Introducing the Short-Time Fourier Kolmogorov Arnold Network: A Dynamic Graph CNN Approach for Tree Species Classification in 3D Point Clouds

Accurate classification of tree species based on Terrestrial Laser Scanning (TLS) and Airborne Laser Scanning (ALS) is essential for biodiversity conservation. While advanced deep learning models for 3D point cloud classification have demonstrated strong performance in this domain, their high complexity often hinders the development of efficient, low-computation architectures. In this paper, we introduce STFT-KAN, a novel Kolmogorov-Arnold network that integrates the Short-Time Fourier Transform (STFT), which can replace the standard linear layer with activation. We implemented STFT-KAN within a lightweight version of DGCNN, called liteDGCNN, to classify tree species using the TLS data. Our experiments show that STFT-KAN outperforms existing KAN variants by effectively balancing model complexity and performance with parameter count reduction, achieving competitive results compared to MLP-based models. Additionally, we evaluated a hybrid architecture that combines MLP in edge convolution with STFT-KAN in other layers, achieving comparable performance to MLP models while reducing the parameter count by 50% and 75% compared to other KAN-based variants. Furthermore, we compared our model to leading 3D point cloud learning approaches, demonstrating that STFT-KAN delivers competitive results compared to the state-of-the-art method PointMLP lite with an 87% reduction in parameter count.

Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds

The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributions into a Hilbert space via the Optimal Transport maps from a fixed reference distribution, and this linearization allows downstream tasks to be completed using off the shelf (linear) machine learning algorithms. We provide a case study of performing ML on 3D scans of lemur teeth, where the original questions of classification, clustering, dimension reduction, and data generation reduce to simple linear operations performed on the LOT embedded representations.

PointABM:Integrating Bidirectional State Space Model with Multi-Head Self-Attention for Point Cloud Analysis

Mamba, based on state space model (SSM) with its linear complexity and great success in classification provide its superiority in 3D point cloud analysis. Prior to that, Transformer has emerged as one of the most prominent and successful architectures for point cloud analysis. We present PointABM, a hybrid model that integrates the Mamba and Transformer architectures for enhancing local feature to improve performance of 3D point cloud analysis. In order to enhance the extraction of global features, we introduce a bidirectional SSM (bi-SSM) framework, which comprises both a traditional token forward SSM and an innovative backward SSM. To enhance the bi-SSM's capability of capturing more comprehensive features without disrupting the sequence relationships required by the bidirectional Mamba, we introduce Transformer, utilizing its self-attention mechanism to process point clouds. Extensive experimental results demonstrate that integrating Mamba with Transformer significantly enhance the model's capability to analysis 3D point cloud.

PointDGMamba: Domain Generalization of Point Cloud Classification via Generalized State Space Model

Domain Generalization (DG) has been recently explored to improve the generalizability of point cloud classification (PCC) models toward unseen domains. However, they often suffer from limited receptive fields or quadratic complexity due to the use of convolution neural networks or vision Transformers. In this paper, we present the first work that studies the generalizability of state space models (SSMs) in DG PCC and find that directly applying SSMs into DG PCC will encounter several challenges: the inherent topology of the point cloud tends to be disrupted and leads to noise accumulation during the serialization stage. Besides, the lack of designs in domain-agnostic feature learning and data scanning will introduce unanticipated domain-specific information into the 3D sequence data. To this end, we propose a novel framework, PointDGMamba, that excels in strong generalizability toward unseen domains and has the advantages of global receptive fields and efficient linear complexity. PointDGMamba consists of three innovative components: Masked Sequence Denoising (MSD), Sequence-wise Cross-domain Feature Aggregation (SCFA), and Dual-level Domain Scanning (DDS). In particular, MSD selectively masks out the noised point tokens of the point cloud sequences, SCFA introduces cross-domain but same-class point cloud features to encourage the model to learn how to extract more generalized features. DDS includes intra-domain scanning and cross-domain scanning to facilitate information exchange between features. In addition, we propose a new and more challenging benchmark PointDG-3to1 for multi-domain generalization. Extensive experiments demonstrate the effectiveness and state-of-the-art performance of our presented PointDGMamba.

PointMT: Efficient Point Cloud Analysis with Hybrid MLP-Transformer Architecture

In recent years, point cloud analysis methods based on the Transformer architecture have made significant progress, particularly in the context of multimedia applications such as 3D modeling, virtual reality, and autonomous systems. However, the high computational resource demands of the Transformer architecture hinder its scalability, real-time processing capabilities, and deployment on mobile devices and other platforms with limited computational resources. This limitation remains a significant obstacle to its practical application in scenarios requiring on-device intelligence and multimedia processing. To address this challenge, we propose an efficient point cloud analysis architecture, \textbf{Point} \textbf{M}LP-\textbf{T}ransformer (PointMT). This study tackles the quadratic complexity of the self-attention mechanism by introducing a linear complexity local attention mechanism for effective feature aggregation. Additionally, to counter the Transformer's focus on token differences while neglecting channel differences, we introduce a parameter-free channel temperature adaptation mechanism that adaptively adjusts the attention weight distribution in each channel, enhancing the precision of feature aggregation. To improve the Transformer's slow convergence speed due to the limited scale of point cloud datasets, we propose an MLP-Transformer hybrid module, which significantly enhances the model's convergence speed. Furthermore, to boost the feature representation capability of point tokens, we refine the classification head, enabling point tokens to directly participate in prediction. Experimental results on multiple evaluation benchmarks demonstrate that PointMT achieves performance comparable to state-of-the-art methods while maintaining an optimal balance between performance and accuracy.

PADRe: A Unifying Polynomial Attention Drop-in Replacement for Efficient Vision Transformer

We present Polynomial Attention Drop-in Replacement (PADRe), a novel and unifying framework designed to replace the conventional self-attention mechanism in transformer models. Notably, several recent alternative attention mechanisms, including Hyena, Mamba, SimA, Conv2Former, and Castling-ViT, can be viewed as specific instances of our PADRe framework. PADRe leverages polynomial functions and draws upon established results from approximation theory, enhancing computational efficiency without compromising accuracy. PADRe's key components include multiplicative nonlinearities, which we implement using straightforward, hardware-friendly operations such as Hadamard products, incurring only linear computational and memory costs. PADRe further avoids the need for using complex functions such as Softmax, yet it maintains comparable or superior accuracy compared to traditional self-attention. We assess the effectiveness of PADRe as a drop-in replacement for self-attention across diverse computer vision tasks. These tasks include image classification, image-based 2D object detection, and 3D point cloud object detection. Empirical results demonstrate that PADRe runs significantly faster than the conventional self-attention (11x ~ 43x faster on server GPU and mobile NPU) while maintaining similar accuracy when substituting self-attention in the transformer models.

TripletMix: Triplet Data Augmentation for 3D Understanding

Data augmentation has proven to be a vital tool for enhancing the generalization capabilities of deep learning models, especially in the context of 3D vision where traditional datasets are often limited. Despite previous advancements, existing methods primarily cater to unimodal data scenarios, leaving a gap in the augmentation of multimodal triplet data, which integrates text, images, and point clouds. Simultaneously augmenting all three modalities enhances diversity and improves alignment across modalities, resulting in more comprehensive and robust 3D representations. To address this gap, we propose TripletMix, a novel approach to address the previously unexplored issue of multimodal data augmentation in 3D understanding. TripletMix innovatively applies the principles of mixed-based augmentation to multimodal triplet data, allowing for the preservation and optimization of cross-modal connections. Our proposed TripletMix combines feature-level and input-level augmentations to achieve dual enhancement between raw data and latent features, significantly improving the model's cross-modal understanding and generalization capabilities by ensuring feature consistency and providing diverse and realistic training samples. We demonstrate that TripletMix not only improves the baseline performance of models in various learning scenarios including zero-shot and linear probing classification but also significantly enhances model generalizability. Notably, we improved the zero-shot classification accuracy on ScanObjectNN from 51.3 percent to 61.9 percent, and on Objaverse-LVIS from 46.8 percent to 51.4 percent. Our findings highlight the potential of multimodal data augmentation to significantly advance 3D object recognition and understanding.

Mamba3D: Enhancing Local Features for 3D Point Cloud Analysis via State Space Model

Existing Transformer-based models for point cloud analysis suffer from quadratic complexity, leading to compromised point cloud resolution and information loss. In contrast, the newly proposed Mamba model, based on state space models (SSM), outperforms Transformer in multiple areas with only linear complexity. However, the straightforward adoption of Mamba does not achieve satisfactory performance on point cloud tasks. In this work, we present Mamba3D, a state space model tailored for point cloud learning to enhance local feature extraction, achieving superior performance, high efficiency, and scalability potential. Specifically, we propose a simple yet effective Local Norm Pooling (LNP) block to extract local geometric features. Additionally, to obtain better global features, we introduce a bidirectional SSM (bi-SSM) with both a token forward SSM and a novel backward SSM that operates on the feature channel. Extensive experimental results show that Mamba3D surpasses Transformer-based counterparts and concurrent works in multiple tasks, with or without pre-training. Notably, Mamba3D achieves multiple SoTA, including an overall accuracy of 92.6% (train from scratch) on the ScanObjectNN and 95.1% (with single-modal pre-training) on the ModelNet40 classification task, with only linear complexity.

Nearest Neighbors Meet Deep Neural Networks for Point Cloud Analysis

Performances on standard 3D point cloud benchmarks have plateaued, resulting in oversized models and complex network design to make a fractional improvement. We present an alternative to enhance existing deep neural networks without any redesigning or extra parameters, termed as Spatial-Neighbor Adapter (SN-Adapter). Building on any trained 3D network, we utilize its learned encoding capability to extract features of the training dataset and summarize them as prototypical spatial knowledge. For a test point cloud, the SN-Adapter retrieves k nearest neighbors (k-NN) from the pre-constructed spatial prototypes and linearly interpolates the k-NN prediction with that of the original 3D network. By providing complementary characteristics, the proposed SN-Adapter serves as a plug-and-play module to economically improve performance in a non-parametric manner. More importantly, our SN-Adapter can be effectively generalized to various 3D tasks, including shape classification, part segmentation, and 3D object detection, demonstrating its superiority and robustness. We hope our approach could show a new perspective for point cloud analysis and facilitate future research.

Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers

We propose a new class of linear Transformers called FourierLearner-Transformers (FLTs), which incorporate a wide range of relative positional encoding mechanisms (RPEs). These include regular RPE techniques applied for nongeometric data, as well as novel RPEs operating on the sequences of tokens embedded in higher-dimensional Euclidean spaces (e.g. point clouds). FLTs construct the optimal RPE mechanism implicitly by learning its spectral representation. As opposed to other architectures combining efficient low-rank linear attention with RPEs, FLTs remain practical in terms of their memory usage and do not require additional assumptions about the structure of the RPE-mask. FLTs allow also for applying certain structural inductive bias techniques to specify masking strategies, e.g. they provide a way to learn the so-called local RPEs introduced in this paper and providing accuracy gains as compared with several other linear Transformers for language modeling. We also thoroughly tested FLTs on other data modalities and tasks, such as: image classification and 3D molecular modeling. For 3D-data FLTs are, to the best of our knowledge, the first Transformers architectures providing RPE-enhanced linear attention.