Latent Space Representations Under Equivariance and Data Augmentation

Authored by Krishna Sri Ipsit Mantri, Gerrit Hübsch, Zorah Lähner
Published in The German Conference on Pattern Recognition (GCPR) 2026

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Abstract

We study how explicit symmetry constraints and data augmentation shape the latent representations of neural networks. Although both strategies often achieve comparable performance, it remains unclear whether they induce similar internal representations. We investigate this question across three symmetry settings: rotational invariance in CNN classifiers, permutation invariance in PointNet architectures, and circular-translation equivariance in convolutional autoencoders. We compare the global geometry, local equivariant structure, and functional compatibility of the resulting latent spaces using complementary metrics: CKA, PWCCA, G-EED, and linear model stitching. Across all experiments, data augmentation and explicitly equivariant models frequently exhibit strong agreement under standard similarity metrics. However, this apparent alignment does not imply functional interchangeability. Despite high global similarity, stitched models consistently suffer substantial performance degradation, indicating that the underlying representations remain incompatible under point-wise linear alignment. Explicit symmetry constraints further produce the strongest local invariance according to G-EED, whereas augmentation only partially reproduces these properties. Finally, the gap between augmentation and architectural equivariance diminishes when symmetry transformations are only approximately realized, such as interpolated image rotations. Together, our results highlight a fundamental distinction between representational similarity and functional compatibility in symmetry-aware representation learning.

Resources

It was accepted for an Oral presentation and is based on master’s thesis of Gerrit Hübsch.

Bibtex

    @inproceedings{ mantri2026latent, 
    		author 	= { Krishna Sri Ipsit Mantri and Gerrit Hübsch and Zorah Lähner },
        	title 	= { Latent Space Representations Under Equivariance and Data Augmentation },
       		booktitle = { The German Conference on Pattern Recognition (GCPR) },
        	year 	= { 2026 },
    	}