Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy

Rixon Crane, Fahira Afzal Maken, Nicholas Lawrance, Stanislav Funiak, Kasra Khosoussi, Ming Xu, Russell Tsuchida
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:21638-21649, 2026.

Abstract

We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg–Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-crane26a, title = {Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy}, author = {Crane, Rixon and Afzal Maken, Fahira and Lawrance, Nicholas and Funiak, Stanislav and Khosoussi, Kasra and Xu, Ming and Tsuchida, Russell}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {21638--21649}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/crane26a/crane26a.pdf}, url = {https://proceedings.mlr.press/v306/crane26a.html}, abstract = {We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg–Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.} }
Endnote
%0 Conference Paper %T Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy %A Rixon Crane %A Fahira Afzal Maken %A Nicholas Lawrance %A Stanislav Funiak %A Kasra Khosoussi %A Ming Xu %A Russell Tsuchida %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-crane26a %I PMLR %P 21638--21649 %U https://proceedings.mlr.press/v306/crane26a.html %V 306 %X We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg–Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.
APA
Crane, R., Afzal Maken, F., Lawrance, N., Funiak, S., Khosoussi, K., Xu, M. & Tsuchida, R.. (2026). Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:21638-21649 Available from https://proceedings.mlr.press/v306/crane26a.html.

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