Fast Quaternion Product Units for Learning Disentangled Representations in $\mathbb {SO}(3)$

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

doi:10.1109/tpami.2022.3202217

Cited by 13 publications

(5 citation statements)

References 53 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

View full text Add to dashboard Cite

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“…This is required for QNN composed out of standard quaternion valued building blocks like fully connected or convolution layer, which can easily be checked by using the identity function as the activation function, contrary to e.g. [50] where custom quaternion valued architectures are non-linear by itself. Also, all used activation functions are suitable to be used for gradient based optimization during the training phase and can be incorporated in arbitrary QNN architectures.…”

Section: Discussionmentioning

confidence: 99%

“…A further application of recurrent quaternion models is [18] where quaternion RNNs, specifically Quaternion Gated Recurrent Units are applied on sensor fusion for navigation and human activity recognition. Finally, [52] proposes quaternion product units and uses them to human action and hand action recognition. Furthermore, they utilize them for point cloud classification.…”

Section: Related Workmentioning

confidence: 99%

“…For our compression algorithm, we chose 40 chunks of length eight, yielding a compression-rate of factor two. Hence, we obtain data in the shape (N, 52,4,40) and (N, 208, 40).…”

Section: A Experimental Setupmentioning

confidence: 99%

“…Also utilizing quaternion properties, [8] proposes an isotropic activation to be used in combination with pure quaternions. Contrary, [50] designed custom quaternion product units which are non-linear itself, hence don't require a further non-linearity.…”

Section: Quaternion Activationsmentioning

confidence: 99%

See 2 more Smart Citations

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements. After introducing the underlying dual quaternion math, we derive dual quaternion valued neural network layer which are generally applickable to all sorts of problems which can benefit from a mathematical description in dual quaternion space. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the rigid bodies interactions efficiently, we incorporate a novel attention mechanism employing dual quaternion algebra. The introduced architecture is trainable by means of gradient based algorithms. We apply our approach to a parcel prediction problem where a rigid body with an initial position, orientation, velocity and angular velocity moves through a fixed simulation environment which exhibits rich interactions between the parcel and the boundaries. There we can show that the dual quaternion valued models outperform their counterparts operation on the real numbers, confirming the successful introduction of an inductive bias through the usage of dual quaternion math. Furthermore, we used an advantageous custom data augmentation technique specifically tailored for the usage with our dual quaternion valued input data. INDEX TERMSdual quaternion attention, dual duaternion neural networks, hypercomplex neural networks, rigid body dynamics

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Rotation invariance and equivariance in 3D deep learning: a survey

Fei,

Deng

2024

Artif Intell Rev

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Deep neural networks (DNNs) in 3D scenes show a strong capability of extracting high-level semantic features and significantly promote research in the 3D field. 3D shapes and scenes often exhibit complicated transformation symmetries, where rotation is a challenging and necessary subject. To this end, many rotation invariant and equivariant methods have been proposed. In this survey, we systematically organize and comprehensively overview all methods. First, we rewrite the previous definition of rotation invariance and equivariance by classifying them into weak and strong categories. Second, we provide a unified theoretical framework to analyze these methods, especially weak rotation invariant and equivariant ones that are seldom analyzed theoretically. We then divide existing methods into two main categories, i.e., rotation invariant ones and rotation equivariant ones, which are further subclassified in terms of manipulating input ways and basic equivariant block structures, respectively. In each subcategory, their common essence is highlighted, a couple of representative methods are analyzed, and insightful comments on their pros and cons are given. Furthermore, we deliver a general overview of relevant applications and datasets for two popular tasks of 3D semantic understanding and molecule-related. Finally, we provide several open problems and future research directions based on challenges and difficulties in ongoing research.

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Fast Quaternion Product Units for Learning Disentangled Representations in $\mathbb {SO}(3)$

Cited by 13 publications

References 53 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

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Rotation invariance and equivariance in 3D deep learning: a survey

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