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Register a new userParticle Cloud Generation with Message Passing Generative Adversarial Networks
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Added by
Raghav Kansal
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In high energy physics (HEP), jets are collections of correlated particles produced ubiquitously in particle collisions such as those at the CERN Large Hadron Collider (LHC). Machine-learning-based generative models, such as generative adversarial networks (GANs), have the potential to significantly accelerate LHC jet simulations. However, despite jets having a natural representation as a set of particles in momentum-space, a.k.a. a particle cloud, to our knowledge there exist no generative models applied to such a dataset. We introduce a new particle cloud dataset (JetNet), and, due to similarities between particle and point clouds, apply to it existing point cloud GANs. Results are evaluated using (1) the 1-Wasserstein distance between high- and low-level feature distributions, (2) a newly developed Fr{e}chet ParticleNet Distance, and (3) the coverage and (4) minimum matching distance metrics. Existing GANs are found to be inadequate for physics applications, hence we develop a new message passing GAN (MPGAN), which outperforms existing point cloud GANs on virtually every metric and shows promise for use in HEP. We propose JetNet as a novel point-cloud-style dataset for the machine learning community to experiment with, and set MPGAN as a benchmark to improve upon for future generative models.
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We consider representation learning from 3D graphs in which each node is associated with a spatial position in 3D. This is an under explored area of research, and a principled framework is currently lacking. In this work, we propose a generic framework, known as the 3D graph network (3DGN), to provide a unified interface at different levels of granularity for 3D graphs. Built on 3DGN, we propose the spherical message passing (SMP) as a novel and specific scheme for realizing the 3DGN framework in the spherical coordinate system (SCS). We conduct formal analyses and show that the relative location of each node in 3D graphs is uniquely defined in the SMP scheme. Thus, our SMP represents a complete and accurate architecture for learning from 3D graphs in the SCS. We derive physically-based representations of geometric information and propose the SphereNet for learning representations of 3D graphs. We show that existing 3D deep models can be viewed as special cases of the SphereNet. Experimental results demonstrate that the use of complete and accurate 3D information in 3DGN and SphereNet leads to significant performance improvements in prediction tasks.
Graph neural networks (GNNs) are a powerful inductive bias for modelling algorithmic reasoning procedures and data structures. Their prowess was mainly demonstrated on tasks featuring Markovian dynamics, where querying any associated data structure depends only on its latest state. For many tasks of interest, however, it may be highly beneficial to support efficient data structure queries dependent on previous states. This requires tracking the data structures evolution through time, placing significant pressure on the GNNs latent representations. We introduce Persistent Message Passing (PMP), a mechanism which endows GNNs with capability of querying past state by explicitly persisting it: rather than overwriting node representations, it creates new nodes whenever required. PMP generalises out-of-distribution to more than 2x larger test inputs on dynamic temporal range queries, significantly outperforming GNNs which overwrite states.
With many frameworks based on message passing neural networks proposed to predict molecular and bulk properties, machine learning methods have tremendously shifted the paradigms of computational sciences underpinning physics, material science, chemistry, and biology. While existing machine learning models have yielded superior performances in many occasions, most of them model and process molecular systems in terms of homogeneous graph, which severely limits the expressive power for representing diverse interactions. In practice, graph data with multiple node and edge types is ubiquitous and more appropriate for molecular systems. Thus, we propose the heterogeneous relational message passing network (HermNet), an end-to-end heterogeneous graph neural networks, to efficiently express multiple interactions in a single model with {it ab initio} accuracy. HermNet performs impressively against many top-performing models on both molecular and extended systems. Specifically, HermNet outperforms other tested models in nearly 75%, 83% and 94% of tasks on MD17, QM9 and extended systems datasets, respectively. Finally, we elucidate how the design of HermNet is compatible with quantum mechanics from the perspective of the density functional theory. Besides, HermNet is a universal framework, whose sub-networks could be replaced by other advanced models.
The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs). To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks (GNNs) with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline.
In recent studies, neural message passing has proved to be an effective way to design graph neural networks (GNNs), which have achieved state-of-the-art performance in many graph-based tasks. However, current neural-message passing architectures typically need to perform an expensive recursive neighborhood expansion in multiple rounds and consequently suffer from a scalability issue. Moreover, most existing neural-message passing schemes are inflexible since they are restricted to fixed-hop neighborhoods and insensitive to the actual demands of different nodes. We circumvent these limitations by a novel feature-message passing framework, called Graph Multi-layer Perceptron (GMLP), which separates the neural update from the message passing. With such separation, GMLP significantly improves the scalability and efficiency by performing the message passing procedure in a pre-compute manner, and is flexible and adaptive in leveraging node feature messages over various levels of localities. We further derive novel variants of scalable GNNs under this framework to achieve the best of both worlds in terms of performance and efficiency. We conduct extensive evaluations on 11 benchmark datasets, including large-scale datasets like ogbn-products and an industrial dataset, demonstrating that GMLP achieves not only the state-of-art performance, but also high training scalability and efficiency.
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