ADMP-GNN dynamically adjusts message-passing layers for better graph learning performance.
problem Fixed message-passing steps in GNNs do not account for nodes' varying computational needs.
method Proposes ADMP-GNN, which dynamically adjusts the number of message-passing layers for each node.
result Improves performance on node classification tasks compared to baseline GNN models.
Paper interprets contrastive learning dynamics using message passing.
problem Lack of rigorous understanding of contrastive learning dynamics.
method Casts contrastive objective into message passing scheme on augmentation graph.
result The learning dynamics of contrastive learning can be theoretically characterized.
Analyze message passing algorithms using free probability theory.
problem Dynamics of message passing algorithms for probabilistic models.
method Use freeness assumptions of random matrix theory.
result Recover and analyze properties of message passing algorithms.
The Duffing oscillator's parameters are identified online using variational message passing.
problem Estimating parameters of a nonlinear Duffing oscillator in real-time.
method Variational message passing on a factor graph of the Duffing oscillator's generative model.
result The online inference procedure performs as well as offline methods.
DRew dynamically rewires message passing to improve long-range tasks.
problem Over-squashing in MPNNs due to local message passing.
method Layer-dependent rewiring and delay mechanism for gradual densification.
result DRew outperforms graph Transformers and multi-hop MPNNs on long-range tasks.
Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian pro…
Agent uses message passing to optimize robot navigation, balancing exploration and exploitation.
problem Optimizing robot navigation in continuous-valued spaces with uncertainty.
method Autoregressive active inference agent using message passing on a factor graph.
result Agent modulates action based on predictive uncertainty, leading to better model of dynamics.
New framework for estimating treatment effects in experiments with network interference.
problem Network interference biases traditional treatment effect estimations in randomized experiments.
method Causal message-passing framework based on high-dimensional approximate message passing.
result Practical algorithm to estimate total treatment effect in multi-period experiments.
DYMAG uses dynamic waveforms to improve graph neural networks.
problem Improving graph neural networks for better graph understanding.
method DYMAG employs dynamical system-based waveforms for message aggregation in graph neural networks.
result DYMAG outperforms baseline models in graph recovery, property prediction, and random graph generation.
PMP extends GNNs to handle past states efficiently.
problem Efficient querying of data structures dependent on previous states.
method Persistent Message Passing (PMP) which persists past states through new nodes.
result Significantly outperforms GNNs in handling out-of-distribution data.
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
problem Learning in Restricted Boltzmann Machines (RBMs) with complex dependencies.
method Dynamical mean-field theory applied to RBMs with rectangular coupling matrices drawn from a bi-rotation invariant ensemble.
result The algorithm converges globally under a stability criterion, with rates matching numerical simulations.
Graph neural networks are explained through heat diffusion analogy.
problem Limitations of graph neural networks (oversmoothing, oversquashing).
method Analogizing message passing in GNNs to heat dynamics.
result Fundamental understanding of GNNs and improved model design.
AMP method reconstructs rank-one matrices from noisy data efficiently.
problem Reconstructing rank-one matrices with prior structural information from noisy observations.
method Approximate Message Passing (AMP) with random initialization.
result AMP from random initialization converges rapidly and globally.
New algorithms improve rank one signal estimation from noisy data.
problem Estimating a rank one signal matrix from corrupted data with rotationally invariant noise.
method Developed approximate message-passing algorithms exploiting eigenvalues and iterates denoisers.
result Achieves optimal asymptotic estimation error among iterative algorithms.
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some a…
Modern methods for learning over graph input data have shown the fruitfulness of accounting for relationships among elements in a collection. However, most methods that learn over set input data use only rudimentary approaches to exploit intra-collection relationships. In this work we introduce Deep Message Passing on …
New algorithm for signal estimation in noisy matrix models.
problem Signal estimation in rectangular spiked matrix models with rotationally invariant noise.
method Orthogonal Approximate Message Passing (OAMP) algorithm for signal estimation.
result Optimal OAMP algorithm minimizes mean-squared error and achieves Bayes-optimal performance.
Efficient algorithm learns Independent Cascade model from partial network observations.
problem Learning accurate spreading models from limited network data.
method Scalable dynamic message-passing approach for parameter learning.
result Improved prediction of marginal probabilities compared to original model.
Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many…
New framework predicts AMP behavior in spiked models for finite iterations.
problem Understanding AMP dynamics in high-dimensional spiked models.
method Developed a non-asymptotic framework for AMP in spiked matrix estimation.
result Predicted AMP behavior for up to O(polylognn) iterations in Z2 synchronization. AIF improves physical AI agents' performance in dynamic environments.
problem Physical AI agents are less capable than biological agents in open-ended real-world environments.
method Developed from probability theory, Bayesian machine learning, variational inference, and Active Inference (AIF), grounded in the Free Energy Principle.
result AIF minimizes variational free energy and is well-suited to physical constraints.
We analyze oversquashing in topological message-passing using relational structures.
problem Oversquashing in topological message-passing remains understudied.
method A unifying axiomatic framework that bridges graph and topological message-passing.
result Potential to advance topological deep learning.
Message passing is the key to graph neural networks, but new terms are needed to avoid confusion.
problem Current methods of graph neural networks cannot solve all problems over given input graphs.
method Demonstrates that any function of interest can be expressed using pairwise message passing over a modified graph.
result Message passing is the fundamental approach for graph neural networks, and new terms are needed to avoid confusion.
New algorithm estimates influence in social networks without sampling.
problem Estimating the number of influenced nodes in social networks.
method Dynamic message-passing approach for scalable influence estimation.
result Upper bound on expected spread for general graphs, exact for treelike networks.
Graph Network-based Simulators learn complex physics simulations.
problem Simulating complex physical systems with high accuracy and scalability.
method Graph Network framework for particle dynamics, learned message-passing.
result Model generalizes well to different conditions and scales, robust to hyperparameters.
GemNet improves molecular predictions by overcoming graph neural network limitations.
problem Graph neural networks struggle with distinguishing certain types of molecular graphs.
method Discretized geometric message passing neural network (GemNet) with spherical representations.
result GemNet outperforms previous models on molecular datasets by 34-20%.
New graph coarsening method preserves GNN message-passing signals.
problem Preserving GNN message-passing on coarsened graphs.
method Proposed a new oriented message-passing operation for coarsened graphs.
result Improved node classification results compared to naive methods.
Study on convergence of graph neural networks on random graphs.
problem Convergence of message passing graph neural networks on large random graphs.
method Extended convergence results to a broad class of aggregation functions using McDiarmid inequality.
result Non-asymptotic bounds for convergence quantified with high probability.
It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it difficult to define structural metrics. In this work, we apply deep learning algori…
TGR rewires temporal graphs to improve TGNN performance.
problem Temporal graphs in evolving networks can suffer from under-reaching and over-squashing issues.
method TGR uses expander graph propagation to create message-passing highways between temporally distant nodes.
result TGR achieves state-of-the-art results on temporal graph benchmarks.
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
Topo-MLP learns network representations without message passing.
problem Lack of efficient higher-order network modeling methods.
method Proposes Topo-MLP, a simplicial neural network algorithm using MLP and HONC loss.
result Demonstrates improved robustness and efficiency in representation learning.
A new aggregation strategy improves GNN performance and learning dynamics.
problem Improving expressivity and learning dynamics of GNNs.
method Proposes a variance-preserving aggregation function (VPA) for GNNs.
result VPA leads to increased predictive performance and improved learning dynamics.
New method estimates treatment effects in complex interference settings.
problem Challenges in estimating treatment effects due to unknown interference.
method Higher-order causal message passing for non-linear feature learning.
result Effective estimation of treatment effect dynamics in complex interference.
Introduces P-tensors for generalized higher-order message passing in graph neural networks.
problem Expanding the expressive power of graph neural networks through higher-order structures.
method Introduces P-tensors to define the most general form of permutation equivariant message passing.
result Achieves state-of-the-art performance on molecular datasets.
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most ca…
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…
Convex message passing algorithms converge to a fixed point.
problem Understanding convergence properties of convex message passing methods.
method Proving convergence of coordinate descent applied to piecewise-affine convex objectives, and showing this applies to various message passing methods.
result The iterates converge to a fixed point of the method, and the algorithm terminates in a known number of iterations.
New algorithms accelerate MAP inference in Markov fields with faster convergence.
problem Finding the most likely configuration in discrete-valued Markov random fields.
method Entropy-regularized linear programming with accelerated gradient methods.
result Accelerated algorithms find optimal solutions faster, especially when the LP is tight.
Combines PCA and message passing for better graph node embeddings.
problem Challenges of learning long-range dependencies in graph data.
method PCAPass: PCA + message passing for unsupervised node embeddings.
result Empirically shows competitive performance on node classification benchmarks.
The paper sets limits for GNNs solving PDEs to avoid under-reaching phenomenon.
problem Under-reaching phenomenon in GNNs solving PDEs.
method Sharp lower bounds for message-passing iterations based on PDE characteristics.
result Proposed lower bounds ensure efficient information propagation in GNNs.
New method solves group synchronization with cycle-edge message passing.
problem Solving group synchronization with adversarial or uniform corruption and small noise.
method Cycle-edge message passing procedure using cycle consistency information.
result Exact recovery and linear convergence guarantees under adversarial corruption.
Proves formula for reconstruction performance in generalized linear models.
problem Analyzing reconstruction performance in generalized linear models with arbitrary bounded spectrum.
method Message passing algorithms and dynamical system stability analysis.
result Analytical formula confirms replica method conjecture for convex models.
Enhances graph neural networks with structural message-passing for better generalization.
problem Limited representation power and inability to learn basic graph topological properties.
method Proposes a framework that includes a one-hot encoding of nodes and parametrized message and update functions ensuring permutation equivariance.
result Achieves state-of-the-art results on molecular graph regression on the ZINC dataset.