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Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…

Machine Learning · Computer Science 2023-10-31 Arnab Kumar Mondal , Siba Smarak Panigrahi , Sékou-Oumar Kaba , Sai Rajeswar , Siamak Ravanbakhsh

Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces discontinuities that can affect stability during training,…

Machine Learning · Computer Science 2026-04-17 Ya-Wei Eileen Lin , Ron Levie

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to…

Machine Learning · Computer Science 2023-07-10 Sékou-Oumar Kaba , Arnab Kumar Mondal , Yan Zhang , Yoshua Bengio , Siamak Ravanbakhsh

In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries…

Machine Learning · Computer Science 2024-11-05 George Ma , Yifei Wang , Derek Lim , Stefanie Jegelka , Yisen Wang

Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations…

Robotics · Computer Science 2025-11-20 Jian Deng , Yuandong Wang , Yangfu Zhu , Tao Feng , Tianyu Wo , Zhenzhou Shao

Canonicalization provides an architecture-agnostic method for enforcing equivariance, with generalizations such as frame-averaging recently gaining prominence as a lightweight and flexible alternative to equivariant architectures. Recent…

Machine Learning · Computer Science 2024-06-19 Nadav Dym , Hannah Lawrence , Jonathan W. Siegel

Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an…

Machine Learning · Computer Science 2026-04-14 Kusha Sareen , Daniel Levy , Arnab Kumar Mondal , Sékou-Oumar Kaba , Tara Akhound-Sadegh , Siamak Ravanbakhsh

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…

Machine Learning · Computer Science 2024-04-16 Jinwoo Kim , Tien Dat Nguyen , Ayhan Suleymanzade , Hyeokjun An , Seunghoon Hong

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field…

Machine Learning · Computer Science 2025-10-01 Gerrit Gerhartz , Peter Lippmann , Fred A. Hamprecht

While rule-based attribution methods have proven useful for providing local explanations for Deep Neural Networks, explaining modern and more varied network architectures yields new challenges in generating trustworthy explanations, since…

Machine Learning · Computer Science 2022-02-15 Franz Motzkus , Leander Weber , Sebastian Lapuschkin

Fine-grained visual classification (FGVC) tasks, such as insect and bird identification, demand sensitivity to subtle visual cues while remaining robust to spatial transformations. A key challenge is handling geometric biases and noise,…

Computer Vision and Pattern Recognition · Computer Science 2025-10-10 Johann Schmidt , Sebastian Stober

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as…

Machine Learning · Computer Science 2026-02-17 Cai Zhou , Zijie Chen , Zian Li , Jike Wang , Kaiyi Jiang , Pan Li , Rose Yu , Muhan Zhang , Stephen Bates , Tommi Jaakkola

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…

Computer Vision and Pattern Recognition · Computer Science 2021-04-06 Zezhou Cheng , Jong-Chyi Su , Subhransu Maji

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

Numerical Analysis · Mathematics 2024-03-18 Matthias Beckmann , Nick Heilenkötter

The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solvers, recent works have shown that Lie point symmetries can be…

Machine Learning · Computer Science 2025-03-06 Zakhar Shumaylov , Peter Zaika , James Rowbottom , Ferdia Sherry , Melanie Weber , Carola-Bibiane Schönlieb

Learning representations of two views of data such that the resulting representations are highly linearly correlated is appealing in machine learning. In this paper, we present a canonical correlation guided learning framework, which allows…

Machine Learning · Computer Science 2024-10-01 Zhiwen Chen , Siwen Mo , Haobin Ke , Steven X. Ding , Zhaohui Jiang , Chunhua Yang , Weihua Gui

Constructing model-agnostic group equivariant networks, such as equitune (Basu et al., 2023b) and its generalizations (Kim et al., 2023), can be computationally expensive for large product groups. We address this problem by providing…

Machine Learning · Computer Science 2024-10-08 Razan Baltaji , Sourya Basu , Lav R. Varshney

Visual Imitation learning has achieved remarkable progress in robotic manipulation, yet generalization to unseen objects, scene layouts, and camera viewpoints remains a key challenge. Recent advances address this by using 3D point clouds,…

Robotics · Computer Science 2025-11-11 Zhiyuan Zhang , Zhengtong Xu , Jai Nanda Lakamsani , Yu She

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Machine Learning · Computer Science 2021-03-31 Allan Zhou , Tom Knowles , Chelsea Finn
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