under non-IID and unbalanced data settings for nonconvex optimization.
FAVANO improves federated learning for resource-constrained environments.
problem Asynchronous communication in federated learning leads to bias and scalability issues.
method FAVANO is a novel asynchronous federated learning framework for resource-constrained environments.
result FAVANO outperforms existing methods on standard benchmarks.
FedCD improves non-IID federated learning performance.
problem Learning from non-IID data in federated learning.
method FedCD dynamically groups devices with similar data.
result FedCD achieves higher accuracy and faster convergence.
DSVGD improves federated learning with fewer communication rounds.
problem Federated learning scalability and trustworthiness.
method Distributed Stein Variational Gradient Descent (DSVGD) for non-parametric Bayesian inference.
result DSVGD achieves comparable accuracy and scalability to other methods, with well-calibrated predictions.
Sketching improves federated learning privacy without sacrificing performance or accuracy.
problem Privacy concerns in federated learning training.
method Sketching algorithms to enhance privacy.
result Sketching can provide strong privacy guarantees for federated learning.
FedGRU uses federated learning to predict traffic flow accurately while preserving user privacy.
problem Developing accurate traffic flow prediction while protecting user privacy.
method Federated Learning, Secure Parameter Aggregation, Joint Announcement Protocol, Ensemble Clustering.
result FedGRU achieves 90.96% higher prediction accuracy than advanced deep learning models.
RPN reduces communication costs in federated learning.
problem Efficient communication in federated learning with complex models.
method Residual Pooling Network (RPN) for compression.
result RPN achieves similar performance with reduced data transmission.
Federated Extra-Trees protects privacy while improving machine learning performance.
problem Scattered data and privacy concerns in machine learning.
method Local differential privacy in federated trees model.
result Improved accuracy and robustness in federated machine learning.
New algorithm tracks subspaces with missing and corrupted data, simpler and federated.
problem Subspace tracking with missing and corrupted data.
method Proposes a novel algorithm that does not assume piecewise constant subspace changes and is simpler.
result Guarantees for both subspace tracking with missing data and outliers.
This paper analyzes the convergence of Federated Average under relaxed assumptions.
problem Lack of theoretical analysis for Federated Average under assumptions beyond smoothness.
method Relaxing assumptions of strong smoothness to semi-smoothness and semi-Lipschitz properties, and introducing a bound on the gradient.
result Provides a theoretical convergence study on Federated Learning under new assumptions.
Optimizes communication in federated learning using rate-distortion theory.
problem Reduces communication cost in federated learning while maintaining model accuracy.
method Applies rate-distortion theory to model updates, proposing distortion as a proxy for accuracy.
result Near-optimal communication reduction, outperforming other methods on a FL benchmark.