65 research outputs found
QDC: Quantum Diffusion Convolution Kernels on Graphs
Graph convolutional neural networks (GCNs) operate by aggregating messages
over local neighborhoods given the prediction task under interest. Many GCNs
can be understood as a form of generalized diffusion of input features on the
graph, and significant work has been dedicated to improving predictive accuracy
by altering the ways of message passing. In this work, we propose a new
convolution kernel that effectively rewires the graph according to the
occupation correlations of the vertices by trading on the generalized diffusion
paradigm for the propagation of a quantum particle over the graph. We term this
new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In
addition, we introduce a multiscale variant that combines messages from the QDC
operator and the traditional combinatorial Laplacian. To understand our method,
we explore the spectral dependence of homophily and the importance of quantum
dynamics in the construction of a bandpass filter. Through these studies, as
well as experiments on a range of datasets, we observe that QDC improves
predictive performance on the widely used benchmark datasets when compared to
similar methods
Recommended from our members
A Correlated-Polaron Electronic Propagator: Open Electronic Dynamics beyond the Born-Oppenheimer Approximation
In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based on the ab initio Hamiltonian, and is thus well-defined apart from any phenomenological choice of basis states or electronic system-bath coupling model. The equation-of-motion for the density matrix we derive includes non-Markovian and non-perturbative bath effects and can be used to simulate environmentally broadened electronic spectra and dissipative dynamics, which are subjects of recent interest. The theory also goes beyond the adiabatic Born-Oppenheimer approximation, but with computational cost scaling such as the Born-Oppenheimer approach. Example propagations with a developmental code are performed, demonstrating the treatment of electron-correlation in absorption spectra, vibronic structure, and decay in an open system. An untransformed version of the theory is also presented to treat more general baths and larger systems.Chemistry and Chemical Biolog
A correlated-polaron electronic propagator: open electronic dynamics beyond the Born-Oppenheimer approximation
In this work we develop a theory of correlated many-electron dynamics dressed
by the presence of a finite-temperature harmonic bath. The theory is based on
the ab-initio Hamiltonian, and thus well-defined apart from any
phenomenological choice of collective basis states or electronic coupling
model. The equation-of-motion includes some bath effects non-perturbatively,
and can be used to simulate line- shapes beyond the Markovian approximation and
open electronic dynamics which are subjects of renewed recent interest. Energy
conversion and transport depend critically on the ratio of electron-electron
coupling to bath-electron coupling, which is a fitted parameter if a
phenomenological basis of many-electron states is used to develop an electronic
equation of motion. Since the present work doesn't appeal to any such basis, it
avoids this ambiguity. The new theory produces a level of detail beyond the
adiabatic Born-Oppenheimer states, but with cost scaling like the
Born-Oppenheimer approach. While developing this model we have also applied the
time-convolutionless perturbation theory to correlated molecular excitations
for the first time. Resonant response properties are given by the formalism
without phenomenological parameters. Example propagations with a developmental
code are given demonstrating the treatment of electron-correlation in
absorption spectra, vibronic structure, and decay in an open system.Comment: 25 pages 7 figure
Graph Neural Networks as Gradient Flows: understanding graph convolutions via energy
Gradient flows are differential equations that minimize an energy functional
and constitute the main descriptors of physical systems. We apply this
formalism to Graph Neural Networks (GNNs) to develop new frameworks for
learning on graphs as well as provide a better theoretical understanding of
existing ones. We derive GNNs as a gradient flow equation of a parametric
energy that provides a physics-inspired interpretation of GNNs as learning
particle dynamics in the feature space. In particular, we show that in graph
convolutional models (GCN), the positive/negative eigenvalues of the channel
mixing matrix correspond to attractive/repulsive forces between adjacent
features. We rigorously prove how the channel-mixing can learn to steer the
dynamics towards low or high frequencies, which allows to deal with
heterophilic graphs. We show that the same class of energies is decreasing
along a larger family of GNNs; albeit not gradient flows, they retain their
inductive bias. We experimentally evaluate an instance of the gradient flow
framework that is principled, more efficient than GCN, and achieves competitive
performance on graph datasets of varying homophily often outperforming recent
baselines specifically designed to target heterophily.Comment: First two authors equal contribution; 39 page
Graph Neural Networks for Link Prediction with Subgraph Sketching
Many Graph Neural Networks (GNNs) perform poorly compared to simple
heuristics on Link Prediction (LP) tasks. This is due to limitations in
expressive power such as the inability to count triangles (the backbone of most
LP heuristics) and because they can not distinguish automorphic nodes (those
having identical structural roles). Both expressiveness issues can be
alleviated by learning link (rather than node) representations and
incorporating structural features such as triangle counts. Since explicit link
representations are often prohibitively expensive, recent works resorted to
subgraph-based methods, which have achieved state-of-the-art performance for
LP, but suffer from poor efficiency due to high levels of redundancy between
subgraphs. We analyze the components of subgraph GNN (SGNN) methods for link
prediction. Based on our analysis, we propose a novel full-graph GNN called
ELPH (Efficient Link Prediction with Hashing) that passes subgraph sketches as
messages to approximate the key components of SGNNs without explicit subgraph
construction. ELPH is provably more expressive than Message Passing GNNs
(MPNNs). It outperforms existing SGNN models on many standard LP benchmarks
while being orders of magnitude faster. However, it shares the common GNN
limitation that it is only efficient when the dataset fits in GPU memory.
Accordingly, we develop a highly scalable model, called BUDDY, which uses
feature precomputation to circumvent this limitation without sacrificing
predictive performance. Our experiments show that BUDDY also outperforms SGNNs
on standard LP benchmarks while being highly scalable and faster than ELPH.Comment: 29 pages, 19 figures, 6 appendice
- …