# Formalizing Neurath's Ship: Approximate Algorithms for Online Causal Learning

arXiv: https://arxiv.org/abs/1609.04212 · HTML: https://mlsanity.com/paper/1609.04212/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2016.

## Built on by (most cited first, 12 of 12)

- [Visual cognition in multimodal large language models](https://mlsanity.com/paper/2311.16093/) (2023)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Reinforcement Learning with Simple Sequence Priors](https://mlsanity.com/paper/2305.17109/) (2023)
- [Active Reasoning in an Open-World Environment](https://mlsanity.com/paper/2311.02018/) (2023)
- [Actively learning to learn causal relationships](https://mlsanity.com/paper/2206.09777/) (2022)
- [Simulated Annealing Enhances Theory-of-Mind Reasoning in Autoregressive Language Models](https://mlsanity.com/paper/2601.12269/) (2026)
- [Causality in the human niche: lessons for machine learning](https://mlsanity.com/paper/2506.13803/) (2025)
- [What Is Worth Representing? Representational Empowerment for Continual Model Construction](https://mlsanity.com/paper/2609.02322/) (2026)
- [Building Object-based Causal Programs for Human-like Generalization](https://mlsanity.com/paper/2111.12560/) (2021)
- [Disentangled Representations for Causal Cognition](https://mlsanity.com/paper/2407.00744/) (2024)
- [Understanding Human Limits in Pattern Recognition: A Computational Model of Sequential Reasoning in Rock, Paper, Scissors](https://mlsanity.com/paper/2508.06503/) (2025)
- [Hypothesis Generation and Inductive Inference in Children and Language Models](https://mlsanity.com/paper/2605.24528/) (2026)

## Abstract (arXiv)

Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of four experiments.