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PointMamba: A Simple State Space Model for Point Cloud Analysis

Dingkang Liang, Xin Zhou, Wei Xu, Xingkui Zhu, Zhikang Zou, Xiaoqing Ye, Xiao Tan, Xiang Bai

arXiv:2402.10739v5cs.CV

TL;DR

PointMamba targets the quadratic computational cost of Transformer attention while preserving global modeling for point-cloud analysis. It uses space-filling-curve tokenization and a simple non-hierarchical Mamba encoder, achieving superior performance across datasets with lower GPU memory usage and FLOPs. The paper presents these results as evidence of SSM potential for 3D vision.

  • Problem

    Transformer attention provides global modeling for point clouds but has quadratic complexity, motivating a linear-complexity alternative with comparable global modeling capacity.

  • Method

    PointMamba serializes point clouds with space-filling curves and processes the resulting tokens using a plain, non-hierarchical Mamba encoder.

  • Results

    PointMamba achieves superior performance across various datasets while significantly reducing GPU memory usage and FLOPs.

  • Takeaways & Limitations

    The results underscore the potential of SSMs, particularly Mamba, for point-cloud analysis and future 3D vision foundation models.

  • Takeaways & Limitations

    The paper focuses only on point-cloud analysis and uses only point clouds as training data, leaving unified multi-task and multimodal models for future work.

Abstract

from arXiv · show

Transformers have become one of the foundational architectures in point cloud analysis tasks due to their excellent global modeling ability. However, the attention mechanism has quadratic complexity, making the design of a linear complexity method with global modeling appealing. In this paper, we propose PointMamba, transferring the success of Mamba, a recent representative state space model (SSM), from NLP to point cloud analysis tasks. Unlike traditional Transformers, PointMamba employs a linear complexity algorithm, presenting global modeling capacity while significantly reducing computational costs. Specifically, our method leverages space-filling curves for effective point tokenization and adopts an extremely simple, non-hierarchical Mamba encoder as the backbone. Comprehensive evaluations demonstrate that PointMamba achieves superior performance across multiple datasets while significantly reducing GPU memory usage and FLOPs. This work underscores the potential of SSMs in 3D vision-related tasks and presents a simple yet effective Mamba-based baseline for future research. The code will be made available at \url{https://github.com/LMD0311/PointMamba}.

1 Introduction

PointMamba addresses the quadratic cost of Transformer attention by combining space-filling-curve tokenization with a simple, non-hierarchical Mamba encoder for global point-cloud modeling. It reports superior performance across datasets while reducing computational costs.

  • Point cloud analysis supports applications including robotics, autonomous driving, and augmented reality but is challenging because point clouds are irregular and sparse.
  • Transformer attention captures point relationships and supports global modeling, but its quadratic complexity creates substantial computational costs for long sequences and low-resource devices.
  • PointMamba introduces a point-cloud State Space Model intended as a simple alternative to Transformers with global modeling and linear complexity.
  • Space-filling curves scan key points from different directions, converting unstructured point clouds into regular sequences whose tokens support local and global modeling.
  • PointMamba uses a plain, non-hierarchical Mamba backbone and an MAE-like pretraining strategy that randomizes serialization across a predefined serialization bank.
  • PointMamba achieves superior performance across datasets while reducing GPU memory usage and FLOPs through Mamba's linear complexity.

2 Related work

Related work establishes Transformers as effective global-modeling architectures for point clouds but highlights their quadratic attention cost. The paper positions PointMamba as a simple attention-free SSM alternative with linear complexity.

  • Point Cloud Transformers: Point-cloud Transformers use global attention and encoder-decoder pretraining designs, but attention has time complexity O(n^2d), constraining efficiency as sequence length grows.
  • PointMamba: This work focuses on a simple attention-free SSM that retains the Transformer's global-modeling advantages for point-cloud analysis.
  • State Space Models: State Space Models provide an alternative for sequential data, with S4 offering contextualization and strong performance on lengthy sequences.
  • Point Cloud Transformers: The efficiency comparison removes both Point-MAE and PointMamba tokenizers and feeds each model a predefined sequence to isolate structural efficiency.
  • State Space Models: Prior work applies Mamba and related SSMs across images, graphs, medical segmentation, video understanding, and generative modeling, while point-cloud applications remain limited.

3 Preliminaries

The preliminaries introduce state-space sequence modeling and space-filling curves as foundations for PointMamba. Selective SSMs make parameters input-dependent, while Hilbert variants preserve spatial locality during serialization.

  • State Space Model: An SSM maps an input state to an output through an implicit latent state, and S4 parameterizes the system with A, B, C, and sampling step size ∆.
  • State Space Model: S4 discretizes its continuous system using the zero-order hold rule to obtain discrete parameters A and B.
  • State Space Model: Fixed parameters across time steps give conventional SSMs a linear time-invariant structure that limits their ability to handle varied input sequences.
  • Selective SSM: Selective SSMs make B, C, and ∆ functions of the input, producing a time-variant model; PointMamba uses a hardware-aware S6 implementation with linear complexity.
  • Space-filling curve: Space-filling curves traverse discrete higher-dimensional spaces while preserving spatial proximity, and PointMamba uses Hilbert and Trans-Hilbert variants for point-cloud serialization.

4 PointMamba

PointMamba organizes irregular point clouds into serialized tokens using space-filling curves and processes them with a simple, non-hierarchical Mamba encoder. Its bidirectional serialization design supplies global context while retaining linear-complexity modeling.

  • Point scanning and tokenization: PointMamba samples key points with FPS, scans them using Hilbert and Trans-Hilbert curves, and forms KNN patches for token embedding.The resulting serialized tokens receive order indicators identifying their scanning strategy.
  • Point scanning and tokenization: Order indicators transform tokens from different scanning strategies into distinct latent spaces before Mamba encoding.This preserves the distinction between tokens sharing centers but having different serialization orders.
  • Mamba encoder: The encoder stacks plain, non-hierarchical Mamba blocks with layer normalization, SelectiveSSM, depth-wise convolution, and residual connections.The design intentionally avoids complex structural additions.
  • Mamba encoder: Hilbert serialization accumulates global information that informs subsequent Trans-Hilbert tokens, enabling globally aware sequence modeling.Each Trans-Hilbert point is informed by the previously processed Hilbert sequence.
  • Evaluation: PointMamba surpasses various Transformer-based point-cloud analysis methods despite using a very simple Mamba block.The supplied table caption identifies ScanObjectNN object-classification evaluation and reports overall accuracy and parameter counts, but provides no values here.
  • Serialization-based mask modeling: During pre-training, PointMamba randomly selects a space-filling curve for serialization-based mask modeling and reconstructs masked patches with Chamfer distance.Different serialized tokens receive different order indicators during this process.

5 Experiments

PointMamba is evaluated across classification, few-shot learning, and part segmentation, alongside efficiency and component ablations. It achieves competitive or superior results while reducing computational costs and benefiting from its scanning and selective-SSM design choices.

  • Classification: PointMamba surpasses Point-MAE by 1.55%, 1.38% and 0.27% on ScanObjectNN OBJ-BG, OBJ-ONLY and PB-T50-RS, respectively.These gains use less computational cost and also exceed PointGPT-S by 0.93%, 0.17% and 0.14% across the same variants.
  • Classification: PointMamba achieves the best ModelNet40 classification results among various self-supervised Transformer methods, surpassing Point-MAE and PointGPT-S by 0.4% and 0.3%.Compared with cross-modal ACT, it reduces parameters and FLOPs by about 44% and 38%, respectively.
  • Few-shot learning: PointMamba shows competitive results in ModelNet40 few-shot learning with limited data, including +1.0% mean accuracy over ACT in one reported setting.The experiments use n-way, m-shot configurations and report mean accuracy with standard deviation across 10 experiments per setting.
  • Part segmentation: PointMamba demonstrates highly competitive performance against Transformer-based counterparts on ShapeNetPart part segmentation.The evaluation reports mIoU for all classes and all instances.
  • Structural efficiency: 30.2×, 24.9×, and 5.2× improvements over PointMAE are reported for inference speed, GPU memory, and FLOPs when sequence length exceeds 32,768.The comparison highlights increasing efficiency advantages on long point-token sequences.
  • Ablation studies: Combining Hilbert and Trans-Hilbert scanning surpasses random serialization by 1.20% and 1.73% on two datasets, while order indicators yield 94.32% and 92.60% accuracy.The order indicator adds only 1.5k parameters and distinguishing the two scanning strategies improves performance.

6 Conclusion

PointMamba is a simple Mamba-based point-cloud method that uses space-filling-curve tokenization and a plain, non-hierarchical Mamba architecture for global modeling with linear complexity.

  • PointMamba combines a space-filling curve-based point tokenizer with a plain, non-hierarchical Mamba architecture.
  • PointMamba achieves global modeling with linear complexity while reducing GPU memory and FLOPs.
  • PointMamba delivers state-of-the-art performance across various point-cloud datasets despite its structural simplicity.
  • The results highlight the potential of SSMs, particularly Mamba, for handling point-cloud data and constructing 3D vision foundation models.

Appendix A Theoretically Analysis

The appendix analyzes Selective SSM as a masked, causal self-attention-like operation whose input-dependent parameters determine token interactions.

  • Selective SSM computes per-time B_t, C_t, and ∆_t from each input x_t using linear projections and softplus.
  • Ignoring the residual connection D, the output sequence is obtained by expanding the state-space recurrence over the input sequence.
  • The expanded operation can be represented in matrix form through a transfer matrix W relating the output sequence to the input sequence.
  • The lower-triangular structure of W makes the operation resemble causal self-attention with a lower-triangular mask.
  • The appendix approximates softplus with ReLU when simplifying the transfer-matrix expression.
  • Selective SSM represents token influence through Q_i and K_j, while T_i,j models token significance from x_i to x_j.

A.2 Global modeling of PointMamba

PointMamba obtains global information by combining two space-filling-curve serializations, allowing one serialized half to receive information from the other while retaining a simple design.

  • A.2 Global modeling of PointMamba: The input sequence has even length and is split into Hilbert and Trans-Hilbert serialized halves.
  • A.2 Global modeling of PointMamba: The partitioned transfer structure contains a cross-block Y that is associated with both serialized halves.
  • A.2 Global modeling of PointMamba: The hidden-space output is organized across the two sequence halves, with separate X and Z blocks and an interaction block Y.
  • A.2 Global modeling of PointMamba: Serialized points from Trans-Hilbert can receive global information from Hilbert serialization.
  • PointMamba surpasses concurrent state-space methods while using reduced computational overhead and retaining vanilla Mamba without complex modular designs.

Appendix C More experimental resutls

The appendix provides implementation details, downstream evaluation settings, masking and classification-token analyses, and qualitative segmentation results.

  • Table 10 reports implementation details for pre-training and downstream tasks.
  • ShapeNetCore pre-training uses approximately 51K samples across 55 categories, 1,024 input points, 64 patches, and 300 epochs.
  • Downstream experiments evaluate classification on ScanObjectNN and ModelNet40 and segmentation on ShapeNetPart using multiple serialization strategies.
  • Table 11 reports pre-training loss and fine-tuning accuracy for different masking strategies.
  • Table 12 reports fine-tuning accuracy for different classification-token settings.
  • Figure 7 presents qualitative mask predictions on the ShapeNet validation set.

C.2 Additional ablation study

The additional ablations examine masking strategies and classification-token usage in PointMamba. Random masking of 60% of point patches and removing [CLS] with average pooling are identified as effective choices.

  • The ablation studies evaluate several hyper-parameters of PointMamba.
  • Masking strategy for pre-training: Randomly masking 60% of point patches achieves good performance in the serialization-based mask-modeling paradigm.This is compared with block masking, which creates a more challenging reconstruction target.
  • Usage of classification token: Without [CLS], average pooling of the final block’s output yields the best classification results for PointMamba.

Appendix D Qualitative Analysis

Qualitative analyses show PointMamba reconstructing masked patches effectively and producing highly competitive part-segmentation predictions on ShapeNet-based validation sets.

  • Mask modeling: Despite masking 60% of serialization-based point tokens, PointMamba effectively reconstructs the masked patches on ShapeNet validation data.An asymmetric vanilla Mamba autoencoder extracts point features for reconstruction.
  • Part segmentation: PointMamba shows highly competitive part-segmentation results on the ShapeNetPart validation set.The qualitative comparison includes ground-truth and predicted results.
  • Part segmentation: Figure 8 presents qualitative PointMamba part-segmentation results on ShapeNetPart.
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