Parameter is Not All You Need: Starting from Non-Parametric Networks for 3D Point Cloud Analysis

TL;DR

This work revisits non-learnable components in 3D point cloud processing and introduces Point-NN, a training-free, non-parametric network built from FPS, $k$-NN, and pooling, augmented by trig-based positional encodings. It demonstrates that Point-NN can achieve competitive results across shape classification, few-shot learning, part segmentation, and 3D object detection, and can further serve as a parameter-efficient architectural base (Point-PN) or a plug-and-play module to boost existing models without re-training. The paper also provides extensive ablations to justify the design choices (PosE, local geometry weighting, memory-based prediction) and discusses why trig functions capture useful high-frequency spatial patterns in 3D data. Overall, the approach offers a compelling, low-parameter alternative that complements learned models and hints at broader applicability of non-parametric methods in 3D vision.

Abstract

We present a Non-parametric Network for 3D point cloud analysis, Point-NN, which consists of purely non-learnable components: farthest point sampling (FPS), k-nearest neighbors (k-NN), and pooling operations, with trigonometric functions. Surprisingly, it performs well on various 3D tasks, requiring no parameters or training, and even surpasses existing fully trained models. Starting from this basic non-parametric model, we propose two extensions. First, Point-NN can serve as a base architectural framework to construct Parametric Networks by simply inserting linear layers on top. Given the superior non-parametric foundation, the derived Point-PN exhibits a high performance-efficiency trade-off with only a few learnable parameters. Second, Point-NN can be regarded as a plug-and-play module for the already trained 3D models during inference. Point-NN captures the complementary geometric knowledge and enhances existing methods for different 3D benchmarks without re-training. We hope our work may cast a light on the community for understanding 3D point clouds with non-parametric methods. Code is available at https://github.com/ZrrSkywalker/Point-NN.

Figures (9)

• Figure 1: The Pipeline of Non-Parametric Networks. Point-NN is constructed by the basic non-parametric components without any learnable operators. Free from training, Point-NN can achieve favorable performance on various 3D tasks.
• Figure 2: Two Applications of Point-NN. (a) As a non-parametric framework to construct parametric networks by simply inserting linear layers. (b) As a plug-and-play module to enhance already trained networks without re-training.
• Figure 3: Non-Parametric Encoder of Point-NN. We first utilize trigonometric functions, denoted as $\operatorname{PosE}(\cdot)$, to encode raw points into high-dimensional vectors, and then adopt non-learnable operations to hierarchically aggregate local features.
• Figure 4: Point-Memory Bank of Point-NN. We construct the memory bank by caching training-set features via the non-parametric encoder. Then, the test point cloud is simply classified by similarity matching without training.
• Figure 5: The Pipeline of Point-PN. Given the non-parametric framework of Point-NN, we simply construct the parametric derivative, Point-PN, by inserting linear layers into every stage of the encoder. Performance gain of using linear layers of A$\sim$E is shown in Table \ref{['t1']}.