analiza aiqbench
This paper presents a plug-and-play module that enforces SE(2) invariance—handling both translation and rotation—without altering standard CNN components like nonlinearities or normalization layers. By deriving feature maps provably optimal under classical invariant theory, the approach achieves competitive accuracy with significantly lower computational cost than existing equivariant methods. The work advances efficient neural architecture design by theoretically and empirically clarifying the relationship between equivariance and invariance for improved model robustness.
On Making $\mathrm{SE}(2)$-Invariant Networks Optimal
arXiv:2610.17424v1 Announce Type: cross Abstract: Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks are a canonical example, encoding translation equivariance. Extending this inductive bias to richer symmetry groups such as $\mathrm{SE}(2)$ in the most effective way possible is an ongoing architectural and computational challenge. Building on classical invariant theory, we derive invariant feature maps that are provably optimal: minimal and information-preserving with respect to the symmetry group. Our construction is designed to integrate seamlessly into standard architectures, requiring no modification to nonlinearities or normalization layers. As a concrete implementation, we introduce a plug-and-play module for convolutional neural networks that enforces $\mathrm{SE}(2)$ invariance, capturing both translations and rotations within standard architectures. The resulting models are both efficient and expressive. Experiments show competitive or improved accuracy compared to state-of-the-art equivariant methods at significantly lower computational cost. Finally, we provide a theoretical and empirical analysis of the relationship between equivariance and invariance, offering insight into their roles in controlling robustness and flexibility.
Abstract:Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks are a canonical example, encoding translation equivariance. Extending this inductive bias to richer symmetry groups such as $\mathrm{SE}(2)$ in the most effective way possible is an ongoing architectural and computational challenge. Building on classical invariant theory, we derive invariant feature maps that are provably optimal: minimal and information-preserving with respect to the symmetry group. Our construction is designed to integrate seamlessly into standard architectures, requiring no modification to nonlinearities or normalization layers. As a concrete implementation, we introduce a plug-and-play module for convolutional neural networks that enforces $\mathrm{SE}(2)$ invariance, capturing both translations and rotations within standard architectures. The resulting models are both efficient and expressive. Experiments show competitive or improved accuracy compared to state-of-the-art equivariant methods at significantly lower computational cost. Finally, we provide a theoretical and empirical analysis of the relationship between equivariance and invariance, offering insight into their roles in controlling robustness and flexibility.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.17424 [cs.LG]
(or arXiv:2610.17424v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.17424 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 262 cuvinte
Subiecte conexe
Challenge: Hand coding weights for efficient sequence memorisation
AI Alignment Forum · 23 iul. 2026
Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise
arXiv · 16 iun. 2026
GEM Training: How Meta Doubled the Efficiency of Its LLM-Scale Ads Foundation Model
Meta Engineering · 3 aug. 2026
On the Limits of Maximal Coding Rate Reduction for Out-of-Distribution Generalisation
arXiv · 21 sept. 2026