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We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our $\beta$-TCVAE (Total Correlation Variational Autoencoder), a refinement of the…

Machine Learning · Computer Science 2019-04-24 Ricky T. Q. Chen , Xuechen Li , Roger Grosse , David Duvenaud

In many data analysis tasks, it is beneficial to learn representations where each dimension is statistically independent and thus disentangled from the others. If data generating factors are also statistically independent, disentangled…

Machine Learning · Statistics 2019-12-12 Harshvardhan Sikka , Weishun Zhong , Jun Yin , Cengiz Pehlevan

$\beta$-VAE is a follow-up technique to variational autoencoders that proposes special weighting of the KL divergence term in the VAE loss to obtain disentangled representations. Unsupervised learning is known to be brittle even on toy…

Machine Learning · Computer Science 2022-01-03 Miroslav Fil , Munib Mesinovic , Matthew Morris , Jonas Wildberger

Disentangled and interpretable latent representations in generative models typically come at the cost of generation quality. The $\beta$-VAE framework introduces a hyperparameter $\beta$ to balance disentanglement and reconstruction…

Machine Learning · Computer Science 2025-07-10 Anshuk Uppal , Yuhta Takida , Chieh-Hsin Lai , Yuki Mitsufuji

The performance of $\beta$-Variational-Autoencoders ($\beta$-VAEs) and their variants on learning semantically meaningful, disentangled representations is unparalleled. On the other hand, there are theoretical arguments suggesting the…

Machine Learning · Computer Science 2021-02-16 Dominik Zietlow , Michal Rolinek , Georg Martius

We develop a generalisation of disentanglement in VAEs---decomposition of the latent representation---characterising it as the fulfilment of two factors: a) the latent encodings of the data having an appropriate level of overlap, and b) the…

Machine Learning · Statistics 2019-06-13 Emile Mathieu , Tom Rainforth , N. Siddharth , Yee Whye Teh

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback--Leibler (KL) divergence in…

Fluid Dynamics · Physics 2026-04-21 Zhiyuan Wang , Iacopo Tirelli , Stefano Discetti , Andrea Ianiro

We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned…

One major challenge of disentanglement learning with variational autoencoders is the trade-off between disentanglement and reconstruction fidelity. Previous studies, which increase the information bottleneck during training, tend to lose…

Machine Learning · Computer Science 2023-10-05 Jiantao Wu , Shentong Mo , Xiang Yang , Muhammad Awais , Sara Atito , Xingshen Zhang , Lin Wang , Xiang Yang

This paper challenges the common assumption that the weight $\beta$, in $\beta$-VAE, should be larger than $1$ in order to effectively disentangle latent factors. We demonstrate that $\beta$-VAE, with $\beta < 1$, can not only attain good…

Machine Learning · Computer Science 2020-10-02 Huajie Shao , Haohong Lin , Qinmin Yang , Shuochao Yao , Han Zhao , Tarek Abdelzaher

A variational autoencoder (VAE) is a probabilistic machine learning framework for posterior inference that projects an input set of high-dimensional data to a lower-dimensional, latent space. The latent space learned with a VAE offers…

Machine Learning · Computer Science 2022-11-16 Rafael Pastrana

Variational autoencoders (VAEs) often struggle to represent non-commutative structure in learned latent spaces. Symmetry-aware VAEs commonly address this issue by enforcing commutativity through algebraic regularization, which is…

Machine Learning · Computer Science 2026-05-25 Tahereh Dehdarirad , Michael Felsberg , Gabriel Eilertsen , Ziliang Xiong

Posterior collapse plagues VAEs for text, especially for conditional text generation with strong autoregressive decoders. In this work, we address this problem in variational neural machine translation by explicitly promoting mutual…

Computation and Language · Computer Science 2019-09-23 Arya D. McCarthy , Xian Li , Jiatao Gu , Ning Dong

Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but…

Machine Learning · Computer Science 2020-07-02 Xiaojiang Yang , Wendong Bi , Yitong Sun , Yu Cheng , Junchi Yan

While disentangled representations have shown promise in generative modeling and representation learning, their downstream usefulness remains debated. Recent studies re-defined disentanglement through a formal connection to symmetries,…

Machine Learning · Computer Science 2024-11-04 Cristian Meo , Louis Mahon , Anirudh Goyal , Justin Dauwels

We present a framework for learning disentangled representation of CapsNet by information bottleneck constraint that distills information into a compact form and motivates to learn an interpretable factorized capsule. In our $\beta$-CapsNet…

Computer Vision and Pattern Recognition · Computer Science 2022-09-13 Ming-fei Hu , Jian-wei Liu

Beta-VAE is a very classical model for disentangled representation learning, the use of an expanding bottleneck that allow information into the decoder gradually is key to representation disentanglement as well as high-quality…

Machine Learning · Computer Science 2023-03-28 Zhouzheng Li , Hao Liu

In this paper, we propose a novel model called Learnable VAE (L-VAE), which learns a disentangled representation together with the hyperparameters of the cost function. L-VAE can be considered as an extension of \b{eta}-VAE, wherein the…

Machine Learning · Computer Science 2025-07-04 Hazal Mogultay Ozcan , Sinan Kalkan , Fatos T. Yarman-Vural

Paradoxically, a Variational Autoencoder (VAE) could be pushed in two opposite directions, utilizing powerful decoder model for generating realistic images but collapsing the learned representation, or increasing regularization coefficient…

Machine Learning · Computer Science 2022-03-30 Trung Ngo , Najwa Laabid , Ville Hautamäki , Merja Heinäniemi

Finding disentangled representation plays a predominant role in the success of modern deep learning applications, but the results lack a straightforward explanation. Here we apply the information bottleneck method and its $\beta$-VAE…

Strongly Correlated Electrons · Physics 2022-07-01 Dongchen Huang , Danqing Hu , Yi-feng Yang
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