Unified framework for differentiable graph partitioning with probabilistic cuts.
problem Lack of general guarantees and principled gradients in prior probabilistic relaxations of graph cuts.
method Unified probabilistic framework covering a wide class of cuts, including Normalized Cut, with tight analytic upper bounds.
result Rigorous, numerically stable foundation for scalable, differentiable graph partitioning.
The paper compares PINN methods for solving drift-diffusion equations on metric graphs.
problem Solving drift-diffusion equations on metric graphs using machine learning.
method Comparison of physics-informed neural networks (PINNs) for solving drift-diffusion equations on metric graphs.
result PINNs offer a flexible and versatile tool for solving parameter identification or optimization problems on metric graphs.
Graph neural controlled differential equations learn graph dynamics from vertex observations.
problem Predicting future states of dynamical systems on graphs with limited vertex data.
method Incorporates graph topology information into NCDE to predict graph dynamics.
result Informed NCDE requires fewer parameters and lower MAE compared to previous methods.
Differentially private graph learning via bounded sensitivity PPR.
problem Protecting user data in graph learning algorithms.
method Proposes a sensitivity-bounded personalized PageRank (PPR) algorithm.
result Achieves similar accuracy to non-private algorithms with large degrees.
Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchica…
AMES framework selects optimal embedding space for latent graph inference.
problem No principled method for choosing the best embedding space for latent graph inference.
method Differentiable AMES framework using backpropagation to select optimal embedding space.
result Consistently achieves comparable or superior results across multiple datasets.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
Graph-based multimodal federated learning for HAR improves accuracy and privacy.
problem Challenges in HAR due to noisy data, incomplete measurements, and privacy concerns.
method Proposes GraMFedDHAR, a Graph-based Multimodal Federated Learning framework for HAR tasks, using modality-specific graphs, residual GCNs, and attention-based fusion.
result Experimental results show up to 13 percent performance improvement for MultiModalGCN under differential privacy constraints.
INDEQS: A Graph-Based Neural Controlled Differential Equation Framework for Forecasting
problem Forecasting time series with neural networks
method Incorporating prior knowledge of a directed graph
result Outer informedness consistently improves forecasting accuracy
A new layer learns abstract relations from graph structure using finite-state automata.
problem Learning abstract relations from graph structure for program analysis.
method Relaxing the problem into learning finite-state automata policies on a graph-based POMDP and training these policies using implicit differentiation.
result GFSA layer finds shortcuts in grid-world graphs and reproduces simple static analyses on Python programs.
Hybrid model combines neural networks and fluid dynamics for efficient, generalized simulations.
problem Inefficient and poor generalization of deep learning approximations of fluid dynamics.
method Combines graph neural networks with a differentiable PDE solver inside a neural network.
result Hybrid model generalizes well to new scenarios and outperforms both neural network and traditional methods.
MissNODAG learns cyclic causal graphs from incomplete data.
problem Causal discovery in systems with feedback loops and missing data.
method Differentiable framework integrating additive noise model and expectation-maximization.
result MissNODAG uncovers cyclic structures and missingness mechanisms from partially observed data.
PGFL framework learns personalized models with differential privacy.
problem Privacy-preserving personalized learning for diverse data.
method Exploits model similarities and differential privacy (zero-concentrated).
result Algorithm converges to optimal solutions with linear time complexity.
Storchastic improves stochastic AD for complex models in RL and VI.
problem Handling intractable expectations in RL and VI.
method Introduces Storchastic, a framework for AD of stochastic computation graphs with various gradient estimation methods.
result Provable unbiasedness and variance reduction for higher-order gradients.
COSMO learns DAG structure without acyclicity constraints.
problem Learning DAG structure from data efficiently and without constraints.
method Differentiable approximation of smooth orientation matrix.
result COSMO converges to acyclic solutions without evaluating acyclicity.
A new neural network layer integrates graph learning into classification tasks.
problem Lack of relational information in standard deep learning architectures for label predictions.
method Derives backpropagation equations for a differentiable graph learning layer.
result Smooth label transitions, improved generalization, and robustness to adversarial attacks.
Paper analyzes multi-attribute data to estimate differences in Gaussian graphical models.
problem Estimating differences in two Gaussian graphical models with similar structure.
method Group lasso penalized D-trace loss function and ADMM algorithm for optimization.
result Consistency in support recovery and estimation in high-dimensional settings established.
Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes ar…
A new graph neural network framework captures long-range interactions efficiently.
problem Efficiently modeling long-range interactions in graph neural networks for PDEs.
method Proposes a multi-level graph neural network framework using multipole methods.
result Captures interaction at all ranges with only linear complexity, learning discretization-invariant solution operators.
Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.
problem Publishing graph node vectors can leak sensitive individual information.
method SE-PrivGEmb, a skip-gram based technique with a unified noise tolerance mechanism and negative sampling probabilities.
result Our method outperforms existing methods in structural equivalence and link prediction tasks.
New method resolves inconsistency in learning directed acyclic graphs using penalized likelihood.
problem Inconsistency of ℓ1-penalized likelihood in learning directed acyclic graphs. method Developed a hybrid differentiable structure learning method based on ℓ0-penalized likelihood with hard acyclicity constraint. result Demonstrated and explained why ℓ1-penalized likelihood is fundamentally inconsistent in identifying true structure up to Markov equivalence classes. Neural networks improve predictions of complex network dynamics.
problem Improving neural network predictions for complex network dynamics.
method Extended neural network models to complex systems, ensuring they conform to dynamical model assumptions and using a statistical significance test.
result Achieved advanced generalization of neural network predictions for complex systems.
Graph Gaussian processes use Matérn models for better function learning.
problem Lack of Gaussian process models for graph input spaces.
method Stochastic partial differential equation characterization of Matérn Gaussian processes.
result Graph Matérn Gaussian processes inherit properties of Euclidean and Riemannian models and can be trained efficiently.
Graph neural networks learn PDEs from sparse, irregular data.
problem Learning PDEs from irregularly spaced data.
method Continuous-time differential model with graph neural networks for arbitrary discretizations.
result Efficient inference with continuous-time adjoint method.
Critical graphs of quadratic differentials equidistribute in moduli space.
problem Distribution of critical graphs in moduli space.
method Study of Jenkins-Strebel differentials and their critical graphs.
result Critical graphs equidistribute to the Kontsevich measure.
Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the prior one. With a long history in scientific computing, many coarsening strategies…
Study neural architectures on learned latent graphs using Schrödinger dynamics.
problem Understanding neural architectures on learned latent graphs.
method Optimizes over stratified moduli space of weighted graphs with Kähler-Hessian metric.
result Multilayer stationary networks are equivalent to global stationary problems on supra-graphs.
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filte…
Paper presents voxel graph operators for vector data models.
problem Efficient conversion and analysis of geometric models.
method Topological voxelization, graph construction, differential operator derivation.
result Discrete differential and integral operators from voxel complexes.
Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we propose a novel GNN architecture for learning representations on Riemannian man…
Study uniformly differentiable graphs in Carnot groups, proving area formulas.
problem Characterize uniformly differentiable intrinsic graphs in Carnot groups.
method Characterize uniform intrinsic differentiability via Hölder properties of projections of vector fields.
result Explicit area formula for uniformly intrinsically differentiable maps in Carnot groups.
DiSC detects feature clusters that differentiate between conditions.
problem Identifying subsets of features that differentiate between two conditions.
method Construct feature graphs, compute connectivity differences using spectral clustering.
result DiSC uncovers features that better differentiate between conditions.
SPOT improves differentiable causal discovery by estimating skeleton posterior for latent confounders.
problem Scalable and accurate estimation of causal skeletons in the presence of latent confounders.
method SPOT (Skeleton Posterior-guided OpTimization) framework that estimates skeleton posterior and integrates it with differentiable causal discovery.
result SPOT enhances differentiable causal discovery by reducing the search space and improving accuracy.
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph p-Laplacian. Unlike the …
Study uses graph techniques to understand meromorphic quadratic differential strata.
problem Understanding the topology of meromorphic quadratic differential strata.
method Exchange graph techniques to study fundamental groups; generalizes relations for mixed-angulations.
result Explicit presentations of fundamental groups in genus-zero case with four singularities.
CASPER improves DAG structure learning by integrating graph structure into score function.
problem Discovering suboptimal DAGs and model vulnerabilities in causal discovery.
method CASPER integrates graph structure into the score function as a new measure in the causal space, enhancing DAG structure learning via adaptive attention to DAG-ness.
result CASPER outperforms state-of-the-art methods in terms of accuracy and robustness.
New method recovers graph latent positions under edge differential privacy.
problem Recovering latent graph information from privatized graphs.
method Applying geometric insights to adjust statistical inference for privatized graphs.
result Achieves consistent recovery of latent positions under local edge differential privacy constraints.
Neural ODEs control graph dynamics with low energy feedback.
problem Controlling complex dynamical systems on graphs.
method Neural Ordinary Differential Equation Control (NODEC) framework.
result NODEC learns low-energy control signals for graph dynamical systems.
FuDGE estimates differences between functional graphs in high-dimensional settings.
problem Estimating differences between two undirected functional graphical models with shared structures.
method FuDGE: A method that directly estimates the functional differential graph without first estimating individual graphs.
result FuDGE consistently estimates the functional differential graph in high-dimensional settings.
New kernel speeds up graph regression in physics.
problem Handling large, sparse graphs with continuous node attributes in physics.
method Introduced Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel for Gaussian process regression.
result The SWWL kernel is efficient and positive definite, reducing complexity.
New method denoises graph signals using wavelets, scalable for large graphs.
problem Denoising graph signals with overcomplete tight frames and correlated noise.
method Data-driven wavelet tight frame, Stein's unbiased risk estimate, Chebyshev-Jackson polynomial approximations, Monte-Carlo strategy.
result Method scales to large graphs and finds applications in differential privacy.
Neural GDEs improve graph prediction by blending discrete structures and differential equations.
problem Dynamic graph prediction challenges in irregularly sampled data.
method Continuous-depth graph neural networks (GNNs) with Neural GDEs.
result Neural GDEs enhance performance across various applications.
Privacy-preserving GNNs for graph data with sensitive node data.
problem Privacy concerns in learning node representations for graphs with sensitive data.
method Developed a privacy-preserving GNN learning algorithm based on Local Differential Privacy (LDP). Proposed an LDP encoder, an unbiased rectifier, and a denoising mechanism (KProp).
result Our method maintains a satisfying level of accuracy with low privacy loss.
Paper estimates differences in conditional independence graphs from time-dependent data.
problem Estimating changes in conditional dependencies between two time series with known similar structure.
method Penalized D-trace loss function approach in the frequency domain, using Wirtinger calculus, with convex and non-convex penalties.
result Established sufficient conditions for consistency and graph recovery in high-dimensional settings.
Study automorphisms of smooth curve graphs on surfaces.
problem Understanding automorphisms of fine curve graphs.
method Examined automorphisms of continuously differentiable curves on surfaces.
result Automorphisms on surfaces of genus ≥ 2 are induced by homeomorphisms.
New method recovers transportable DAG structures from different datasets.
problem Inference of DAG structures is computationally expensive and lacks transportability.
method Introduces D-Struct, a differentiable architecture that recovers transportable DAG structures.
result D-Struct recovers transportable DAG structures from different datasets.
Paper develops a consistent algorithm for learning graph structure from continuous-time stochastic differential equations.
problem Learning structure from continuous-time stochastic differential equations.
method Score-based structure learning using Neural Ordinary Differential Equations with adaptive regularization.
result The method consistently recovers directed graphs of local independencies in systems of stochastic differential equations.
Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications ranging from social science, biomedicine, and particle physics to computer vision,…