# Identifiability of deep generative models without auxiliary information

Source: [Identifiability of deep generative models without auxiliary information](<https://www.sota2.com/research/paper/68fa59bd1e209131ce9b9cdc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-04T05:18:39.051Z

Authors: Bohdan Kivva, Goutham Rajendran, Pradeep Ravikumar, Bryon Aragam

Published: 2022-06-20T23:24:48.000Z

## Abstract

We prove identifiability of a broad class of deep latent variable models that (a) have universal approximation capabilities and (b) are the decoders of variational autoencoders that are commonly used in practice. Unlike existing work, our analysis does not require weak supervision, auxiliary information, or conditioning in the latent space. Specifically, we show that for a broad class of generative (i.e. unsupervised) models with universal approximation capabilities, the side information $u$ is not necessary: We prove identifiability of the entire generative model where we do not observe $u$ and only observe the data $x$. The models we consider match autoencoder architectures used in practice that leverage mixture priors in the latent space and ReLU/leaky-ReLU activations in the encoder, such as VaDE and MFC-VAE. Our main result is an identifiability hierarchy that significantly generalizes previous work and exposes how different assumptions lead to different "strengths" of identifiability, and includes certain "vanilla" VAEs with isotropic Gaussian priors as a special case. For example, our weakest result establishes (unsupervised) identifiability up to an affine transformation, and thus partially resolves an open problem regarding model identifiability raised in prior work. These theoretical results are augmented with experiments on both simulated and real data.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Causal Representation Learning on Synthetic Numerical Experiments](<https://www.sota2.com/research/sota/causal-representation-learning-on-synthetic-numerical-experiments.md>): Causal Representation Learning; Synthetic Numerical Experiments; R^2 Stage 1: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2206.10044>)

[PDF](<https://arxiv.org/pdf/2206.10044.pdf>)