# Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learning

arXiv: https://arxiv.org/abs/2511.08240 · HTML: https://mlsanity.com/paper/2511.08240/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 30 of 30)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [On the Universality of Rotation Equivariant Point Cloud Networks](https://mlsanity.com/paper/2010.02449/) (2020)
- [SOE-Net: A Self-Attention and Orientation Encoding Network for Point Cloud based Place Recognition](https://mlsanity.com/paper/2011.12430/) (2020)
- [PointSIFT: A SIFT-like Network Module for 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/1807.00652/) (2018)
- [Rotation-Invariant Local-to-Global Representation Learning for 3D Point Cloud](https://mlsanity.com/paper/2010.03318/) (2020)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (2022)
- [Global Context Aware Convolutions for 3D Point Cloud Understanding](https://mlsanity.com/paper/2008.02986/) (2020)
- [Clustering based Point Cloud Representation Learning for 3D Analysis](https://mlsanity.com/paper/2307.14605/) (2023)
- [Deep Positional and Relational Feature Learning for Rotation-Invariant Point Cloud Analysis](https://mlsanity.com/paper/2011.09080/) (2020)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [The Devil is in the Pose: Ambiguity-free 3D Rotation-invariant Learning via Pose-aware Convolution](https://mlsanity.com/paper/2205.15210/) (2022)
- [Endowing Deep 3D Models with Rotation Invariance Based on Principal Component Analysis](https://mlsanity.com/paper/1910.08901/) (2019)
- [LSK3DNet: Towards Effective and Efficient 3D Perception with Large Sparse Kernels](https://mlsanity.com/paper/2403.15173/) (2024)
- [Learning Rotation-Invariant Representations of Point Clouds Using Aligned Edge Convolutional Neural Networks](https://mlsanity.com/paper/2101.00483/) (2021)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [An intuitive multi-frequency feature representation for SO(3)-equivariant networks](https://mlsanity.com/paper/2405.04537/) (2024)
- [SPE-Net: Boosting Point Cloud Analysis via Rotation Robustness Enhancement](https://mlsanity.com/paper/2211.08250/) (2022)

## Abstract (arXiv)

Point cloud processing has become a cornerstone technology in many 3D vision tasks. However, arbitrary rotations introduce variations in point cloud orientations, posing a long-standing challenge for effective representation learning. The core of this issue is the disruption of the point cloud's intrinsic directional characteristics caused by rotational perturbations. Recent methods attempt to implicitly model rotational equivariance and invariance, preserving directional information and propagating it into deep semantic spaces. Yet, they often fall short of fully exploiting the multiscale directional nature of point clouds to enhance feature representations. To address this, we propose the Direction-Perceptive Vector Network (DiPVNet). At its core is an atomic dot-product operator that simultaneously encodes directional selectivity and rotation invariance--endowing the network with both rotational symmetry modeling and adaptive directional perception. At the local level, we introduce a Learnable Local Dot-Product (L2DP) Operator, which enables interactions between a center point and its neighbors to adaptively capture the non-uniform local structures of point clouds. At the global level, we leverage generalized harmonic analysis to prove that the dot-product between point clouds and spherical sampling vectors is equivalent to a direction-aware spherical Fourier transform (DASFT). This leads to the construction of a global directional response spectrum for modeling holistic directional structures. We rigorously prove the rotation invariance of both operators. Extensive experiments on challenging scenarios involving noise and large-angle rotations demonstrate that DiPVNet achieves state-of-the-art performance on point cloud classification and segmentation tasks. Our code is available at https://github.com/wxszreal0/DiPVNet.