  Existing Transformer-based models for point cloud analysis suffer from
quadratic complexity, leading to compromised point cloud resolution and
information loss. In contrast, the newly proposed Mamba model, based on state
space models (SSM), outperforms Transformer in multiple areas with only linear
complexity. However, the straightforward adoption of Mamba does not achieve
satisfactory performance on point cloud tasks. In this work, we present
Mamba3D, a state space model tailored for point cloud learning to enhance local
feature extraction, achieving superior performance, high efficiency, and
scalability potential. Specifically, we propose a simple yet effective Local
Norm Pooling (LNP) block to extract local geometric features. Additionally, to
obtain better global features, we introduce a bidirectional SSM (bi-SSM) with
both a token forward SSM and a novel backward SSM that operates on the feature
channel. Extensive experimental results show that Mamba3D surpasses
Transformer-based counterparts and concurrent works in multiple tasks, with or
without pre-training. Notably, Mamba3D achieves multiple SoTA, including an
overall accuracy of 92.6% (train from scratch) on the ScanObjectNN and 95.1%
(with single-modal pre-training) on the ModelNet40 classification task, with
only linear complexity.
