Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs

Hee-Jun Jung, Jaehyoung Jeong, Kangil Kim
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4798-4806, 2026.

Abstract

Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains challenging. In this paper, we propose a novel method, called \textit{Multiple Invertible and Partial-Equivariant Transformation} (MIPE-Transformation), which integrates two main parts: (1) \textit{Invertible and Partial-Equivariant Transformation} (IPE-Transformation), guaranteeing an invertible latent-to–transformed-latent mapping while preserving partial input-to-latent equivariance in the transformed latent space; and (2) \textit{Exponential-Family Conversion} (EF-Conversion) to extend the standard Gaussian prior to an approximate exponential family via a learnable conversion. In experiments on the 3D Cars, 3D Shapes, and dSprites datasets, MIPE-Transformation improves the disentanglement performance of state-of-the-art VAEs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-jung26a, title = { Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs }, author = {Jung, Hee-Jun and Jeong, Jaehyoung and Kim, Kangil}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4798--4806}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/jung26a/jung26a.pdf}, url = {https://proceedings.mlr.press/v300/jung26a.html}, abstract = { Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains challenging. In this paper, we propose a novel method, called \textit{Multiple Invertible and Partial-Equivariant Transformation} (MIPE-Transformation), which integrates two main parts: (1) \textit{Invertible and Partial-Equivariant Transformation} (IPE-Transformation), guaranteeing an invertible latent-to–transformed-latent mapping while preserving partial input-to-latent equivariance in the transformed latent space; and (2) \textit{Exponential-Family Conversion} (EF-Conversion) to extend the standard Gaussian prior to an approximate exponential family via a learnable conversion. In experiments on the 3D Cars, 3D Shapes, and dSprites datasets, MIPE-Transformation improves the disentanglement performance of state-of-the-art VAEs. } }
Endnote
%0 Conference Paper %T Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs %A Hee-Jun Jung %A Jaehyoung Jeong %A Kangil Kim %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-jung26a %I PMLR %P 4798--4806 %U https://proceedings.mlr.press/v300/jung26a.html %V 300 %X Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains challenging. In this paper, we propose a novel method, called \textit{Multiple Invertible and Partial-Equivariant Transformation} (MIPE-Transformation), which integrates two main parts: (1) \textit{Invertible and Partial-Equivariant Transformation} (IPE-Transformation), guaranteeing an invertible latent-to–transformed-latent mapping while preserving partial input-to-latent equivariance in the transformed latent space; and (2) \textit{Exponential-Family Conversion} (EF-Conversion) to extend the standard Gaussian prior to an approximate exponential family via a learnable conversion. In experiments on the 3D Cars, 3D Shapes, and dSprites datasets, MIPE-Transformation improves the disentanglement performance of state-of-the-art VAEs.
APA
Jung, H., Jeong, J. & Kim, K.. (2026). Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4798-4806 Available from https://proceedings.mlr.press/v300/jung26a.html.

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