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Efficient Graph Field Integrators Meet Point Clouds
Krzysztof Choromanski · Arijit Sehanobish · Han Lin · YUNFAN ZHAO · Eli Berger · Tetiana Parshakova · Qingkai Pan · David Watkins · Tianyi Zhang · Valerii Likhosherstov · Somnath Basu Roy Chowdhury · Kumar Avinava Dubey · Deepali Jain · Tamas Sarlos · Snigdha Chaturvedi · Adrian Weller

Thu Jul 27 04:30 PM -- 06:00 PM (PDT) @ Exhibit Hall 1 #533
We present two new classes of algorithms for efficient field integration on graphs encoding point cloud data. The first class, $\mathrm{SeparatorFactorization}$ (SF), leverages the bounded genus of point cloud mesh graphs, while the second class, $\mathrm{RFDiffusion}$ (RFD), uses popular $\epsilon$-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g. shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (in particular for mesh-dynamics modeling) as well as Wasserstein distance computations for point clouds, including the Gromov-Wasserstein variant.

Author Information

Krzysztof Choromanski (Google DeepMind & Columbia University)
Arijit Sehanobish (Kensho Technologies)
Han Lin (Columbia University)

Columbia master student major in computer science. Research interests focus on the theories of structured random featuresfor kernel approximation and their applications to build efficient Transformers and GNNs.

YUNFAN ZHAO (Columbia University)
Eli Berger (University of Haifa)
Tetiana Parshakova (Stanford)
Qingkai Pan (Columbia University)
Qingkai Pan

I got my undergraduate degree in Machine Learning at Carnegie Mellon University, and I’m currently finishing off my master's degree in Computer Science at Columbia University graduating on May 12, 2023. I have done several publications and internships on Machine Learning Engineering, Data Science and Software Engineering, where my most recent internship at Elementary Robotics focuses on implementing an end-to-end ML pipeline for image-based anomaly detection. You can contact krishna@elementaryrobotics.com (VP of Machine Learning) and dat@elementaryml.com (Director of Machine Learning Team) for further details. I’m proficient in python and C programming and use pytorch as my primary ML programming language. My google scholar profile is https://scholar.google.com/citations?user=Broaf5YAAAAJ&hl=en.

David Watkins (The Boston Dynamics AI Institute)
David Watkins

I’m the Foudation Models Lead Research Scientist at the Boston Dynamics AI Institute. I develop robotic systems across several domains including assistive care, real-world, simulation, and video games. I work with several different robotic technologies including robots from Fetch, Kinova, Staubli, Barrett, Seed, and Intel Realsense. I’ve worked on projects sponsored or afficilated with the Army Research Lab, Google Robotics, NSF, and NVIDIA. I’ve contributed to a number of open source frameworks, including GraspIt!. I am a PhD from the Columbia Robotics Lab at Columbia University, under supervision of Prof. Peter Allen. My dissertation, Learning Mobile Manipulation, present a novel methodology for manipulating objects without the need for localization at runtime. While at the Columbia Robotics Lab and as an undergrad at Columbia University, I have either published or helped publish multiple research papers, assisted in teaching multiple courses, and participated in multiple entrepreneurship endeavours. More information about me is available in my curriculum vitae or my resume.

Tianyi Zhang (Columbia University)
Valerii Likhosherstov (University of Cambridge)
Somnath Basu Roy Chowdhury (UNC Chapel Hill)
Kumar Avinava Dubey (Google Research)
Deepali Jain (Google)
Tamas Sarlos (Google)
Snigdha Chaturvedi (Department of Computer Science, University of North Carolina, Chapel Hill)
Adrian Weller (University of Cambridge, Alan Turing Institute)
Adrian Weller

Adrian Weller is Programme Director for AI at The Alan Turing Institute, the UK national institute for data science and AI, and is a Turing AI Fellow leading work on trustworthy Machine Learning (ML). He is a Principal Research Fellow in ML at the University of Cambridge, and at the Leverhulme Centre for the Future of Intelligence where he is Programme Director for Trust and Society. His interests span AI, its commercial applications and helping to ensure beneficial outcomes for society. Previously, Adrian held senior roles in finance. He received a PhD in computer science from Columbia University, and an undergraduate degree in mathematics from Trinity College, Cambridge.

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