Related papers: Learning Invariant Representations Of Planar Curve…

In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…

Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Augmentation-based self-supervised learning methods have shown remarkable success in self-supervised visual representation learning, excelling in learning invariant features but often neglecting equivariant ones. This limitation reduces the…

We propose Graph Contrastive Learning (GraphCL), a general framework for learning node representations in a self supervised manner. GraphCL learns node embeddings by maximizing the similarity between the representations of two randomly…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…

Deep learning is changing many areas in molecular physics, and it has shown great potential to deliver new solutions to challenging molecular modeling problems. Along with this trend arises the increasing demand of expressive and versatile…

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Graph representation learning is fundamental for analyzing graph-structured data. Exploring invariant graph representations remains a challenge for most existing graph representation learning methods. In this paper, we propose a cross-view…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…

We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…

Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…