Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space

• URL: http://arxiv.org/abs/2605.15368v1
• Date: Thu, 14 May 2026 19:47:43 GMT
• Title: Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space
• Abstract summary: Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning.<n>In this paper, we propose sampling in feature space, replacing geometrically dense samples with representative samples selected by feature similarity.<n>Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well.
• Score: 4.089404117494378
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

Related papers

• EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs [12.013314817711054]
  We introduce EqGINO, a geometrically robust framework that enforces isotropy in the spectral domain.<n>Our method robustly models coordinate-invariant physical laws on complex irregular 3D geometries.
  arXiv  Detail & Related papers  (2026-06-02T07:23:06Z)
• Tail-Aware Post-Training Quantization for 3D Geometry Models [58.79500829118265]
  Post-Training Quantization (PTQ) enables efficient inference without retraining.<n>PTQ fails to transfer effectively to 3D models due to intricate feature distributions and prohibitive calibration overhead.<n>We propose TAPTQ, a Tail-Aware Post-Training Quantization pipeline for 3D geometric learning.
  arXiv  Detail & Related papers  (2026-02-02T07:21:15Z)
• Efficient Continuous Group Convolutions for Local SE(3) Equivariance in 3D Point Clouds [5.659343611352998]
  We present an efficient, continuous, and local SE(3) equivariant convolution layer for point cloud processing.<n>Our approach achieves competitive or superior performance across a range of datasets and tasks, including object classification and semantic segmentation.
  arXiv  Detail & Related papers  (2025-02-11T12:15:56Z)
• Deep Learning as Ricci Flow [38.27936710747996]
  Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. We show that the transformations performed by DNNs during classification tasks have parallels to those expected under Hamilton's Ricci flow. Our findings motivate the use of tools from differential and discrete geometry to the problem of explainability in deep learning.
  arXiv  Detail & Related papers  (2024-04-22T15:12:47Z)
• From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity [54.01594785269913]
  We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. The training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset.
  arXiv  Detail & Related papers  (2023-09-28T15:19:30Z)
• 3D Adversarial Augmentations for Robust Out-of-Domain Predictions [115.74319739738571]
  We focus on improving the generalization to out-of-domain data. We learn a set of vectors that deform the objects in an adversarial fashion. We perform adversarial augmentation by applying the learned sample-independent vectors to the available objects when training a model.
  arXiv  Detail & Related papers  (2023-08-29T17:58:55Z)
• Leveraging SO(3)-steerable convolutions for pose-robust semantic segmentation in 3D medical data [2.207533492015563]
  We present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics. These networks are robust to data poses not seen during training, and do not require rotation-based data augmentation during training. We demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks.
  arXiv  Detail & Related papers  (2023-03-01T09:27:08Z)
• Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration [77.99182201815763]
  Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets.
  arXiv  Detail & Related papers  (2022-02-08T16:16:11Z)
• Revisiting Transformation Invariant Geometric Deep Learning: An Initial Representation Perspective [38.314914702299056]
  We propose Transformation In Neural Networks (TinvNN), a straightforward and general plug-in for geometric data.<n>Specifically, we realize transformation invariant and distance-preserving initial point representations by modifying multi-dimensional scaling.<n>We prove that TinvNN can strictly guarantee transformation invariant, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Geometry-Contrastive Transformer for Generalized 3D Pose Transfer [95.56457218144983]
  The intuition of this work is to perceive the geometric inconsistency between the given meshes with the powerful self-attention mechanism. We propose a novel geometry-contrastive Transformer that has an efficient 3D structured perceiving ability to the global geometric inconsistencies. We present a latent isometric regularization module together with a novel semi-synthesized dataset for the cross-dataset 3D pose transfer task.
  arXiv  Detail & Related papers  (2021-12-14T13:14:24Z)
• Training or Architecture? How to Incorporate Invariance in Neural Networks [14.162739081163444]
  We propose a method for provably invariant network architectures with respect to group actions. In a nutshell, we intend to 'undo' any possible transformation before feeding the data into the actual network. We analyze properties of such approaches, extend them to equivariant networks, and demonstrate their advantages in terms of robustness as well as computational efficiency in several numerical examples.
  arXiv  Detail & Related papers  (2021-06-18T10:31:00Z)
• DyCo3D: Robust Instance Segmentation of 3D Point Clouds through Dynamic Convolution [136.7261709896713]
  We propose a data-driven approach that generates the appropriate convolution kernels to apply in response to the nature of the instances. The proposed method achieves promising results on both ScanetNetV2 and S3DIS. It also improves inference speed by more than 25% over the current state-of-the-art.
  arXiv  Detail & Related papers  (2020-11-26T14:56:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.