Quaternion Product Units for Deep Learning on 3D Rotation Groups

Zhang, Xuan; Qin, Shaofei; Xu, Yi; Xu, Hongteng

doi:10.1109/cvpr42600.2020.00733

Cited by 13 publications

(5 citation statements)

References 27 publications

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“…It ensures global completeness of model only with message passing in 1-hop neighborhood to avoid time-consuming calculations like torsion in SphereNet or dihedral angles in GemNet. There are also some other studies [199,309,298,292] exploiting the quaternion algebra to represent the 3D rotation group, which mathematically ensures SO(3) invariance during the inference. Specifically, Yue et al [292] constructs quaternion message-passing module to distinguish the molecular conformations caused by bond torsions.…”

Section: Tablementioning

confidence: 99%

Single-cell atlas of a non-human primate reveals new pathogenic mechanisms of COVID-19

Han

Wei

Liu

et al. 2020

Preprint

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Stopping COVID-19 is a priority worldwide. Understanding which cell types are targeted by SARS-CoV-2 virus, whether interspecies differences exist, and how variations in cell state influence viral entry is fundamental for accelerating therapeutic and preventative approaches. In this endeavor, we profiled the transcriptome of nine tissues from a Macaca fascicularis monkey at single-cell resolution. The distribution of SARS-CoV-2 facilitators, ACE2 and TMRPSS2, in different cell subtypes showed substantial heterogeneity across lung, kidney, and liver. Through co-expression analysis, we identified immunomodulatory proteins such as IDO2 and ANPEP as potential SARS-CoV-2 targets responsible for immune cell exhaustion. Furthermore, single-cell chromatin accessibility analysis of the kidney unveiled a plausible link between IL6-mediated innate immune responses aiming to protect tissue and enhanced ACE2 expression that could promote viral entry. Our work constitutes a unique resource for understanding the physiology and pathophysiology of two phylogenetically close species, which might guide in the development of therapeutic approaches in humans.Bullet pointsWe generated a single-cell transcriptome atlas of 9 monkey tissues to study COVID-19.ACE2+TMPRSS2+ epithelial cells of lung, kidney and liver are targets for SARS-CoV-2.ACE2 correlation analysis shows IDO2 and ANPEP as potential therapeutic opportunities.We unveil a link between IL6, STAT transcription factors and boosted SARS-CoV-2 entry.

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Section: Tablementioning

confidence: 99%

Single-cell atlas of a non-human primate reveals new pathogenic mechanisms of COVID-19

Han

Wei

Liu

et al. 2020

Preprint

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“…Global SE(3)-Invariance Our QMP is SE(3)-invariant. As shown in Proposition 1 in (Zhang et al 2020), for arbitrary two quaternions…”

Section: Theoretical Properties and Rationality Analysismentioning

confidence: 87%

“…Besides our QMP module, some quaternion-based neural networks have been built for modeling graphs (Zhu et al 2018;Zhang et al 2020) and point clouds (Shen et al 2020), e.g., the QuaterNet in (Pavllo, Grangier, and Auli 2018), the quaternion convolution neural network in (Zhu et al 2018), and the quaternion product unit (QPU) (Zhang et al 2020;Qin et al 2022). Among these models, the QPU model applies a similar technical route, aggregating 3D rotations by chained Hamilton product.…”

Section: Connections To Related Workmentioning

confidence: 99%

A Plug-and-Play Quaternion Message-Passing Module for Molecular Conformation Representation

Yue,

Luo,

2024

AAAI

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Graph neural networks have been widely used to represent 3D molecules, which capture molecular attributes and geometric information through various message-passing mechanisms. This study proposes a novel quaternion message-passing (QMP) module that can be plugged into many existing 3D molecular representation models and enhance their power for distinguishing molecular conformations. In particular, our QMP module represents the 3D rotations between one chemical bond and its neighbor bonds as a quaternion sequence. Then, it aggregates the rotations by the chained Hamilton product of the quaternions. The real part of the output quaternion is invariant to the global 3D rotations of molecules but sensitive to the local torsions caused by twisting bonds, providing discriminative information for training molecular conformation representation models. In theory, we prove that considering these features enables invariant GNNs to distinguish the conformations caused by bond torsions. We encapsulate the QMP module with acceleration, so combining existing models with the QMP requires merely one-line code and little computational cost. Experiments on various molecular datasets show that plugging our QMP module into existing invariant GNNs leads to consistent and significant improvements in molecular conformation representation and downstream tasks.

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“…For 3D skeletons, the QuaterNet [5] performs human skeleton action prediction by predicting the relative rotation of each joint in the next step with unit quaternion representation. In our previous work [48], we develop a preliminary version of the proposed quaternion product unit (QPU), which achieves encouraging performance on learning rotation-invariant skeleton representation models. In this paper, we will further study the QPU in-depth, improving its implementations and making it more applicable to various data and tasks.…”

Section: Quaternion-based Models and Learning Algorithmsmentioning

confidence: 99%

Fast Quaternion Product Units for Learning Disentangled Representations in SO(3)

Qin¹,

Zhang²,

Xu³

et al. 2022

Preprint

Self Cite

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Real-world 3D structured data like point clouds and skeletons often can be represented as data in a 3D rotation group (denoted as $\mathbb{SO}(3)$). However, most existing neural networks are tailored for the data in the Euclidean space, which makes the 3D rotation data not closed under their algebraic operations and leads to sub-optimal performance in 3D-related learning tasks. To resolve the issues caused by the above mismatching between data and model, we propose a novel non-real neuron model called \textit{quaternion product unit} (QPU) to represent data on 3D rotation groups. The proposed QPU leverages quaternion algebra and the law of the 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted chain of Hamilton products. We demonstrate that the QPU mathematically maintains the $\mathbb{SO}(3)$ structure of the 3D rotation data during the inference process and disentangles the 3D representations into ``rotation-invariant'' features and ``rotation-equivariant'' features, respectively. Moreover, we design a fast QPU to accelerate the computation of QPU. The fast QPU applies a tree-structured data indexing process, and accordingly, leverages the power of parallel computing, which reduces the computational complexity of QPU in a single thread from $\mathcal{O}(N)$ to $\mathcal {O}(\log N)$. Taking the fast QPU as a basic module, we develop a series of quaternion neural networks (QNNs), including quaternion multi-layer perceptron (QMLP), quaternion message passing (QMP), and so on. In addition, we make the QNNs compatible with conventional real-valued neural networks and applicable for both skeletons and point clouds. Experiments on synthetic and real-world 3D tasks show that the QNNs based on our fast QPUs are superior to state-of-the-art real-valued models, especially in the scenarios requiring the robustness to random rotations.<br>

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Quaternion Product Units for Deep Learning on 3D Rotation Groups

Cited by 13 publications

References 27 publications

Single-cell atlas of a non-human primate reveals new pathogenic mechanisms of COVID-19

Single-cell atlas of a non-human primate reveals new pathogenic mechanisms of COVID-19

A Plug-and-Play Quaternion Message-Passing Module for Molecular Conformation Representation

Fast Quaternion Product Units for Learning Disentangled Representations in SO(3)

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