{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T05:33:22Z","timestamp":1782365602686,"version":"3.54.5"},"reference-count":47,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T00:00:00Z","timestamp":1773705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Youth Program of the National Natural Science Foundation of China","award":["62406208"],"award-info":[{"award-number":["62406208"]}]},{"name":"International Cooperation Program of the Science and Technology Department of Sichuan Province","award":["2025YFHZ0237"],"award-info":[{"award-number":["2025YFHZ0237"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recent years have seen remarkable progress in deep learning on 3D point clouds, with hierarchical architectures becoming standard. Most work has focused on developing increasingly complex operators, such as self-attention, while enhancing the representational capacity of efficient point-wise MLP-based backbones has received less attention. We address this issue by proposing a differentiable module that learns to impose a task-driven canonical structure on local point sets. Our proposed SMA (Sort\u2013Mix\u2013Attend) layer dynamically serializes a neighborhood by generating a geometric basis and using a differentiable sorting mechanism. This enables an efficient MLP-based network to model rich feature interactions, adaptively modulating features prior to the final symmetric aggregation function. We demonstrate that SMA effectively enhances standard backbones for 3D classification and segmentation. Specifically, integrating SMA into PointNeXt-S achieves an Overall Accuracy (OA) of 88.3% on the challenging ScanObjectNN dataset, an improvement of 0.6% over the baseline. Furthermore, it boosts the classic PointNet++ architecture by a significant 5.2% in OA. We also introduce a highly efficient SMA-Tiny variant that achieves 86.0% OA with only 0.3 M parameters, proving the structural superiority, computational cost-effectiveness, and practical significance of our method for real-world 3D perception tasks.<\/jats:p>","DOI":"10.3390\/s26061888","type":"journal-article","created":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T14:03:27Z","timestamp":1773756207000},"page":"1888","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Improved Point Cloud Representation via a Learnable Sort\u2013Mix\u2013Attend Mechanism"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-6126-7293","authenticated-orcid":false,"given":"Yuyan","family":"Zhang","sequence":"first","affiliation":[{"name":"Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xi","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhang","family":"Yi","sequence":"additional","affiliation":[{"name":"Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5297-7046","authenticated-orcid":false,"given":"Lei","family":"Xu","sequence":"additional","affiliation":[{"name":"Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu 610065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, M., Yue, G., Xiong, J., and Tian, S. (2024). Intelligent point cloud processing, sensing, and understanding. Sensors, 24.","DOI":"10.3390\/books978-3-7258-0242-5"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, M., and Tian, S. (2025). A brief introduction to intelligent point cloud processing, sensing, and understanding: Part ii. Sensors, 25.","DOI":"10.3390\/s25051310"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, W., Sun, J., Li, W., Hu, T., and Wang, P. (2019). Deep learning on point clouds and its application: A survey. Sensors, 19.","DOI":"10.3390\/s19194188"},{"key":"ref_4","first-page":"1","article-title":"Compression approaches for LiDAR point clouds and beyond: A survey","volume":"21","author":"Wang","year":"2025","journal-title":"Acm Trans. Multimed. Comput. Commun. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, M., Huang, R., Dong, H., Lin, D., Song, Y., and Xie, W. (2024, January 20\u201327). msLPCC: A multimodal-driven scalable framework for deep LiDAR point cloud compression. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i6.28362"},{"key":"ref_6","unstructured":"Quan, S., Yu, J., Nie, Z., Wang, M., Feng, S., An, P., and Yang, J. (2024). Deep learning for 3d point cloud enhancement: A survey. arXiv."},{"key":"ref_7","unstructured":"Wang, J., Fei, B., Edirimuni, D.d.S., Liu, Z., He, Y., and Lu, X. (2025). A survey of deep learning-based point cloud denoising. arXiv."},{"key":"ref_8","unstructured":"Zhang, Y.X., Gui, J., Yu, B., Cong, X., Gong, X., Tao, W., and Tao, D. (2024). Deep learning-based point cloud registration: A comprehensive survey and taxonomy. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"110532","DOI":"10.1016\/j.patcog.2024.110532","article-title":"Advancements in point cloud data augmentation for deep learning: A survey","volume":"153","author":"Zhu","year":"2024","journal-title":"Pattern Recognit."},{"key":"ref_10","unstructured":"Qi, C.R., Yi, L., Su, H., and Guibas, L.J. (2017, January 4\u20139). Pointnet++: Deep hierarchical feature learning on point sets in a metric space. Proceedings of the Advances in Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chen, J., Kakillioglu, B., Ren, H., and Velipasalar, S. (2022, January 18\u201324). Why discard if you can recycle?: A recycling max pooling module for 3d point cloud analysis. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.00064"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1145\/3326362","article-title":"Dynamic graph cnn for learning on point clouds","volume":"38","author":"Wang","year":"2019","journal-title":"ACM Trans. Graph. (ToG)"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xiang, T., Zhang, C., Song, Y., Yu, J., and Cai, W. (2021, January 11\u201317). Walk in the cloud: Learning curves for point clouds shape analysis. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Virtual.","DOI":"10.1109\/ICCV48922.2021.00095"},{"key":"ref_14","unstructured":"Thomas, H., Qi, C.R., Deschaud, J.E., Marcotegui, B., Goulette, F., and Guibas, L.J. (November, January 27). Kpconv: Flexible and deformable convolution for point clouds. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Choy, C., Gwak, J., and Savarese, S. (2019, January 16\u201320). 4d spatio-temporal convnets: Minkowski convolutional neural networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00319"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hu, Q., Yang, B., Xie, L., Rosa, S., Guo, Y., Wang, Z., Trigoni, N., and Markham, A. (2020, January 14\u201319). Randla-net: Efficient semantic segmentation of large-scale point clouds. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtual.","DOI":"10.1109\/CVPR42600.2020.01112"},{"key":"ref_17","first-page":"28119","article-title":"Assanet: An anisotropic separable set abstraction for efficient point cloud representation learning","volume":"34","author":"Qian","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s41095-021-0229-5","article-title":"Pct: Point cloud transformer","volume":"7","author":"Guo","year":"2021","journal-title":"Comput. Vis. Media"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, H., Jiang, L., Jia, J., Torr, P.H., and Koltun, V. (2021, January 11\u201317). Point transformer. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Virtual.","DOI":"10.1109\/ICCV48922.2021.01595"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yu, X., Tang, L., Rao, Y., Huang, T., Zhou, J., and Lu, J. (2022, January 18\u201324). Point-bert: Pre-training 3d point cloud transformers with masked point modeling. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.01871"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Pang, Y., Wang, W., Tay, F.E., Liu, W., Tian, Y., and Yuan, L. (2022). Masked autoencoders for point cloud self-supervised learning. Proceedings of the European Conference on Computer Vision, Tel Aviv, Israel, 23\u201327 October 2022, Springer.","DOI":"10.1007\/978-3-031-20086-1_35"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Qin, Z., Yu, H., Wang, C., Guo, Y., Peng, Y., and Xu, K. (2022, January 18\u201324). Geometric transformer for fast and robust point cloud registration. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.01086"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Park, J., Lee, S., Kim, S., Xiong, Y., and Kim, H.J. (2023, January 18\u201322). Self-positioning point-based transformer for point cloud understanding. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada.","DOI":"10.1109\/CVPR52729.2023.02089"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, S., Liu, X., Kong, L., Xu, J., Hu, C., Fang, G., Li, W., Zhu, J., and Wang, X. (2025, January 11\u201315). PointLoRA: Low-rank adaptation with token selection for point cloud learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR52734.2025.00619"},{"key":"ref_25","unstructured":"Wu, P., Chai, B., Li, H., Zheng, M., Peng, Y., Wang, Z., Nie, X., Zhang, Y., and Sun, X. (March, January 25). Spiking point transformer for point cloud classification. Proceedings of the AAAI Conference on Artificial Intelligence, Philadelphia, PA, USA."},{"key":"ref_26","unstructured":"Liang, D., Zhou, X., Xu, W., Zhu, X., Zou, Z., Ye, X., Tan, X., and Bai, X. (2024). Pointmamba: A simple state space model for point cloud analysis. arXiv."},{"key":"ref_27","unstructured":"Zhang, T., Yuan, H., Qi, L., Zhang, J., Zhou, Q., Ji, S., Yan, S., and Li, X. (March, January 25). Point cloud mamba: Point cloud learning via state space model. Proceedings of the AAAI Conference on Artificial Intelligence, Philadelphia, PA, USA."},{"key":"ref_28","unstructured":"Li, Z., Ai, Y., Lu, J., Wang, C., Deng, J., Chang, H., Liang, Y., Yang, W., Zhang, S., and Zhang, T. (March, January 25). Pamba: Enhancing global interaction in point clouds via state space model. Proceedings of the AAAI Conference on Artificial Intelligence, Philadelphia, PA, USA."},{"key":"ref_29","unstructured":"He, Q., Zhang, J., Peng, J., He, H., Li, X., Wang, Y., and Wang, C. (March, January 25). Pointrwkv: Efficient rwkv-like model for hierarchical point cloud learning. Proceedings of the AAAI Conference on Artificial Intelligence, Philadelphia, PA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zheng, L., Xia, Q., Chen, X., Liu, Z., and Wen, C. (2025). WinMamba: Multi-Scale Shifted Windows in State Space Model for 3D Object Detection. arXiv.","DOI":"10.1609\/aaai.v40i16.38347"},{"key":"ref_31","first-page":"81489","article-title":"Voxel mamba: Group-free state space models for point cloud based 3d object detection","volume":"37","author":"Zhang","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hilbert, D. (1935). \u00dcber die stetige Abbildung einer Linie auf ein Fl\u00e4chenst\u00fcck. Dritter Band: Analysis\u00b7 Grundlagen der Mathematik\u00b7 Physik Verschiedenes: Nebst Einer Lebensgeschichte, Springer.","DOI":"10.1007\/978-3-662-38452-7"},{"key":"ref_33","unstructured":"Morton, G.M. (1966). A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing, IBM Ltd."},{"key":"ref_34","first-page":"23192","article-title":"Pointnext: Revisiting pointnet++ with improved training and scaling strategies","volume":"35","author":"Qian","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wu, X., Jiang, L., Wang, P.S., Liu, Z., Liu, X., Qiao, Y., Ouyang, W., He, T., and Zhao, H. (2024, January 17\u201321). Point Transformer V3: Simpler Faster Stronger. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR52733.2024.00463"},{"key":"ref_36","unstructured":"Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J. (2015, January 7\u201312). 3d shapenets: A deep representation for volumetric shapes. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA."},{"key":"ref_37","unstructured":"Uy, M.A., Pham, Q.H., Hua, B.S., Nguyen, T., and Yeung, S.K. (November, January 27). Revisiting point cloud classification: A new benchmark dataset and classification model on real-world data. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1145\/2980179.2980238","article-title":"A scalable active framework for region annotation in 3d shape collections","volume":"35","author":"Yi","year":"2016","journal-title":"ACM Trans. Graph. (ToG)"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Armeni, I., Sener, O., Zamir, A.R., Jiang, H., Brilakis, I., Fischer, M., and Savarese, S. (2016, January 27\u201330). 3d semantic parsing of large-scale indoor spaces. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.170"},{"key":"ref_40","unstructured":"Qi, C.R., Su, H., Mo, K., and Guibas, L.J. (2017, January 21\u201326). Pointnet: Deep learning on point sets for 3d classification and segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA."},{"key":"ref_41","first-page":"7537","article-title":"Fourier features let networks learn high frequency functions in low dimensional domains","volume":"33","author":"Tancik","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_42","unstructured":"Prillo, S., and Eisenschlos, J. (2020, January 12\u201318). Softsort: A continuous relaxation for the argsort operator. Proceedings of the International Conference on Machine Learning. PMLR, Virtual."},{"key":"ref_43","unstructured":"Bengio, Y., L\u00e9onard, N., and Courville, A. (2013). Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv."},{"key":"ref_44","unstructured":"Ma, X., Qin, C., You, H., Ran, H., and Fu, Y. (2022). Rethinking network design and local geometry in point cloud: A simple residual MLP framework. arXiv."},{"key":"ref_45","unstructured":"Li, Y., Bu, R., Sun, M., Wu, W., Di, X., and Chen, B. (2018, January 2\u20137). Pointcnn: Convolution on x-transformed points. Proceedings of the Advances in Neural Information Processing Systems, San Diego, CA, USA."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Deng, X., Zhang, W., Ding, Q., and Zhang, X. (2023, January 18\u201322). Pointvector: A vector representation in point cloud analysis. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada.","DOI":"10.1109\/CVPR52729.2023.00912"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Lai, X., Liu, J., Jiang, L., Wang, L., Zhao, H., Liu, S., Qi, X., and Jia, J. (2022, January 18\u201324). Stratified transformer for 3d point cloud segmentation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.00831"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/6\/1888\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T11:17:01Z","timestamp":1773832621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/6\/1888"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,17]]},"references-count":47,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["s26061888"],"URL":"https:\/\/doi.org\/10.3390\/s26061888","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,17]]}}}