Geometric Feature Embedding for Effective 3D Few-Shot Class Incremental Learning

We sincerely appreciate your insightful feedback, which has guided us in refining the manuscript and addressing key concerns. Below, we provide detailed responses to each of your questions, supported by additional analyses and clarifications.

Q1: Clarification of Ablation Studies in Table 3
A1: Thank you for prompting us to clarify this section. Table 3 systematically evaluates the contributions of two critical components in the geometric feature extraction module:

• Dynamic Geometric Projection Clusters: These clusters are constructed via spectral clustering and Laplacian eigenmaps to encode shared geometric structures.
• Attention Weights for Basis Vectors: Learnable weights prioritize cluster centers relevant to incremental tasks.

The ablation settings are:

• Row 1: Raw point cloud features without DGPC.

• Row 2: DGPC with equal weights for all basis vectors.

• Row 3: DGPC + learnable attention weights.
  Key findings are now presented more succinctly:

• DGPC Necessity: Removing DGPC (Row 1) degrades average accuracy by 2.7%, as raw features fail to integrate geometric-textual semantics.

• Attention Mechanism: Adding learnable weights (Row 3) improves harmonic accuracy by 2.1% over Row 2, demonstrating adaptive weighting’s role in suppressing noise and outliers.

The results validate that DGPC and attention weights synergistically enhance stability and discriminability. These results are now contextualized in Section 4.4, and additional visualization examples are available in Figure 2 of the anonymous link. We previously did not express this clearly, but based on your feedback, we will restructure the table and discussion for better interpretability.

Q2: Visualization of Dynamic Projection Clusters
A2: To validate the effectiveness of dynamic geometric feature projection clusters during incremental learning, we visualize the geometric features extracted by DGPC at each incremental stage, as shown in Figure 2 of the anonymous link. Visualizations reveal that DGPC-enhanced features exhibit tighter intra-class clustering and clearer inter-class separation. These results demonstrate that DGPC effectively encodes task-invariant geometric priors, enabling robust feature extraction across incremental phases. We have integrated key examples into the main text in our revised version.

Q3: Implementation Details of the Transformer Encoder
A3: The Transformer encoder comprises 2 standard layers, each with 8-head self-attention. We have enhanced the implementation details section in the revised version to include more comprehensive information.

Q4: Design Principles of Figure 1
A4: We sincerely appreciate your guidance in improving Figure 1's clarity. In light of your thoughtful suggestions, we have reorganized and optimized Figure 1 (detailed in Figure 1 of the anonymous link) to improve its clarity. It now contains 7 comparisons:

1. SOTA Baselines: Methods (1)-(2) adopt strategies from C3PR [1] and FoundationModel [2].
2. Cross-Combination Strategies: Methods (3)-(7) integrate various prompt styles with distinct training strategies.

For detailed explanations of Figure 1, we sincerely invite you to consult our response to Reviewer 8rPH's Question 2.

Q5: Linking Observations to Robust Feature Learning
A5: We appreciate your guidance in strengthening this connection. The experiments (lines 87-93) demonstrate that complex prompt designs yield inferior performance compared to simple prompts. This observation highlights a critical limitation: existing methods overly rely on manually crafted text semantics while failing to autonomously extract geometry-aware robust features from 3D point clouds. Consequently, models exhibit excessive sensitivity to textual variations and struggle to adapt to distribution shifts in incremental phases with limited samples.

3D-FLEG addresses this by:

1. Geometric Feature Embedding: Explicitly encoding spatial structures into prompts via dynamic projection clusters, bypassing dependency on complex text engineering.
2. Unified Optimization: Forcing joint alignment between geometric features and text semantics during incremental training, enabling the model to prioritize discriminative cross-modal patterns from sparse data.

By incorporating supplementary experiments, enhanced visualizations, and expanded explanations, we sincerely hope to have addressed all raised concerns. Please let us know if you feel any additional adjustments would better address your concerns.

References

[1] Canonical shape projection is all you need for 3d few-shot class incremental learning, ECCV 2024.

[2] Foundation Model-Powered 3D Few-Shot Class Incremental Learning via Training-Free Adaptor, ACCV 2024.

Thank you for your insightful feedback, which has helped us significantly improve the clarity and rigor of our manuscript. Below are our detailed responses:

Q1: Claims (Laplacian Eigenmaps, AdaptiveAvgPool1d, geometric feature) are not well supported

A1: (1) Laplacian Eigenmaps for Geometric Structure Extraction
Theoretically, Laplacian Eigenmaps minimizes $\sum_{i,j} (y_i - y_j)^2 W_{ij}$, where $y_i, y_j$ are low-dimensional representations of data points $x_i, x_j$, and $W_{ij}$ reflects their proximity ($W_{ij}=e^{-\frac{\|x_i-x_j\|^2}{t}}$ if neighbors; otherwise, $W_{ij}=0$). This ensures nearby points in the original space remain close in the reduced space. Using the graph Laplacian $L=D-W$, the problem reduces to minimizing $y^T L y$. The eigenvectors of $L$ capture the manifold's structure, preserving local geometry effectively. A similar theoretical analysis appears in [1].

Besides, we have additionally conducted an ablation study to validate the role of Laplacian Eigenmaps as given below, demonstrating a 1.8% improvement in accuracy when utilized. We have incorporated the comprehensive theoretical proof and analysis in our revised paper.

A1: (2) AdaptiveAvgPool1d for Fine-Grained Features
We apologize for the confusion caused by the description of "fine-grained" features. You are right that traditional average pooling (AvgPool) typically extracts globally smoothed features. AdaptiveAvgPool1d in 3D-FLEG differs by dynamically adjusting pooling windows to capture local geometric statistics rather than fixed-window averaging. Specifically, it quantifies geometric attribute distributions across localized regions along the channel dimension, enabling fine-grained pattern extraction [2], where "fine-grained" refers to the statistical representation of local geometric details. We have revised our manuscript to clarify this distinction and articulate our design rationale.

A1: (3) Modality Abstraction Alignment
We have strengthened Section 4.3 to clarify the modality abstraction alignment: A dual-pooling strategy (Eq. 5) extracts multi-scale geometric features, bridging the gap between text and point cloud details. The Transformer encoder (Eq. 6) then refines these features, emphasizing geometry relevant to text prompts and reducing noise. Cross-entropy loss (Eq. 8) ensures consistency in the shared semantic space, aligning geometric and textual abstractions.

Q2: Cross-Dataset Superiority

A2: Thank you for prompting this critical analysis. 3D-FLEG’s cross-dataset superiority stems from its geometry-centric design:

• Dynamic Projection Clusters capture task-invariant geometric patterns, which generalize across synthetic-to-real domains.
• Geometric Feature Embedding directly fuses these features with text semantics, bypassing domain-specific text variations.

This synergy enables 3D-FLEG to achieve 7% higher accuracy in cross-dataset tasks. We have revised Section 4.3 to clarify this mechanism.

Q3: Symbol Confusion and Misspellings

A3: Thank you for highlighting these inconsistencies. We have reviewed the manuscript and made corrections to the symbols and typographical errors to improve clarity and rigor.

Q4: Detailed Descriptions of Prompt and Training Strategies in Figure 1

A4: We appreciate your suggestion to improve Figure 1. We have detailed the experimental setup principles with relevant citations. For further details, please see our response to Reviewer 8rPH's Q2. The "Alignment Module and Dual Cache System" requires caching five samples per class, causing significant computational and memory overhead. In contrast, our geometric embedding module integrates geometric features directly with text prompts, eliminating the need for complex alignment training and caching.

Q5：Clarification on Initial Features ${featBase}_i$ and ${featPoint}_i$

A5： To address this ambiguity, we have revised Section 3 to explicitly define:

${featBase}_i$ : Features extracted from base-class data using the frozen Uni3D encoder. These features are used to construct dynamic geometric projection clusters.
${featPoint}_i$ : Features processed during incremental training from the same Uni3D encoder. These are dynamically reprojected through DGPC using learnable attention weights to extract geometric features.

Your feedback has guided us in refining both the theoretical foundations and presentation of our work. All revisions have been incorporated into the manuscript.

References

[1] Laplacian eigenmaps for dimensionality reduction and data representation, Neural computation 2003.

[2] Point cloud segmentation of overhead contact systems with deep learning in high-speed rails, Journal of Network and Computer Applications 2023.

Thank you for your thoughtful and constructive feedback. We deeply appreciate your insights, which have guided us in refining our manuscript. Below, we outline the specific revisions made in response to your concerns:

Q1: Ablation Studies on the Number of Clusters
A1: We deeply appreciate your guidance on this critical aspect. Honestly speaking, we have added a detailed ablation analysis of the number of clusters in Table 6 of Appendix D (also given below), demonstrating how it affects model performance. Note that the cluster numbers are the same as the Basis Vectors Count in our experiments, as each cluster center is adaptively mapped to a corresponding basis vector within the projection space during dynamic projection cluster construction. As shown in Table 6, aligning cluster numbers with the base model's feature dimension (1024 in our case) balances information retention for accuracy and the redundancy of basis vectors. We have also included additional sensitivity analyses on cluster update rates as given in Fig. 6 of Appendix D. We have revised our manuscript to emphasize these findings more clearly in the main paper.

Q2：Impact of Prompt Style on Model Performance
A2: Thank you for highlighting the importance of prompt-style analysis. We implemented a more comprehensive comparison of the 7 experimental configurations. They include:

1. SOTA Baselines: Methods (1)-(2) adopt strategies from C3PR [1] and FoundationModel [2].
2. Cross-Combination Strategies: Methods (3)-(7) integrate various prompt styles with distinct training strategies.

From that, we recorded and provided a new Figure 1 (now visible in Figure 1 of the anonymous link) in our revised version.

As shown in Figure 1, the performance of our geometric embedding (Method 7) remains stable across prompt variations, proving reduced dependency on prompt quality. This demonstrates that geometric feature embedding alleviates reliance on prompt quality by encoding structural priors, ensuring stable performance even under variations in prompt style. Compared with "Alignment Module + Dual Cache System" (Method 2), which caches 5 samples per class, our strategy replays only a single sample and achieves 7% higher accuracy with lower memory overhead.

Q3：Cited related papers
A3: We sincerely appreciate the suggestion. The following works have been incorporated to strengthen our related works review:

1. Geometric Word-Based Segmentation [3]: Validates cluster-driven feature learning, aligning with our dynamic projection cluster design. (We have added it to Section 3.3 in our revised paper.)
2. 3D Few-Shot Generalization [4]: Highlights domain adaptation challenges, motivating our geometry-centric approach for cross-dataset robustness. (We have added it to Section 3.4 in our revised paper.)
3. Multimodal Fusion [5]: Supports our cross-modal alignment strategy via joint geometric-textual optimization. (We have added it to Section 3.4 in our revised paper.)

These references are now cited in relevant sections as indicated in the corresponding bracket.

We hope our revised works have addressed your concerns. Should further clarifications or adjustments be needed, we are fully committed to incorporating your guidance. Thanks for your feedback, as it is invaluable in refining our work.

References

[1] Canonical shape projection is all you need for 3d few-shot class incremental learning, ECCV 2024.

[2] Foundation Model-Powered 3D Few-Shot Class Incremental Learning via Training-free Adaptor, ACCV 2024.

[3] Generalized Few-Shot Point Cloud Segmentation Via Geometric Words, ICCV 2023.

[4] Rethinking Few-shot 3D Point Cloud Semantic Segmentation, CVPR 2024.

[5] Multimodality Helps Few-shot 3D Point Cloud Semantic Segmentation, ICLR 2025.