# Machine-learning optimized measurements of chaotic dynamical systems via the information bottleneck

arXiv: https://arxiv.org/abs/2311.04896 · HTML: https://mlsanity.com/paper/2311.04896/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 76 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 14 of 14)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations](https://mlsanity.com/paper/1704.00648/) (2017)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [Distributed Variational Representation Learning](https://mlsanity.com/paper/1807.04193/) (2018)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)
- [Predictive information in a sensory population](https://mlsanity.com/paper/1307.0225/) (2013)
- [The extent and drivers of gender imbalance in neuroscience reference lists](https://mlsanity.com/paper/2001.01002/) (2020)
- [Quantitative Evaluation of Gender Bias in Astronomical Publications from Citation Counts](https://mlsanity.com/paper/1610.08984/) (2016)
- [Information decomposition in complex systems via machine learning](https://mlsanity.com/paper/2307.04755/) (2023)
- [Interpretability with full complexity by constraining feature information](https://mlsanity.com/paper/2211.17264/) (2022)
- [Citation inequity and gendered citation practices in contemporary physics](https://mlsanity.com/paper/2112.09047/) (2021)
- [Entropy-based Generating Markov Partitions for Complex Systems](https://mlsanity.com/paper/1711.09072/) (2017)

## Built on by (most cited first, 3 of 3)

- [Partial information decomposition: redundancy as information bottleneck](https://mlsanity.com/paper/2405.07665/) (2024)
- [Emergence of Physical Intelligence via Controllable Information Production](https://mlsanity.com/paper/2601.22449/) (2026)
- [Surveying the space of descriptions of a composite system with machine learning](https://mlsanity.com/paper/2411.18579/) (2024)

## Abstract (arXiv)

Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is challenging, and has generally required intimate knowledge of the dynamics in the few cases where it has been done. We establish an equivalence between a perfect measurement and a variant of the information bottleneck. As a consequence, we can employ machine learning to optimize measurement processes that efficiently extract information from trajectory data. We obtain approximately optimal measurements for multiple chaotic maps and lay the necessary groundwork for efficient information extraction from general time series.