# Learning from What's Right and Learning from What's Wrong

arXiv: https://arxiv.org/abs/2112.14045 · HTML: https://mlsanity.com/paper/2112.14045/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2021.

## Built on by (most cited first, 5 of 5)

- [Causal models in string diagrams](https://mlsanity.com/paper/2304.07638/) (2023)
- [Towards Compositional Interpretability for XAI](https://mlsanity.com/paper/2406.17583/) (2024)
- [Jeffrey's update rule as a minimizer of Kullback-Leibler divergence](https://mlsanity.com/paper/2502.15504/) (2025)
- [Pearl's and Jeffrey's Update as Modes of Learning in Probabilistic Programming](https://mlsanity.com/paper/2309.07053/) (2023)
- [On Lockean beliefs that are deductively closed and minimal change](https://mlsanity.com/paper/2507.06042/) (2025)

## Abstract (arXiv)

The concept of updating (or conditioning or revising) a probability distribution is fundamental in (machine) learning and in predictive coding theory. The two main approaches for doing so are called Pearl's rule and Jeffrey's rule. Here we make, for the first time, mathematically precise what distinguishes them: Pearl's rule increases validity (expected value) and Jeffrey's rule decreases (Kullback-Leibler) divergence. This forms an instance of a more general distinction between learning from what's right and learning from what's wrong. The difference between these two approaches is illustrated in a mock cognitive scenario.