Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding

Jincen Jiang; Qianyu Zhou; Yuhang Li; Kui Su; Meili Wang; Jian Chang; Jian Jun Zhang; Xuequan Lu

cs.CVMar 21, 2026

Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding

Authors: Jincen Jiang, Qianyu Zhou, Yuhang Li, Kui Su, Meili Wang, Jian Chang, Jian Jun Zhang, Xuequan Lu

Organizations: Bournemouth University · Jilin University · The University of Western Australia · Hangzhou City University ·

Abstract

While recent Transformer and Mamba architectures have advanced point cloud representation learning, they are typically developed for single-task or single-domain settings. Directly applying them to multi-task domain generalization (DG) leads to degraded performance. Transformers effectively model global dependencies but suffer from quadratic attention cost and lack explicit structural ordering, whereas Mamba offers linear-time recurrence yet often depends on coordinate-driven serialization, which is sensitive to viewpoint changes and missing regions, causing structural drift and unstable sequential modeling. In this paper, we propose Structure-Aware Domain Generalization (SADG), a Mamba-based In-Context Learning framework that preserves structural hierarchy across domains and tasks. We design structure-aware serialization (SAS) that generates transformation-invariant sequences using centroid-based topology and geodesic curvature continuity. We further devise hierarchical domain-aware modeling (HDM) that stabilizes cross-domain reasoning by consolidating intra-domain structure and fusing inter-domain relations. At test time, we introduce a lightweight spectral graph alignment (SGA) that shifts target features toward source prototypes in the spectral domain without updating model parameters, ensuring structure-preserving test-time feature shifting. In addition, we introduce MP3DObject, a real-scan object dataset for multi-task DG evaluation. Comprehensive experiments demonstrate that the proposed approach improves structural fidelity and consistently outperforms state-of-the-art methods across multiple tasks including reconstruction, denoising, and registration.

Figures & tables

Figure 1: Overview of our SADG . (a) During training, point clouds from multiple source domains are partitioned into local patches and serialized into structure-aware sequences using the Centroid Distance Spectrum (CDS) and Geodesic Curvature Spectrum (GCS), which preserve global topology and local geometric continuity. The serialized sequences are then processed by Mamba blocks under the Hierarchical Domain-Aware Modeling (HDM) mechanism, which stabilizes intra-domain structure and fuses inter-domain relations. (b) At test time, the Spectral Graph Alignment (SGA) performs structure-aware shifting that guides target features toward source prototypes in the spectral domain without updating model parameters, enabling robust generalization to unseen target domains across multiple tasks.

Figure 2: Comparison of different serialization strategies. The proposed CDS and GCS maintain transformation invariance and structural consistency across unaligned real-scan objects, providing a stable foundation for domain-generalized 3D understanding.

Figure 3: Hierarchical Domain-Aware Modeling (HDM) cascades intra-domain structural modeling and inter-domain relational fusion.

Method	Setting	ModelNet			ShapeNet			ScanNet			ScanObjectNN			MP3DObject
Method	Setting	Rec.	Den.	Reg.	Rec.	Den.	Reg.	Rec.	Den.	Reg.	Rec.	Den.	Reg.	Rec.	Den.	Reg.
PointNet [ 62 ]	General	20.56	27.15	17.19	19.84	32.99	19.57	23.73	30.27	19.49	21.74	33.97	21.62	22.63	35.24	23.17
DGCNN [ 77 ]	General	19.17	26.91	17.41	21.18	26.97	19.05	21.73	30.35	17.51	24.88	33.08	18.85	21.83	38.10	21.82
PCT [ 17 ]	General	16.98	25.10	14.50	18.39	24.59	15.28	18.76	27.03	16.99	19.50	29.98	15.71	18.91	28.74	16.49
Point-MAE [ 60 ]	General	14.77	21.53	13.42	16.82	23.91	14.36	16.16	24.54	16.79	19.27	28.69	15.74	20.39	27.28	17.13
PointMamba [ 43 ]	General	16.47	23.13	13.65	16.33	25.24	14.96	15.61	22.43	14.30	17.16	25.44	17.64	20.16	27.08	17.40

Table 1: Comparison on the multi-domain and multi-task benchmark. All models are trained on four source domains and directly evaluated on the remaining one. Evaluation metric: Chamfer Distance (CD,

\times 10^{-3}

, lower is better).

Serialization Variants
Variant	Reconstruction	Denoising	Registration
Z-order Scanning	7.32	12.47	6.29
Hilbert Curve	6.23	11.13	7.68
w/o CDS	4.75	10.69	6.17
w/o GCS	5.82	8.92	4.43
Ours (full SAS)	3.55	6.61	2.84

Table 2: Ablation study on the proposed components.

Figure 4: Comparison between naive serialization variants and our method, highlighting stable topology and geometry in 3D objects.

Figure 5: Qualitative results on synthetic (ModelNet) and real-scan (MP3DObject) targets. Our method recovers both detailed geometry and smooth surfaces. For visualization, MP3DObject instances are rendered after aligning their non-canonical orientations.

Figure 6: t-SNE visualization of latent features. The Input plot shows encoder-only features, while the latter two depict representations after Mamba-based sequential modeling.

Variant	NPR $\uparrow$	Avg. CD $\downarrow$	Runtime / batch $\downarrow$
Naive BFS (CPU)	1.00	4.27	2.22s
Spectral CDS (GPU, ours)	0.97	4.33	0.75s

Table 3: Naive BFS vs. spectral CDS under MP3DObject as target.

Figure 7: Illustration of why Euclidean distance fails on curved surfaces: straight-line distances shortcut across the token, whereas geodesic distances correctly follow the intrinsic surface geometry.

Method	Topo-NPR $\uparrow$	Geo-NPR $\uparrow$
Z-order	0.59	0.48
Hilbert curve	0.62	0.48
SAS (CDS+GCS, ours)	0.69	0.67

Table 4: Neighborhood preservation rate under random rotations (higher is better). Our serialization preserves intrinsic neighborhoods more faithfully than coordinate-driven baselines.

Variant	Reconstruction	Denoising	Registration
Naive FPS order	7.73	13.64	7.54
Random traversal	8.17	12.92	7.24
SAS (CDS+GCS, ours)	3.55	6.61	2.84

Table 5: Ablations of serialization strategies on MP3DObject. Naive FPS order and random traversal are clearly inferior to our structure-aware serialization.

Kernel setting	Avg. CD	Comment
Fixed $\sigma=\gamma=0.05$	5.76	too local, sensitive to noise
Fixed $\sigma=\gamma=0.10$	5.02	tuned baseline
Fixed $\sigma=\gamma=0.20$	5.52	overly smooth, loses detail
Adaptive (median-based, ours)	4.33	robust across categories

Table 6: Fixed vs. data-adaptive kernel scales on MP3DObject. We report average Chamfer Distance (CD

\times 10^{-3}

) over reconstruction, denoising, and registration. Data-adaptive scales based on median distances provide robust performance without tuning.

Variant	Reconstruction	Denoising	Registration
w/ concat	5.40	7.11	4.23
w/ interleave (ours)	3.55	6.61	2.84

Table 7: Interleaving vs. concatenation in HDM on MP3DObject. Interleaving tokens from both domains enables more effective cross-domain information flow.

Variant	Reconstruction	Denoising	Registration
No SGA	11.95	17.38	9.43
Simple feature shift	7.62	12.56	7.96
SGA (ours)	3.55	6.61	2.84

Table 8: SGA vs. simple feature shifting on MP3DObject. Spectral alignment yields consistently better domain generalization.

Setting	Avg. CD	Comment
$\alpha=0.0$ (no SGA)	12.92	no alignment applied
$\alpha=0.5$ (fixed)	6.77	improves over no alignment
$\alpha=1.0$ (fixed)	10.20	over-alignment, less stable
Adaptive (cosine, ours)	4.33	similarity-based, best overall

Table 9: Effect of alignment strength in SGA on MP3DObject. We report average Chamfer Distance (CD

\times 10^{-3}

) over three tasks.

Method	SAS (s)	Fwd. (s)	SGA (s)	Total (s)	FLOPs (G)	Params (M)
DG-PIC [ 28 ]	–	0.94	–	0.94	21.07	27.57
SADG (ours)	0.33	0.25	0.17	0.75	14.89	18.87

Table 10: Runtime breakdown and model complexity.

Dataset	Curvature	Missing	Noise	Orientation
ModelNet	low	low	low	low
ShapeNet	low–mid	low	low	low
ScanNet	mid	mid–high	mid	mid
ScanObjectNN	mid–high	high	high	high
MP3DObject	high	high	high	high

Table 11: Qualitative characterization of datasets along four difficulty dimensions. “Low / mid / high” indicate relative levels to highlight trends. MP3DObject sits at the most challenging end across all dimensions.

Figure 8: Visual comparison of datasets. MP3DObject instances present complex indoor objects in cluttered scenes with substantial occlusions and highly varied poses. For visualization clarity, MP3DObject samples are shown in a manually aligned canonical view; all training and evaluation use the original unaligned scans.

Figure 9: MP3DObject per-class visualization in original and aligned poses. For each class, we show several instances in their original unaligned pose (left of each pair) and in a manually aligned pose (right of each pair) to facilitate visual inspection. The original pose distribution is highly diverse, reflecting realistic scanning conditions. Alignment is applied only for visualization; all training and evaluation in our experiments use the original unaligned MP3DObject scans.

Figure 10: Qualitative comparisons on different target domains.

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Deformation-based In-Context Learning for Point Cloud Understanding

Chengxing Lin, Jinhong Deng, Yinjie Lei, Wen Li

Shenzhen Institute for Advanced Study, UESTC · School of Computer Science and Engineering, UESTC · Sichuan University

Point Cloud Denoising Point Cloud Learning In-Context Learning Point Cloud Understanding Point Cloud Registration

Open paper AskPDF arXiv

Recent advances in point cloud In-Context Learning (ICL) have demonstrated strong multitask capabilities. Existing approaches typically adopt a Masked Point Modeling (MPM)-based paradigm for point cloud ICL. However, MPM-based methods directly predict the target point cloud from masked tokens without leveraging geometric priors, requiring the model to infer spatial structure and geometric details solely from token-level correlations via transformers. Additionally, these methods suffer from a training-inference objective mismatch, as the model learns to predict the target point cloud using target-side information that is unavailable at inference time. To address these challenges, we propose DeformPIC, a deformation-based framework for point cloud ICL. Unlike existing approaches that rely on masked reconstruction, DeformPIC learns to deform the query point cloud under task-specific guidance from prompts, enabling explicit geometric reasoning and consistent objectives. Extensive experiments demonstrate that DeformPIC consistently outperforms previous state-of-the-art methods, achieving reductions of 1.6, 1.8, and 4.7 points in average Chamfer Distance on reconstruction, denoising, and registration tasks, respectively. Furthermore, we introduce a new out-of-domain benchmark to evaluate generalization across unseen data distributions, where DeformPIC achieves state-of-the-art performance.

Abstract

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