# L-VAE: Variational Auto-Encoder with Learnable Beta for Disentangled Representation

arXiv: https://arxiv.org/abs/2507.02619 · HTML: https://mlsanity.com/paper/2507.02619/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 53 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [DRIT++: Diverse Image-to-Image Translation via Disentangled Representations](https://mlsanity.com/paper/1905.01270/) (2019)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Unsupervised Learning of Disentangled Representations from Video](https://mlsanity.com/paper/1705.10915/) (2017)
- [Learning to Decompose and Disentangle Representations for Video Prediction](https://mlsanity.com/paper/1806.04166/) (2018)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [FD-GAN: Generative Adversarial Networks with Fusion-discriminator for Single Image Dehazing](https://mlsanity.com/paper/2001.06968/) (2020)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [S3VAE: Self-Supervised Sequential VAE for Representation Disentanglement and Data Generation](https://mlsanity.com/paper/2005.11437/) (2020)
- [HoloGAN: Unsupervised learning of 3D representations from natural images](https://mlsanity.com/paper/1904.01326/) (2019)
- [Theory and Evaluation Metrics for Learning Disentangled Representations](https://mlsanity.com/paper/1908.09961/) (2019)
- [Simple and Effective VAE Training with Calibrated Decoders](https://mlsanity.com/paper/2006.13202/) (2020)
- [Semi-Supervised StyleGAN for Disentanglement Learning](https://mlsanity.com/paper/2003.03461/) (2020)
- [Exploring Disentangled Feature Representation Beyond Face Identification](https://mlsanity.com/paper/1804.03487/) (2018)
- [Cross-Spectral Face Hallucination via Disentangling Independent Factors](https://mlsanity.com/paper/1909.04365/) (2019)
- [Beta-VAE Reproducibility: Challenges and Extensions](https://mlsanity.com/paper/2112.14278/) (2021)
- [ControlVAE: Tuning, Analytical Properties, and Performance Analysis](https://mlsanity.com/paper/2011.01754/) (2020)

## Built on by (most cited first, 2 of 2)

- [ManiVID-3D: Generalizable View-Invariant Reinforcement Learning for Robotic Manipulation via Disentangled 3D Representations](https://mlsanity.com/paper/2509.11125/) (2025)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)

## Abstract (arXiv)

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 beta-VAE, wherein the hyperparameter, beta, is empirically adjusted. L-VAE mitigates the limitations of beta-VAE by learning the relative weights of the terms in the loss function to control the dynamic trade-off between disentanglement and reconstruction losses. In the proposed model, the weight of the loss terms and the parameters of the model architecture are learned concurrently. An additional regularization term is added to the loss function to prevent bias towards either reconstruction or disentanglement losses. Experimental analyses show that the proposed L-VAE finds an effective balance between reconstruction fidelity and disentangling the latent dimensions. Comparisons of the proposed L-VAE against beta-VAE, VAE, ControlVAE, DynamicVAE, and σ-VAE on datasets, such as dSprites, MPI3D-complex, Falcor3D, and Isaac3D reveals that L-VAE consistently provides the best or the second best performances measured by a set of disentanglement metrics. Moreover, qualitative experiments on CelebA dataset, confirm the success of the L-VAE model for disentangling the facial attributes.