This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
New perspective on federated learning as posterior inference, improving optimization.
problem Optimizing global models in distributed learning settings.
method Formulated as posterior inference problem, using MCMC for approximate inference and federated averaging for refinement.
result Federated posterior averaging (FedPA) outperforms existing methods on benchmarks.
Global and local blowups of manifolds are proven equivalent.
problem Equivalence of global and local blowups in differential topology.
method Proof of equivalence between global and local constructions of blowups.
result Global and local constructions of blowups are shown to be equivalent.
A note on learning with agents having global perspectives and a principal optimizing their performance.
problem Learning with dynamic-optimizing principal-agent setting, where agents have global views and the principal optimizes performance.
method Empirical-likelihood estimator under conditional moment restrictions model, considering agents' out-of-sample and private dataset performances.
result A coherent mathematical argument for the learning process in this framework.
P3I learns holistic scene representations from a single image.
problem Inferring camera poses, object locations, and global scene structures from a single image.
method Combines search-based and gradient-based algorithms.
result P3I outperforms baselines on various image manipulation tasks.
Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.
problem Understanding the complexity of Covid-19 data across countries.
method Used a Bayesian mixture model (Hidalgo) to estimate intrinsic dimensionality.
result Covid-19 data projects onto two low-dimensional manifolds without significant loss of information.
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define co…
We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These h…
The fragmentation of production across countries has become an important feature of the globalization in recent decades and is often conceptualized by the term, global value chains (GVCs). When empirically investigating the GVCs, previous studies are mainly interested in knowing how global the GVCs are rather than how …
SogCLR uses small batch sizes for global contrastive learning, achieving similar performance to SimCLR.
problem Existing contrastive learning methods require large batch sizes or large feature dictionaries.
method SogCLR, a memory-efficient Stochastic Optimization algorithm for global contrastive learning.
result SogCLR with small batch sizes (e.g., 256) achieves similar performance to SimCLR with large batch sizes (e.g., 8192).
We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time singularities, and constructions of self-similar solutions.
The paper constructs Levi flat structures using structure sheaves and differential complexes.
problem Global solvability and regularity of Levi flat structures.
method Employing formal integrability and differential complexes, the paper constructs a resolution for the structure sheaf.
result Global exactness and Sobolev regularity of the differential complex for Levi flat structures.
Theoretical study explains why federated optimization fails to achieve perfect fitting.
problem Performance degradation in federated optimization under data heterogeneity.
method Assumption of distinct local optima due to client data heterogeneity.
result The global objective has a lower bound that prevents perfect fitting of all client data.
We derive a representation formula for the tensorial wave equation $\Box_\bg φ^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any dimension.
New framework for DNN training guarantees convergence to global minimum.
problem Training deep neural networks to converge to global minimum.
method Reformulated minimization problem with recursive algorithmic framework, using bounded style assumptions.
result Convergence to an ε-(global) minimum with O(1/ε^3) gradient computations.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
problem Understanding the effectiveness of tree-based methods in finite-sample settings, especially symbolic feature selection.
method Local ranking perspective, finite-sample analysis, oracle bounds, posterior contraction results, concordant divergence statistics.
result New insights and statistics for evaluating symbolic feature mappings.
Deep neural networks perform well on local tasks but struggle with global tasks.
problem Understanding the limitations of overparameterized deep neural networks in learning global functions.
method Introduced k-local and k-global functions to study the interplay between depth and function locality. result Depth is beneficial for learning local functions but detrimental to learning global functions.
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle theory. From this perspective, we obtain a global geometric proof on a generalized 3-d…
Framework for analyzing dynamic topological changes in point clouds using persistent homology and dynamic optimal transport.
problem Analyzing transient structural reorganizations during dynamic phase transitions in time-evolutionary point clouds.
method Hierarchical dynamic evaluation framework driven by topological and hypergraph reconstruction strategy.
result Combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.
Model strategic interactions between market makers and traders to optimize execution.
problem Optimizing execution in markets with strategic interactions.
method Stochastic game modeling with FBSDEs and decoupling approach.
result Established Nash equilibria and global well-posedness for specific models.
Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of …
Survey of global geometry for double field theory.
problem Global description of double field theory geometry.
method Review of Courant algebroids, metric algebroids, AKSZ construction, para-Hermitian geometry.
result Global description of doubled geometry and topological models.
The abstract introduces golden Finsler structures and explores their local and global properties.
problem Investigating geometric properties of golden Finsler structures.
method Local and global analysis of golden Finsler structures, including explicit computations and transformations.
result Proved that golden Finsler structures cannot be projectively related.
Study explores embedding signature-changing manifolds into higher-dimensional spaces.
problem Smooth metric signature changes in spacetimes.
method Global isometric embeddings into higher-dimensional pseudo-Euclidean spaces.
result Explicit constructions of global embeddings into Minkowski and Misner spaces.
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses
Multivariate time series (MTS) forecasting is widely used in various domains, such as meteorology and traffic. Due to limitations on data collection, transmission, and storage, real-world MTS data usually contains missing values, making it infeasible to apply existing MTS forecasting models such as linear regression an…
Study fragility in global financial indices using network analysis.
problem Monitor fragility in global financial indices.
method Network-based approach to analyze daily closing prices of global financial indices.
result Network-centric measures reveal fragility in global financial indices.
Global Autoregressive Models (GAMs) are a recent proposal [Parshakova et al., CoNLL 2019] for exploiting global properties of sequences for data-efficient learning of seq2seq models. In the first phase of training, an Energy-Based model (EBM) over sequences is derived. This EBM has high representational power, but is u…
In this paper, we provide an integrated systems modeling approach to analyzing global externalities from a microeconomic perspective. Various forms of policy (fiscal, monetary, etc.) have addressed flaws and market failures in models, but few have been able to successfully eliminate modern externalities that remain an …
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometric model for equivariant cohomotopy which works for any compact Lie group G. In the special case when G is finite or a torus, we show that ou…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of compl…
Replica exchange Langevin diffusion accelerates nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Replica exchange Langevin diffusion, discretization analysis.
result Replica exchange accelerates convergence to global minima.
Empirical evidence suggests that neural networks with ReLU activations generalize better with over-parameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameterized convolutional net…
QP perspective on Poisson-Lie T-duality topology changes.
problem Understanding Poisson-Lie T-duality through QP manifolds.
method QP manifolds and canonical transformations for symplectic reductions.
result Canonical transformations mediate Poisson-Lie T-duality.
New approach to principal groupoid bundles with connections using dg-Lie groupoids.
problem Developing a new perspective on principal bundles with connections.
method Using dg-Lie groupoids and additional adjustment data for Lie groupoids.
result Adjusted connections provide a global formulation of curved Yang-Mills-Higgs theories.
Max-pooling architectures are theoretically analyzed and shown to be globally optimized and generalize well.
problem Theoretical understanding and optimization of max-pooling in deep learning architectures.
method Theoretical analysis of a convolutional max-pooling architecture, focusing on a pattern detection problem.
result Max-pooling architectures can be globally optimized and generalize well, even for highly over-parameterized models.
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse topology from which generalizable physical features can be extracted. We advocate…
We establish that first-order methods avoid saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical s…
FedBE aggregates local models into a robust global model via Bayesian inference.
problem Challenges in aggregating non-i.i.d. local models into a global model in federated learning.
method FedBE uses Bayesian inference to sample and combine higher-quality global models from local models.
result FedBE leads to more robust aggregation of local models into a global model, especially when data is non-i.i.d.
SAGE quantifies feature importance in machine learning models.
problem Understanding the role of individual features in complex models.
method Formalizing predictive power through model-based and universal measures, and introducing SAGE for efficient calculation.
result SAGE assigns more accurate feature importance values than other methods.
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
The paper discusses scalable learning for wireless data-driven systems.
problem Expanding data volume and model complexity limit centralized learning solutions.
method Discusses scalable architecture and local learning strategies.
result Promising research directions in scalable data-driven wireless communications.
Mercat preserves angles to create accurate low-dimensional embeddings.
problem Reconstructing global relationships in low-dimensional embeddings.
method Reconstructing angles between data points to preserve both local and global structures.
result Mercat yields good reconstruction across various experiments and metrics.
We solve the optimization of two-layer ReLU networks using convex math.
problem Optimizing two-layer ReLU neural networks.
method Exact characterization of optimal solutions via convex optimization.
result We prove that all globally optimal solutions can be found via convex optimization.
Paper analyzes SHB method for neural networks, proving stability, connectivity, and global convergence.
problem Theoretical understanding of SHB method for neural networks.
method Mean-field analysis of SHB dynamics related to a partial differential equation.
result SHB method converges to global optimum and exhibits stability and connectivity.
The paper explores how topology affects the solvability of first-order differential equations.
problem The solvability of first-order differential equations and the role of topology.
method Analysis of de Rham cohomology to determine global integrability and uniqueness of solutions.
result Triviality of the first de Rham cohomology group is a fundamental requirement for global integrability and uniqueness of solutions.
In this paper we establish a constructive method in order to show global existence and regularity for a class of degenerate parabolic Cauchy problems which satisfy a weak Hoermander condition on a subset of the domain where the data are measurable and which have regular data on the complementary set of the domain. This…
OceanForecastBench offers a comprehensive benchmark for data-driven ocean forecasting models.
problem Lack of open-source, standardized benchmarks for data-driven ocean forecasting models.
method Proposes OceanForecastBench, a benchmark with high-quality data and evaluation pipeline.
result Offers the most comprehensive benchmarking framework for data-driven ocean forecasting.