Novel CG-EGNNs learn equivariant functions from Clifford algebras.
problem Lack of equivariance in high-order graph neural networks.
method Integrates high-order local structures with Clifford algebras for equivariant learning.
result CG-EGNNs outperform previous methods on various benchmarks.
This work proposes a geometric approach to equivariant message passing on Riemannian manifolds.
problem Efficiently processing data on Riemannian manifolds with equivariance.
method Geometric insight into equivariant message passing on Riemannian manifolds, using an equivariant embedding and diffusion process.
result A new class of equivariant GNNs on Riemannian manifolds.
Generative model designs highly designable proteins using geometric algebra.
problem Creating proteins with diverse and statistically accurate secondary structures.
method Introduced a geometric algebra flow matching model (FrameFlow) with Clifford Frame Attention (CFA) for protein backbone design.
result Achieved high designability, diversity, and novelty in protein backbone sampling.
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.
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.
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.
MACE uses higher-order messages to create fast, accurate force fields.
problem Creating fast and accurate force fields in computational chemistry and materials science.
method Introducing MACE, an equivariant MPNN model that uses four-body messages.
result MACE reduces the required number of message passing iterations to just two, achieving state-of-the-art accuracy.
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…
MPLP learns neural network weights by treating operations as message-passing agents.
problem Training neural networks using gradient-based methods.
method MPLP abstracts neural network operations as message-passing agents, updating internal states and passing messages.
result MPLP outperforms traditional gradient-based methods on simple feed-forward neural networks.
DimeNet uses directional message passing to improve molecular predictions.
problem Lack of directional information in graph neural networks for molecules.
method Directional message passing, rotationally equivariant embeddings, spherical functions.
result DimeNet outperforms previous GNNs by 76% on MD17 and 31% on QM9.
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.
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.
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.
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 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.
Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. In this work, we propose a relational message passing method for knowledge graph completion. Different from existing embedding-based methods, relational message passing only considers edge features (i.e., relation types)…
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.
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.
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.
Develops a Gaussian-based message-passing algorithm for noisy matrix completion.
problem Noisy matrix completion problems.
method Gaussian parameterized belief propagation algorithm.
result Advantages over traditional methods in non-Gaussian noise scenarios.
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.
A new neural network model for molecular graphs that learns efficiently and accurately.
problem Learning on molecular graphs with cycles and complex structures.
method Hierarchical inter-message passing using raw graph and junction tree representations.
result The model outperforms classical GNNs in detecting cycles and is efficient to train.
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.
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%.
Steerable E(3) Graph Neural Networks incorporate geometric and physical covariant information.
problem Incorporating covariant information like position, force, velocity, or spin in graph neural networks.
method Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that use steerable MLPs to incorporate geometric and physical covariant information.
result SEGNNs improve upon classic linear point convolutions and recent equivariant graph networks that send invariant messages.
New algorithm minimizes FE objectives for synthetic AIF agents.
problem Minimizing Free Energy for synthetic active inference agents.
method Variational message passing on Constrained FFGs.
result Message passing algorithms induce epistemic behavior in AIF agents.
PushNet efficiently and adaptively pushes messages in neural networks, improving performance.
problem Inefficient and inflexible synchronous message passing in neural networks.
method Asynchronous message passing with adaptive receptive fields and multiple scale correlations.
result PushNet outperforms competitors in semi-supervised node classification on multiple datasets.
Chance-constrained ActInf allows for small violations of constraints to drive goal-directed behavior.
problem Goal-directed behavior constrained by prior beliefs.
method Introducing chance constraints to ActInf, allowing for small violations of constraints.
result Chance-constrained ActInf allows for a trade-off between robust control and chance constraint violation.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
SpatialSim benchmarks machine learning in recognizing object spatial configurations.
problem Machine learning in recognizing precise geometrical configurations of groups of objects.
method SpatialSim benchmark with tasks of Identification and Comparison, using Graph Neural Networks (MPGNNs).
result MPGNNs outperform baselines in recognizing spatial configurations, highlighting current limits.
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…
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…
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
problem Handling multi-channel graph signals with limited architectures.
method BankGCN decomposes multi-channel signals into subspaces and uses adapted filters for each subspace.
result BankGCN achieves excellent performance in graph classification on benchmark datasets.
A training-free message passing module improves hypergraph neural networks.
problem Computational intensive training process in hypergraph neural networks.
method Decoupling hypergraph structural information from model learning stage.
result TF-HNN achieves superior performance and training efficiency.
Gradient Gating improves deep GNNs by modulating message passing updates.
problem Oversmoothing and performance degradation in deep GNNs.
method Gradient gating mechanism for multi-rate message passing.
result G2 framework alleviates oversmoothing and achieves state-of-the-art performance. ALBU improves LDA performance on small datasets.
problem Limited data impairs variational Bayes in LDA.
method Approximate Loopy Belief message passing algorithm.
result ALBU learns latent distributions more accurately than VB, especially for smaller data sets.
LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.
problem Limitations of specialized layers in Lorentz-equivariant neural networks.
method LLoCa framework using local reference frames and geometric message passing.
result Models achieve competitive and state-of-the-art accuracy on particle physics tasks.
Bayesian method for multivariate autoregressive models with exogenous inputs.
problem Estimating uncertainties in autoregressive models with exogenous inputs.
method Recursive Bayesian estimation via message passing in a factor graph.
result Produces full posterior distributions for autoregressive coefficients and noise precision.
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message p…
Optimal graph classification uses message-passing neural networks.
problem Node classification on sparse graphs with fixed feature dimensions.
method Asymptotic local Bayes optimality, message-passing graph neural networks.
result Optimal message-passing architecture interpolates between MLP and convolution.
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
A new algorithm improves topic model accuracy in small data sets.
problem Limited data leads to inaccurate topic model identification.
method Developed a novel variational message passing algorithm (ALBU) for LDA.
result ALBU learns latent distributions more accurately than Variational Bayes (VB) in small data sets.