# Comparing the information content of probabilistic representation spaces

arXiv: https://arxiv.org/abs/2405.21042 · HTML: https://mlsanity.com/paper/2405.21042/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 72 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 30 of 38)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [What shapes feature representations? Exploring datasets, architectures, and training](https://mlsanity.com/paper/2006.12433/) (2020)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Are Disentangled Representations Helpful for Abstract Visual Reasoning?](https://mlsanity.com/paper/1905.12506/) (2019)
- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [Variational Autoencoders Pursue PCA Directions (by Accident)](https://mlsanity.com/paper/1812.06775/) (2018)
- [Explorations in Homeomorphic Variational Auto-Encoding](https://mlsanity.com/paper/1807.04689/) (2018)
- [Learning Disentangled Representations via Mutual Information Estimation](https://mlsanity.com/paper/1912.03915/) (2019)
- [Unsupervised Model Selection for Variational Disentangled Representation Learning](https://mlsanity.com/paper/1905.12614/) (2019)
- [Disentanglement via Latent Quantization](https://mlsanity.com/paper/2305.18378/) (2023)
- [Estimating Mixture Entropy with Pairwise Distances](https://mlsanity.com/paper/1706.02419/) (2017)
- [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015)
- [The Training Process of Many Deep Networks Explores the Same Low-Dimensional Manifold](https://mlsanity.com/paper/2305.01604/) (2023)
- [Locally Weighted Ensemble Clustering](https://mlsanity.com/paper/1605.05011/) (2016)
- [Representational dissimilarity metric spaces for stochastic neural networks](https://mlsanity.com/paper/2211.11665/) (2022)

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

- [From independent patches to coordinated attention: Controlling information flow in vision transformers](https://mlsanity.com/paper/2602.04784/) (2026)
- [Surveying the space of descriptions of a composite system with machine learning](https://mlsanity.com/paper/2411.18579/) (2024)

## Abstract (arXiv)

Probabilistic representation spaces convey information about a dataset and are shaped by factors such as the training data, network architecture, and loss function. Comparing the information content of such spaces is crucial for understanding the learning process, yet most existing methods assume point-based representations, neglecting the distributional nature of probabilistic spaces. To address this gap, we propose two information-theoretic measures to compare general probabilistic representation spaces by extending classic methods to compare the information content of hard clustering assignments. Additionally, we introduce a lightweight method of estimation that is based on fingerprinting a representation space with a sample of the dataset, designed for scenarios where the communicated information is limited to a few bits. We demonstrate the utility of these measures in three case studies. First, in the context of unsupervised disentanglement, we identify recurring information fragments within individual latent dimensions of VAE and InfoGAN ensembles. Second, we compare the full latent spaces of models and reveal consistent information content across datasets and methods, despite variability during training. Finally, we leverage the differentiability of our measures to perform model fusion, synthesizing the information content of weak learners into a single, coherent representation. Across these applications, the direct comparison of information content offers a natural basis for characterizing the processing of information.