# Half-VAE: An Encoder-Free VAE to Bypass Explicit Inverse Mapping

arXiv: https://arxiv.org/abs/2409.04140 · HTML: https://mlsanity.com/paper/2409.04140/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 6 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [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)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Implicit Neural Representations for Variable Length Human Motion Generation](https://mlsanity.com/paper/2203.13694/) (2022)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Longitudinal Variational Autoencoder](https://mlsanity.com/paper/2006.09763/) (2020)
- [Decoupling Local and Global Representations of Time Series](https://mlsanity.com/paper/2202.02262/) (2022)
- [Gradient Origin Networks](https://mlsanity.com/paper/2007.02798/) (2020)

## Built on by (most cited first, 5 of 5)

- [PDGMM-VAE: A Variational Autoencoder with Adaptive Per-Dimension Gaussian Mixture Model Priors for Nonlinear ICA](https://mlsanity.com/paper/2603.23547/) (2026)
- [Half-AVAE: Adversarial-Enhanced Factorized and Structured Encoder-Free VAE for Underdetermined Independent Component Analysis](https://mlsanity.com/paper/2506.07011/) (2025)
- [Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICA](https://mlsanity.com/paper/2508.09721/) (2025)
- [SAHMM-VAE: A Source-Wise Adaptive Hidden Markov Prior Variational Autoencoder for Unsupervised Blind Source Separation](https://mlsanity.com/paper/2603.25776/) (2026)
- [StrTransformer: Source-Wise Structured Transformers for Unsupervised Blind Source Recovery](https://mlsanity.com/paper/2605.25648/) (2026)

## Abstract (arXiv)

Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a variety of problems, including those related to causal inference. Variational inference, a subset of Bayesian inference, is primarily used to efficiently approximate complex posterior distributions. Variational Autoencoders (VAEs), which combine variational inference with deep learning, have become widely applied across various domains. This study explores the potential of VAEs for solving inverse problems, such as Independent Component Analysis (ICA), without relying on an explicit inverse mapping process. Unlike other VAE-based ICA methods, this approach discards the encoder in the VAE architecture, directly setting the latent variables as trainable parameters. In other words, the latent variables are no longer outputs of the encoder but are instead optimized directly through the objective function to converge to appropriate values. We find that, with a suitable prior setup, the latent variables, represented by trainable parameters, can exhibit mutually independent properties as the parameters converge, all without the need for an encoding process. This approach, referred to as the Half-VAE, bypasses the inverse mapping process by eliminating the encoder. This study demonstrates the feasibility of using the Half-VAE to solve ICA without the need for an explicit inverse mapping process.