DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Authors: Changshuo Wang
Xiang Fang
Prayag Tiwari
Venue: ICML 2025 poster (2025)
Keywords: Dynamic Convolution
Taylor Series
Prototype Completion
Few-shot
Point Cloud
Semantic Segmentation
Primary area: applications->computer_vision

Abstract: Few-shot point cloud semantic segmentation effectively addresses data scarcity by identifying unlabeled query samples through semantic prototypes generated from a small set of labeled support samples. However, pre-training-based methods suffer from domain shifts and increased training time. Additionally, existing methods using DGCNN as the backbone have limited geometric structure modeling capabilities and struggle to bridge the categorical information gap between query and support sets. To address these challenges, we propose DyPolySeg, a pre-training-free Dynamic Polynomial fitting network for few-shot point cloud semantic segmentation. Specifically, we design a unified Dynamic Polynomial Convolution (DyPolyConv) that extracts flat and detailed features of local geometry through Low-order Convolution (LoConv) and Dynamic High-order Convolution (DyHoConv), complemented by Mamba Block for capturing global context information. Furthermore, we propose a lightweight Prototype Completion Module (PCM) that reduces structural differences through self-enhancement and interactive enhancement between query and support sets. Experiments demonstrate that DyPolySeg achieves state-of-the-art performance on S3DIS and ScanNet datasets.

DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Changshuo Wang' Xiang Fang?
Prayag Tiwari3
Abstract
Supaot
Fasaskk -C.TMM
Few-shot point cloud semantic segmentation ef- fectively addresses data scarcity by identifying unlabeled query samples through semantic pro- totypes generated from a small set of labeled support samples. However, pre-training-bun methods suffer from domain shifts and increased training time. Additionally, existing methods using DGCNN as the backbone have limited geometric structure modeling capabilities and struggle to bridge the categorical information gap between query and support sets. To ad- dress these challenges, we propose DyPolySeg. a pre-training-free Dynamic Polynomial fitting net- work for few-shot point cloud semantic segmenta- tion. Specifically, we design a unified Dynamic Polynomial Convolution (DyPolyCome Conv) that ex- tracts flat and detailed features of local geometry through Low-order Convolution (LoConv) and Dynamic High-order Convolution (DyHoConv). complemented by Mamba Block for capturing global context information. Furthermore, we pro- pose lightweight Prototype Completion Module (PCM) that reduces structural differences through eeff-enhancement and interactive enhancement between query and support sets. Experiments demonstrate that DyPolySeg achieves sfate-of-the- art performance on S3DIS and ScanNet datasets.
teput Botay
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Stritted Imaderre
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Saggen
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Priserpe Modile
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Figure I. Architectural comparison of representative few-shot point cloud segmentation methods. (a) Conventional approaches (Zhao al., 2021b; He et al., 2023) rely pre- pre-trained DGCNN backbones coupled with various prototype alignment modules. (b) SegPN (Zhu et al., 2024) eliminates the need for pre- te-irranning but suffers from limited representational capacity. (c) COSeg (An et al., 2024) adopts pre-trained Straight Transformer architecture and processes 20,480 points to mitigate foreground information leak- age. (d) Our proposed DyPolySeg innovatively models local struc- tures through polynomial fitting and incorporates lightweight prototype completion module enhanced performance.
spanning autonomous driving (Zhao al., 2023; Chib & Singh, 2023), robotics (Soori et al., 2023; Goel & Gupta, 2020), and augmented reality (Devagiri et al., 2022; Sereno et al., 2020). Despite its significance, the acquisition of large-scale annotated point cloud data(Jiang et al., 2023) remains a eesource-intensive challenge, requiring substantial human effort and time investment. This limitation signifi- cantly constrains the practical deployment of deep learning methods (Ning et al., 2024a; Wang al., 2021; 2023; Ning et al., 2024b; Yu et al., 2024) in real-world scenarios. To address this fundamental challenge, researchers (Li et al., 2024; Xiong et al., 2024) have increasingly turned to few- shot learning approaches for point cloud segmentation tasks.
1. Introduction
Point cloud semantic segmentation (Xu et al., 2024; Zhang et al., 2023b; 2024b; He et al., 2024) serves as a fundamen- tal task in 3D scene understanding, with critical applications
Few-shot point cloud semantic segmentation represents an innovative paradigm that leverages semantic prototypes de- rived from limited set of labeled support samples effec- tively identify and segment unlabeled query samples. As illustrated in Fig. 1(a), this field was pioneered by Zhao et al. (Zhao et al., 2021b), who introduced the AttMPTI method based on a pre-trained DGCNN (Wang et al., 2019). Their groundbreaking work established foundation that
'Cyber Security Research Center, Nanyang Technological University, Singapore "ERI@N, Interdisciplinary Graduate Pro- gramme, Nanyang Technological University. Singapore "Shool of Information Technology, Halmstad University, Sweden. Corre- spondence to: Xiang Fang <xfang9508 goai..com>>
Proceedings of the nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
subsequent research has built upon, with various approaches (Mao al., 2022; Lai al., 2022a; Zhu al., 2023) pro- gressively enhancing segmentation performance. While Zhu et al. (Zhu et al., 2024) made significant strides with their pre-training-free SegNN approach (Fig. 1(b)), their model's capability in local structure representation remains limited. An et al. (An et al., 2024) proposed COSeg (Fig. I())), intro- ducing a novel upproach to prevent foreground leakage by expanding input points 20,480 through uniform sampling. However, this methodology can lead to suboptimal scenar- ios where foreground information either becomes extremely sparse or is entirely absent from the sampled points.
We develop a unified Dynamic Polynomial Convolu- tion (DyPolyConv) that precisely captures local geo- metric structures through the synergistic combination of low-order convolution (LoConv) and dynamic high- order convolution (DyHoConv).
We introduce an efficient Prototype Completion Mod- ule (PCM) that effectively minimizes structural dif- ferences through self-enhancement and interactive en- hancement modules between query and support sets.
2. Related Works
Current sho-shot point cloud segmentation methods ( (Wang et al., 2025b; Zhao et al., 2021b; Mao al., 2022; Zhu et al., 2023; 2024; He et al., 2023; An al., 2024) face three criti- cal challenges: First, pre-training on "seen" categories be- fore fine-tuning on "unseen" ones increases computational cost and leads to domain shifts. Second, using DGCNN as backbone limits the model's ability to capture complex 3D geometric structures, particularly crucial in few-shot scenarios. Finally, the limited support samples fail to fully represent category distributions, creating biased prototypes that affect feature matching accuracy between query and support sets.
2.1. Point Cloud Semantic Segmentation
Point cloud semantic segmentation (Wang et al., 2022a; Wu et al., 2022; He & Ding, 2024; Zhang et al., 2024a; Wang et al., 2022b) represents a fundamental task in 3D scene understanding, focusing on assigning semantic labels to in- dividual points within a point cloud. PointNet (Qi et al., 20) pioneered this field by introducing direct point cloud processing through shared MLPs and global max pooling, though its capacity for local feature extraction remained lim- ited. Subsequent research has primarily focused on enhane- ing local feature representation capabilities. PointNet++ (Qi et al., 2017b) advanced the field by implementing hierarchi- cal sampling and local feature aggregation, while DGCNN (Wang et al., 2019) introduced the innovative EdgeConv op- eration to capture point relationships through dynamically constructed local graph structures.
To address these challenges, we propose DyPolySeg, an innovative pre-training-free dynamic polynomial fitting net- work. First, we introduce a unified Dynamic Polynomial Convolution (DyPolyConv) that combines geometry-pie -rriorrr----o-----o driven low-order convolution (LoConv) and dynamic high- order convolution (DyHoConv) for local geometric feature modeling. LoConv efficiently captures basic flat informa- tion through position encoding, while DyHoConv adaptively models complex local details through learned spatial priors, integrating high-order convolution weights and power expo- nents. Second, we incorporate Mamba Block to establish a robust "local-global" structure through strategic stacking of DyPolyConv and Mamba Block, effectively fusing lo- cal geometric features with global semantic information. Finally, we develop a lightweight stackable Prototype Com- pletion Module (PCM) featuring Self-Enbancement Module (SEM) and Interactive Enhancement Module (IEM): the former learns feature distribution patterns within query and support sets, while the latter refines prototype bias through fine-grained feature correspondence. Multiple stacked PCM modules enable gradual reduction of structural differences, enhancing segmentation accuracy.
Recent years have witnessed significant advancements through three main approaches: Transformer-based architec- tures (Zhao al., 2021a; Lai et al., 2022b; Wang al., 2024), Mamba-based models (Liang et al., 2024b; Han et al., 2024), and self-supervised pre-training strategies (Chen et al., 2024: Pang et al., 2022). Point Transformer (Zhao et al., 2021a) effectively leveraged self-attention mechanisms to capture long-range dependencies, while PointMamba (Liang et al., 2024b) innovatively employed space-filling curves for efficient point tokenization and uti- lized a non-hierarchical Mamba encoder as its backbone. DAPT (Zhou et al., 2024) introduces novel dynamic adapter and seamlessly integrates with prompt tuning, sub- stantially reduces training costs while achieving impressive performance. PointGST (Liang et al., 2024a) innovatively proposes fine-tuning in spectral domain, resulting in sig- nificantly reduced training parameters and superior perfor- mance across diverse point cloud tasks. PointGPT (Chen et al., 2024) introduced novel point cloud autoregressive generation task for pre-training transformer models, achiev- ing superior performance in downstream point cloud under- standing tasks. While these approaches demonstrate impres- sive performance in fully supervised scenarios Shi et al., 2023; Ning et al., 2023; Wang et al., 2025d;a;c; Fang et al.,
strucuree
Our contributions are summarized as follows:
We propose DyPolySeg, novel framework that achieves comprehensive scene understanding through an innovative "local-globll" structure constructed by strategically integrating dynamic polynomial convolu- tion and Mamba Block.
2

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DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
2025), they heavily rely on large-scale annotated datasets and struggle generalize effectively to novel categories or data-scarce environments.
We then present our Dynamic Polynomial Convolution (Dy- PolyConv) with its design principles and theoretical guaran- tees. Subsequently, we introduce our Prototype Completion Module (PCM) and its innovative mechanisms. Finally, we detail the complete DyPolySeg architecture (see 2).
2.2. Few-shot Point Cloud Semantic Segmentation
Few-shot point cloud semantic segmentation addresses the challenge of learning semantic segmentation capabilities for new categories with limited annotated data. AtMMPTI (Zhao et al., 2021b) established the foundation for this field by achieving few-shot segmentation through multi- protoippr generation and label propagation. Subsequent research has advanced along three primary directions: feature enhance- ment, prototype optimization, and domain adaptation.
3.1. Preliminary
3. 3.1.1. PROBLEM DEFINITION
In few-shot point cloud semantic segmentation, we adopt an episodic learning paradigm where the dataset is divided into seen classes Czeen and unseen classes Cunseen. Each task is formulated as an N-way K-shot problem with a support set m= > and a query set Q [T
S {(Tg.) Mg. Mr)*)) N,K
In the feature enhancement domain, BFG (Mao et al., 2022) introduced bilateral feature globalization to improve per- formance through feature interaction between support and query sets, while SCAT (Zhang et al., 2023a) leveraged hierarchical attention mechanisms to capture long-range dependencies. For prototype optimization, PAP (He al., 2023) enhanced prototype representation through adaptive prototype adaptation and projection strategies.
Here, IT.k E (x+())++) represents the k-th point cloud sample of the n-th class in the support set, where T denotes the number of points, 3 represents 3D coordinates (z; y. z), and C indicates additional feature dimensions. Each support sample is paired with a binary segmentation mask M RTx1, The query set contains H samples, where each I E RTx((++)) represents point cloud to be segmented. The objective is to leverage K labeled samples from N classes in the support set S to segment query samples into N target classes plus one background class.
Recent works have introduced sophisticated approaches: DLE (Li et al., 2024) incorporated structural information for precise target region localization while minimizing back- ground interference, utilizing intra-target similarities for complete target segmentation. DENet (Xiong et al., 2024) comprehensively addressed intra-class diversity and seman- tic inconsistency through bilateral mutual aggregation module and consistency purification strategy. GPCPR (Wei et al., 2024) innovatively leveraged LL LLM-generated content and pseudo-query context to optimize prototypes, effectively mitigating categorical information bias.
3.1.2. TAYLOR SERIES
Taylor series (Rudin et al., 1964) serves as a fundamen- tal mathematical tool that enables the representation of a function through an infinite sum of terms derived from its derivatives at a specific point. Formally, for sufficiently smooth function f(x), its Taylor series expansion at point zo is given by:
Recent architectural innovations include SegNN (Zhu al., 2024), which introduced both parameter-free and parame- terized variants achieving competitive performance without pre-training. COSeg (An et al., 2024) proposed a novel approach to prevent foreground leakage by expanding in- put points to 20,480, though this strategy can potentially lead to sparse foreground representation or information loss. TaylorSeg (Wang et al., 2025b), a pretraining-fiet network for few-shot point cloud semantic segmentation, uses Tay- lorConv, inspired by Taylor series, to fit local structures as polynomials. It includes -on-aramettri TaylorSeg-Ni and parametric TaylorSeg-Po with an Adaptive Push-Pull module to align feature distributions, achieving high perfor- mance without pretraining.
20
f(n) (20) (r xo)",
f(xo) +
(I)
n
where ((n)(())) denotes the n-th order derivative of func- tion fi) evaluated at point xo. This series enables accurate local approximation of function values by leveraging in- formation about the function's 's derivatives at a single point, making particularly suitable for modeling complex geo- metric structures in point clouds.
3.1.3. DYNAMIC CONVOLUTION
Traditional convolution operations with fixed kernels inher- ently limit the model's adaptability to diverse local struc- tures. Dynamic convolution (Yang et al., 2019) overcomes this limitation by introducing adaptive weight generation based on input characteristics. In the context of point clouds, dynamic convolution is formulated as:
3. Method
In this section, we first formalize the few-shot point cloud semantic segmentation problem and establish its theoretical
foundations based on Taylor series and dynamic convolution.
gi =
(pr, (p.KKp)) eN)),,
(2)
3

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DyPolySeg: Taylor Sespes-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Support Mask
Support
Eaiboktngg Laces
Suppost
Coarse Protatyppe
Upparepling
Groun truth
DyPuy
ReS+Omppnn
DylolyDev
Mambb Boodkatoock Block
PCM
ESSHChoupkng
Manabo Block
Unowemphon
PCM
Query
Refined Protalypes
CB Loes
Queey
Feel.
(a) SyPalySeg
Albrrtion wdight
Libeer
Cos
Casine S Smiliorit
Explicil Structure
Doff
IN
Layer Normalizaion
Embediiing
A déition
Dut Product
Linee
Linarr
Multpiccation
Activation Function
Polynomial Fitting
LoCour
CyPolyConv
(c) Mamba Block
Figure 2. Architectural overview of DyPolySeg. (a) Pipeline architecture: an embedding layer for point cloud representation, feature extraction modules (FPS, DyPolyConv, DyHoConv, and Mamha Block), Prototype Complction Module (PCM), and segmentation layer for query point clouds. (b) The DyPolyConv module combines attention-hased weight generation with polynomial fitting for local geometric feature extraction. (c) The Mamba Block architecture integrates linear transformations, selective kernel convolutions, and normalization for global context modeling.
where Ii represents the output feature, A denotes ag- gregation function (e.g., max pooling summation), M defines point p, 's local neighborhood, K (p:, Pý) represents dynamically generated convolution weights, and fy indi- cates the input feature of neighborhood point Py-
ric features. Our approach can be formulated as:
9i = (ff
3: (L, fi)
(4)
LoConu
DyHooComv
The core innovation lies in the generation of convolution weights K (pt,P;). These weights computed dynami- cally through a weighted combination of base matrices:
where &p denotes shared MIP, 3r represents attention coef- ficients, L is the number of high-order convolutions, and ny denotes the power exponent for the I-th convolution.
The high-order convolution operation h is defined as:
M
K K(p.. P.)
Σ
am Pm)
M((f, - fa)") A(T(s, (N()))
(5)
with transformation function:
T(f.ff) W (f, fi) - fo)l
) |wy -wy. (fs
where (W., m J.M denotes base weight matrices, Omn (Pi. P,) represents combination coefficients generated by neural net- works based on spatial relationships between and pý. and M indicates the number of base matrices.
[w (f) -0)
f()l. (6)
where | denotes element-wise absolute value, s {0, 1} controls the sign function, and learnable parameter.
3.2. Dynamic Polynomial Convolution
Our transformation function T(-) exhibits remarkable gen- erality. It reduces to Affine basis function (ABF) (Rosen- blatt, 1958) when 8 = 1, n 1, and f; 0:
Inspired by Taylor series (Rudin et al., 1964), we propose novel dynamic polynomial convolution (DyPolyConv) that models local structures through multi-order point convolu- tions, enabling accurate representation of complex geomet-
Wj Sj
T =
Juy fz1t = w/ fz.
(7)
W/ f5

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DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Furthermore, it becomes radial basis function (RBF) (Moody & Darken, 1989) when and 2:
3.3.3. COMPUTATIONAL EFFICIENCY OPTIMIZATION
To address computational burden and numerical instability from exponential operations, employ logarithmic space transformation:
Wj (fz [t) T = (13 -1)²=
w/ (Jz fi)l wy - -
(8)
T(,, [J) = sgn(Ja, ". log(l,, -U3 (1i-J0]++ +e), (14)
3.3. Improving Dynamic Polynomial Convolution
where = 10 prevents numerical instability. This trans- formation reduces computational complexity from O(n²) ) to (n log n) while improving numerical stability and mem- ory efficiency, making it suitable for large-scale point cloud processing.
While our basic Dynamic Polynomial Convolution frame- work provides a solid foundation for capturing complex local geometric structures, practical applications require bal- ancing expressive power with computational efficiency. To address limitations in our initial formulation, enhance model performance through three complementary optimiza- tion strategies:
3.4. Prototype Completion Module
Few-shot point cloud segmentation faces a critical chal- lenge: limited semantic information in support sets and class discrepancies between support and query sets affect semantic matching accuracy, leading to incorrect segmen- tation results. To address this problem, we propose lightweight stackable Prototype Completion Module (PCM) that aims to effectively reduce the feature gap between sup- port and query sets while maintaining computational effi- ciency. PCM comprises two complementary components: Self-Enhancement Module (SEM) and Interactive Enhance- ment Module (IEM).
3.3.1. ENHANCED LOW-ORDER CONVOLUTION
The original low-order convolution primarily focuses on center point features and cannot effectively capture compre- hensive local structural information. We extend the func- tionality by incorporating neighboring point information:
gL = A(p(f))lp E (p:)),
where 9L represents the enhanced output features, A denotes max pooling, and &p is a shared MIP. This improvement enables the model to observe the entire local region's 's feature distribution, providing richer contextual information.
First, we obtain rough prototype features V through sup- port set features and support set masks. Then, we extract representative scene features from support and query sets through max pooling:
3.3.2. EXPLICIT STRUCTURE INTEGRATION
F q = MaxPool( F, = MM
(15)
To enhance spatial relationship perception, explicitly integrate geometric relationships through comprehensive spatial features:
where Fg E R DxC and F, E RxC represent the pooled features of query set and support set S respectively, / de- notes the pooled feature dimension (typically much smaller than the original point count), and C' represents the number of feature channels. This step significantly reduces memory consumption while preserving global semantic information, providing computationally efficient representations for sub- sequent cross-set feature comparisons.
h [p., Pj. Ps: Pj.ll E I
(10)
where h, contains center point coordinates, neighborhood coordinates, relative displacement, and Euclidean distance. These features generate three key adaptive parameters:
w/ = h1 Van
(11)
1.4.1. SELF-ENIANCEMENN MODULE
31 exp(h, Vi)
SEM is designed to enhance prototype representational (12) power by exploring intra-set feature distributions, reducing intra-set class diversity. It achieves this goal by computing auto-correlation matrices:
Σt exp(h, V.)
1, ifo 0.5
(13)
0. otherwise
G FFFFFg. F.=
(16)
where VA, V1, V, E 1lu are learnable transforma- tion matrices. The learnable parameter enables automatic switching between affine and radial basis function behaviors based on local geometric context, significantly enhancing adaptability to different geometric shapes.
where G,,, G. E RCXC are the auto-correlation matrices for query and support sets respectively, capturing relation- ships between feature channels within each set. These ma- trices reveal internal structural patterns in the feature space that can be used to improve prototype discriminability.
5

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DyPolySeg:
Taylor Scries-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
SEM subsequently generates attention-based enhanced pro- totypes:
process. Each PCM layer can further reduce structural differ- ences between support and query sets, improving prototype quality.
A = (U,G,)/ A, = -,-
(17)
Vselt (I @ V) + (A, o V),
(18)
3.5. DyPolySeg Overview
where Ug U, E RRCC are learnable weight matrices used transform auto-correlation matrices into attention weights, denotes the Sigmoid function, VD is a normalization factor, Ay A, E CRCxC are attention weight matrices, @ represents element-wise multiplication, Φ1 is a transforma- tion function, V E [B(++IxCC* represents initial prototype features (including prototypes for N target classes and background class), and well represents the self-enhanced prototype features.
As shown in Figure 2, we propose DyPolySeg, formulating few-shot point cloud semantic segmentation as a dual opti- mization problem that combines local structure modeling with prototype matching.
Our framework adopts an encoder-decoder architecture. The encoder consists of stacked "local-global" blocks that in- tegrate DyPolyConv for local structural feature extraction and Mamba blocks for global context modeling. The de- coder progressively recovers point cloud resolution through inverse interpolation. A lightweight Prototype Completion Module bridges the semantic gap between support and query sets by generating discriminative prototypes for both target classes and background. The final segmentation is obtained by computing similarities between query point features and the refined prototypes.
This design enables the model to learn feature distribution patterns within each set and use them to guide prototype enhancement, reducing intra-set class diversity.
3.4.2. INTERACTIVE ENHANCEMENT MODULE
While SEM focuses on intra-set feature enhancement, IEM concentrates on eliminating domain gaps by modeling con- sistency and differences between support and query sets.
4. Experiments
IEM first computes cross-set correlation matrices:
4.1. Datasets and Evaluation Metrics
C = F=FFFF.)VVD
(19)
Our experiments utilize three distinct point cloud datasets.
where C E C represents correlations between query and support set features, and vD is normalization factor. This matrix captures shared information and differences between the two sets, providing important reference for subsequent prototype refinement.
The S3DIS dataset (Armeni et al., 2016) encompasses RGB point clouds collected from 272 rooms distributed across 6 indoor environments, with points categorized into 13 seman- tic labels (12 categories and clutter). Following established protocols (Zhao et al., 2021b), we process each scene into Im x Im blocks, extracting 2048 points per block, yielding 7547 blocks in total.
IEM leverages this cross-set correlation information to en- rich prototype semantics:
For additional validation, we employ the ScanNet dataset (Dai et al., 2017), comprising 1513 scanned in- door scenes. The dataset features comprehensive point- wise annotations across 20 semantic categories, excluding unannotated regions. Our preprocessing pipeline (Zhao et al., 2021b) generates 36350 blocks, maintaining consis- tent 1048-point sampling per block.
Amntrr = V). A. = softmax (C), (20)
where A. CRC is the cross-set correlation matrix nor- malized through softmax, @22 is a transformation function, and Ajster represents interactive enhancement-bee based proto- type features. This step enables the model to learn shared patterns between support and query sets, helping prototypes adapt to feature distributions across different domains.
To evaluate classification capabilities, we incorporate ScanObjectNN (Uy et al., 2019), real-world point cloud dataset that surpasses ModelNet40 in complexity through its inclusion of background elements and occlusion effects. This collection encompasses 2902 objects across 15 cate- gories, with our evaluation focusing on its most challenging variant (PB T50 TS).RS)
The final refined prototypes are obtained through residual connections:
V out V + Ainter + V,
(21)
where Vou E (N+))xC represents the final prototype fea- tures by PCM. The residual connection design ensures loss- less information transmission, avoiding feature degradation problems while facilitating gradient backpropagation.
Evaluation Metrics. we adopt the standard mean Intersec- tion over Union (mIoU) metric across all categories.
The design of the PCM module allows it to be stacked in multiple layers, forming a progressive prototype refinement
6

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DyPolySeg:
Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Table 1. Few-shot Results (%) ) on S3DIS. S, denotes the split i is used for testing, Avg their average mloU.
2-way
3-way
Methods
Param.
1-shot
S-shot S]
1 1-shot
5-shot
Su
Avg
S
Aug
Su
Avg
St
Avg
DGCNN (Wang al., 2019)
0.62 M
36.34
38.79
37.57
56.49
56,99
56.74
30.05
32.19
31.12
46.88
47.57
47.23
ProtoNet (Snell et al., 2017)
0.27 M
48.39
49.98
49.19
57.34
63.22
60.28
40.81
45.07
42.94
49.05
53.42
51.24
MPTI (Zhao et al., 1021bb
0.29 M
52.27
51.48
51.88
58.93
60.56
59.75
44.27
46.92
45.60
$1.74
48.57
50.16
ARMPTI (Zhao et al., 1b)
0.37 M
53.77
55.94
54.86
61.67
67.02
64.35
45,18
49.27
47.23
54,92
56.79
55.86
BFG (Mau et al., 2022)
55.60
55.98
55.79
63.71
66.62
65.17
46.18
48.36
47.27
55.05
57.80
56,43
2CBR (Zhu et al., 2023)
0.35 M
55.89
61.99
58.94
63.55
67.51
65.53
46.51
53.91
50.21
55.51
58.07
56,79
PAP3D (He et al., 2023)
2.45 M
59.45
66.08
62,76
65.40
70.30
67.85
48.99
56.57
52.78
61,27
60.81
61.04
Seg-PN(Zhu et al., 2024)
0.24 M
64.84
67.98
66.41
67.63
71.48
69.56
59.11
60.42
59.77
59.48
64.72
62.10
DyPolySeg
2.64 M
72.02
73.82
72.92
75.99
75.32
75.66
64.54
67.93
66.24
65.61
70.22
67.92
Improvement
+7.18
+5.84
+6.51
+8.36
+3.84
+6.10
+5.43
+7.51
+6,47
+6.13
+5.50
+5.82
4.2. Implementation Details
validate the effectiveness of our proposed modules.
We implement DyPolySeg using PyTorch on an NVIDIA RTX 4090 GPU. For model configuration, we use k-NN with 16 nearest neighbors in DyPolyConv, set max pooling stride to 32 in PCM, and stack three basic blocks combin- ing DyPolyConv and Mamba Block for the encoder. Our experiments focus on N-way K-shot settings (N E (2,3). K E {1, 5)) with 100 test episodes.
Results on ScanNet Dataset. As shown in Table 2, ex- perimental results on ScanNet dataset further validate the exceptional performance of DypolySeg. In the 2-way 1-shot setting, our method achieves 71.89% mIoU, significantly outperforming Seg-PN (63.74%) by 8. 1.1.. This improve- ment demonstrates our method's robust capability with lim- ited labeled samples. In the 2-way 5-shot scenario, DyPoly- Seg achieves 72.46% mIoU, surpassing Seg-Ph Beg-PN (68.07%) by 4.39%. The performance remains strong in more chal- lenging 3-way settings, where DyPolySeg reaches 69.45% mloU in 1-shot and 69. 18% in 5-shot configurations, ex- ceeding Seg-PN by 5.87% and 3.58% respectively. These consistent improvements across different settings further validate the effectiveness of our approach.
For training, we divide dataset classes into seen and un- seen subsets, constructing episodes with randomly selected support and query samples. We use cross-entropy loss and AdamW optimizer with learning rate 0.001, halved every 7000 iterations. Data augmentation includes random rota- tion, translation, and point jittering for improved robustness.
4.3. Comparison with Existing Methods
4.4. Ablation experiments
To evaluate method, we conduct comparisons with state-of-the-art approaches including DGCNN (Wang et al., 2019), ProtoNet (Snell et al., 2017), MPTI (Zhao et al., 2021b), AμMPTI (Zhao et al., 2021b), BFG (Mao et al., 2022). 2CBR (Zhu et al., 2023), PAP3D (He et al., 2023), and Seg-PN (Zhu et al., 2024).
4.4.1. IMPACT OF DIFFERENT MODULES
Table 3 demonstrates the critical contributions of each mod- ule in our DyPolySeg framework. The model with only LoConv achieves a modest average mIoU of 48.68%, while introducing DyHoConv improves performance to 50.25%, highlighting its potential in capturing local geometric fea- tures. Adding the Mamba Block further enhances perfor- mance to 53.28% mloU, showing its effectiveness in cap- turing global context. Notably, incorporating PCM dramat- ically boosts performance to 70.48% mloU, revealing its crucial role in bridging semantic information gaps between support and query sets. The optimal performance of 72.92% mloU is achieved when all modules are combined, validat- ing the synergistic effect of our complete architecture.
As shown in Table 1, experimental results the S3DIS dataset demonstrate the significant performance ad advantages of our proposed DyPolySeg across various few-shot set- tings. In the 2-way I-shot scenario, our method achieves 72.92% mloU, substantially outperforming the previous state-of-the-art method Seg-PN (66.41 %) by 6.51 %. The performance gains become more pronounced in the 5-shot settings, where DyPolySeg achieves 75.66% mIoU in the 2-way scenario, surpassing Seg-PN (69.56%) by 6.10%. In the more challenging 3-way settings, our method continues to demonstrate exceptional performance- achieving 66.24% mloU in the 1-shot scenario and 67.92% in the 5-shot set- ting, outperforming Seg-PN by significant margins of 6.47% and 5. 5.82% respectively. These consistent improvements
4.4.2. IMPACT OF DIFFERENT NUMBERS OF ENCODER LAYERS
As shown in Figure 3, while Seg-NN and Seg-PN show modest improvements with increasing depth, DyPolySeg
7

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DyPolySeg:
Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Table 2. Few-shot Results (%) on SeanNet. S, denotes the split is used for testing. Aug their average mloU.
2-way
3-way
Methods
Param.
1-shot
S-shot S;
1 1-shot
5-shot
Avg
Aug
Su
Avg
St
Avg
DGCNN (Wang al., 2019)
1.43 M
31.55
28.94
30.25
42.71
37.24
39.98
23.99
19.10
21.55
34.93
28.10
31.52
ProtoNet (Snell et al., 2017)
0.27 M
33.92
30.95
32.44
45.34
42.01
43.68
28.47
26.13
27.30
37.36
34.98
36.17
MPTI (Zhao et al., 2021bb
0.29 M
39.27
36.14
37.71
43.59
45.25
29.96
27.26
28.61
38.14
34.36
36.25
AuMPTI (Zhao et al., 202 2021b)
0.37 M
42.55
40.83
41.69
54.00
50.32
52.16
35.23
30.72
32.98
46,74
40.80
43.77
BFG (Mao et al., 2022)
42.15
40.52
41.34
51.23
49.39
50.31
34.12
31.98
33.05
46.25
41.38
43.82
2CBR (Zhu al., 2023)
0.35 M
50.73
47.66
49.20
52.35
47.14
49.75
47.00
46.36
46.68
45.06
39.47
42.27
PAP3D (He et al., 2023)
2.45 M
57.08
55.94
56.51
64,55
59.64
62.10
55.27
55.60
55,44
$9.02
53.16
56.09
Seg-PN (Zhu et al., 2024)
0.24 M
63.15
64.32
63.74
67.08
69.05
68.07
61.80
65.34
63.57
62.94
68.26
65.60
DyPolySeg
2.64 M
71.05
72.73
71.89
71.25
73.66
72.46
67.65
71.24
69.45
68.73
69.18
Improvement
+7.90
+8.41
+8.15
+4.17
14.61
+4,39
+5.85
+5.90
+5.87
+5,79
+1,36
+3,58
Table Effect of different modules on S3DIS under 1-way-l-shol settings the So and S1 split.
Table 4. Effect increasing HoConv numbers in DyHoConv mod- ule. Results (%) reported S3DIS dataset
LoCoav DyHoConw
Mamba
PCM
Sq
91
Ang
2-way- I-shot
3-way-1 wway-I-shot
Number
x
47.32
50.05
48.68
So
S1
Aug
So
S₁
Aug
48.64
51.86
50.25
1
68.76
69.89
69.33
62.11
65.46
63.79
X
x
49.75
52.97
51.36
2
69.47
70.07
69.77
62.66
65.95
64.31
$2.21
53.28
4
70.28
71.13
70.71
63.45
66.54
65.00
V
x
V
70.12
70.84
70.48
6
71.14
72.06
71.60
64.01
67.17
65.59
72.02
73.82
72.92
8
72.02
73.82
72.92
64.54
67.93
66.24
Geg
7342
Suy PM
EyPetyJeg
Table S. Effect of different composition of PCM on S3DIS under 2/3-way-1 settings on the S, and S split.
6.5
2-way- I-sotl-shot
3-way-I-she 1-shot
SEM
IEM
Sg
5
Aug
S.
8
Auy
22-
X
X
49.17
52.32
50.75
43.34
46.12
44.73
x
70.15
71.03
70.59
63.67
68.42
66.05
68.44
71.66
70.05
62.74
67.35
65.05
/
v
72.02
73.82
72.92
64.54
67.93
66.24
264
with two convolutions, a 1.38% improvement with four con- volutions, and reaching 71.60% mloU with six convolutions in the 2-way setting. The optimal performance is achieved with eight HoConvs, yielding 72.92% mloU for 2- way and 66. 66.24% for 3-way settings. This trend indicates that ad- ditional HoConvs enhance the capture of local geometric features, while the diminishing returns suggest eight layers as an optimal configuration.
Figure 3. Performance comparison with varying encoder layers under 2-way- 1-sho setting on S3DIS dataset.
demonstrates substantial and consistent performance gains. Starting from 36.4% mloU with one layer, our method pro- gressively improves to 58.4%, 65.1%, and peaks at 72.02% with four encoder layers. The performance plateaus beyond four layers, suggesting optimal balance between model capacity and complexity.
4.4.4. ABLATION STUDY PCM
As shown in Table removing both SEM and IEM mod- ules causes significant performance degradation, with mloU dropping to 50.75% and 44.73% for 2-way and 3-way set- tings respectively. Each individual module demonstrates substantial effectiveness: SEM alone achieves 70.59% and 66.05% mIoU, while IEM alone reaches 70.05% and 65.05% mloU in 2-way and 3-way settings. The combination of both
4.4.3. ABLATION STUDY OF DYHOCONV
As shown in Table 4, our model demonstrates consistent improvement with increasing number of HoConvs. Starting from a single convolution (69.33% mloU in 2-way, 63.79% in 3-way), we observe progressive gains; a 0.44% increase
8

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DyPolySeg:
Taylor Sespes-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
Table Effect of the number of PCM. We report the results (%)
60
under 2/3 2/3-way-1 shot settings on S3DIS datasets.
Number
2-way-1-shor
3-way-1-shan
20
20-
So
Si
Aug
Sg
Si
Avg
0
49.17
52.32
50.75
43.34
46.12
44.73
68.42
70.18
69.30
61.47
66.89
64.18
-0
2
72.02
73.82
72.92
64.54
67.93
66.24
70.02
71.24
70.63
64.32
67.24
65.78
-00
-50
(a) Point-BERT
(b) DyPalySog
modules yields optimal performance with 72.92% mIoU in 2-way and 66.24% in way settings, validating the syner- gistic effect of our SEM and IEM design.
Figure 4. t-SNE visualization comparing the feature spaces of Point-BERT and DyPolySeg on the ScanObjectNN.
4.4.5. IMPACT OF NUMBER OF PCM
As shown in Table 6, without any PCM, the model's perfor- mance is significantly low, with an average mloU of 50.75% in 2-way and 44.73% in 3-way settings. Introducing a single PCM dramatically improves performance to 69.30% and 64.18% 18%, respectively. The optimal performance is achieved with PCM layers, reaching 72.92% mIoU in the 2-way set- ting and 66.24% in the 3-way setting. Interestingly, adding third PCM slightly reduces performance to 70.63% % and 65.78%, suggesting that two layers represent the optimal balance for prototype refinement. This indicates that while initial prototype completion significantly enhances feature representation, excessive stacking may introduce unneces- sary complexity or feature redundancy.
validates the effectiveness of our architecture design.
Visualization in Figure 3 compares feature distributions between Point-BERT (Yu al., 2022) and DyPolySeg on ScanObjectNN dataset. Our method achieves more compact within-class clustering and clearer between-class separation, indicating superior shape-aware representation learning.
5. Conclusion
In this paper, we present DyPolySeg, novel framework for few-shot point cloud semantic segmentation. Our method addresses two critical challenges through: (1) dynamic polynomial fitting network with DyPolyConv for effective local geometric modeling, and (2) a lightweight Prototype Completion Module (PCM) for enhanced prototype rep- resentation. The integration of DyPolyConv and Mamba Block in encoder-decoder architecture enables compre- hensive capture of both local geometric details and global semantic context. Extensive experiments demonstrate that DyPolySeg not only advances the state-of-the-art in few- shot point cloud segmentation but also provides valuable insights for future 3D vision research.
Table The accuracy (%) DyPolySeg on ScanObjectNN. means unknown.
Methods
Venue
Accuracy
PointNet (Qi et al., 2017a)
CVPR2017
68.2
PoimNett+ (Qi et al., 201 7h)
NIPS2017
77.9
DGCNN (Wang al., 2019)
ACM TOG2019
78.1
Point BERT (Yu al., 2022)
CVPR2022
83.1
Point-MAF (Pang et al., 2022)
BOCV2022
85.2
PuinIMPP (Ma et al., 2022)
ICLR2022
85.4
Impact Statement
RespSurf-UJ (Ran et al,, 2022)
CVPR2022
86.0
PoimtNeXi-S (Qian al., 2022)
NIPS2022
87.7
The proposed DyPolySeg framework advances few-shot point cloud semantic segmentation, contributing to robust and efficient 3D scene understanding. This technology has broad applications in autonomous navigation, assistive robotics, and augmented reality, potentially accelerating their deployment for societal benefit.
Point- PN (7hang et al., 2023c)
CVPR2023
87.1
PCM (Zhang et al., 2024c)
AAAI2025
88.1
PointMamba (Liang 2024b)
NeurIPS20224
89.3
DyPolySeg (our)
JCML2025
90.8
While promising, we acknowledge potential privacy con- cerns regarding point cloud data usage and the need to address potential biases in training data that could affect different populations. We encourage the research commu- nity to proactively consider these broader impacts in future developments.
4.5. Other Point Cloud Understanding Tasks
As shown in Table 7, DyPolySeg achieves 90.8% accuracy on ScanObjectNN with only 2.64M parameters, demon- strating competitive performance against recent methods like PCM (34.2M) and Mamba3D (16.9M). This efficiency

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DyPolySeg: Taylor Series-Inspired Dynamic Polynomial Fitting Network for Few-shot Point Cloud Semantic Segmentation
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12


Reviews:
[{"review_id": "cnm2W9rFbL", "reviewer": "Reviewer_KVRZ", "summary": "This paper points out that there are three main limitations in the existing methods. First, the methods based on pre-training have domain transfer and increase training time. Second, the current method mainly relies on DGCNN as the backbone, which affects the modeling of several structures of the point cloud. Third, the current method does not completely solve the domain differences between the query set and the support set. In response to these three problems, this paper mainly made three innovations: In order to solve problems one and two, this paper designed a DyPolySeg model, which does not require pre-training, and the proposed DyPolyConv has strong representation capabilities. In order to solve problem three, the author proposed a lightweight PCM to solve the problem of domain differences. The author verified the effectiveness of the proposed method through a large number of experiments.", "questions": "", "limitations": "", "rating": 5, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "First of all, we would like to thank the reviewers for their time in reviewing our manuscript and providing constructive comments. We have carefully addressed your questions below.\n\n**Concern 1:** Although this article mentions the improvement of computing efficiency, the author does not seem to provide the time required for inference and the size of memory required, which is also an important indicator. It is recommended that the author provide these data.\n\n**Reply:** Thank you for your valuable suggestion. We have conducted a comprehensive efficiency analysis of DyPolySeg on the S0 subset of the S3DIS dataset. Our experiments show that for the 2-way-1-shot setting, the model requires 21 seconds for inference and occupies 1.08G of video memory on an NVIDIA RTX 4090 GPU. In comparison with state-of-the-art methods, DyPolySeg demonstrates competitive efficiency while achieving superior performance. For instance, PAP3D requires approximately 35 seconds and 1.56G memory under the same conditions. Additionally, during the training phase, our model converges in about 1.2 hours, significantly faster than the 4.7 hours required by PAP3D. We will include these detailed efficiency metrics in the final version of our paper, providing a more complete evaluation of our method's practical advantages.\n\n**Concern 2:** I found that the datasets used by the author are all indoor point cloud datasets. I want to know whether the method proposed by the author and other authors can be applied to outdoor scene point cloud datasets?\n\n**Reply:** Thank you for raising this important question about generalizability. As demonstrated by our experimental results on ScanObjectNN (which contains diverse object classes), our method shows strong generalization capabilities. The fundamental principles behind DyPolySeg—dynamic polynomial fitting for local geometric modeling and prototype completion for feature enhancement—are designed to capture essential geometric patterns that exist in both indoor and outdoor environments. While our current research focuses on indoor point cloud datasets due to their prevalence in few-shot segmentation benchmarks, we believe DyPolySeg can be effectively extended to outdoor scenes such as autonomous driving scenarios with appropriate adaptation to handle the increased scale and sparsity characteristics of outdoor point clouds. In future work, we plan to explicitly evaluate our method on outdoor datasets like SemanticKITTI to further validate its versatility across different domains.\n\n**Concern 3:** In Table 3, the author should also provide experimental results without LoConv?\n\n**Reply:** We appreciate your suggestion for this additional ablation study. We have conducted the requested experiment, and without LoConv, DyPolySeg achieves 46.95% mIoU on S0 and 49.87% on S1, with an average result of 48.41%. This represents a significant drop of 23.17% compared to our full model (71.58% mIoU), highlighting the crucial role of LoConv in capturing essential flat geometric features. This result aligns with our theoretical foundation in Taylor series approximation, where lower-order terms provide fundamental structural information that higher-order terms build upon. The substantial performance degradation without LoConv empirically validates our design choice of combining low-order and high-order convolutions for comprehensive geometric modeling. We will incorporate this informative ablation study in the final version of our paper to provide a more complete analysis of our model components.\n\n**Concern 4:** Does the model in Table 7 use PCM? If not, it needs to be explained in the text.\n\n**Reply:** Thank you for pointing out this ambiguity. The model used for experiments in Table 7 (ScanObjectNN classification) does not incorporate the PCM module. For these experiments, we utilized only the DyPolySeg encoder as the backbone, followed by a classifier consisting of a fully connected layer, global pooling, and other standard classification components. This is because PCM is specifically designed to address prototype bias in few-shot segmentation scenarios through feature enhancement between support and query sets, which is not applicable to the standard classification task on ScanObjectNN. The strong performance (92.8% accuracy) achieved with just our backbone architecture demonstrates the effectiveness of our DyPolyConv and Mamba Block combination for general point cloud representation learning. We will explicitly clarify this architectural difference in the final version to avoid confusion and provide a more precise description of our experimental setup.", "claims_and_evidence": "The method proposed in the paper is supported by some mathematical theories. Specifically, the author's proposed DyPloyConv establishes a connection with Taylor series, points out the relationship between them, and provides a mathematical theoretical basis for the design of the convolution. In order to verify the effectiveness of the proposed method, the author not only conducted experiments on S3DIS and ScanNet data but also conducted a large number of experiments on each module. In addition, the versatility of the proposed DyPloyConv was verified on the ScanObjectNN dataset.", "methods_and_evaluation_criteria": "Yes. The proposed methods and evaluation criteria make sense for the problem or application.", "theoretical_claims": "I have checked the correctness for theoretical claims. The authors clearly introduce the relationship between the proposed DyPolyConv and Taylor series, as well as the situation of the convolution under some special settings (ABF and RBF), verifying the universality of the convolution and supported by mathematical formulas.", "experimental_designs_or_analyses": "I check the validity of the experimental designs and analyses. I think they are reasonable. For example, the authors used standard evaluation indicators and conducted experiments on standard datasets (S3DIS and ScanNet). In order to verify the universality of DyPolyConv, experiments were also conducted on ScanobjectNN.", "relation_to_broader_scientific_literature": "The author discussed previous point cloud basic models, such as PointNet, PointNet++, DGCNN, PointTransformer, and PointMamba series of work, and recognized their contributions. Based on them, the author proposed a novel DyPolyConv, which showed certain effects on the 3D point cloud classification dataset. The author also discussed the limitations of the current few-shot point cloud semantic segmentation work (Seg-NN, COSeg), and proposed some improvement measures.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n\n1. Inspired by Taylor series, this paper proposes a novel DyPolyConv for local structure representation of point clouds and verifies the versatility of the convolution.\n\n2. This paper designs a lightweight PCM module to bring the features of the Gallery set and the features of the Query set closer, greatly improving the performance of semantic segmentation of few-shot point clouds.\n\nWeaknesses:\n\n1. Although this article mentions the improvement of computing efficiency, the author does not seem to provide the time required for inference and the size of memory required, which is also an important indicator. It is recommended that the author provide these data.\n\n2. I found that the datasets used by the author are all indoor point cloud datasets. I want to know whether the method proposed by the author and other authors can be applied to outdoor scene point cloud datasets?\n\n3. In Table 3, the author should also provide experimental results without LoConv?\n\n4. Does the model in Table 7 use PCM? If not, it needs to be explained in the text.", "other_comments_or_suggestions": "It is recommended that the author provide some examples of segmentation failure, which may be of great help in understanding the article.", "questions_for_authors": "The author can respond with reference to the weaknesses and other suggestions I have raised.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "guEsjoasTt", "reviewer": "Reviewer_XJbF", "summary": "The paper argues that few-shot point cloud semantic segmentation models are constrained by their pretraining models and introduces a pre-training-free Dynamic Polynomial Fitting network. The network comprises DyPolyConv for local feature extraction and the Mamba Block for global feature extraction. Additionally, a PCM module is incorporated to reduce discrepancies between query and support sets.", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you to the reviewer for your time and suggestions, and to the other reviewers for their recognition of our paper. We have carefully addressed your concerns. The specific responses are shown below, and we hope we have resolved your questions.\n\n**Concern 1:** The Method section lacks clarity, and the motivation behind certain design choices is not well explained. For instance, it is unclear how the Dynamic Polynomial Convolution module is enhanced and what the underlying motivation for these choices is.\n\n**Reply:** Our methods chapter is clearly organized. We have structured Section 3 systematically, beginning with the problem definition (Section 3.1), introducing our novel DyPolyConv (Section 3.2), enhancing it (Section 3.3), and then presenting PCM (Section 3.4) before tying everything together (Section 3.5). In Section 3.2, we explicitly establish the connection between Taylor series and our Dynamic Polynomial Convolution, explaining how this mathematical foundation motivated our design choices to capture complex geometric structures.\n\nRegarding the specific enhancements in Section 3.3, each component has a clear motivation:\n- The Enhanced Low-order Convolution (Section 3.3.1) enriches the description of local point cloud structures by moving beyond simple mapping of center point features, which alone cannot effectively capture the overall geometric context.\n- The Explicit Structure Integration (Section 3.3.2) deliberately incorporates geometric relationships to enable DyPolyConv to effectively capture spatial arrangements within local structures, providing crucial spatial context.\n- The learnable parameter s increases DyPolyConv's flexibility.\n- The Computational Efficiency improvements (Section 3.3.3) replace exponential operations with logarithmic transformations for three key reasons: (1) reducing computational complexity from O(n²) to O(n log n), (2) enhancing numerical stability by avoiding overflow/underflow issues during backpropagation, and (3) reducing GPU memory consumption by approximately 15% during training.\n\nDue to page limitations, some explanations might be concise and we will expand these sections in the revised version.\n\n**Concern 2:** And the formulas in Section 3.3 are confusing—for example, the role of s in Eq. 15 is not clearly defined in the context of the Dynamic Polynomial Convolution.\n\n**Reply:** Thank you for highlighting this issue. The parameter s in Equation 15 is a binary switch that controls whether sign information is preserved (s=1) or discarded (s=0) during feature transformation. This key parameter allows DyPolyConv to adapt between directional sensitivity (when s=1, similar to Affine Basis Functions) and magnitude-only processing (when s=0, similar to Radial Basis Functions). The value of parameter s is typically set manually, which presents a significant challenge in determining flexible settings. Therefore, we adopted the approach in Equation 15 to learn parameter s in a flexible, learnable manner. We will further revise Section 3.3 in the final version to explicitly define the role of s and explain its geometric interpretation.\n\n**Concern 3:** There are missing ablation studies to show how the Dynamic Polynomial Convolution specifically contributes to performance improvements over other 3D convolution operations.\n\n**Reply:** Thank you for this valuable suggestion. As recommended, we conducted a comprehensive comparison between our DyPolyConv and four state-of-the-art 3D convolution operations for local point cloud aggregation. The experimental results are shown in the following table:\n\n| 3D Convolution Operations | S₀ | S₁ | Avg |\n|---------------------------|----|----|-----|\n| PointNet++[1] | 68.57 | 69.83 | 69.20 |\n| PointMLP[2] | 68.76 | 69.92 | 69.34 |\n| DGCNN[3] | 70.32 | 71.34 | 70.83 |\n| RepSurf[4] | 70.45 | 71.26 | 70.86 |\n| DyPolyConv(our) | **71.21**| **71.94**| **71.58**|\n\n[1] Pointnet++: Deep hierarchical feature learning on point sets in a metric space.\n[2] Rethinking network design and local geometry in point cloud: A simple residual MLP framework.\n[3] Dynamic graph cnn for learning on point clouds.\n[4] Surface representation for point clouds.\n\nResults show DyPolyConv outperforms all compared methods on both S3DIS dataset splits in the 2-way-1-shot setting. With an average mIoU of 71.58%, it surpasses RepSurf by 0.72%, DGCNN by 0.75%, PointNet++ by 2.38%, and PointMLP by 2.24%. This confirms the effectiveness of our polynomial fitting approach for geometric feature extraction in few-shot point cloud segmentation. We will add this analysis to better highlight DyPolyConv's contributions in our revised paper.\n\n**Concern 4:** And the paper lacks clarity and is not well structured. Clearer writing is needed.\n\n**Reply:** Our paper follows standard technical structure with clear Introduction, comprehensive Related Works, hierarchically organized Method section, and standard Experiments format. We will review our manuscript to further improve clarity.", "claims_and_evidence": "The paper makes a claim that pretraining models limit few-shot performance and the claim is supported by the experiments in the paper.", "methods_and_evaluation_criteria": "The evaluation criteria and datasets used make sense for the problem. However, the Method section lacks clarity, and the motivation behind certain design choices is not well explained. For instance, it is unclear how the Dynamic Polynomial Convolution module is enhanced and what the underlying motivation for these choices is. And the formulas in Section 3.3 are confusing—for example, the role of $s$ in Eq. 15 is not clearly defined in the context of the Dynamic Polynomial Convolution.", "theoretical_claims": "Not related.", "experimental_designs_or_analyses": "The experiments are conducted on two standard datasets and prove the effectiveness of the proposed method. However, the paper misses some important ablation studies to verify the designed components, such as specifically showing how Dynamic Polynomial Convolution improves performance compared to other 3D convolutions.", "relation_to_broader_scientific_literature": "The proposed designs do not overlap with other papers.", "essential_references_not_discussed": "Not related.", "other_strengths_and_weaknesses": "No.", "other_comments_or_suggestions": "No.", "questions_for_authors": "There are missing ablation studies to show how the Dynamic Polynomial Convolution specifically contributes to performance improvements over other 3D convolution operations. And the paper lacks clarity and is not well structured. Clearer writing is needed.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Hfcj5B7NBP", "reviewer": "Reviewer_wrBV", "summary": "The authors propose a novel framework for semantic segmentation of few-shot point clouds, called DyPolySeg. This framework consists of two parts. The first part is composed of an encoder and a decoder for representation learning of point clouds. In the encoder part, the authors propose a novel DyPolyConv. The second part is a PCM module for improving the performance of semantic segmentation of few-shot point clouds. The overall framework does not require pre-training. The authors conducted a large number of experiments in various few-shot settings and verified that this method achieved the best performance.\n\n## update after rebuttal\nI thank the authors for their comprehensive and detailed responses to my questions. After reading their rebuttal, I believe the authors have addressed all the issues I raised. I consider the manuscript to have met the acceptance standards, and I will maintain my score.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the reviewers' positive comments on our manuscript and their valuable suggestions. We have responded to all your questions in detail, as follows:\n\n**Concern 1:** Although the method proposed by the author achieves the best performance, I would like to know that the author claims to have proposed a lightweight PCM but does not explain in the article how lightweight the module is. Please provide this information.\n\n**Reply:** Thank you for your question about PCM's efficiency. Our PCM module contains only 0.1M parameters, which accounts for just 7% of the entire model's parameters (1.42M total), making it significantly more lightweight than comparable modules in other architectures. For context, prototype enhancement modules in competing methods like PAP3D require approximately 0.5-0.6M parameters, 5-6 times larger than our PCM.\nDespite its compact design, PCM substantially improves performance - when added to the baseline model, it increases mIoU from 53.28% to 71.58% (an 18.3% absolute improvement) as shown in Table 3. This demonstrates PCM's exceptional parameter efficiency. Additionally, we tested DyPolySeg on the S0 subset of the S3DIS dataset and found that the 2-way-1-shot inference time was 21 seconds and occupied 1.08G video memory, with PCM adding only 3 seconds to the inference time compared to the backbone alone. We will add these detailed efficiency metrics in the final version to better quantify PCM's lightweight nature.\n\n**Concern 2:** I would like to know whether the PCM proposed by the author is universal and can be used in other methods?\n\n**Reply:** Yes, PCM is designed as a universal module that can be integrated into other few-shot point cloud segmentation frameworks. We conducted additional experiments applying PCM to baseline methods like AttMPTI and Seg-PN, resulting in performance improvements of 3.8% and 2.1% respectively on S3DIS. PCM's design is agnostic to the specific feature extraction backbone, requiring only query and support features as input. We will add these cross-method integration results to the paper to demonstrate PCM's universality.\n\n**Concern 3:** The content of Section 3.3.3 is too thin. The author should explain why the exponential operation is replaced by the logarithmic operation and what are the benefits of doing so.\n\n**Reply:** Thank you for this insightful suggestion. We will significantly expand Section 3.3.3 to provide a more comprehensive explanation of our logarithmic transformation approach. The replacement of exponential operations with logarithmic transformations was motivated by multiple critical considerations: (1) Computational efficiency: Logarithmic operations reduce the computational complexity from O(n²) to O(n log n), resulting in a 35% reduction in forward pass computation time during training. (2) Numerical stability: Exponential operations with high-power values can quickly lead to overflow (extremely large values) or underflow (extremely small values approaching zero) issues, particularly when processing point clouds with large spatial variations. Our logarithmic transformations maintain stable gradients during backpropagation, reducing gradient vanishing/explosion issues and improving convergence speed by approximately 20%. (3) Memory efficiency: Our logarithmic approach reduces GPU memory consumption by approximately 15% during training compared to direct exponential implementation. (4) Precision preservation: For high-order polynomial terms (n>2), logarithmic space calculations preserve numerical precision better, resulting in more accurate geometric modeling.\n\nWe conducted ablation experiments comparing direct exponential implementation versus our logarithmic approach, finding that the logarithmic version not only trains faster (1.2 hours vs. 1.8 hours) but also achieves better final performance (71.58% vs. 69.27% mIoU). We will incorporate these explanations and quantitative benefits in the revised paper.\n\n**Concern 4:** The output of the cosine similarity calculation between the query feature and PCM in Figure 2 (a) should point to the predicted image, right? Rather than the predicted image point to cos?\n\n**Reply:** Thank you for pointing out the arrow error. There is indeed a directional error in Figure 2(a). The arrow should point from the cosine similarity calculation to the prediction image, not the other way around. We will correct this in the final version to accurately reflect the information flow in our architecture.\n\n**Concern 5:** The schematic diagram of polynomial fitting in Figure 2 (b) is not clear enough. It is recommended that the author improve the clarity of this sub-graph.\n\n**Reply:** Thank you for your feedback on Figure 2(b). In the revised version, we will redesign this figure to improve its resolution.", "claims_and_evidence": "Yes. The claims made by the authors are well supported. In particular, the experimental results and ablation studies on the S3DIS and ScanNet datasets well support the authors' claims.", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes. The author explains the relationship between DyPolyConv and Taylor series very well, providing a clear theoretical basis for his method.", "experimental_designs_or_analyses": "Yes. The authors evaluate the superiority of their method compared with the SOTA methods on the S3DIS and ScanNet datasets in Tables 1 and 2, and verify the effectiveness of each component through ablation experiments.", "relation_to_broader_scientific_literature": "The author's method has made some progress and has promoted the field of point cloud few-shot semantic segmentation. In particular, the author has solved the pre-training constraints of the current method and has also shown advantages in the new setting (COSeg).", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "**Strengths:**\n1. The authors proposed a novel framework for semantic segmentation of few-shot point clouds, called DyPolySeg. \n2. nspired by Taylor series, the authors proposed a novel convolution to effectively solve the problem of local aggregation of point clouds. \n3. The authors proposed a lightweight PCM to effectively solve the problem of domain differences between query and gallery.\n\n**Weaknesses:**\n1. Although the method proposed by the author achieves the best performance, I would like to know that the author claims to have proposed a lightweight PCM but does not explain in the article how lightweight the module is. Please provide this information. \n2. I would like to know whether the PCM proposed by the author is universal and can be used in other methods? \n3. The content of Section 3.3.3 is too thin. The author should explain why the exponential operation is replaced by the logarithmic operation and what are the benefits of doing so.", "other_comments_or_suggestions": "1. The output of the cosine similarity calculation between the query feature and PCM in Figure 2 (a) should point to the predicted image, right? Rather than the predicted image point to cos? \n2. The schematic diagram of polynomial fitting in Figure 2 (b) is not clear enough. It is recommended that the author improve the clarity of this sub-graph.", "questions_for_authors": "See Weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wlblebRfQ8", "reviewer": "Reviewer_7yxm", "summary": "The author proposed an interesting method to solve the problem of semantic segmentation of few-shot point clouds. Specifically, the author proposed a local feature aggregation convolution inspired by Taylor series, and built the entire model backbone on this basis. To specifically solve the problem of semantic segmentation of few-shot point clouds, the author proposed a novel PCM module, which is a lightweight module that effectively solves the difference between gallery set features and query set features through self-attention mechanism and cross-attention, and verifies the effectiveness of the method on multiple datasets and tasks.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your recognition of our method and detailed review. We have responded to your concerns in detail and hope to address all your questions.\n\n**Concern 1:** Although the method has achieved certain advancement, I think it is also necessary to think about the complexity of the model, but I did not see any analysis of the model complexity in the article. I suggest that the author can analyze it.\n\n**Reply:** Thank you for your question. We have analyzed the model complexity of DyPolySeg and will include this in the final version. Specifically, our complete model contains 1.42M parameters, with DyPolyConv accounting for 0.97M parameters and PCM comprising only 0.1M parameters. For computational complexity, DyPolySeg requires 1.08G of video memory and has an inference time of 21 seconds for a 2-way-1-shot task on the S3DIS dataset (S0 split) using an NVIDIA RTX 4090. This is comparable to Seg-PN while achieving significantly better performance, and much more efficient than heavier models like PAP3D (2.45M parameters). Additionally, during the training phase, our model requires 1.2 hours, which is shorter than PAP3D (4.7h).\n\n**Concern 2:** Regarding DyPolyConv, I see that it is a unified point cloud representation convolution, especially its two special cases are ABF and RBF, but the article does not provide their sources, and the author needs to cite them correctly.\n\n**Reply:** Thank you for your suggestion. We will properly cite the sources for ABF and RBF in the final version. Specifically, we will reference the work by Radial Basis Functions by Buhmann (2003, \"Radial Basis Functions: Theory and Implementations\") and for Affine Basis Functions, we will cite the work by Duchon (1977, \"Splines minimizing rotation-invariant semi-norms in Sobolev spaces\"). These references provide the theoretical foundations for these special cases of our DyPolyConv.\n\n**Concern 3:** The author may need to provide more detailed motivation and analysis for the design of PCM to help understand how it effectively solves the prototype bias problem in few-shot learning.\n\n**Reply:** Thank you for this valuable suggestion. We will substantially expand our explanation of PCM's motivation, design principles, and effectiveness in addressing prototype bias in the revised paper.\nThe fundamental challenge in few-shot point cloud segmentation is that limited support samples often fail to fully represent the distribution of their respective classes, creating biased prototypes that lead to inaccurate feature matching. This \"prototype bias\" is particularly severe in point cloud data due to geometric variations within the same semantic category.\nOur PCM addresses this challenge through two complementary mechanisms: (1) Self-Enhancement Module (SEM): This component learns the internal feature distribution patterns within each set independently. By computing self-correlation matrices (Eq. 18) and generating attention-based prototypes (Eq. 19-20), SEM captures class-specific characteristics that might be missing from sparse support samples. This self-attention mechanism effectively expands the representational capacity of prototypes beyond the limited samples provided. (2) Interactive Enhancement Module (IEM): While SEM focuses on internal distributions, IEM establishes fine-grained feature correspondences between support and query sets through cross-correlation (Eq. 21). This bidirectional knowledge transfer refines prototypes by incorporating query-specific contextual information, allowing adaptation to the target scene's characteristics.\n\n**Concern 4:** It is recommended that the author add an introduction to Mamba content.\n\n**Reply:** We appreciate this suggestion. We will include a dedicated subsection explaining Mamba's architecture for point cloud processing.\n\nMamba is a state-of-the-art sequence modeling architecture introduced by Gu et al. (2023, \"Mamba: Linear-Time Sequence Modeling with Selective State Spaces\") that employs Selective State Space Models (SSMs) for efficient long-range dependency modeling. Unlike attention-based mechanisms that scale quadratically with sequence length, Mamba achieves linear complexity through structured state space representations. In our context, Mamba's key components offer specific advantages for point cloud processing: (1) Selective State Space Module (SSM): Enables efficient sequence modeling with Θ(L) complexity (where L is sequence length) compared to Θ(L²) in attention-based approaches. This is particularly advantageous for processing dense point clouds. (2) Data-dependent Selection Mechanism: Dynamically adjusts receptive fields based on input characteristics, allowing adaptive focus on relevant spatial regions in point clouds. (3) Bidirectional Processing: Captures global context from multiple directions, complementing our DyPolyConv's local geometric modeling by providing crucial long-range dependencies.", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "yes", "theoretical_claims": "Yes. I checked some of their design theory. They designed DyPolyConv starting from Taylor series and provided the geometry of this convolution in the supplementary material.", "experimental_designs_or_analyses": "Yes. I think the authors’ experiments are quite comprehensive. They not only conducted experiments and ablation experiments on few-shot point cloud semantic segmentation tasks, but also conducted experiments on point cloud classification tasks.", "relation_to_broader_scientific_literature": "The author mentioned the most advanced work in the introduction, related work and experimental comparison. I think the author's work is at the forefront in this direction.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "1. This paper proposes a very expressive point cloud representation network, especially in few-shot scenarios.\n2. Specifically, the DyPolyConv proposed by the author is very interesting. It provides a new perspective for modeling the geometric structure of point clouds and has strong interpretability.\n3. The author also provides a lightweight PCM module to reduce domain differences.\n\nAlthough I think the author's method is novel and effective in some aspects, there are several issues that need to be addressed:\n1. Although the method has achieved certain advancement, I think it is also necessary to think about the complexity of the model, but I did not see any analysis of the model complexity in the article. I suggest that the author can analyze it.\n2. Regarding DyPolyConv, I see that it is a unified point cloud representation convolution, especially its two special cases are ABF and RBF, but the article does not provide their sources, and the author needs to cite them correctly.\n3. The author may need to provide more detailed motivation and analysis for the design of PCM to help understand how it effectively solves the prototype bias problem in few-shot learning.\n4. It is recommended that the author add an introduction to Mamba content.", "other_comments_or_suggestions": "1. The caption of Figure 1 is too long;\n2. The clarity of Figure 3 can be adjusted.", "questions_for_authors": "I don't have any other specific questions, and I need the author to answer the questions in the weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper presents a compelling and well-executed framework, DyPolySeg, for few-shot point cloud semantic segmentation, introducing a pretraining-free approach that combines a novel Taylor series-inspired DyPolyConv for expressive local feature learning and a lightweight PCM module for mitigating domain differences between support and query sets. Across four reviewers, the method is consistently recognized for its theoretical grounding, experimental rigor on multiple benchmarks, and practical contribution to advancing 3D few-shot learning. While some reviewers request additional clarity on specific design motivations and model complexity, these concerns are outweighed by the paper's novelty, strong empirical results, and detailed supplementary material. I recommend acceptance and encourage the authors to further strengthen the camera-ready version by including computational efficiency analysis, clarifying PCM’s design choices, and improving figure clarity.
Decision: Accept (poster)