# What Capable Agents Must Know: Selection Theorems for Robust Decision-Making under Uncertainty

arXiv: https://arxiv.org/abs/2603.02491 · HTML: https://mlsanity.com/paper/2603.02491/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 24 of its 72 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [Training Agents Inside of Scalable World Models](https://mlsanity.com/paper/2509.24527/) (2025)
- [Robust agents learn causal world models](https://mlsanity.com/paper/2402.10877/) (2024)
- [EfficientZero V2: Mastering Discrete and Continuous Control with Limited Data](https://mlsanity.com/paper/2403.00564/) (2024)
- [Taking AI Welfare Seriously](https://mlsanity.com/paper/2411.00986/) (2024)
- [Task-Driven Convolutional Recurrent Models of the Visual System](https://mlsanity.com/paper/1807.00053/) (2018)
- [A Theory of Consciousness from a Theoretical Computer Science Perspective: Insights from the Conscious Turing Machine](https://mlsanity.com/paper/2107.13704/) (2021)
- [General agents contain world models](https://mlsanity.com/paper/2506.01622/) (2025)
- [Neural Foundations of Mental Simulation: Future Prediction of Latent Representations on Dynamic Scenes](https://mlsanity.com/paper/2305.11772/) (2023)
- [Brain-Model Evaluations Need the NeuroAI Turing Test](https://mlsanity.com/paper/2502.16238/) (2025)
- [The Optimal Choice of Hypothesis Is the Weakest, Not the Shortest](https://mlsanity.com/paper/2301.12987/) (2023)
- [Emergent Causality and the Foundation of Consciousness](https://mlsanity.com/paper/2302.03189/) (2023)
- [Is Complexity an Illusion?](https://mlsanity.com/paper/2404.07227/) (2024)
- [General Agents Contain World Models, even under Partial Observability and Stochasticity](https://mlsanity.com/paper/2602.03146/) (2026)
- [AI Consciousness is Inevitable: A Theoretical Computer Science Perspective](https://mlsanity.com/paper/2403.17101/) (2024)
- [Intrinsic Goals for Autonomous Agents: Model-Based Exploration in Virtual Zebrafish Predicts Ethological Behavior and Whole-Brain Dynamics](https://mlsanity.com/paper/2506.00138/) (2025)
- [Affordances Enable Partial World Modeling with LLMs](https://mlsanity.com/paper/2602.10390/) (2026)
- [Calculating Mutual Information between a Reward Maximizer and its Environment](https://mlsanity.com/paper/2602.12963/) (2026)

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

- [Contravariance Theory: Strong Alignment for Minimal Solutions to Hard Tasks](https://mlsanity.com/paper/2607.08561/) (2026)
- [Approximate Homomorphisms and Convergent Representations in Transducers](https://mlsanity.com/paper/2608.20428/) (2026)

## Abstract (arXiv)

As artificial agents become increasingly capable, what internal structure is necessary for an agent to act competently under uncertainty? Classical results show that optimal control can be implemented using belief states or world models, but not that such representations are required. We prove quantitative "selection theorems" showing that strong task performance (low average-case regret) forces world models, belief-like memory and -- under task mixtures -- persistent regime-tracking variables resembling functional primitives of emotion, along with informational modularity under block-structured tasks. Our results cover stochastic policies, partial observability, and evaluation under task distributions, without assuming optimality, determinism, or access to an explicit model. Technically, we reduce predictive modeling to binary "betting" decisions and show that regret bounds limit probability mass on suboptimal bets, enforcing the predictive distinctions needed to separate high-margin outcomes. In fully observed settings, this yields approximate recovery of the interventional transition kernel; under partial observability, it implies necessity of predictive state and belief-like memory, addressing an open question in prior world-model recovery work.