Coarse-to-Fine 3D Part Assembly via Semantic Super-Parts and Symmetry-Aware Pose Estimation
Authors: Xinyi Zhang
Bingyang Wei
Ruixuan Yu
Jian Sun
Venue: NeurIPS 2025 poster ()
Keywords: 3D part assembly; semantic super-parts; dual-range feature propagation; symmetry-aware supervision
Primary area: applications
TL;DR: We propose CFPA for 3D part assembly that integrates semantic super-parts, dual-range feature propagation, and symmetry-aware supervision, achieving SOTA accuracy, consistency, and diversity on standard benchmarks.

Abstract: We propose a novel two-stage framework, Coarse-to-Fine Part Assembly (CFPA), for 3D shape assembly from basic parts. Effective part assembly demands precise local geometric reasoning for accurate component assembly, as well as global structural understanding to ensure semantic coherence and plausible configurations. CFPA addresses this challenge by integrating semantic abstraction and symmetry-aware reasoning into a unified pose prediction process. In the first stage, semantic super-parts are constructed via an optimal transport formulation to capture high-level object structure, which is then propagated to individual parts through a dual-range feature propagation mechanism. The second stage refines part poses via cross-stage feature interaction and instance-level geometric encoding, improving spatial precision and coherence. To enable diverse yet valid assemblies, we introduce a symmetry-aware loss that jointly models both self-symmetry and inter-part geometric similarity, allowing for diverse but structurally consistent assemblies. Extensive experiments on the PartNet benchmark demonstrate that CFPA achieves state-of-the-art performance in assembly accuracy, structural consistency, and diversity across multiple categories.

Coarse-to-Fine 3D Part Assembly via Semantic Super-Parts and Symmetry-Aware Pose Estimation
Xinyi Zhang'; Bingyang
Yu (E3) Jiin Sun
School of Airspace Science and Engineering, Shandong University, Weihai 264209. China Schooo of Mathematics and Statistics, Xi' an Jiaotong University, Xi'an an 710049, China Pazhou Laboratory (Huangpu), Guangzhou, Guangdong 510555, China (zhangxiny1123, weibingyang! (aaggl.mmmll... sdu. edu. en, yuruixuan@sdu. edu. cn, jiansun@x tu. edu. cn
Abstract
We propose novel two-stage framework, Coarse-to-Fine Part Assembly (CFPA), for 3D shape assembly from basic parts. Effective part assembly demands precise local geometric reasoning for accurate component assembly, as well as global structural understanding to ensure semantic coherence and plausible configurations. CFPA addresses this challenge by integrating semantic abstraction and symmetry- aware reasoning into a unified pose prediction process. the first stage, semantic super-parts are constructed via optimal transport formulation to capture high- level object structure, which then propagated to individual parts through a dual- range feature propagation mechanism. The second stage refines part poses via cross- stage feature interaction and instance-level geometric encoding, improving spatial precision and coherence. To enable diverse yet valid assemblies, introduce a symmetry-awand loss that jointly models both self-symmetry and inter-part geometric similarity, allowing for diverse but structurally consistent assemblies. Extensive experiments on the PartNet benchmark demonstrate that CFPA achieves state-of the-art performance in assembly accuracy, structural consistency, and diversity across multiple categories. Code is available at https: httpp://gitai gighhu..... com/ zhangxiny1364/CPA.
Introduction
3D part assembly, the task of estimating accurate 6-DoF poses for set of basic parts to reconstruct coherent 3D shape, is a fundamental yet challenging problem in robotics, vision, and digital design [I] 55. This task is particularly challenging due to the complex geometric dependencies between parts, the absence of explicit semantic structure, the pervasive presence of symmetries, and the vast number of potential combinations.
Recent advances 3D part assembly have focused on modeling structural dependencies among parts. Graph-based approaches 6 7 encode local geometric relationships through message passing on learned part graphs, but their receptive field often limited and insufficient for capturing high-level object structure. Transformer-based methods g g improve long-range reasoning by leveraging global self-attention, yet they typically process parts as flat sequences and struggle to encode hicrarchical permutationninvariin semantics. Generative approaches, including VAEs [00,, GANs (II) and score-based diffusion models [12], attempt to model joint distributions over object structure and part-level geometry 15.15). While powerful, they often rely implicit, handcrafted, or fixed part hierarchies, which can be brittle and category-specific. To address this, we propose to learn high-
"Equal contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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level semantic parts via optimal transport, which provide meaningful guidance for subsequent coarse-to-fine pose prediction and support more coherent and semantically aware assembly.
Beyond semantic reasoning, another challenge in 3D part assembly is handling symmetry within indi- vidual parts and geometrically similar parts, common in real-world objects like self-symmetric chair seats or repeated structures like chair legs. These symmetries lead to multiple valid configurations that are indistinguishable under standard supervision. Some methods address this by introducing instance encoding, losses, or constraints to discourage geometrically similar parts from occupying equivalent position 8 16] Others reduce part-wise pose ambiguity through part pose normalization and further leverage part-level geometric similarity to model part relations O g 17 [8]. Furthermore, some methods exploit symmetry to reduce complexity during fragment reassembly by aligning parts based on their symmetric relationships [1]. However, most existing methods focus on precise part assembly and overlook the interchangeable structural roles of self-symmetric parts or parts with minor geometric differences. In contrast, our approach jointly models both intra-part and inter-part symmetries, enabling the generation of accurate, diverse, and structurally plausible assemblies.
In this paper, we propose CFPA (Coarse-to-Fine Part Assembly), a two-stage framework that jointl models semantic structure and geometrie symmetry. It first performs coarse pose estimation by constructing semantic super-parts via optimal transport, which guides prediction through novel dual-range feature propagation. The part poses are then refined using stoss-stage interaction and instance-level geometry encoding to enhance spatial precision and structural coherence. CFPA further incorporates a symmetry-awand
loss that supervises multiple consistent pose configurations by explicitly modeling both intra-part and inter-part symmetries. Experiments on PartNet show that CFPA outperforms prior methods pose accuracy, structural consistency, and assembly diversity.
2 Related Work
3D Part Assembly 3D part assembly, which aims to estimate 6-DoF poses for object parts to form coherent shapes, has evolved from rule-based and probabilistic approaches modern deep learning frameworks. Early methods 22) relied on handcrafted rules or statistical models to retrieve and align parts from shape repositories. With the rise of deep learning, recent methods focus on learning inter-part relationships and global structure directly from data. Graph-based models [6] 7 24 capture local dependencies via message passing, while Transformer-basedd frameworks 8
enable long-range reasoning and instance-level disambiguation through attention mechanisms and structural constraints. To improve diversity and probabilistic modeling, generative methods such as VAEs, GANs, and diffusion models have been explored [15, 26 27]. fask-specific strategies have also been designed, and Li et al. (28) propose precise alignment through peg-hole constraints, while guided approaches such as GPAT 229. Img-PA [18] and Imagine [30] leverage external cues like planning sequences or images. Despite these advances, many existing methods lack explicit semantic structuring and struggle with symmetry- induced uncertainties, which are critical for producing consistent and diverse assemblies in complex scenarios. Our work addresses these gaps by introducing semantic super-parts and symmetry-ave reasoning for pose prediction.
Multi-scale Feature for Shape Generation Multi-scale feature modeling (3:35]] plays a crucial
role in modeling complex object structures. Early works such as StructureNet [36] and PT2PC [37] introduced hierarchical representations via trees and graphs to encode semantic part relationships, mainly for shape generation. Later, assembly-focssed models like DGL 66 and RGL 7 extended this idea by leveraging graph neural networks to reason over both global context and local interactions during part refinement. Recent transformer-baa models further expand multi-scale reasoning. SPAFormer [38] integrates global attention with
symmetry grouping to enhance long- range dependencies, while 3DHPA [17] models part-whole hierarchies through super-part message passing based on geometric similarity. The works of [18] 36 39) also conduct feature interaction within geometrically similar part sets. In parallel, Score-PA [S] employs diffusion processes to jointly learn global and local feature distributions for generative assembly. However, prior methods commonly rely on fixed part groupings and uniform feature aggregation, which limits their ability to model both overall structure and detailed geometry, especially for repetitive or symmetric parts. We learn semantic part abstractions a data-driven way and adaptively propagate global and local context to improve structural alignment.
2

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Cross Stage
Allention
Couine Estimation
Short- Range Propagatiin
Pose Prediction
MITA
Point
MHHA
Super-Parts Parts Constraction
Shape Loss
4000
Instance Encoding
Long-Range Progagation
Byal.awaee
Coarse Pose Estimation with Super-Part
Pose Refinement
Loss Function
Figure 1: Pipeline of our CFPA. We first perform coarse pose estimation using super-parts derived via optimal transport, followed by pose refinement through cross-stage interactions. A symmetry-anve loss is proposed to improve pose accuracy while allowing structurally consistent variations.
Symmetry for Shape Understanding Symmetry is fundamental property in 3D shapes, playing a crucial role in structural reasoning and part assembly. It includes self-symmetry, where part remains invariant under transformations like rotation, translation, and reflection, and inter-part geometric similarity, where multiple parts share nearly identical shapes. Early works focused on detecting reflective and rotational symmetries for shape matching and alignment [40 [4] Later methods integrated symmetry into deep models for structural generation, such as StructureNet [6], which encodes symmetric part relationships via hierarchical graphs, well as SAGNet [45 and ShapeFlow [46), which treat symmetry as an inductive bias to guide part deformation. SDM-NET implicitly encodes symmetry in latent codes to guide part generation. Recent methods like DGL
6
Score-PA [15]. and Img- -Pg [18] group geometrically similar parts for feature interaction, while SPAFormer [38] and 3DHPA [17 PCA or bounding box similarity to enhance attention during part assembly. Symmetry is also particularly critical in deterministic fragment assembly, where it guides the precise reconstruction broken objects using symmetry- -based priors to align fractured parts [16 [9 21 These approaches typically encode symmetry as architectural prior. In this work, we model inter-part similarity to enhance representations and further propose a symmetry-awan loss that accounts for both self-symmetry and geometric similarity, enabling diverse yet valid assemblies.
3 Method
Let {Pi) denote a set of 3D part point clouds, where each part P. E Dx3 contains D points.
1N 1N Our goal is to predict the corresponding 6-DoF part poses (t) r lim1, where t E R is the translation vector and rf R is the rotational quaternion. The assembled shape is then given by
S* U (rā P. 12), with denoting the rotation operation, which can be implemented via Rodrigues' formula 48 and U denoting the union operation.
Effective 3D part assembly requires not only the precise prediction of part poses for correct component assembly, but also deep understanding of the global structure to ensure semantic consistency and generate plausible configurations. We propose CFPA (Coarse-to-FF framework that integrates structural priors, geometric reasoning, and symmetry-aweer aware supervision into the pose prediction pipeline. The overall architecture is illustrated in Figure [ begins with coarse pose estimation using semantic super-parts and dual-range feature propagation strategy (Section (.11), followed by a pose refinement stage that leverages cross-stage attention and instance encoding (Section 3.2). Additionally, we introduce symmetry-ave loss that encourages both pose accuracy and assembly diversity (Section 3.3 by exploiting intra-part and inter-part symmetries.
Part Assembly), a two-stage
3.1 Coarse Pose Estimation with Semantic Super-Part
We conduct coarse part-wise poses estimation guided by semantic super-parte which serve as high- level structural priors capturing object-level semantics. These super-parts are constructed via an optimal transport formulation that yields compact and coherent part groupings in feature space. Their representations are then propagated to individual parts through a dual-range mechanism that integrates both local and global structural cues, enabling accurate pose prediction.

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3.1.1 Semantic Super-Parts Construction via Optimal Transport
Given a set of parts {P.) we first extract part-wise features {fi] using shared lightweight PointNet [49]. To capture the high-level structural information of the object, we then construct set of semantic super-parts {hj} عرر from {fr) with M I N. These super-parts serve as compact, semantically meaningful representations that encode the global structure of the target shape.
To encourage compact and semantically consistent part grouping, we formulate the assignment of part features to super-parte parts an nngropy-regularized optimal transport problem. which provides principled and differentiable way to compute soft assignments. Specifically, we learn a transport matrix T' = {Tiz} IR x that defines soft correspondences between individual part features and super-part part representations. Each super-part is then computed as weighted aggregation of part features according to the transport matrix T:
h Σ Tyfi j M.
The transport matrix 7 can be obtained by minimizing the following entropy-regularized objective using Sinkhorn's algorithm [50]:
N ΣΣ
M
N
M Tú log Tij.
T arg min
Ci
-C
where Cip = (Jis hy) denotes the inner product cost between part feature Si and super-part feature hy, and > 0 is regularization coefficient that balances transport cost and entropy.
The resulting semantic super-parts (hr) encapsulate the global structural context implied by the input part set. These high-level representations serve as semantic anchors for subsequent dual-range feature propagation, providing informative priors for coarse part-wise pose estimation.
3.1.2 Dual-Range Feature Propagation
Leveraging the semantic super-parts, propose dual-ran aual-range feature propagation to enhance part features by incorporating the local and global structural context, supporting accurate pose prediction.
Short-Range Feature Propagation To embed localized structural priors into part features, we perform short-range propagation from the nearest semantic super-part. For each part feature fi we identify its closest super-part from {h, { via Euclidean distance in the feature space, denoted by hū- The paired representations of fa, hi are then concatenated and passed through multi-layer perceptron (MLP) to produce enhanced representation:
= MLP ([/i, ht)), 1, N.
This operation enriches part representations with structural priors from their nearest semantic super- parts. The features ) preserve local geometric detail while integrating contextual cues from nearest semantic super-part, enabling more coherent representations for downstream pose estimation.
Long-Range Feature Propagation To capture holistic structural dependencies at the global scale, introduce long-range feature propagation mechanism that integrates semantic information from all super-parts and reinforces spatial coherence through geometry-aware message passing. Specifically, we compute the -ase attention-weighee aggregation over all super-parts
M
S2B
Σ
Onj (hy Wv), with {ar)), = Softmax (((AW))(,
(4)
where WK, Wv. WQ are learnable projection matrices. This mechanism enables each part selec- tively integrate high-level semantic cues from the entire structural representation. To promote spatial coherence and suppress isolated responses, we further refine the attended features through message passing among geometrically similar parts:
S2B MP
Σ
Big.
S2B
i= 1, =1,.., N,
(5)
(ER())

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where (i) denotes the set of geometrically similar parts to i, and B:g is normalized affinity weights for the subgraph of geometrically similar parts (details in Appendix). The final long-range propagated feature is obtained by fusing original part feature Si and refined representation J52B-MP through MLP:
MLP [[ (SBBMMP)) i= 1 N.
This long-range propagation complements the short-range path by incorporating global semantic structure and promoting geometric consistency across parts, leading to more contextually informed part representations for downstream pose prediction.
3.1.3 Coarse Part Pose Estimation
Based on the short-range and long-range propagated features (ft N and {f:);= we estimate the coarse poses for individual parts. For each part, the two features are concatenated and passed through a multi-head attention (MHA) module to capture inter-pant part dependencies:
[oorse N Ti=1
MHA ( AIVE))
The resulted coarse features ( li=1 then processed by MLP to predict rigid transformation,
consisting of rotational quaternion rę and translation vector tú, and the transformed part P. is achieved:
rs. MLP(J, ((uurs)) (
P: r4 o P.+ i= 1=1,...,N N.
By integrating semantic priors from super-parts and capturing structural dependencies via dual- range propagation, the coarse stage yields an initial pose estimation that is globally coherent and semantically informed. This provides reliable initialization for subsequent pose refinement.
3.2 Pose Refinement
Building upon the coarsely transformed parts {P.) we perform pose refinement by incorporating coarse-stage semantic guidance and modeling part-level geometric relations.
Specifically, we first extract part-wise features from (P.) using shared, lightweight Point- Net [49], which produces the feature {g: J These features serve queries in cross-stage attention module, with keys and values taken from the coarse-stage features [o Ji=1 The re- sulting attended features {g.1 encode coarse-to-fine guidance for each part. To further enhance spatial coherence and structural consistency, we incorporate instance encoding {e which en- codes geometric similarity and inter-part relations following [8] (details in Appendix). Finally, we concatenate 9i, e, for each part, and apply MHA to obtain refined part feature {Reeliiee 1.V regress the final pose by MLP:
Ji=1 and
ReRliine N
Ji=l MHA (119, Gi, m))) ri
MLP (FReeliee) i= I,.,,
(9)
where r and t denote the predicted rotational quaternion and translation vector for part P., respec- tively. The final transformed part and the assembled shape are computed as:
o S = =UUP.. P. 1=1
(10)
This refinement stage enhances transformation precision by combining semantic guidance from the coarse stage with fine-grained geometric reasoning, ultimately yielding more accurate part-wise pose predictions and structurally coherent assemblies.
3.3 Training Objective
We design the training objective optimize part-level pose accuracy and global structural consistency, while allowing symmetry-consisten diversity part configurations, through a combination of part, shape, and symmetry-awant losses defined follows.
5

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Part and Shape Losses Denoting the predicted pose for part P. as F(P.) = fri,t;) accurate part placement, we supervise the predicted transformation against its ground-truth pose {r ( using standard part loss 15
(t.tt,, , to ensure
15
Purt Σ Lpoce (F(P)), GT (,,",,,)))) )),T))
(11)
with (F(P), (1 GT 1..TT = 11 1 + yde (rī o P,, o P.).
where de denotes the Chamfer distance [8]] between transformed point clouds, and 7 balances translation and rotation terms. To further encourage global consistency, we supervise the assembled shape S against the ground-truth shape geT by shape loss
[7]:
Lshape = de (S SUT).
(12)
The part and shape losses provide complementary supervision at the local and global levels, jointly promoting accurate pose estimation and structurally coherent assemblies.
Symmetry-Aware Loss To support diverse yet semantically valid part configurations, we introduce symmetry-aware loss that explicitly accommodates multiple pose solutions induced by inherent part symmetries. accounts for two cases, (1) self-symmetry where a part is indistinguishable from its flipped counterpart (e.g., chair seat symmetric under vertical flipping as in Figure 2). and (2) inter- part geometric similarity where parts with nearly identical shapes can assume interchangeable roles (e.g., chair legs). These symmetries imply that structurally equivalent assemblies may admit multiple plausible configurations. Instead of enforcing a unique canonical pose, we select the best-aligned symmetric variant during training, enabling robust and symmetry-consiseee learning.
For self-symmetry, we consider all sign-flipped variants of the ground truth pose {x.²T " denoted as {To {r." "x.")) Drez,, where E z represents flipping operation along x-, y- and z-axis having 2 = 8 possible transformations. We select the flip 7f that yields the lowest pose error with respect to the predicted pose F(P.):
self-sym
T arg min Lpose (F(P.), (1. (TT).
(13)
TE22
geo. similarity
To further account for assembly diversity arising from geomet-
rically similar parts, we identify the set Mi()) of ground-truth Figure 2: Parts with self- self-symmetry indices whose axis-aligned bounding box differences from P. and geometric similarity in chair.
below a fixed threshold. The symmetry-awar loss encourages consistency between thr predicted pose F(P;) and the most similar flipped ground-truth pose this set, where each candidate uses its own optimal self-symmetry transformation 7J obtained from Eq. (3)
Lyym
min Teose (F(P.). (r (T)). jER())
(14)
This formulation strengthens pose supervision by leveraging symmetry to accommodate diverse yet semantically valid configurations, while maintaining consistent with ground-truth transformations.
Total Training Objective We define the total training objective as weighted combination of part loss, shape loss, and symmetry-awen loss as:
Crart + LShope + AL
(15)
where À is hyper- parem--arreeter balancing contribution of symmetry-aware loss in the overall optimization.
Experiment
Implementation Details We implement CFPA in PyTorch [51] using AdamW optimizer [52] with batch size 64. Following 66 PCA and added with random noise during training. We adopt Min-of-N (MoN) strategy optimization. The model learns M-16 super-part parts and uses 8-head attention in all MHA layers. Key hyper-parameters set 1=10- y= 10, and 0 Code will be released if paper is accepted.
7 [3] [7]. all the input parts are centralized and normalized by
(53) for

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Table 1: Comparison for assembly accuracy evaluated by SCD, PA, and CA.
SCD(10 3)
PA(S) f
CA(%) f
Methods
Chair
Table
Lamp
Chair
Table
Lamp
Chair
Table
Lamp
B-Global
1.46
1.12
0.79
15.70
15.37
22.61
9.90
33.84
B-LSTM 55
2.35
1.71
0.90
8,08
10.55
24.68
10.05
18.28
30.23
DGL
0.91
0.50
0.93
39.00
49.51
33.33
23.87
39.96
41.70
Scorc-PA 15
0.71
0.42
1.11
44.51
52.78
34.32
30.32
40.59
49.07
1ET
1.34
0.89
37.60
48.86
32.86
25.44
40.35
52.75
SPAForer 38
0.67
0.38
55.88
64.38
36,39
57.60
RGL 7
0.98
0.40
1.05
48.85
55.13
35,54
30.68
41,41
50.09
3DHPA
12
0.51
0.32
0.82
63.01
64.58
33.49
48.28
58,00
62.01
Ours
0.49
0.33
0.77
69.24
68.48
36.35
49.20
58.51
63.32
Table Comparison for assembly accuracy with mPA, mCA metrics.
mPA(%) (%)
mCA(S))
Methods
Chair
Table
Lamp
Chair
Tahle
Lamp
B-Global 18 34
28.01
44.55
37.03
29.05
44.27
42.34
B-I.STM 55
14.49
15.92
43.75
18.91
31.77
43.21
DGL 6
52.85
60.46
49.17
41,62
54.94
57.52
Score-P4
58.80
65.61
49.06
43.96
53.72
62.55
IET 8
49.29
59.34
48.29
42.51
55.27
64.47
RGL 7
59.40
53.05
50.12
47.28
56.51
62.07
3DHPA
77.06
75.06
48.47
64.47
71.00
75.81
Ours
81.28
78.57
52.84
65.73
71.84
76.58
Dataset In line with prior studies [688 15 18, 54 55,, we evaluate our method on the PartNet dataset (56). focusing on the three largest object categories: Chair (6.323 shapes), Table (8,218 shapes), and Lamp (2,207 shapes). We follow the official data splits for every categories, using 70% of the shapes for training, 10% for validation, and the remaining 20% for testing.
Evaluation Metrics Following prior work 668 15 18 54 55,, we evaluate assembly performance using five metrics: (1) Shape Chamfer Distance (SCD), which measures the geometric similarity between assembled and ground-truth shapes; (2) Part Accuracy (PA), which assesses the correctness of predicted part transformations based on a predefined distance threshold; (3) Connectivity Accuracy (CA), which evaluates whether adjacent parts in the assembled shape are correctly connected within specified threshold; (4) Quality-Diversiity Score (QDS) and (5) Weighted QDS (WQDS) [15], both of which quantify the diversity and structural plausibility of generated assemblies. Detailed definitions of all metrics are provided in the Appendix.
4.1 Results and Comparisons
We evaluate assembly accuracy on Chair, Table, and Lamp categories using SCD, PA, and CA, with PA and CA computed under a Chamfer distance threshold of 0.01. As shown in Table ] CFPA achieves the best results in 8 out of cases and ranks second in the remaining one, demonstrating its effectiveness in both part assembly accuracy and structural consistency.
We also report PA and CA under varying thresholds (0.01-0.05), with performance curves in Figure and average results in Table 2 CFPA consistently outperforms others across all settings. Notably, the work 3DHPA [17], which employs geometry- bbased super-part also performs well on CA. highlighting the benefit of hierarchical structural priors. Detailed values are in the Appendix.
We further evaluate assembly diversity using QDS and WQDS. As shown in Table CFPA achieves the highest WQDS across all categories and the highest QDS on Chair, indicating its ability to generate shape diverse yet structurally valid assemblies.

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Chair
Table
Lamp
Port Awcounnco
Purt Aecuteeut
-3
35
33
Score
RCL
80
DGL
IET
Acoricy
Carrectiiity Accmmog)
Connodivlte Accaroo)
60
S
20
6.31
0.2
0.33
0.08
0.55
40
0.31
082
0.03
0.04
8.55
40
0.0L
6.82
0:02
0.04
0.05
Chamfer
Figure 3: Performance curves of our CFPA and compared models the Chair, Table and Lamp
categories under Chamfer distance threshold ranging from 0.01 to 0.05. Best viewed in color
Table 3: Comparison of assembled shape diversity evaluated using QDS and WQDS.
QDS(10-9) f
WQDS(10-9)
Methods
Chair
Table
Lamp
Chair
Table
Lamp
B B-Global 1
54
0.15
0.20
0.76
1.25
1.40
0.58
B-LSTM
3.92
1.33
3.05
1.26
0.55
2.01
DGL 6
1.69
3,05
1.84
1.35
2.97
1.73
Score PA 15
3.36
9.17
6.83
1.70
3.81
2.82
IET
3.33
6.22
1.85
2.35
3.43
RGL
5.85
7.55
6.37
2.09
3.51
3.15
3DHPA
4.42
7.15
4.67
1.90
3.80
3.16
Ours
6.71
7.28
5.65
2.75
3.92
3.74
4.2 Ablation Study
Table 4: Ablation study papper--rtts...
Effectiveness of Super-Part. CFPA predicts coarse part poses with the help of semantic super-parts constructed via optimal transport (OT) the feature space. compare ith with three variants: 1) CFPA-w/o-SP, which removes super-part guidance; 2) CFPA-GE-SP. which builds super-parts based on geometric similarity:
Methods
SCD(10 PA(%) f CA(S))
1) SPPS-
0.54
66.75
47.75
2) CFPA-GE-SP
0.53
67.60
47.97
CFPA-KM-SP
0.54
69.20
47.48
CFPA
0.49
69.24
49.20
3) CFPA-KM-SP, which uses K-means clustering [57 to build semantic super-parts based on basic part features. As shown in Table 4 super-part guidance improves performance, with OT-based construction achieving the best results over heuristic variants.
Effectiveness of Dual-Range Feature Propa- gation. CFPA incorporates both short-range and long-range feature propagation to transfer information from super-pase parts to individual parts.
Table 5: Ablation study designs in the coarse pose estimation stage and pose refinement stage.
Methods
SCD(10 3) PA(%)* CA(%) )
We evaluate three ablated variants: 4) CFPA-
CFPA-w/-SSRE
0.57
66.77
44.71
w/o-SRFP, which removes short-range propaga- tion; 5) CFPA-W/O-LRFP,, which removes long-
CFPA-W/-LRRF
0.51
68.93
47.56
6) CFPA-W/O-MP
0.60
63.60
40.28
7) CFPA-W/O-CA
0.51
67.47
44.42
range propagation; 6) CFPA-W/O-MP, which
CFPA-w/O-IE
0.55
64.81
44.44
omits feature refinement by message passing within geometrically similar parts defined in
CFPA
0.49
69.24
49.20

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IKGL
Score
HPA
Ours
Ground Truch
Table
Lamp
Figure 4: Qualitative results on the Chair, Table and Lamp categories.
Eq. (5), As shown in Table[5] all variants exhibit degraded performance, underscoring the importance of both propagation mechanisms.
Effectiveness of Operations in Pose Refinement Stage. We assess the impact of cross-stage attention and instance encoding by ablating each component with 7) CFPA-w/oCA., which removes cross-stage attention; 8) CFPA-w/O-IE, which removes instance encoding. As shown in Table 5 both variants yield reduced performance, confirming the effectiveness of incorporating coarse-stage guidance and geometric relationships.
Effectiveness of Symmetry-Aware Loss. The symmetry-aware loss addresses both self- symmetry and geometric similarity among in- terchangeable parts. We ablate three variants: 9) CFPA-w/O-SS, which removes self-symmetry supervision; 10) CFPA-w/O-GS, which removes constraints on geometrically similar parts; 11) CFPA-w/O-SL,, which disables the symmetry- aware loss entirely. As shown in Table removing either component degrades performance, confirm- ing the effectiveness of symmetry-awann supervision.
Table 6: Ablation study symmetry-aware loss.
Methods
SCD(10 34 PA(%)
CA(%) 1
9) CFPA-w/O-SS
0.51
67.86
47.24
10) CFPA-w/o-GS
0.51
68.98
47.49
11) CFPA-w/O-SL
0.52
67.51
47.17
CFPA
0.49
69.24
49.20
4.3 Qualitative Results
Figure presents the qualitative results on Chair, Table and Lamp categories. Our method pro- duces more reasonable and structurally coherent assemblies compared to previous methods. The generated shapes by our CFPA demonstrate as- sembly diversity arising from self-symmetric components and geometrically similar parts, while preserving overall structural validity.
Coarsc Pose Extination
Refremmnt
Estimetion
Figure 5 illlstrates the coarse-to-fine assembly process. Starting with PCA-normalized parts as inputs, the Coarse Pose Estimation stage es- timates intiill part poses (2nd column). In the Pose Refinement stage, part poses are refined to produce more accurate and structurally coherent assembly configurations (3rd column), leading to final shapes that closely match ground truth.
Eutmative
Refremrree
Irpute
Cranc Aseembby
Final Assamblyy
Ground Trull
Figure 5: Visualization of coarse-to-fine progress.
More experimental details, ablation studies, and visualization provided in the Appendix.

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Conclusion
We propose CFPA, a coarse-to fine framework for 3D part assembly that integrates semantic super- parts, dual-range feature propagation, and symmetry-awand supervision. By jointly modeling global structure and geometric symmetry, CFPA enables accurate and diverse part assemblies. Extensive experiments show that it achieves tate-of-theeart performance in assembly accuracy, structural consistency, and diversity across multiple categories. In future work, we plan to extend CFPA to fragment reassembly and explore unsupervised learning enhance robustness on unseen parts.
Limitation CFPA is designed for part-level assembly with semantically meaningful components and is not directly applicable to fragment reassembly involving irregular or incomplete parts. Extending the framework handle such cases is a promising direction.
Impact Statement This work contributes 3D part assembly by introducing coarse-to to-fiee framework that unifies semantic abstraction and symmetry-awan reasoning. By explicitly modeling hierarchical structure and geometric symmetry, our method improves both accuracy and diversity in assembly tasks. The proposed approach can benefit downstream applications in 3D design, CAD modeling, and intelligent robotic assembly. This work poses no ethical concerns.
Acknowledgments and Disclosure of Funding
This work was supported by NSFC with grant numbers 62306167, 12125104, 12426313, and project ZR2024QA161, ZR2023QG143 supported by Shandong Provincial Natural Science Founda- tion. is also funded by National Social Science Fund Project (25CJY023).
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Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, or originality the research, declaration is not required.
Answer: [NA]
The core method development in this research does not involve LLMs any important, original, or non-standard components. There is no evidence that LLMs were used in way that affects the core methodology. scientific rigorousness, or originality of the research.
Justification:
Guidelines:
The answer NA means that the method development in this research does involve LLMs as any important, original, or non-standard components.
Please refer to our LLM policy (https: http://eeeuu..eeeeeee cc/Conffrrences/2255 /LLM) for what should or should not be described.
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Appendix
A Model Details
Physical meaning & intuitive interpretation of super-part from OT Physically, as Eq. (1), each super-part is weighted aggregation of basic part features learned via optimal transport, forming compact prototypes that encode multiple related parts. Intuitively, these super-parts group function- ally geometrically similar parts into semantic clusters, providing mid-level abstractions without predefined hierarchies.
Details on Geometrically Similar Part Set and Normalized Affinity Weights In Eq. (5) of the main paper, we construct a graph to facilitate message passing among geometrically similar parts, thereby enhancing feature consistency across structurally related components. In this graph, each node represents an individual part, and edges are formed based on geometric similarity. This process involves two steps: (1) constructing the sets of geometrically similar parts, and (2) computing normalized affinity weights.
To determine geometric similarity, we follow [6] and compare the axis-aligned bounding box sizes of each part. Two parts are considered similar if the absolute difference their bounding box sizes below a predefined threshold (set to 0.1). These geometrically similar parts, such as chair arms legs, are grouped into fully connected subgraphs to enable dense information exchange. Parts that do not belong to any similarity sets are treated structurally unique and form isolated subgraphs; these subgraphs are fully connected internally to ensure message propagation. Figure A. visualizes an example of the graph resulting from chair model.
For each subgraph, we assign uniform affinity weights guide message passing. For given part P; and its geometrically similar part P P)E0()). compute the normalized affinity weight as:
8i
Vg E (((1),
(16)
1((1)'
where [ denotes the number of parts in the geometrically similar set for part P.. This uniform weighting avoids bias toward any individual part and ensures stable and balanced feature aggregation within each subgraph.
Graph for Chair
Subgraph
Subgraph
Subgraph
Back Right Leg
Book
Left
Prost Lef
Laft Anm
Right Arm
Frone Right Lag
Figure A.1: Graph for chair. Nodes represent individual parts, and edges denote connectivity based on geometric similarity. Subgraphs and contain geometrically similar parts (c.g.. arms, legs) which are fully connected to facilitate message passing. Subgraph 2 consists of geometrically isolated parts (e.g., back, cushion, seat base) that do not belong to any geometrically similar part set, and they fully connected to enable massage passing among structurally unique parts.
Details on Pose Retinement Stage by incorporating cross-stage attention and instance encoding, enabling more accurate and structurally consistent pose estimation.
The pose refinement stage enhances part-level representations
The cross-stage attention mechanism utilizes coarse features (f[Coars)) Ji=l keys and values, and part features (g, N. queries, where all feature vectors are of dimension 256. We implement
21

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multi-head attention (MHA) with 8 heads operating in 32-dimensional subspace using scaled dot-product attention.
For instance encoding, following 8 we employ a 40-dimensional embedding { as a unique instance encoding vector for part formed by concatenating inter-class encoding that uniquely identifies each individual part and an intra-class encoding that establishes relationships among geometrically-simiee parts.
For pose prediction, we first pass the concatenated features [9 e;] through MHA with 8-head to facilitate part-to- sto-part information exchange. The output features are then processed by multilayer perceptron (MLP) with dimensions [1024, 512, 7] using ReLU activations, where the final layer predicts rotational quaternion and translation vector for each part.
Details on Lightweight PointNet The input part features are extracted using a shared PointNet [49 applied to the part point clouds. An MIP (with dimensions [64, 256, 512, 1024) is first applied to transform the 3-dimensional point positions into 1024-dimensional features, and then a global max- pooling operation is applied to aggregate point-level features into compact part-wise representation, which is further processed through three fully connected layers (with dimensions [1024, 512, 256]) to obtain a final 256-dimensional embedding for each part.
Computational cost of the proposed components To evaluate the computational of our proposed components, we report key metrics for single forward pass with batch size of 64, including the number of parameters (Million, M), GPU memory usage (GB), forward time (ms), and GFLOPS, We analyze the CFPA model and its variants, each excluding specific components as: 1)-2) STPA-w/o-refine/cconne MHA that exclude the multi-head attention
pose refinement/coarse pose estimation stage; 3) CFPA-w/o-OT that removes the OT-based super-part construction; 4)-5) CFPA-W/O-SRFPII.RU that remove the short-/long-range feature propagation; 6) CFPA-w/O-MP that removes the message passing in long-range feature propagation; 7) CFPA-w/o-CA that removes the cross-stage attention; 8) CFPA-W/-SLL that removes the symmetry-aware loss. also report the computational cost of the bascline method that removes all of the above components.
As shown in Table A.1 compared to the full CFPA model. Notably, some of these components are specifically designed to operate based on the relationships between parts and super-parts rather than directly on point clouds, with the maximum number of parts limited to 20 and super-parts to 16. This design inherently requires only small computational cost. Additionally, certain components, such as OT, short-range feature propagation, and message passing, do not introduce any learnable parameters, further contributing to their relatively low computational cost.
removing these components leads to reduction in computational cost
Table A.1: Computational cost comparisons.
Method
(Mara.(M)
GPU Memory(GB)
Forward time(ms)
GFLOPS
baseline
21.33
24.05
641.36
86.22
I) CFPA-w/orefine MHA
22.90
24.28
674.80
86.26
2) CFPA-w/o-coarse MHA
25.14
26.72
772.09
86.30
3) CFPA-w/O-OT
25.89
26.80
657.87
86.34
4) CFPA--/O-SRFP
25.89
26.36
804.91
86.34
5) CFPA-W/O-LRTP
25.76
24.68
778.68
86.33
6) CFPA-w/O-MP
25.89
24.60
791.31
86.34
7) CFPA-W/O-CA
25.63
25.71
698.05
86.33
8) CFPS-w/O-SL
25.89
26.60
802.72
86.34
CFPA
25.89
27.04
806.80
86.34
B Experiment Details
The model trained for 500 epochs using a batch size of 64 across NVIDIA RTX 4090 GPUs. We adopt the AdamW optimizer with initial learning rate of 7.5 10-5 and weight decay
22

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of 1 x 10-4. A cosine annealing learning rate schedule is applied with a decay factor of 100 to progressively reduce the learning rate over the training process.
Each input 3D part is represented as a point cloud containing 1,000 points, which are sampled by Farthest Point Sampling [58]. To ensure consistency and invariance to translation and rotation, all parts are pre-aligned to canonical coordinate system by Principal Component Analysis (PCA).
B.1 Evaluation Metrics
We evaluate our method using five commonly adopted metrics in part assembly tasks: Shape Chamfer Distance (SCD), Part Accuracy (PA), Connectivity Accuracy (CA), Quality-Diversic Score (QDS), and Weighted Quality-Diversity Score (WQDS). The definitions of these metrics are provided below.
Shape Chamfer Distance (SCD) The Shape Chamfer Distance (SCD) quantifies the geometric discrepancy between two point clouds by computing the average nearest-neighbor distance between points in each set. Formally, given two point sets X' and Y, the Chamfer distance is defined as:
de 37)
Σ
min || - v11 + Σ
min || - -v12
(17)
Mey
ZEX
BEY
In our case, SCD is computed between the predicted assembled shape S and the ground truth shape SGT, i.e., (S" SGT).
Part Accuracy (PA) It evaluates the proportion of parts whose transformed point clouds, using the predicted transformations, yield accurate geometric alignment with their ground-truth counterparts, as measured by the Chamfer Distance. Specifically, is defined as:
N
1 N
PA
Σ 1 (de (T (P.), (P)),T(((P)) (P.) < TT))
(18)
where 1(-) indicator function. T(P:) and ( represent the transformed part point clouds using the predicted and ground-truth transformations, respectively. d, represents the Chamfer distance, and Tp the predefined threshold.
Connectivity Accuracy (CA) It measures the structural correctness of pairwise part connections in the assembled shape. For each contact point pair {cīy, CyJ in the ground-truth object space, where cy is the point on part i closest to part j and Gj. is the corresponding nearest point on part j to part i. we identify their corresponding coordinates in the canonical part spaces (normalized using PCA) as {cij. Ctyl }. The predicted transformations Tú, Ty are then applied to these canonical points, and their distance is measured in the predicted assembled space. The connectivity accuracy defined as:
CA
Σ (cire
1 (d TT (c5x)) TT),
(19)
C
where C denotes the set of all contact point pairs in the assembly, d is the Euclidean distance, and To the predefined threshold.
Meanwhile, following [17], we apply mean part accuracy (mPA) and mean connectivity accuracy (mCA) for more comprehensive evaluation as follows:
1
mPA-
Σ PA, mCA
E
Σ CA,
(20)
TEE
T.E5
where E (0.01, 0.02, 0.03, 0.04, 0.05) represents predefined set of Chamfer distance thresholds.
Quality-Diversitn Score (QDS) Following [1 17 we use QDS to jointly evaluate the structural quality and geometric diversity of generated assemblies, which is defined as:
N
QDS
Σ de (S; (CA(S;) > T.)) 1 (CA(S)) > Ty): 1==1
(21)
No
where 1(.) is indicator function, and (.).) is Chamfer distance. The threshold Ty is set to 0.5. QDS incorporates quality constraints by excluding pairs with low assembly quality, simultaneously evaluating both diversity and quality of the generated shapes.
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Weighted Quality-Diversife Score WQDS is the weighted QDS with the connectivity accuracy, prioritizing assembled shapes with qugh-quality connections between parts:
WQDS = N2
Σ de (3) CA (5)) CA (5)) (CA (S) (CA Tq). (22)
B.2 Experimental Results under Multiple Thresholds
Tables B.I.B.B.. report detailed numerical results corresponding to Figure 2 in the main paper, present- ing PA and CA for our CFPA and several state-of-the-an baselines across range of Chamfer distance thresholds (0.01-0.05) on the Chair, Table, and Lamp categories. The consistently superior perfor- mance of CFPA across all thresholds and object classes highlights its robustness and effectiveness in achieving accurate and structurally coherent part assemblies.
Table B.1: Comparisons on Chair category PA CA at Chamfer distance thresholds of 0.01 to 0.05.
PA(S)
CA(S) f
Method
0.01
0.02
0.03
0.04
0.05
AVG
0.01
0.02
0.03
0.04
0.05
AVG
B-Global 18 54
15.70
22.02
28.72
34.74
38.86
28.01
9.90
23.04
31.06
38.00
43.26
29.05
B-LSTM 55
8.08
12.36
15.46
17.39
19.14
14.49
10.04
15.29
19.58
23.20
26.44
18.91
DGL 0
39.00
49.45
55.25
58.96
61.30
52.85
23.87
35.50
44.01
50.35
55.12
41.62
RGL /
56.02
64.71
65,41
59.40
30.68
54.80
59.62
47.28
Score-PA 15
44.51
56. 14
61.33
64.81
67.11
58.80
30.32
38.63
46.66
52.36
56.58
43.96
IET 8
37.60
38.37
53.65
57.43
59.39
49.29
25.44
37.46
44.97
50.14
54.56
42.51
3DHPA
63.01
82,93
84.71
77.06
48.28 18.28
67.16
71.80
75.12
64.47
69.24
86.36
88.10
81.28
49.20
61.66
68.79
73.06
75.95
65.73
Table B.2: Comparisons on Table category of PA CA at Chamfer distance thresholds of 0.01 to 0.05.
PA(%)
CA(3)) f
Method
0.01
0.02
0.03
0.04
0.05
AVG
0.01
0.02
0.03
0.04
0.05
AVG
B-Global
BN 54
15.37
43.56
49.77
54.69
59.36
44.55
33.84
35.98
44.10
50.58
$6.86
44.27
B-LSTM 55
10.55
13.80
16.10
18.55
20.58
15.92
18.28
26.27
32.64
38.21
43.43
31.77
DGL G
49.51
56,21
62.44
66.74
70.28
60.46
39.96
50.03
57.68
62.72
66.50
54.94
RGL V
55.13
73.65
75.90
53.05
$1.80
58.60
64.19
66.57
56.51
Score-PA 15
52.78
61.68
67.38
71.48
74.72
65.61
40.59
47.96
55.29
60.16
64.62
$3.72
IET 8
48.86
55,99
60.64
64.37
66.84
59.34
40.35
50.66
57.23
62.26
65.84
55.27
3DHPA
64.58
72.62
79.69
81.89
75.06
58.00
73.23
77.01
79.79
71.00
68.48
76.17
80.10
83.07
85.04
78.57
58.51
77.88
80.24
71.84
Table B.3: Comparisons on Lamp category of PA / CA at Chamfer distance thresholds 0.01 to 0.05.
PA(%) f
CA(S) f
Method
0.01
0.02
0.03
0.04
0.05
AVG
0.01
0.02
0.03
0.04
0.05
AVG
B-Global
13 54)
22.61
31.38
38.85
42.56
49.77
37.03
18.60
35.79
46.13
52.42
58.74
42.34
B-LSTM 55
29.59
38.80
45.78
50.13
54.47
43.75
28.31
38.83
44.85
49.45
54.60
43.21
DGL G
33.33
44.83
51.45
56.71
59.91
49.17
41.70
50.60
60.36
67.23
71.08
57.52
RGL 7
35.54
46.40
51.68
56.95
60.05
50.12
50.09
56.23
64.43
67.53
72.08
62.07
Score-PA
15
34.32
44.71
51.04
56.58
60.
49.06
49.07
$7.24
65.42
71.38
76.29
62.55
IET 8
32.86
43.15
49.56
56.14
59.73
48.29
52.75
57.65
66.52
70.87
74.56
64.47
3DHPA
33.67
42.42
49.97
55.89
60.41
48.47
62.01
72.32
78.09
82,13
84.52
75.81
36.35
47.81
54.91
60.15
64.68
52.84
62.45
74.02
78.64
82.67
85.12
76.58
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B.3 Details on Ablation Study in the Main Paper
Details for CFPA-W/o-PP In Table of the main paper, we conduct an ablation study to assess the contribution of semantic super-parts In the CFPA-w/o-PP variant, the coarse pose estimation stage performed without leveraging super-paa part. Instead, the dual-range feature propagation is applied directly to the raw part-level features extracted from the input point clouds by PointNet [49]
Details for CFPA-GE-SP In the experiment of CFPA-GE-SP, we construct the super-pan based on geometric similarity, and the parts with similar axis-aligned bounding boxes are considered to belong to the same super-part. The feature of each super-part is obtained by applying max- max-pooling over the features of its constituent parts which are extracted by PointNet 449
Details for CFPA-KM-SP For the model of CFPA-KM-SP. we employ K-means clustering (57 on all the part features extracted by PointNet [49]. The process begins by randomly initializing M clustering centroids and then assigning each part feature to its nearest centroid with Euclidean distance. Each centroid then itcratively updated by averaging the features assigned to it.
Details for CFPA-w/O-SS In Table 6 of the main paper, we perform an ablation study to evaluate the impact of the symmetry awarre loss, particularly its treatment of self-symmetry and inter-pant geometric similarity. In the CFPA-w/o-SS variant, we disable the self-symmetyy supervision and retain only the constraint on geometrical similar parts. Specifically, the symmetry- loss is modified to compare the predicted pose of each part against the ground-truti poses of geometrically similar counterparts, defined as:
min ( (ry .t,
(23)
(EQ(()
where 12(1) denotes the set of parts geometrically similar P,, and F(P,) is the predicted pose of part P.. This variant allows us to isolate and assess the contribution of self-symmetry modeling within the overall symmetry-aware supervision.
Details for CFPA-w/O-GS In the CFPA-w/O-GS variant, we ablate the geometric similarity compo- nent of the symmetry-awen loss while only retaining supervision celf-symmetry. Specifically, only symmetric transformations for ground-truth part are considered during training. The loss is:
N
Caol.Gs GS Sym
min (F(.)) TEZ?
GTT).. (1 .44
(24)
where 2 represents the set of eight possible axis-flipping transformations, and To fr (((T) denotes the flipped version of ground-truth part under transformation This formulation evaluates the effect of modeling self-symmetry isolation, without considering inter-part geometric similarity.
C More Ablation Studies
Effectiveness of Super-Pat Numbers. The number of semantic super-parts (M) is a critical factor in the performance of CFPA. A small M may group functionally distinct parts, resulting the loss of structural detail, and a large M may overemphasize local features while compromising global coherence. The results on Chair category (Figure C.I indicate that the optimal performance is achieved at M = 16.
in Loss Function. The hyper-parameter X in the overall loss modulates the influence of the symmetry-awar loss term relative to the part-level and shape-level supervision objec- tives. To investigate its effect, we conduct an ablation study on the Chair category by varying À and reporting the corresponding
Effectiveness of
Table C.I: Ablation study on hyper-parameteer in loss.
X
SCD(10-3)
PA(%)
CA(%)
0.1
0.49
69.24
49.20
0.51
68.86
47.85
10
0.52
69.45
47.08
performance in Table C.T The results indicate that setting À 0.1 yields the best performance.
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Part Accuracy (PA)
Connectivity Accuracy (CA)
Shape Chamfer Distance (SCD)
80
60
0/6
Connectivity Accuracy11))
Shage Chamfer Distance :10
Port Accuracy(%s)
0.53
10
53.02
50
25.0
41/02
0.90
65-
45
0.45
0.40
12
16
Number super-parts
Number super-parts
Number of super-parts
Figure C.I: Performance curves in PA, CA and SCD for CFPA with varying super-parts numbers.
Effectiveness of Graph Construction based on Geometric Similarity In Eq. (5), mes- sage passing performed on a part graph constructed according geometric similar- ity, as described in Section Parts with sim- ilar axis-aligned bounding boxes grouped into subgraphs, while geometrically unique
Table C.2: Ablation study on graph construction.
Methods
SCD(10
PA(%) f CA(%)
12) CFPA-WO-UPC
0.54
68.05
46.77
13) CFPA-FC-UP
0.53
68.78
47.53
CFPA
0.53
68.48
48.48
parts without similar counterparts also grouped into fully connected subgraph. To evaluate the effectiveness of this graph construction strategy. we compare two alternative designs: 12) CFPA-w/o- UPC. where geometrically unique parts remain isolated and do not communicate with other parts; 13) CFPA-FC-UP. where each unique part is fully connected to all other parts. The results presented in Table C.2 validate the effectiveness of our proposed balanced graph construction. By preserving geometric similarity through subgraphs and modeling functional relationships among unique parts, CFPA achieves the best performance.
Performance of the proposed symmetry-aware loss other baselines To evaluate the general- ization ability of the proposed symmetry-aween aware loss, we conducted experiments by integrating it into various baseline methods. As shown in Table C.3 the models equipped with our symmetry-aver loss (* -w/-SL, where represents the baselines) achieve improved performance.
These results demonstrate that the symmetry-avee but also generalizable across diverse baseline methods. This further validates its robustness and applicability in 3D part assembly tasks.
loss is not only effective within framework
Table C.3: Comparison different baselines with our symmetry-aware loss.
Method
SCD4
PA(%)*
CA(%)1
QDS(10- 5)t
WQDS(10-5) 55t
B-Global 18
54
1.46
15.70
9.90
0.15
1.25
B-Global-w/-SI
1.21
18.10
12.92
0.43
1.21
B-LSTM 55
2.35
8.08
10.05
3.92
1.26
B-LSTM-W/SSL
2.35
9.34
11.25
4.03
1.33
DGL 6
0.91
39.00
23.87
1.69
1.35
DGL-w/-SL
0.87
41.77
29.51
1.66
1.73
RGL 7
0.98
48.85
30.68
5.85
2.09
RGL-w/-SL
0.92
49.15
33.27
5.91
1.55
Score-PA Sare-PA [15]
0.71
44.51
30.32
3.36
1.70
PA-w/-SL
0.65
43.77
31.32
5.11
1.41
IET 8
1.34
37.60
25,44
3.33
1.85
IET-w/-SL
1.21
38.53
27.21
3.33
1.93
3DHPA 17
0.51
63.01
48.28
4.42
1.90
3DHPA-W/SL
0.51
66.34
47.21
4.82
2.01
26

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D More Visualization Results
We provide more visualization results for instances from the Chair, Table, and Lamp categories in Figure D.I] Figure|D.2 and Figure [.3] respectively. Compared previous methods, our model generates assembly results that align more closely with ground-truth configurations, indicating superior accuracy. In particular, our approach effectively captures diverse assembly variations (c.g.. different arrangements of chair and table legs), showcasing its robustness and adaptability in the 3D part assembly task.
FEFfE
EEEEE
DGL
FEEE
Score
HPA
Ours
Ground Truth
Figure D.1: Qualitative results on the Chair category.
DGL
Score
HPA
Ours
Ground Truth
Figure D.2: Qualitative results on the Table category.
27

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DGL
Score
HPA
Ground Truth
Figure D.3: Qualitative results on the Lamp category.
28


Reviews:
[{"review_id": "hgoSqYinWp", "reviewer": "Reviewer_jLDf", "summary": "This paper introduces CFPA , a two-stage deep learning framework for 3D shape assembly that predicts  poses for individual parts to reconstruct coherent 3D shapes. The key innovation lies in constructing semantic super-parts through optimal transport to capture high-level object structure, followed by dual-range feature propagation that integrates both local and global structural information. The method addresses critical challenges in part assembly including complex geometric dependencies, symmetry handling, and the need for both precise local reasoning and global structural understanding. Experimental results on the PartNet benchmark demonstrate state-of-the-art performance across Chair, Table, and Lamp categories, achieving superior assembly accuracy, structural consistency, and assembly diversity compared to existing methods.", "questions": "- What is the physical meaning and intuitive interpretation of the super-part features constructed via optimal transport formulation? How do these semantic super-parts conceptually differ from simpler global feature aggregation approaches[1] or utilize graph neural network-based feature aggregation and message passing between different parts[2], what are the fundamental theoretical advantages and principled design motivations behind constructing these intermediate semantic super-parts?\n\n- While the empirical results demonstrate the effectiveness of optimal transport-based super-part construction, could the authors provide theoretical analysis or intuitive explanations for why the entropy-regularized optimal transport formulation is particularly well-suited for this hierarchical part grouping task? And why inner product can serve as a great cost function ? A deeper theoretical understanding of the underlying mechanisms and design principles would significantly strengthen the paper's contribution beyond purely empirical validation.\n\n- The proposed symmetry-aware loss enumerates all eight axis-aligned reflection transformations and selects the one with minimal pose error. However, since reflections are not elements of the SE(3) group, this exhaustive search may introduce unintended chirality issues, potentially producing assemblies with inverted handedness. Moreover, real-world part point clouds can assume arbitrary orientations and need not align with the canonical axes; it is unclear whether the fixed set of eight reflections suffices to capture all symmetry variants under arbitrary poses. Finally, this approach incurs additional computational overhead due to repeated network forward passes for each candidate reflection. Could the authors provide:\n\n  1. A theoretical discussion on how reflecting parts outside SE(3) affects the preservation of chirality and whether any mechanisms ensure consistency of handedness across the assembled shape?\n\n  2. Empirical or analytical justification that the eight axis-aligned reflections are sufficient to cover the full space of self-symmetries for arbitrarily oriented part point clouds?\n\n  3. An evaluation of the added computational cost from multiple forward passes, and potential strategies (e.g., grouping symmetric variants or embedding symmetry into the architecture) to mitigate this overhead while preserving symmetry-aware supervision?\n\n- In Eq.14, there may exists a typo, the subscript $j$ should be $g$\n\n- In Eq.14, could the author clarify why your training objective minimizes the pose differences between geometrically similar parts, rather than encouraging them to occupy distinct positions? Intuitively, one would expect interchangeable components—such as the four legs of a chair—to be driven toward different spatial locations instead of collapsing into the same pose. What is the motivation for favoring minimal pose discrepancy among symmetric parts, and have you considered an alternative formulation that explicitly promotes diversity in their placements?\n\n\n\n[1] Wu, Ruihai, et al. \"Leveraging se (3) equivariance for learning 3d geometric shape assembly.\" *Proceedings of the IEEE/CVF International Conference on Computer Vision*. 2023.\n\n[2] Scarpellini, Gianluca, et al. \"Diffassemble: A unified graph-diffusion model for 2d and 3d reassembly.\" *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*. 2024.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths And Weaknesses\n\n#### Strengths\n\n- **Novel Two-Stage Framework with Semantic Abstraction** The paper introduces a principled coarse-to-fine architecture that first constructs *semantic super-parts* via an entropy-regularized optimal transport formulation and then refines part poses through cross-stage attention and instance-level encoding. This dual-stage design effectively balances global structural understanding with precise local geometric reasoning\n- **Comprehensive Experimental Validation** Extensive experiments on the PartNet benchmark across Chair, Table, and Lamp categories demonstrate SOTA performance in assembly accuracy (SCD, PA, CA), structural consistency, and assembly diversity (QDS, WQDS). The ablation studies systematically quantify the contribution of each component, highlighting the author’s reasons for choosing each module.\n\n#### Weaknesses\n\n- **Insufficient Theoretical Foundations for Design Choices** While the authors provide comprehensive empirical validation demonstrating the effectiveness of each proposed module, the paper would benefit significantly from theoretical analysis or intuitive explanations underlying the design principles and mechanisms. For instance, the optimal transport formulation for semantic super-part construction, the dual-range feature propagation mechanism, and the cross-stage attention design would all benefit from theoretical justification or principled intuition beyond empirical effectiveness. This theoretical gap potentially constrains the generalizability and interpretability of the proposed framework to new scenarios or domains.\n- **Limited Novelty Claims Regarding Symmetry-Aware Loss Terms**  The symmetry-aware loss formulation presented in this work appears to have been explored in prior literature. For example, works such as Manual-PA[1] and other contemporary studies have previously addressed the handling of part self-symmetry and inter-part geometric similarity through specialized loss terms. The reflective symmetry loss and geometric similarity constraints have been incorporated into part assembly frameworks to address pose ambiguities arising from symmetric components. To substantiate the claimed contributions in symmetry-aware modeling, the authors should provide more rigorous comparative analysis or experimental validation demonstrating the specific advantages and innovations of their proposed symmetry-aware loss formulation compared to these existing symmetry-handling approaches. This could include detailed ablation studies comparing different symmetry loss formulations, theoretical analysis of the proposed approach's superiority, or empirical evidence showing improved performance over prior symmetry-aware methods.\n\n- **Computational and Memory Overhead** The construction of semantic super-parts via Sinkhorn’s algorithm, dual-range propagation, and cross-stage attention introduces multiple heavyweight modules and hyperparameters (e.g., number of super-parts, entropy regularization), potentially limiting scalability to larger part sets or high-resolution meshes. Additionally, in the self symmetry part, the proposed method need to compute 8 times of forward propagation, which seems quite heavy.\n\n[1] Zhang, Jiahao, et al. \"Manual-PA: Learning 3D Part Assembly from Instruction Diagrams.\" *arXiv preprint arXiv:2411.18011* (2024).", "was_revised": true, "final_justification": "This paper addresses an important problem in 3D vision and robotics, namely multipart assembly. It introduces CFPA, a two-stage deep learning framework for 3D shape assembly that predicts poses for individual parts to reconstruct coherent 3D shapes. The authors design several modules tailored to the characteristics of this problem and provide extensive experimental evidence demonstrating their effectiveness. The rebuttal is thorough and addresses most of my concerns. Therefore, I recommend that this paper be accepted.", "rebuttal": "***Q1: Physical meaning & intuitive interpretation of super-part from OT.***\n\n**Physically**, as Eq.(1), each  super-part is a weighted aggregation of basic part features learned via optimal transport, forming compact prototypes that encode multiple related parts. **Intuitively**, these super-parts group functionally or geometrically similar parts into semantic clusters, providing mid-level abstractions without predefined hierarchies.\n\n**Visualization:**  Figures are not allowed in rebuttal. We visualize the correspondence between parts and their nearest super-parts identified by transport map $T$. Figures show: 1) parts with similar functions (e.g., chair legs, backs & seats) tend to cluster within the same super-part; 2) unique or uncommon parts (e.g., decorative elements) are tend to be assigned to one specific super-part; 3) the super-parts exhibit semantic consistency across shapes, consistently grouping functionally similar parts.\n\n***Q2: Difference of super-parts from  global [1] or GNN-based aggregation [2]. Motivation & advantage of intermediate super-parts.***\n\n**Difference:** Unlike global feature aggregation [1] that compresses part information into single vector and loses intermediate structures, our super-parts preserve mid-level semantics by clustering parts into coherent groups. Compared to GNN-based method [2] that model inter-part relations via message passing but may suffer from over-smoothing, we build hierarchical representations to encode structural relationships, bridging local details and global organization.\n\n**Motivation & advantage:** Object parts often exhibit similarities in appearance or functionality, naturally forming semantic groups. These relationships provide a foundation for coarse-to-fine approach in part assembly, where intermediate representations help progressively refine local details into coherent structure. This hierarchical design enhances semantic consistency across parts and guides precise part assembly, as validated by ablation study 1)-3) in manuscript.\n\n[1] Wu, R., et al. Leveraging se(3) equivariance for learning 3d geometric shape assembly.\n\n[2] Scarpellini, G., et al. Diffassemble: a unified graph-diffusion model for 2d and 3d reassembly.\n\n***Q3: Why use entropy-regularized OT & inner product.***\n\n**OT** offers a flexible, probabilistic alignment of parts to super-parts, enabling soft associations compared to rigid clustering or geometry-based grouping. **Entropy regularization** ensures smooth assignments, avoids sparsity, and enables efficient Sinkhorn-based computation.\n\nReplacing OT with k-means or geometric grouping (ablation 2)-3) in manuscript), or replacing entropy regularization with attention-based map as in [3] (CFPA-w/-Att.-map in Table R1-1), results in worse performance, highlighting effectiveness of entropy-regularized OT.\n\n**Inner product** measures compatibility between part and super-part by capturing directional similarity in feature space. Its linearity ensures computational efficiency and stability during training. \n\nReplacing  inner product with  $L_2$ distance-based cost function (CFPA-w/-$L_2$-dis. in Table R1-1) resulted in worse performance,  validating its suitability for this task.\n\nTable R1-1. Results on Chair\n\n||SCD($10^{-2}$)↓|PA(\\%)↑|CA(\\%)↑|QDS($10^{-5}$)↑|WQDS($10^{-5}$)↑|\n|---|:---:|:---:|:---:|:---:|:---:|\n|CFPA-w/-Att.-map|0.50|**69.87**|49.07|5.87|2.60|\n|CFPA-w/-$L_2$-dis.|0.51|69.23|48.85|5.08|2.14|\n|CFPA|**0.49**|69.24|**49.20**|**6.71**|**2.75**|\n\n[3] Xin W., et al. Learning generalizable part-based feature representation for 3d point clouds.\n\n***Q4: Physical meaning & intuitive interpretation of dual-range feature propagation & cross-stage attention.***\n\n**Physically**, **Dual-range feature propagation** allows each part to capture both global semantic structure (Eqs.(3-4)) and local geometric details (Eq.(5)), bridging global and local contexts. **Cross-stage attention** leverages coarse-stage semantic cues to refine part features, enabling more accurate pose estimation and consistent assembly.\n\n**Intuitively**, **Dual-range feature propagation** enables each part to integrate local details with global structure, while **cross-stage attention** ensures feature refinement maintains semantic consistency across stages.\n\n***Q5: Analysis/validation on symmetry-aware loss vs other symmetry-handling methods.***\n\n**Analysis**: IET [5] use Chamfer Distance (CD) and instance encoding to address self-symmetry and distinguish similar parts, Li et al. [6] and Manual-PA [4] use Hungarian algorithm for one-to-one matching, with Manual-PA further introducing InfoNCE loss to reduce matching uncertainty. **In contrast**, we minimizes CD over all flipped variants (Eq.(13)) to explicitly model multiple symmetric solutions and avoid bias from uneven point sampling. For geometrically similar parts, we relax strict matching (Eq.(14)) to allow interchangeable roles, enabling structurally equivalent assemblies.\n\n**Validation**: Replacing symmetry-handling loss in Eq.(15) with alternatives from [4–6]  (CFPA-w/-SL in [4]/[5]/[6] in Table R1-2) improves performance over  baseline without symmetry handling (CFPA-w/o-SL). CFPA with our symmetry-aware loss achieves best results, demonstrating the benefit of explicitly modeling symmetric configurations.\n\nTable R1-2. Results with symmetry-handling losses\n||SCD($10^{-2}$)↓|PA(%)↑|CA(%)↑|QDS($10^{-5}$)↑|WQDS($10^{-5}$)↑|\n|----|:--:|:--:|:--:|:--:|:--:|\n|CFPA-w/o-SL|0.52|67.51|47.17|4.60|1.99|\n|CFPA-w/-SL in [4]|0.51|68.72|44.87|4.80|2.02|\n|CFPA-w/-SL in [5]| 0.52|68.74|48.42|4.86|2.06|\n|CFPA-w/-SL in [6]|0.50|69.17|48.35|5.23|2.22|\n|**CFPA**|**0.49**|**69.24**|**49.20**|**6.71**|**2.75**|\n\n[4] Zhang, J., et al. Manual-PA: Learning 3D Part Assembly from Instruction Diagrams.\n\n[5] Zhang, R., et al. 3d part assembly generation with instance encoded transformer.\n\n[6] Li, Y., et al. Learning 3d part assembly from a single image.\n\n***Q6: Are 8 reflections sufficient? How reflection outside SE(3) affects chirality preservation? Computational cost for multiple forward passes and potential strategies.***\n\n**Sufficiency** of the eight axis-aligned reflections is guaranteed because all input parts are pre-aligned using a chirality-preserving PCA method as in DGL [7], before being fed into the model.\n\n**Chirality** is preserved during both training and inference: 1) For inference, input parts are pre-aligned using a chirality-preserving PCA as in DGL [7], and the model predicts rotations with quaternion, ensuring no chirality inversion occurs. (2) For training, although Eq.(13) formulates the reflection-based symmetry constraint as applying reflections to input, in practice, for computational efficiency, we instead apply these reflections only to ground-truth poses of self-symmetric parts.\n\n**Computational cost:** In implementation, the potential computational overhead for symmetry-aware supervision is significantly reduced by applying axis-aligned reflections only to ground-truth poses of self-symmetric parts, rather than reflecting input parts. As in Table R1-4 (last two rows), using symmetry-aware loss does not increase parameter count but leads to increased GPU memory (26.60GB→27.04GB) and forward time (802.72ms→806.80ms).\n\n**Other strategies:** 1）designing symmetry-equivariant architectures to ensure consistent outputs under input reflections; 2）grouping symmetric variants by aggregating losses or sampling representatives; 3）employing hierarchical processing to first capture global symmetries before refining local variations. \n\n[7] Zhan, G., et al. Generative 3d part assembly via dynamic graph learning.\n\n***Q7: Why not encourage distinct placement for collapse?***\n\nBy minimizing prediction differences to the most similar ground-truth counterpart (Eq.(14)), we accommodate multiple plausible part configurations induced by geometric similarity. The part-wise instance encoding and shape loss (Eq.(12)) further maintain coherent global arrangements without collapsing similar parts into identical poses.\n\nAs in Table R1-3., replacing symmetry-aware loss $\\mathcal{L}_{sym}$ in Eq.(15) with distinct-placement constraint as [8] (CFPA-w/-SL in [8]) or using $L_2$ loss (CFPA-w/-SL-$L_2$) on predictions of geometrically similar parts results in worse performance. \n\nTable R1-3. Results with constraints for geometric similar part\n\n| |SCD($10^{-2}$)↓|PA(%)↑|CA(%)↑ | QDS($10^{-5}$)↑|WQDS($10^{-5}$)↑|\n|---|:---:|:---:|:---:|:---:|:---:|\n|CFPA-w/-SL in [8]|0.51|68.82|45.81|4.82|2.04|\n|CFPA-w/-SL-$L_2$|0.55|67.67|42.59|3.27|1.45|\n|**CFPA**|**0.49**|**69.24**|**49.20**|**6.71**|**2.75**|\n\n[8] Zhang, R., et al. Scalable geometric fracture assembly via co-creation space among assemblers.\n\n***Q8: Computational cost of modules.***\n\nTable R1-4. presents computational cost of CFPA and its variants without key modules of semantic super-parts via OT (CFPA-w/o-OT), short/long-range feature propagation (CFPA-w/o-SRFP/LRFP), message passing (CFPA-w/o-MP), cross-stage attention (CFPA-w/o-CA), and symmetry-aware loss (CFPA-w/o-SL). The baseline model refers to CFPA without any of these modules.  '#Para.(M)' is number of parameters(in millions). All variants are tested on Chair with batchsize=64,  forward time is measured for one iteration.\n\nThese modules operate on **part or super-part levels** rather than the point cloud, and the overhead introduced by these components in the full CFPA remains manageable and does not significantly impact scalability.\n\nTable R1-4. Computational cost\n||#Para.(M)|GPU Memory(GB)|Forward time(ms)|GFLOPS|\n|---|:---:|:---:|:---:|:---:|\n|CFPA-w/o-OT|25.89|26.80|657.87|86.34|\n|CFPA-w/o-SRFP|25.89|26.36|804.91|86.34|\n|CFPA-w/o-LRFP|25.76|24.68|778.68|86.33|\n|CFPA-w/o-MP|25.89|24.60|791.31|86.34|\n|CFPA-w/o-CA|25.63|25.71|698.05|86.33|\n|CFPA-w/o-SL|25.89|26.60|802.72|86.34|\n|**CFPA**|**25.89**|**27.04**|**806.80**|**86.34**|\n\n**We will incorporate the analysis on model and experiments, and correct the typo.**"}, {"review_id": "3ywhMIefb8", "reviewer": "Reviewer_7yWx", "summary": "This paper introduces a method to assemble parts togehter. It uses optimal transport to produce a coarse assembly, before refining in the second stage. They train and test on PartNet.", "questions": "Why are only 3 categories of shapes shown in Table 1?\n\n  How do you account for the various possibilities that the same set of parts can assemble to? Is there a way to communicate the desired final assembly through some form of conditioning?", "limitations": "Yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "+ Strengths\n  Thorough comparisons with prior works, substantial improvements demonstrated quantitatively. The methods seem non-trivial, and takes into account many nuanced problems of the part assembly task.\n\n  Additionally, substantial ablations have been done to show the effectiveness of different design decisions.\n\n+ Weaknesses\n\n  The method was only demonstrated on 3 categories of Partnet, hindering how convincing the results are. Moreover, the qualitative results demonstrated in Figure 4 feels a bit underwhelming, especially given the complexity of the method.\n\n  As far as I can tell (please correct if wrong), the models introduced are not conditional on some input image/pointcloud/mesh of the desired final assembly at test time. This strikes me as a little weird, since it's possible to assemble the parts to produce many different, though equality valid, final assemblies. For instance, in the first Column of tables in Figure 4, I would say that \"Score\", \"Ours\" and \"Groundtruth\" all corresponded to equally likely assemblies.\n  `", "was_revised": true, "final_justification": "Hi, thanks for your comprehensive rebuttal, it has addressed  the bulk of my concerns. I've updated the rating accordingly.", "rebuttal": "***Q1: Why are only 3 categories of shapes shown in Table 1?***\n\n\nWe followed the experimental settings of DGL [1], RGL [2], Score-PA [3], IET [4], and 3DHPA [5], which evaluate models on the three largest categories of PartNet. As shown in Table 1 of the manuscript, our CFPA consistently achieves higher overall performance compared to the baseline methods.\n\nIn addition, we conducted experiments on the **Storage** category, with comparative results coppyed from SPAFormer [6]. As illustrated in Table R2-1, our method outperforms the baseline methods on the SCD and PA metrics, while achieving the second highest performance on the CA metric. Together with the results in Table 1, these results  highlight the effectiveness of our model for accurate part assembly.\n\nFurthermore, we performed **few-shot transfer learning** experiments by training our model on the Chair category and fine-tuning it using only 10 shapes from the Table category. As shown in Table R2-2, our fine-tuned model (Ours Chair$\\rightarrow$Table) outperforms both other fine-tuned models (* Chair$\\rightarrow$Table, where * represents competing methods) and our model trained from scratch (Ours trained from scratch). These results underscore the effectiveness of our approach under limited training data and demonstrate its superior generalization capabilities.\n\nTable R2-1. Performance comparison of different methods on Storage\n\n| Methods    | SCD($10^{-2}$)↓ | PA(%)↑    | CA(%)↑    |\n| ---------- | :---: | :---: | :---:|\n| DGL [1]       | 1.21            | 12.39     | 17.23     |\n| LSTM [1]      | 1.19            | 8.50      | 27.14     |\n| RGL [2]       | 0.64            | 48.02     | 38.45     |\n| Score-PA [3]  | 0.69            | 27.68     | 21.82     |\n| IET  [4]      | 0.68            | 29.31     | 22.51     |\n| SPAFormer [6] | 0.45            | 56.11     | 49.98     |\n| 3DHPA [5]       | 0.39            | 67.09     | **57.62** |\n| **Ours**   | **0.33**        | **68.11** | 56.12     |\n\nTable R2-2. Performances of different methods for few-shot transfer learning\n\n| Methods | SCD($10^{-2}$)↓ | PA(%)↑ | CA(%)↑ |\n|---------|:---:|:---:|:---:|\n| Global [1] Chair→Table | 2.97 | 1.87 | 2.11 |\n| DGL [1] Chair→Table | 1.12 | 27.69 | 33.62 |\n| LSTM [1] Chair→Table | 3.31 | 2.56 | 3.45 | \n| RGL [2] Chair→Table | 0.84 | 17.44 | 23.12 |\n| Score-PA [3] Chair→Table | 1.32 | 19.23 | 29.45 | \n| IET [4] Chair→Table | 0.83 | 48.23 | 20.34 | \n| 3DHPA [5] Chair→Table | 0.86 | 36.77 | 34.68 | \n| **Our Chair→Table** | **0.78** | **40.14** | **36.62** |\n| Ours trained from scratch | 1.43 | 15.06 | 22.90 |\n\n[1] Zhan, Guanqi, et al. Generative 3d part assembly via dynamic graph learning. NeurIPS 2020.\n\n[2] Narayan, et al. Rgl-net: A recurrent graph learning framework for progressive part assembly. WACV 2022.\n\n[3] Cheng, Junfeng, et al. Score-pa: Score-based 3d part assembly. BMVC 2023\n\n[4] Zhang, Rufeng, et al. 3d part assembly generation with instance encoded transformer. IEEE Rob. Autom. Lett., 2022, 7(4): 9051-9058.\n\n[5] Du, Bi'an, et al. Generative 3d part assembly via part-whole-hierarchy message passing. CVPR 2024.\n\n[6] Xu, Boshen, et al. SPAFormer: Sequential 3D Part Assembly with Transformers. 3DV 2025.\n\n\n***Q2: The qualitative results demonstrated in Figure 4 feels a bit underwhelming.***\n\n**Unconditional part assembly** is inherently challenging due to the complexity of understanding assembly patterns and accurately placing symmetric or similar parts. Unlike conditional methods, this task operates without predefined guidance, requiring the model to learn intricate relationships between parts. \n\nFrom a **qualitative** perspective, our model demonstrates better connectivity and more reasonable handling of symmetric or similar parts. For example, in the Chair category, it predicts more accurately aligned legs with stronger connectivity. In the Table category, wheels are placed more reasonably, and for Lamps, lampshades are positioned more effectively. These results highlight the robustness of our approach in capturing meaningful part relationships and producing plausible assemblies.\n\n**Quantitatively**, our model consistently outperforms baseline methods across multiple metrics  as detailed in experiment results of the manuscript. These numerical results further validate the effectiveness of our approach in achieving accurate and robust part assemblies.\n\n\n\n\n***Q3: How do you account for multiple possible assemblies for the same set of parts? How to specify the desired final assembly through conditioning?***\n\nWe **explicitly** accounts for multiple possible assemblies. As in Eq.(14), we consider diverse configurations of similar parts to be valid and constrain the prediction of each part to be consistent with the ground truth of its similar counterparts. This ensures structural plausibility while accommodating the inherent ambiguity of symmetric or geometrically similar parts.\n\nTo further **address potential collapse** caused by identical predictions for similar parts, we incorporate part instance encoding during the refinement stage. This mechanism distinguishes individual parts and avoids over-simplification. Additionally, we employ a shape loss (Eq.(12)) to enforce global structural consistency, ensuring that the overall assembly remains coherent while preserving diversity.\n\n3D part assembly with **conditions,** such as images or textual descriptions, offers a promising approach to achieve the desired final configuration. For example, establishing 2D-3D correspondences through projection methods can effectively constrain the uniqueness of 3D assemblies. Additionally, leveraging deterministic relational links between parts in images to guide the modeling of inter-part relationships in 3D space is a worthwhile direction for further investigation.\n\nCurrently, we focus  on unconditional part assembly, where predictions are made without external guidance. We greatly appreciate your suggestion, as integrating conditional information to enable unique and deterministic predictions represents a highly meaningful and valuable avenue for future exploration.\n\n**We sincerely thank you for your thoughtful feedback and valuable suggestions. We will incorporate the additional analysis and experiments into our revised manuscript.**"}, {"review_id": "PTpHCxfJ32", "reviewer": "Reviewer_XKs3", "summary": "This paper is about 3D part assembly. The pipeline is clear, including *Coarse Pose Estimation with Super-Part*, *Pose Refinement*, and *Loss Function*. This paper introduces a dual-range feature propagation strategy to integrate both local and global structural cues. The Pose Refinement part applies a cross-stage attention and instant encoding. The Loss function integrates structural priors, geometric reasoning, and symmetry-aware supervision.", "questions": "1. I would like to see more explanation of the approach, including how the designed method addresses the needs.\n2. More ablation experiments are encouraged.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strength:\n1. The method is easy to understand, and the experiment in the paper is SOTA\n2. This task is interesting, and the comparison with other methods also proves the effectiveness of this method.\n\nWeakness：\n1. Some parts do not have a clear explanation process, like how the semantic super part $ \\{h_{j}\\} _ {j=1}^M $ comes from $\\{h_{j}\\} _ {j=1}^N$ and the geometrically similar parts in line 159.\n2. The ablation study should contain the baseline method; simply removing any single part is not convincing enough.\n3. The method part needs more explanation about how this module solves the issues.", "was_revised": true, "final_justification": "The authors addressed my concerns and questions. I have lifted my ratings.", "rebuttal": "***Q1: How the semantic super part $\\\\{h\\_j\\\\}\\_{j=1}\\^M$ comes from  $\\\\{f_i\\\\}_{i=1}^N$? What is the definition of geometrically similar parts in line 159?***\n\n**(1) Semantic super-parts.**\n\n\nThe  semantic super-parts $\\\\{h\\_j\\\\}\\_{j=1}\\^M$ are computed as **weighted aggregation** of basic part features $\\\\{f_i\\\\}_{i=1}^N$, where the weights are set as  transport map $T$, as formulated in Eq. (1) of the manuscript.\n\nThe **transport map (weight)** $T$ is obtained through an entropy-regularized optimal transport (OT) process, which minimizes the objective function described in Eq. (2) of the manuscript. This optimization is efficiently solved using Sinkhorn's algorithm [1], which iteratively updates the transport map and super-parts until convergence. \n\n\nThese semantic super-parts act as **middle-level** representations and serve as feature prototypes, offering meaningful structural abstractions that facilitate subsequent feature propagation and pose prediction.\n\n\n**(2) Geometrically similar parts.**\n\nWe follow DGL [2] and compare the axis-aligned bounding box sizes of each part. Two parts are considered geometrically similar if the absolute difference in their bounding box sizes is below a predefined threshold (set to 0.1). For example, under this criterion, parts such as the legs of a table or the  seat and backrest of a chair can be identified as geometrically similar if their bounding box size differences satisfy the threshold. This definition for geometrically similar parts is also provided in Appendix A.\n\n[1] Distances, Cuturi M. Sinkhorn. Lightspeed computation of optimal transport. NeurIPS 2013.\n\n[2] Zhan, Guanqi, et al. Generative 3d part assembly via dynamic graph learning. NeurIPS 2020.\n\n***Q2: Ablation study should contain baseline method. More ablation experiments are encouraged.***\n\nWe present the results of our **1) baseline method** and the full CFPA model in Table R3-1. For the baseline, we systematically remove key components of our approach, including semantic super-parts, dual-range feature propagation, cross-stage attention, and the symmetry-aware loss.\n\n\nTo further evaluate the designs in our model, we conduct  **additional ablation studies** as follows.\n\nA. To demonstrate the effectiveness of **entropy-regularized OT** for semantic super-part construction, we conduct experiments with: **2) CFPA-w/-Att.map**: This variant replaces our transport map computed by entropy-regularized OT with an attention-based transport map as used in [3]. **3) CFPA-w/-$L_2$-dis**: This variant replaces the cost function in OT with $L_2$ distance in feature space. The results in Table R3-1 show that these variants achieve lower performance than our full CFPA model,  demonstrating the effectiveness of entropy-regularized OT and inner product as cost function for  semantic super-part construction.\n\n\nB. To evaluate the effectiveness of our  **symmetry-aware loss** for handling  self-symmetric and geometrically similar parts, we conduct experiments with: **4)-6) CFPA-w/-SL in [4]/[5]/[6]**: These variants replace our symmetry-aware loss $\\mathcal{L}_{sym}$ in Eq.(15) with the **symmetry-handling losses** proposed in [4]/[5]/[6]. The results in Table R3-1 show that CFPA with our symmetry-aware loss achieves better performance compared to these symmetry-handling losses, demonstrating its ability to effectively handle self-symmetric and geometrically similar parts.\n\n\nC. To demonstrate the effectiveness of our **symmetry-aware loss** compared to methods that explicitly use **encourage distinct placement losses** for geometrically similar parts, we conduct ablation studies with: **7) CFPA-w/-SL in [7]**: This variant replaces our symmetry-aware loss $\\mathcal{L}\\_{sym}$ in Eq.(15) with the loss function proposed in [7], which encourages distinct placement for geometrically similar parts. **8) CFPA-w/-SL-$L_2$**: This variant replaces our symmetry-aware loss $\\mathcal{L}\\_{sym}$ in Eq.(15) with $L_2$ distance applied within geometrically similar parts. The results in Table R3-1 show that CFPA with our symmetry-aware loss outperforms these variants, highlighting its superiority in handling geometrically similar parts than explicitly enforcing distinct placement.\n \n\n\nWe hope that these comparisons, along with the variants analyzed in the ablation study of the manuscript, provide a thorough and convincing evaluation of our method.\n\n\nTable R3-1. Ablation studies for CFPA\n\n| Method | SCD($10^{-2}$)↓ | PA(%)↑ | CA(%)↑ | QDS($10^{-5}$)↑ | WQDS($10^{-5}$)↑ |\n|--------|:---:|:---:|:---:|:---:|:---:|\n| 1) CFPA-baseline | 1.02 | 44.37 | 38.20 | 0.99 | 0.46 |\n| 2) CFPA-w/-Att.map | 0.50 | **69.87** | 49.07 | 5.87 | 2.60 |\n| 3) CFPA-w/-$L_2$-dis. | 0.51 | 69.23 | 48.85 | 5.08 | 2.14 |\n| 4) CFPA-w/-SL in [4] | 0.51 | 68.72 | 44.87 | 4.80 | 2.02 |\n| 5) CFPA-w/-SL in [5] | 0.52 | 68.74 | 48.42 | 4.86 | 2.06 |\n| 6) CFPA-w/-SL in [6] | 0.50 | 69.17 | 48.35 | 5.23 | 2.22 |\n| 7) CFPA-w/-SL in [7] | 0.51 | 68.82 | 45.81 | 4.82 | 2.04 |\n| 8) CFPA-w/-SL-$L_2$ | 0.55 | 67.67 | 42.59 | 3.27 | 1.45 |\n| **CFPA** | **0.49** | 69.24 | **49.20** | **6.71** | **2.75** |\n\n\n[3] Xin Wei, et al. Learning generalizable part-based feature representation for 3d point clouds. NeurIPS 2022.\n\n\n[4] Zhang, Jiahao, et al.  Manual-PA: Learning 3D Part Assembly from Instruction Diagrams.  arXiv:2411.18011\n\n[5] Zhang, Rufeng, et al. 3d part assembly generation with instance encoded transformer. IEEE Rob. Autom. Lett., 2022, 7(4): 9051-9058.\n\n[6] Li, Yichen, et al. Learning 3d part assembly from a single image. ECCV 2020.\n\n[7] Zhang, Ruiyuan, et al. Scalable geometric fracture assembly via co-creation space among assemblers. AAAI 2024.\n\n\n***Q3: The method part needs more explanation about how this module solves the issues.***\n\nWe adopts **a coarse-to-fine** strategy for 3D part assembly, which face challenges including the **lack of explicit semantic structure**, **difficulties in  integrating semantic information**, **inconsistencies between different prediction stage** and **ambiguities caused by self-symmetry or geometric similarity**. Below, we clarify how each module specifically resolves these issues:\n\n\nA. To address the **lack of explicit semantic structure**, we propose **semantic super-parts** as high-level structural abstractions. These are dynamically constructed via **optimal transport (OT)** (Eqs.(1-2)), avoiding reliance on rigid hierarchies. By grouping semantically similar parts, this module provides a  semantic abstraction for guiding coarse pose estimation. **This mechanism equips the framework with explicit, data-driven semantic structure, thereby improving global structural understanding and the overall quality of assembly.**\n\n\nB. To guide localized feature learning with the learned semantic abstraction, we introduce a **dual-range feature propagation** mechanism. Locally, it captures fine-grained semantic relations between parts and their nearest super-parts (Eq.(3)); globally, it aggregates holistic context via attention (Eq.(4)). **This design ensures that local feature learning is effectively guided by multi-scale high-level semantic structure, enabling precise part placement while maintaining global structural coherence.**\n\n\nC. To **promote consistency between different stages** and **transfer global information from the coarse to the refinement stage**, we introduce a **cross-stage attention** module. By fusing complementary cues across stages, this module enables the refinement process to be guided by global structural context, thereby reducing inconsistencies and improving overall assembly coherence.\n\n\nD. To resolve **ambiguities from self-symmetry and geometric similarity**, we propose a **symmetry-aware loss** that supervises pose prediction with explicit self-symmetry and geometric similarity modeling (Eq.(13), Eq.(14)). This allows the network to tolerate multiple valid configurations for symmetric or interchangeable parts. By doing so, our method accommodates **symmetry-induced ambiguities** and supports **diverse yet valid assembly solutions.**\n\n\nE. Beyond the above designs, to **enhance feature interaction and discrimination**, we  employ **multi-head attention** in both the coarse and refinement stages (Eq.(7), Eq.(9)), facilitating effective information exchange among parts. Furthermore, **message passing among geometrically similar parts** (Eq.(5)) encourages feature consistency for interchangeable components, while an **instance encoding** strategy preserves unique part representations and prevents prediction collapse. \n\n**We sincerely thank you for your feedback and suggestions. We will incorporate the additional analysis and experiments into our revised manuscript.**"}, {"review_id": "gO1f3g6oHq", "reviewer": "Reviewer_JKQa", "summary": "This paper proposes CFPA (Coarse-to-Fine Part Assembly), a novel two-stage framework for 3D part assembly that jointly addresses semantic structuring and geometric symmetry challenges. The method begins with a coarse pose estimation stage, where semantic super-parts are constructed using entropy-regularized optimal transport, providing high-level guidance via dual-range feature propagation. Then it takes a refinement stage that adjusts part poses through cross-stage attention and instance-level geometric encoding. Besides, this paper introduces a symmetry-aware loss that models both self-symmetry and inter-part geometric similarity. Extensive experiments on the PartNet benchmark show its effectiveness.", "questions": "Refer to the Weakness. I will improve my rates when the weaknesses are solved.", "limitations": "The author analyzes the limitations and societal impacts adequately.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Goodness:\n\n1.\tThis paper presents a novel Coarse-to-Fine Part Assembly framework, integrates global structure and local geometric reasoning. Specifically, it takes a coarse pose estimation stage and a refinement stage to enhance accurate and diverse part assemblies.\n\n2.\tThis paper accounts for pose ambiguity caused by symmetry, enabling accurate and diverse configurations.\n\n3.\tExtensive experiments on PartNet demonstrate its effectiveness.\n\n4.\tThis paper is written and organized well.\n\n\nWeakness:\n\n1.\tSince the proposed method has the ability to learn the base part-level shapes based on the semantic guidance, it will be interesting to evaluate its performance on unseen categories.\n\n2.\tThe framework involves multiple attention layers, message passing, and OT computation. It will be interesting to report on the computational cost impact of these components.\n\n3.\tIt will be interesting to add visualization or analysis of learned super-parts or their semantic consistency across shapes.\n\n4.\tIt will be interesting to evaluate the generalization of the proposed symmetry-aware loss on other baselines, for that it is  a problem often overlooked or only heuristically addressed in prior work.\n\n5.\tLack comparison with Imagine [1] in Tab.1.\n\n[1] Imagine: Image-Guided 3D Part Assembly with Structure Knowledge Graph. AAAI 2025.", "was_revised": true, "final_justification": "The authors addressed my concerns and questions.  I have updated my ratings!  Good luck!", "rebuttal": "***Q1: Evaluate the model's performance on unseen category.***\n\nIn the manuscript, we adopt the experimental settings of DGL [1], RGL [2], Score-PA [3], IET [4], and 3DHPA [5] to evaluate models on the **three largest categories of PartNet**, where our model achieves superior performance compared to the baselines.\n\nTo evaluate the performance of our method on **unseen category**, we test with the model trained on Chair category to predict assemblies for shapes in Lamp category. As shown in Table R4-1, our model (Our Chair⟹Lamp) outperformed the baseline methods (* Chair⟹Lamp, where * represents the compared models) on 4 out of 5 metrics (SCD, PA, CA, QDS), achieving second-best performance on WQDS.\n\nThese results demonstrate the **generalization ability** of our approach, which leverages semantic guidance to learn part-level structures and produce coherent and accurate assemblies even for unseen category.\n\nTable R4-1. Performance of models trained on Chair for assembly prediction on unseen Lamp category\n\n| Methods | SCD($10^{-2}$)↓ | PA(%)↑ | CA(%)↑ | QDS($10^{-5}$)↑ | WQDS($10^{-5}$)↑ |\n|------|:---:|:---:|:---:|:---:|:---:|\n| LSTM [1] Chair⟹Lamp | 4.15 | 2.61 | 15.43 | 1.22 | 0.21 |\n| Global [1] Chair⟹Lamp | 3.99 | 1.32 | 12.81 | 1.28 | 0.15 |\n| DGL [1] Chair⟹Lamp | 3.63 | 2.38 | 10.79 | 0.98 | 0.11 |\n| RGL [2] Chair⟹Lamp | 3.61 | 3.20 | 16.22 | 0.94 | 0.14 |\n| Score-PA [3] Chair⟹Lamp | 2.41 | 5.55 | 13.95 | 1.4 | **1.30** |\n| IET [4] Chair⟹Lamp | 4.79 | 1.93 | 11.70 | 1.26 | 0.41 |\n| 3DHPA [5] Chair⟹Lamp | 2.98 | 4.15 | 26.87 | 1.16 | 0.93 |\n| **Our Chair⟹Table** | **2.84** | **5.61** | **28.85** | **1.43** | 1.13 |\n\n\n\n\n\n\n***Q2: Report computational cost of the proposed components.***\n\nTo evaluate the computational cost of our proposed components, we report key metrics for a single forward pass with a batch size of 64, including the number of parameters (Million, M), GPU memory usage (GB), forward time (ms), and GFLOPS. We analyze the CFPA model and its variants, each excluding specific components as: **1)-2) CFPA-w/o-refine/coarse MHA** that exclude the multi-head attention in the pose refinement/coarse pose estimation stage; **3) CFPA-w/o-OT** that removes the OT-based super-part construction; **4)-5) CFPA-w/o-SRFP/LRFP** that remove the short-/long-range feature propagation; **6) CFPA-w/o-MP** that removes the message passing in long-range feature propagation; **7) CFPA-w/o-CA** that removes the cross-stage attention; **8) CFPA-w/o-SL** that removes the symmetry-aware loss. We also report the computational cost of the baseline method that removes all of the above components.\n\n\n\n\nAs shown in Table R4-2, removing these components leads to a reduction in computational cost compared to the full CFPA model. Notably, some of these components are specifically designed to operate based on the relationships between parts and super-parts rather than directly on point clouds, with the maximum number of parts limited to 20 and super-parts to 16. This design inherently requires only a small computational cost. Additionally, certain components, such as OT, short-range feature propagation, and message passing, do not introduce any learnable parameters, further contributing to their relatively low computational cost.\n\nTable R4-2.  Computational cost comparisons\n\n| Method | #Para.(M) | GPU Memory(GB) | Forward time(ms) | GFLOPS |\n|--------|:---:|:---:|:---:|:---:|\n| baseline | 21.33 | 24.05 | 641.36 | 86.22 |\n| 1) CFPA-w/o-refine MHA | 22.90 | 24.28 | 674.80 | 86.26 |\n| 2) CFPA-w/o-coarse MHA | 25.14 | 26.72 | 772.09 | 86.30 |\n| 3) CFPA-w/o-OT | 25.89 | 26.80 | 657.87 | 86.34 |\n| 4) CFPA-w/o-SRFP | 25.89 | 26.36 | 804.91 | 86.34 |\n| 5) CFPA-w/o-LRFP | 25.76 | 24.68 | 778.68 | 86.33 |\n| 6) CFPA-w/o-MP | 25.89 | 24.60 | 791.31 | 86.34 |\n| 7) CFPA-w/o-CA | 25.63 | 25.71 | 698.05 | 86.33 |\n| 8) CFPA-w/o-SL | 25.89 | 26.60 | 802.72 | 86.34 |\n| **CFPA** | **25.89** | **27.04** | **806.80** | **86.34** |\n\n***Q3: It will be interesting to  add visualization or analysis of learned super-parts or their semantic consistency across shapes.***\n\nWhile **figures are not permitted** in this rebuttal, we visualize the correspondence for the basic parts with their nearest super-parts, identified by the minimal cost in the optimal transport map $T$. These visualization reveal several key tendencies:\n\nA. Parts with **similar functions** are mapped to the **same super-part**, showcasing strong semantic coherence. For instance, chair legs are typically grouped into one super-part, while chair backs and seats are often mapped into another super-part, reflecting their interchangeable functional roles.\n\nB. **Unique or uncommon parts**, such as decorative elements or isolated structural pieces, tend to be assigned to  **specific super-part**.\n\n\nC. The learned super-parts demonstrate **semantic consistency across shapes**. For instance, despite variations in chair designs (e.g., chairs with armrests versus those without), parts with similar functions, such as chair legs and seat backs, are consistently grouped into their respective super-parts, while armrests are mapped into separate super-parts. \n\nThese findings highlight the model's ability to capture semantic and functional relationships across shapes, while effectively handling structural variations and unique components. \n\n***Q4: It will be interesting to  evaluate the generalization of the proposed symmetry-aware loss on other baselines.***\n\nTo evaluate the generalization ability of the proposed symmetry-aware loss, we conducted experiments by integrating it into various baseline methods. As shown in Table R4-3, the models equipped with our symmetry-aware loss (* -w/-SL, where * represents the baselines)  achieve improved performance.\n\nThese results demonstrate that the symmetry-aware loss is not only effective within our framework but also generalizable across diverse baseline methods. This further validates its robustness and applicability in 3D part assembly tasks.\n\nTable R4-3. Comparison of different baselines with our symmetry-aware loss\n\n| Method | SCD↓ | PA(%)↑ | CA(%)↑ | QDS(10⁻⁵)↑ | WQDS(10⁻⁵)↑ |\n|--------|:---:|:---:|:---:|:---:|:---:|\n| Global [1] | 1.46 | 15.70 | 9.90 | 0.15 | **1.25** |\n| Global-w/-SL | **1.21** | **18.10** | **12.92** | **0.43** | 1.21 |\n| | | | | | |\n| LSTM [1] | **2.35** | 8.08 | 10.05 | 3.92 | 1.26 |\n| LSTM-w/-SL | **2.35** | **9.34** | **11.25**| **4.03** | **1.33** |\n| | | | | | |\n| DGL [1] | 0.91 | 39.00 | 23.87 | **1.69** | 1.35 |\n| DGL-w/-SL | **0.87** | **41.77** | **29.51** | 1.66 | **1.73** |\n| | | | | | |\n| RGL [2] | 0.98 | 48.85 | 30.68 | 5.85 | **2.09** |\n| RGL-w/-SL | **0.92** | **49.15** | **33.27** | **5.91** | 1.55 |\n| | | | | | |\n| Score-PA [3] | 0.71 | **44.51** | 30.32 | 3.36 | **1.70** |\n| Score-PA-w/-SL | **0.65** | 43.77 | **31.32** | **5.11** | 1.41 |\n| | | | | | |\n| IET [4] | 1.34 | 37.60 | 25.44 | **3.33** | 1.85 |\n| IET-w/-SL | **1.21** | **38.53** | **27.21** | **3.33** | **1.93** |\n| | | | | | |\n| HPA [5] | **0.51** | 63.01 | **48.28** | 4.42 | 1.90 |\n| HPA-w/-SL | **0.51** | **66.34** | 47.21 | **4.82** | **2.01** |\n\n\n***Q5: Lack comparison with Imagine  in Tab.1.***\n\nWe will include a comparison with Imagine [6] in the revised manuscript and clarify the distinctions between the two methods. While both tackle 3D part assembly tasks, Imagine utilizes structural guidance from 2D images, making it a conditional approach. In contrast, our method addresses the task in an unconditional setting. Despite these differences, our method outperforms Imagine in terms of the PA metric on the Chair (69.24% vs 65.88%) and Table (68.48% vs 65.13%) categories.\n\n**We sincerely thank you for your thoughtful feedback and valuable suggestions. We will incorporate the additional analysis and experiments into our revised manuscript.**\n\n\n\n[1] Zhan, Guanqi, et al. Generative 3d part assembly via dynamic graph learning. NeurIPS 2020.\n\n[2] Narayan, et al. Rgl-net: a recurrent graph learning framework for progressive part assembly. WACV 2022.\n\n[3] Cheng, Junfeng, et al. Score-pa: score-based 3d part assembly. BMVC 2023\n\n[4] Zhang, Rufeng, et al. 3d part assembly generation with instance encoded transformer. IEEE Rob. Autom. Lett., 2022, 7(4): 9051-9058.\n\n[5] Du, Bi'an, et al. Generative 3d part assembly via part-whole-hierarchy message passing. CVPR 2024.\n\n[6] Wang, Weihao, et al. Imagine: image-guided 3d part assembly with structure knowledge graph. AAAI 2025."}]

Author rebuttal:

Meta-review: This paper introduces a coarse-to-fine framework for 3D part assembly. The key innovation is the two-stage framework incorporating super-part construction followed by part pose refinement. Most reviewers appreciated the novelty and the comprehensive evaluations, especially the comparisons with baselines, although there was a concern about the lack of theoretical foundations for certain design choices. All reviewers gave positive scores, so this submission is clearly accept. However, the technical innovation is not at the level to be recommended for a spotlight or oral presentation. During the author–reviewer discussion, the authors provided additional experiments such as computation cost analysis, comparisons between the proposed symmetry-aware loss and previous losses, cross-category few-shot transfer results, and ablation studies. These additional results led the reviewers to raise their scores.
Decision: Accept (poster)