On Learning Sets of Symmetric Elements

• URL: http://arxiv.org/abs/2002.08599v4
• Date: Sun, 29 Nov 2020 07:34:07 GMT
• Title: On Learning Sets of Symmetric Elements
• Authors: Haggai Maron, Or Litany, Gal Chechik, Ethan Fetaya
• Abstract summary: This paper presents a principled approach to learning sets of general symmetric elements. We first characterize the space of linear layers that are equivariant both to element reordering and to the inherent symmetries of elements. We further show that networks that are composed of these layers, called Deep Sets for Symmetric Elements (DSS) layers, are universal approximators of both invariant and equivariant functions.
• Score: 63.12061960528641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has been given to the common case where set elements themselves adhere to their own symmetries. That case is relevant to numerous applications, from deblurring image bursts to multi-view 3D shape recognition and reconstruction. In this paper, we present a principled approach to learning sets of general symmetric elements. We first characterize the space of linear layers that are equivariant both to element reordering and to the inherent symmetries of elements, like translation in the case of images. We further show that networks that are composed of these layers, called Deep Sets for Symmetric Elements (DSS) layers, are universal approximators of both invariant and equivariant functions, and that these networks are strictly more expressive than Siamese networks. DSS layers are also straightforward to implement. Finally, we show that they improve over existing set-learning architectures in a series of experiments with images, graphs, and point-clouds.

Related papers

• Cross-composition Feature Disentanglement for Compositional Zero-shot Learning [49.919635694894204]
  Disentanglement of visual features of primitives (i.e., attributes and objects) has shown exceptional results in Compositional Zero-shot Learning (CZSL) We propose the solution of cross-composition feature disentanglement, which takes multiple primitive-sharing compositions as inputs and constrains the disentangled primitive features to be general across these compositions.
  arXiv  Detail & Related papers  (2024-08-19T08:23:09Z)
• RMAFF-PSN: A Residual Multi-Scale Attention Feature Fusion Photometric Stereo Network [37.759675702107586]
  Predicting accurate maps of objects from two-dimensional images in regions of complex structure spatial material variations is challenging. We propose a method of calibrated feature information from different resolution stages and scales of the image. This approach preserves more physical information, such as texture and geometry of the object in complex regions.
  arXiv  Detail & Related papers  (2024-04-11T14:05:37Z)
• Equivariant Architectures for Learning in Deep Weight Spaces [54.61765488960555]
  We present a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trainedvariant. We show how these layers can be implemented using three basic operations.
  arXiv  Detail & Related papers  (2023-01-30T10:50:33Z)
• Deep Diversity-Enhanced Feature Representation of Hyperspectral Images [87.47202258194719]
  We rectify 3D convolution by modifying its topology to enhance the rank upper-bound. We also propose a novel diversity-aware regularization (DA-Reg) term that acts on the feature maps to maximize independence among elements. To demonstrate the superiority of the proposed Re$3$-ConvSet and DA-Reg, we apply them to various HS image processing and analysis tasks.
  arXiv  Detail & Related papers  (2023-01-15T16:19:18Z)
• Rank-Enhanced Low-Dimensional Convolution Set for Hyperspectral Image Denoising [50.039949798156826]
  This paper tackles the challenging problem of hyperspectral (HS) image denoising. We propose rank-enhanced low-dimensional convolution set (Re-ConvSet) We then incorporate Re-ConvSet into the widely-used U-Net architecture to construct an HS image denoising method.
  arXiv  Detail & Related papers  (2022-07-09T13:35:12Z)
• Frame Averaging for Equivariant Shape Space Learning [85.42901997467754]
  A natural way to incorporate symmetries in shape space learning is to ask that the mapping to the shape space (encoder) and mapping from the shape space (decoder) are equivariant to the relevant symmetries. We present a framework for incorporating equivariance in encoders and decoders by introducing two contributions.
  arXiv  Detail & Related papers  (2021-12-03T06:41:19Z)
• Equivariant Maps for Hierarchical Structures [17.931059591895984]
  We show that symmetry of a hierarchical structure is the "wreath product" of symmetries of the building blocks. By voxelizing the point cloud, we impose a hierarchy of translation and permutation symmetries on the data. We report state-of-the-art on Semantic3D, S3DIS, and vKITTI, that include some of the largest real-world point-cloud benchmarks.
  arXiv  Detail & Related papers  (2020-06-05T18:42:12Z)

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.