# A taxonomy of surprise definitions

arXiv: https://arxiv.org/abs/2209.01034 · HTML: https://mlsanity.com/paper/2209.01034/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 95 references that are in the map.
- First posted on arXiv 2 Sep 2022.

## Builds on (most cited first, 9 of 9)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Large-Scale Study of Curiosity-Driven Learning](https://mlsanity.com/paper/1808.04355/) (2018)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [An empirical evaluation of active inference in multi-armed bandits](https://mlsanity.com/paper/2101.08699/) (2021)
- [How particular is the physics of the free energy principle?](https://mlsanity.com/paper/2105.11203/) (2021)
- [Human Inference in Changing Environments With Temporal Structure](https://mlsanity.com/paper/2101.11143/) (2021)
- [One-shot learning and behavioral eligibility traces in sequential decision making](https://mlsanity.com/paper/1707.04192/) (2017)
- [Representation learning with reward prediction errors](https://mlsanity.com/paper/2108.12402/) (2021)

## Built on by (most cited first, 8 of 8)

- [From Curiosity to Competence: How World Models Interact with the Dynamics of Exploration](https://mlsanity.com/paper/2507.08210/) (2025)
- [Measuring Surprise in the Wild](https://mlsanity.com/paper/2305.07733/) (2023)
- [Agent-centric learning: from external reward maximization to internal knowledge curation](https://mlsanity.com/paper/2507.22255/) (2025)
- [Working Paper: Active Causal Structure Learning with Latent Variables: Towards Learning to Detour in Autonomous Robots](https://mlsanity.com/paper/2410.20894/) (2024)
- [SUNTA: Hierarchical Video Prediction with Surprise-based Chunking](https://mlsanity.com/paper/2607.02087/) (2026)
- [Confidence Adjusted Surprise Measure for Active Resourceful Trials (CA-SMART): A Data-driven Active Learning Framework for Accelerating Material Discovery under Resource Constraints](https://mlsanity.com/paper/2503.21095/) (2025)
- [Mutual Information Surprise: Rethinking Unexpectedness in Autonomous Systems](https://mlsanity.com/paper/2508.17403/) (2025)
- [Towards Defining, Measuring, and Leveraging Creativity in AI Applications](https://mlsanity.com/paper/2610.12845/) (2026)

## Abstract (arXiv)

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of surprise in a unifying framework. We first propose a technical classification of these definitions into three groups based on their dependence on an agent's belief, show how they relate to each other, and prove under what conditions they are indistinguishable. Going beyond this technical analysis, we propose a taxonomy of surprise definitions and classify them into four conceptual categories based on the quantity they measure: (i) 'prediction surprise' measures a mismatch between a prediction and an observation; (ii) 'change-point detection surprise' measures the probability of a change in the environment; (iii) 'confidence-corrected surprise' explicitly accounts for the effect of confidence; and (iv) 'information gain surprise' measures the belief-update upon a new observation. The taxonomy poses the foundation for principled studies of the functional roles and physiological signatures of surprise in the brain.