PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets

Authors: Ali Kashefi
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Kolmogorov-Arnold Networks, PointNet, Computer Graphics, Classification, Segmentation

Abstract:
Kolmogorov–Arnold Networks (KANs) have recently gained attention as an alternative to traditional Multilayer Perceptrons (MLPs) in deep learning frameworks. KANs have been integrated into various deep learning architectures such as convolutional neural networks, graph neural networks, and transformers, with their performance evaluated. However, their effectiveness within point-cloud-based neural networks remains unexplored. To address this gap, we incorporate KANs into PointNet for the first time to evaluate their performance on 3D point cloud classification and segmentation tasks. Specifically, we introduce PointNet-KAN, built upon two key components. First, it employs KANs instead of traditional MLPs. Second, it retains the core principle of PointNet by using shared KAN layers and applying symmetric functions for global feature extraction, ensuring permutation invariance with respect to the input features. In traditional MLPs, the goal is to train the weights and biases with fixed activation functions; however, in KANs, the goal is to train the activation functions themselves. We use Jacobi polynomials to construct the KAN layers. We extensively and systematically evaluate PointNet-KAN across various polynomial degrees and special types such as the Lagrange, Chebyshev, and Gegenbauer polynomials. Our results show that PointNet-KAN achieves competitive performance compared to PointNet with MLPs on benchmark datasets for 3D object classification and segmentation, despite employing a shallower and simpler network architecture. We hope this work serves as a foundation and provides guidance for integrating KANs, as an alternative to MLPs, into more advanced point cloud processing architectures.

Decision: reject
Reviewer scores: 3, 3, 5

Reviews and discussion:
<thread>
creation date:
1729692262678

thread_type:
official_review

<thread_object>
creator: reviewer_bvrm

<content>
summary:
This paper is the first to introduce KAN in the 3D domain, replacing MLP with KAN based on PointNet. Experiments are conducted on both classification and segmentation tasks, providing guidance for the subsequent application of KAN in point cloud analysis tasks.

strengths:
This paper is the first to apply KAN to point cloud analysis tasks. The article is logically coherent, with complete formulas, and includes a substantial amount of experimentation to demonstrate the effectiveness of the proposed method, providing valuable guidance for the future development of KAN in point clouds.

weaknesses:
1. Some experimental results are concerning and lack detailed discussion or explanation. For instance, on ModelNet40, there is a significant performance difference for PointNet-KAN depending on whether the input includes normal vectors, suggesting that PointNet-KAN is highly sensitive to input variations. However, the authors did not provide a more thorough investigation or explanation regarding this sensitivity. Additionally, on ShapeNet Part, the performance of PointNet-KAN still falls short compared to PointNet. Furthermore, based on subsequent experimental results, it seems that merely increasing the scale of PointNet-KAN does not address this issue.

2. The robustness experiments only consider variations in point quantity and lack experimental results when increasing noise and rotation.

3. For the classification tasks, experiments were only conducted on the ModelNet40 dataset and the PointNet model. It is recommended to include experiments on the ScanObjectNN dataset as well. Additionally, since PointMLP is also based on MLP, it may be worthwhile to explore embedding KAN into PointMLP.

questions:
1. It is suggested that the authors provide a more detailed discussion and analysis of the experimental results. For example, they should explore why the presence of normal vectors has such a significant impact on the performance of PointNet-KAN on ModelNet40 and why the performance on ShapeNet Part is inferior to that of PointNet.

2. It is recommend that the authors include experiments on the ScanObjectNN dataset to further demonstrate the applicability of PointNet-KAN. Additionally, conducting experiments that address the effects of rotation and noise would provide a more comprehensive assessment of the robustness of PointNet-KAN.

3. Is there more detailed data regarding the $\textbf{influence of the size of tensors and global features}$? This could provide insights into the scalability of PointNet-KAN to some extent.

4. For Figure 2, I suggest adding a visual comparison with other methods to demonstrate the effectiveness of PointNet-KAN.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730295780540

thread_type:
official_review

<thread_object>
creator: reviewer_y4gc

<content>
summary:
he paper integrates KAN into PointNet to propose a PointNet-KAN. It replaces MLPs with KAN and conducts validations on 3D object classification and part segmentation tasks. Compared with PointNet, the PointNet-KAN performs better on classification but maintains similar segmentation results on the ShapeNet part dataset. Overall, this work validates the KAN on 3D point domains but lacks novelty and contributions.

strengths:
Integrating KAN into the 3D domain is interesting and may benefit the field of study.

weaknesses:
1. Limited novelty and contribution.  This paper looks more like a technique report rather than a research paper. It naively uses KAN to replace the MLPs in PointNet without any technique improvements on KAN. It would be more preferable if the paper could adapt KAN in terms of some properties of 3D points, like irregularity and unorderness, to fit the nature of 3D points.

2. Lack of motivation to introduce KAN into 3D point cloud domain. In the Introduction part, the paper mentions that KAN can learn activation functions by itself but does not illustrate other benefits of introducing KAN into the 3D domain. Therefore, it is unclear why to integrate KAN into PointNet.

3. Experiment results are not satisfactory and need more improvements. In terms of Tables 1&2, PointNet-KAN can only marginally surpass PointNet on ModelNet classification and is even lower than PointNet on part segmentation tasks.These weak results fail to validate the effectiveness of the proposed method.

questions:
If the paper aims to validate the effectiveness of replacing KAN with MLPs, how about trying more network architectures?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730704384830

thread_type:
official_review

<thread_object>
creator: reviewer_a2lp

<content>
summary:
The paper replaces Multi-Layer Perceptrons (MLPs) in the PointNet model with Kolmogorov-Arnold Network layers (KANs) to create a point-cloud-based neural network for classification or segmentation tasks on unordered 3D point sets. The proposed approach uses Jacobi polynomials to construct PointNet-KAN and investigate its performance across different polynomial degrees. The paper also includes efforts to examine the effect of special cases of Jacobi polynomials, including Legendre polynomials, Chebyshev polynomials of the first and second kinds, and Gegenbauer polynomials. The paper supports the proposed method with extensive evaluations of PointNet-KAN hyperparameters, such as the degree and type of polynomial used in constructing KANs. PointNet-KAN is a shallower and simpler network compared to PointNet and achieves competitive performance.

strengths:
+ The proposed approach accommodates Jocbi polynomials and special case polynomials and provides experimental results.
+ The paper is well-written and easy to understand.

weaknesses:
- The proposed method evaluation is limited to synthetic datasets. Most recent state-of-the-art 3D Classification methods use real-world datasets such as ScanObjectNN. 
- The time complexity of the pointNet-KAN model during training/testing is not discussed. It is unclear if it is worth replacing MLPs with KANs as the overall accuracy improvements are less significant (< 2%).
- The proposed approach is a straightforward replacement of MLPs by KANs. Although it has limited novelty for a paper in the ICLR main track, it would be a good contribution if submitted to one of the workshops.
- While qualitative results for part segmentation are provided for Jacobi polynomials, the results for special polynomials such as Legendre, Chebyshev, and Gegenbauer polynomials are not provided. 
- Table 3 shows that the increase in Jacobi polynomial degree and the corresponding increase in the number of parameters seem to have marginal improvements in both mean and overall accuracy. So, it is unclear if the increase in accuracy due to the increase in Jacobi polynomial degree from 2 to 4 is due to the increase in the number of parameters only and not due to the proposed approach.
- The mean or overall accuracy for classification and segmentation tasks is lower than that of the original PointNet model (refer to Tables 1 and 2).

questions:
Kindly provide experimental results to back the claim below.

"Using more complex versions of PointNet could introduce other factors that might obscure the direct influence of KANs, making it challenging to determine whether any performance changes are due to the KAN architecture or other network components."
</content>
</thread_object>

</thread>
<thread>
creation date:
1732639576744

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
[Acknowledgment and Request for Reevaluation]

comment:
We sincerely appreciate all the comments, questions, and concerns provided by the reviewers. We have thoroughly answered all the questions, addressed the concerns, and submitted a revised version of the manuscript. We would be grateful if the reviewers could kindly reevaluate our work accordingly. Thank you.
</content>
</thread_object>

</thread>
<thread>
creation date:
1733300029591

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
[Kind Request to the Area Chair: Fair Assessment of Our Submission]

comment:
Dear Area Chair,

We greatly appreciate the efforts of the reviewers in providing feedback on our submission and their valuable time. However, we have concerns that our submission did not receive adequate engagement during the discussion period, and critical aspects of our rebuttal appear to have been overlooked.

Below, we summarize the major additions made to our manuscript in response to the reviewers' requests:

1. We added experiments for classification on **ScanObjectNN**.

2. We integrated KAN into **PointMLP** in addition to its integration into **PointNet**.

Here is a summary of the reviewers' actions during the discussion period:

--> Reviewer **A2LP**: This reviewer never responded to our rebuttal or engaged in the discussion period.

--> Reviewer **y4gC**: Provided a single general comment:

*Thank the authors for providing additional materials. However, the current version still lacks strong motivations and experimental results to support the integration of KAN into point-based methods. I'll keep my rating.*

This feedback does not clarify what specific experiments or additional motivations were expected. Without further details, it was challenging to address these concerns effectively.

--> Reviewer **bvRm**: Requested results for **ScanObjectNN** and integration of KAN into a modern architecture such as **PointMLP**. We provided these results, yet the final comment stated:

*Thank you for your response. Our opinion is consistent with that of the other reviewers, who also question whether KAN is suitable for the modern architecture of point cloud models. Therefore, we will maintain the score.*

This comment appears to disregard our response and newly added experiments with **PointMLP**, which was previously mentioned as an example of a modern architecture by the reviewer.

We are concerned that these issues may have prevented a fair evaluation of our submission. Specifically, the reviewers’ lack of detailed feedback and engagement during the discussion period has left us unclear about their expectations or concerns.

We sincerely hope you can consider these points in your assessment to ensure a fair review of our work.

We highly appreciate your time and considering our concerns.

Best regards,

The Authors
</content>
</thread_object>

</thread>


Metareview:
metareview:
All reviewers unanimously provided negative feedback, primarily concerning why KAN can enhance point cloud parsing, both in terms of innovation and experimental aspects. Although the authors supplemented the relevant experiments as requested during the rebuttal process, the reviewers still held negative views. Their comments are presented as follows.

Reviewer A2LP: The evaluation is limited to synthetic datasets, with no experiments on real-world datasets like ScanObjectNN. The proposed approach lacks significant novelty, as it is primarily a straightforward replacement of MLPs with KANs. Additionally, the time complexity and computational efficiency of PointNet-KAN are not sufficiently explored.

Reviewer y4gC: The paper lacks methodological novelty and appears more like a technical report. The results fail to validate the effectiveness of KAN integration, as PointNet-KAN only marginally outperforms PointNet for classification and underperforms for segmentation. The motivation for introducing KAN into 3D domains is unclear, and the experimental results are not compelling.

Reviewer bvRm:  The experimental results are inconsistent, with PointNet-KAN performing worse than PointNet in segmentation and being highly sensitive to input variations like normal vectors. Robustness experiments are limited and do not address important factors like noise and rotation. The lack of experiments on modern architectures like PointMLP raises concerns about generalizability.

Two reviewers recommended rejection (scores of 3), and one reviewer provided a marginally below acceptance threshold score (5). The reviewers collectively question the contribution and practical relevance of the proposed method. Therefore, my recommendation is to reject the paper.