[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120734-en":3,"doc-seo-120734-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120734,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds","Rotation invariance is a widely used inductive bias in machine learning, delivering strong results in computer vision and 3D chemistry tasks. Yet it remains unclear whether performance mainly comes from rotation invariance or from the complexity of deep neural networks. This work proposes a simple random-features approach to learn rotation-invariant functions for 3D point clouds by extending Rahimi and Recht’s method. Experiments show competitive or better results versus rotation-invariant neural networks on QM7 and QM9, strong general-purpose baselines on ModelNet40, and substantially lower prediction latency than kernel methods.","arXiv :2308 .06271v1 [ cs .CV] 27 Jul 2023  \nRotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds  \nOwen Melia ∗1, Eric Jonas †1, and Rebecca Willett ‡1,2  \n1 Department of Computer Science, University of Chicago, US  \n2 Department of Statistics, University of Chicago, US  \nAbstract  \nRotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many tasks, including molecular property prediction and 3D shape classification. These methods generally either rely on task-specific rotation-invariant features, or they use general-purpose deep neural networks which are complicated to design and train. However, it is unclear whether the success of these methods is primarily due to the rotation invariance or the deep neural networks. To address this question, we suggest a simple and generalpurpose method for learning rotation-invariant functions of three-dimensional point cloud data using a random features approach. Specifically, we extend the random features method of Rahimi and Recht [2007] by deriving a version that is invariant to three-dimensional rotations and showing that it is fast to evaluate on point cloud data. We show through experiments that our method matches or outperforms the performance of general-purpose rotation-invariant neural networks on standard molecular property prediction benchmark datasets QM7 and QM9 . We also show that our method is general-purpose and provides a rotation-invariant baseline on the ModelNet40 shape classification task. Finally, we show that our method has an order of magnitude smaller prediction latency than competing kernel methods.  \n1 Introduction  \nMany common prediction tasks where the inputs are three-dimensional physical objects are known to be rotation-invariant; the ground-truth label does not change when the object is rotated. Building rotation invariance into machine learning models is an important inductive bias for such problems. The common intuition is that restricting the learning process to rotation-invariant models will remove any possibility of poor generalization performance due to rotations of test samples and may improve sample efficiency by reducing the effective complexity of learned models. These ideas have inspired a line of research begun by Kondor et al. [2018], Cohen et al. [2018a], Esteves et al. [2018] into building general-purpose deep neural network architectures that are invariant to rotations of their input. However, in these studies, it is not clear whether the reported high accuracies are due to the expressive power of the neural networks or primarily attributable to rotation invariance. We introduce a rotation-invariant random feature model which helps us explore the impact of rotation invariance alone, outside of the neural network framework. Our method is general-purpose and does not require expert knowledge for feature or architecture design. For certain prediction tasks, our proposed method can be computed with very low prediction latency with only a small reduction in accuracy compared to neural network methods, making it a viable method in a range of applications.  \nIn this paper, we consider prediction problems that are rotation-invariant, that is, the ground-truth response f ∗ (x) = y does not change when an arbitrary rotation is applied to the input x. We represent the input data x as a 3D point cloud, an unordered set of points in R3 possibly with accompanying labels. Common examples of rotation-invariant prediction problems on 3D point clouds include molecular  \n∗ [meliao@uchicago.edu](meliao@uchicago.edu)  \n†[ericj@uchicago.edu](ericj@uchicago.edu)[ ](ericj@uchicago.edu)‡[willett@uchicago.edu](willett@uchicago.edu)  \nFigure 1: An overview of the rotation-invariant random features method. First we construct a feature matrix Φ, de","cbCaioG5bP5SzJHF","https://ap.wps.com/l/cbCaioG5bP5SzJHF","pdf",1912896,1,29,"English","en",105,"# Introduction\n## Rotation-invariant learning motivation\n## Proposed rotation-invariant random feature model\n# Method and evaluation\n## Feature construction and computation overview\n# Experiments\n## Molecular property prediction benchmarks\n## 3D shape classification and latency comparison","[{\"question\":\"What problem does the paper address about rotation-invariant machine learning?\",\"answer\":\"It investigates whether the success of rotation-invariant models comes primarily from rotation invariance itself or from the expressive power of deep neural networks.\"},{\"question\":\"How does the proposed method achieve rotation invariance for 3D point clouds?\",\"answer\":\"It extends Rahimi and Recht’s random features approach by deriving a variant whose features are invariant to three-dimensional rotations, using analytical integration over all rotations and results from SO(3) representation theory.\"},{\"question\":\"What performance and efficiency results are reported?\",\"answer\":\"The method matches or outperforms rotation-invariant neural networks on QM7 and QM9, provides a general-purpose baseline on ModelNet40, and has prediction latency about an order of magnitude lower than competing kernel methods.\"}]","Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds | 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problem does the paper address about rotation-invariant machine learning?","Question",{"text":75,"@type":76},"It investigates whether the success of rotation-invariant models comes primarily from rotation invariance itself or from the expressive power of deep neural networks.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method achieve rotation invariance for 3D point clouds?",{"text":80,"@type":76},"It extends Rahimi and Recht’s random features approach by deriving a variant whose features are invariant to three-dimensional rotations, using analytical integration over all rotations and results from SO(3) representation theory.",{"name":82,"@type":73,"acceptedAnswer":83},"What performance and efficiency results are reported?",{"text":84,"@type":76},"The method matches or outperforms rotation-invariant neural networks on QM7 and QM9, provides a general-purpose baseline on ModelNet40, and has prediction latency about an order of magnitude lower than 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