# GILBO: One Metric to Measure Them All

arXiv: https://arxiv.org/abs/1802.04874 · HTML: https://mlsanity.com/paper/1802.04874/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 9 of 9)

- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [OmniRouter: Budget and Performance Controllable Multi-LLM Routing](https://mlsanity.com/paper/2502.20576/) (2025)
- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [Fracture Detection in Wrist X-ray Images Using Deep Learning-Based Object Detection Models](https://mlsanity.com/paper/2111.07355/) (2021)
- [Information Theoretic Text-to-Image Alignment](https://mlsanity.com/paper/2405.20759/) (2024)
- [Estimators of Entropy and Information via Inference in Probabilistic Models](https://mlsanity.com/paper/2202.12363/) (2022)
- [INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators](https://mlsanity.com/paper/2502.19183/) (2025)
- [IB-GAN: Disentangled Representation Learning with Information Bottleneck Generative Adversarial Networks](https://mlsanity.com/paper/2510.20165/) (2025)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)

## Abstract (arXiv)

We propose a simple, tractable lower bound on the mutual information contained in the joint generative density of any latent variable generative model: the GILBO (Generative Information Lower BOund). It offers a data-independent measure of the complexity of the learned latent variable description, giving the log of the effective description length. It is well-defined for both VAEs and GANs. We compute the GILBO for 800 GANs and VAEs each trained on four datasets (MNIST, FashionMNIST, CIFAR-10 and CelebA) and discuss the results.