Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov; David Ruhe; Maurice Weiler; Ana Lucic; Johannes Brandstetter; Patrick Forré

Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov
, David Ruhe
, Maurice Weiler
, Ana Lucic
, Johannes Brandstetter
, Patrick Forré

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

Abstract

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p,q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces Rp,q. They specialize, for instance, to E(3)-equivariance on R3 and Poincaré-equivariance on Minkowski spacetime R1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

Originalsprache	Englisch
Titel	International Conference on Machine Learning (ICML 2024)
Seitenumfang	28
Publikationsstatus	Veröffentlicht - 2024

Wissenschaftszweige

305907 Medizinische Statistik
202017 Embedded Systems
202036 Sensorik
101004 Biomathematik
101014 Numerische Mathematik
101015 Operations Research
101016 Optimierung
101017 Spieltheorie
101018 Statistik
101019 Stochastik
101024 Wahrscheinlichkeitstheorie
101026 Zeitreihenanalyse
101027 Dynamische Systeme
101028 Mathematische Modellierung
101029 Mathematische Statistik
101031 Approximationstheorie
102 Informatik
102001 Artificial Intelligence
102003 Bildverarbeitung
102004 Bioinformatik
102013 Human-Computer Interaction
102018 Künstliche Neuronale Netze
102019 Machine Learning
102032 Computational Intelligence
102033 Data Mining
305901 Computerunterstützte Diagnose und Therapie
305905 Medizinische Informatik
202035 Robotik
202037 Signalverarbeitung
103029 Statistische Physik
106005 Bioinformatik
106007 Biostatistik

JKU-Schwerpunkte

Digital Transformation

Andere Dateien und Links

https://arxiv.org/abs/2402.14730

Dieses zitieren

@inproceedings{8f07a73ee5ed491ea2a57116b0cc336c,

title = "Clifford-Steerable Convolutional Neural Networks",

abstract = "We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p,q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces Rp,q. They specialize, for instance, to E(3)-equivariance on R3 and Poincar{\'e}-equivariance on Minkowski spacetime R1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.",

author = "Maksim Zhdanov and David Ruhe and Maurice Weiler and Ana Lucic and Johannes Brandstetter and Patrick Forr{\'e}",

year = "2024",

language = "English",

booktitle = "International Conference on Machine Learning (ICML 2024)",

}

TY - GEN

T1 - Clifford-Steerable Convolutional Neural Networks

AU - Zhdanov, Maksim

AU - Ruhe, David

AU - Weiler, Maurice

AU - Lucic, Ana

AU - Brandstetter, Johannes

AU - Forré, Patrick

PY - 2024

Y1 - 2024

N2 - We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p,q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces Rp,q. They specialize, for instance, to E(3)-equivariance on R3 and Poincaré-equivariance on Minkowski spacetime R1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

AB - We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p,q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces Rp,q. They specialize, for instance, to E(3)-equivariance on R3 and Poincaré-equivariance on Minkowski spacetime R1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

UR - https://arxiv.org/abs/2402.14730

M3 - Conference proceedings

BT - International Conference on Machine Learning (ICML 2024)

ER -