A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
kth-order invariant graph networks are as powerful as kth-order WL in distinguishing graphs.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
This thesis explores GNNs, categorizing them into local and global approaches.
Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers. Although this question is answered for the first three examples (for popular tra…
Geometric deep learning predicts knot invariants.
IsoGCNs learn invariant and equivariant graph features for efficient simulations.
ABI adapts to graph data for fast, scalable inference.
Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for graphs are not invariant to the chosen ordering, which might lead to an undesira…
Graph homomorphism numbers embed graphs for classification.
Novel framework improves graph learning for out-of-distribution generalization.
ChebLieNet uses Lie groups to create invariant spectral graph networks.
ISP improves GNN expressivity by stratifying nodes based on graph invariants.
New algorithm uses GNNs to optimize rewards in graph-structured data.
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
Frame Averaging makes neural networks invariant or equivariant to new symmetries.
Proposes local coordinate frames for improving model performance in complex dynamical systems.
Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper, we consider a specific class of invariant and equivariant networks, for which we …
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We find that none of the classical numerical graph invariants by itself allows to s…
The paper presents a method for analyzing shape graphs using specific features.
New invariant for special alternating links based on graph Laplacian.
Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.
A new graph neural network framework captures long-range interactions efficiently.
Graph kernels for metric graphs using tropical algebra.
A new method recovers latent potentials from graph flows, preserving ordering and stability.
Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as…
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervis…
Geometric GNNs improve graph discrimination through GWL.
New LCM aggregator improves GNN performance and efficiency.
We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph representation for graphs of varying dimensions through a differentiable node attention po…
Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaning…
Quantum GNNs outperform classical GNNs in jet tagging.
Explains differences between WL and folklore-WL formulations in graph neural networks.
Framework tackles OOD challenges in molecule property prediction by modeling environments.
Message-passing neural networks (MPNNs) have been successfully applied to representation learning on graphs in a variety of real-world applications. However, two fundamental weaknesses of MPNNs' aggregators limit their ability to represent graph-structured data: losing the structural information of nodes in neighborhoo…
Steerable E(3) Graph Neural Networks incorporate geometric and physical covariant information.
Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and r…
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many s…
Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the ordering of node neighbors, even when there is a geometric interpretation of the …
PARD generates graphs efficiently and invariantly to node ordering.
We introduce a new cohomology theory for planar trivalent graphs with perfect matchings. The graded Euler characteristic of the cohomology is a one variable polynomial called the 2-factor polynomial that, if nonzero when evaluated at one, implies that the perfect matching is even and therefore the graph is 4-face color…
Geometric GNNs model 3D atomic systems with rotations and translations.
Graph neural networks improve with affinity measures from random walks.
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stabili…
We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message passing models, and more powerful spatial variants that exploit local graph structur…
Graph Neural Networks struggle on random graphs without node identifiers.
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…
New invariants distinguish spatial graphs not previously possible.