# Half-AVAE: Adversarial-Enhanced Factorized and Structured Encoder-Free VAE for Underdetermined Independent Component Analysis

arXiv: https://arxiv.org/abs/2506.07011 · HTML: https://mlsanity.com/paper/2506.07011/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 15 of 15)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [Learning Independent Features with Adversarial Nets for Non-linear ICA](https://mlsanity.com/paper/1710.05050/) (2017)
- [Scalable Factorized Hierarchical Variational Autoencoder Training](https://mlsanity.com/paper/1804.03201/) (2018)
- [Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping](https://mlsanity.com/paper/2409.04140/) (2024)
- [VAEs and GANs: Implicitly Approximating Complex Distributions with Simple Base Distributions and Deep Neural Networks -- Principles, Necessity, and Limitations](https://mlsanity.com/paper/2503.01898/) (2025)

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

- [Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICA](https://mlsanity.com/paper/2508.09721/) (2025)
- [AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separation](https://mlsanity.com/paper/2603.14441/) (2026)

## Abstract (arXiv)

This study advances the Variational Autoencoder (VAE) framework by addressing challenges in Independent Component Analysis (ICA) under both determined and underdetermined conditions, focusing on enhancing the independence and interpretability of latent variables. Traditional VAEs map observed data to latent variables and back via an encoder-decoder architecture, but struggle with underdetermined ICA where the number of latent variables exceeds observed signals. The proposed Half Adversarial VAE (Half-AVAE) builds on the encoder-free Half-VAE framework, eliminating explicit inverse mapping to tackle underdetermined scenarios. By integrating adversarial networks and External Enhancement (EE) terms, Half-AVAE promotes mutual independence among latent dimensions, achieving factorized and interpretable representations. Experiments with synthetic signals demonstrate that Half-AVAE outperforms baseline models, including GP-AVAE and Half-VAE, in recovering independent components under underdetermined conditions, as evidenced by lower root mean square errors. The study highlights the flexibility of VAEs in variational inference, showing that encoder omission, combined with adversarial training and structured priors, enables effective solutions for complex ICA tasks, advancing applications in disentanglement, causal inference, and generative modeling.