# The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis

arXiv: https://arxiv.org/abs/2512.23419 · HTML: https://mlsanity.com/paper/2512.23419/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 70 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
- [Variational Intrinsic Control](https://mlsanity.com/paper/1611.07507/) (2016)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [A Definition of Continual Reinforcement Learning](https://mlsanity.com/paper/2307.11046/) (2023)
- [Open-Endedness is Essential for Artificial Superhuman Intelligence](https://mlsanity.com/paper/2406.04268/) (2024)
- [Continual Learning: Applications and the Road Forward](https://mlsanity.com/paper/2311.11908/) (2023)
- [Normalization and effective learning rates in reinforcement learning](https://mlsanity.com/paper/2407.01800/) (2024)
- [Continual Learning as Computationally Constrained Reinforcement Learning](https://mlsanity.com/paper/2307.04345/) (2023)
- [Learning Continually by Spectral Regularization](https://mlsanity.com/paper/2406.06811/) (2024)
- [Embedded Agency](https://mlsanity.com/paper/1902.09469/) (2019)
- [On Value Functions and the Agent-Environment Boundary](https://mlsanity.com/paper/1905.13341/) (2019)
- [Three Dogmas of Reinforcement Learning](https://mlsanity.com/paper/2407.10583/) (2024)
- [Plastic Learning with Deep Fourier Features](https://mlsanity.com/paper/2410.20634/) (2024)
- [Harnessing Discrete Representations For Continual Reinforcement Learning](https://mlsanity.com/paper/2312.01203/) (2023)
- [Position: Lifetime tuning is incompatible with continual reinforcement learning](https://mlsanity.com/paper/2404.02113/) (2024)
- [The Need for a Big World Simulator: A Scientific Challenge for Continual Learning](https://mlsanity.com/paper/2408.02930/) (2024)

## Built on by (most cited first, 1 of 1)

- [World models of environment, agent and joint agent-environment systems](https://mlsanity.com/paper/2608.20401/) (2026)

## Abstract (arXiv)

Continual learning is often motivated by the idea, known as the big world hypothesis, that "the world is bigger" than the agent. Recent problem formulations capture this idea by explicitly constraining an agent relative to the environment. These constraints lead to solutions in which the agent continually adapts to best use its limited capacity, rather than converging to a fixed solution. However, explicit constraints can be ad hoc, difficult to incorporate, and may limit the effectiveness of scaling up the agent's capacity. In this paper, we characterize a problem setting in which an agent, regardless of its capacity, is constrained by being embedded in the environment. In particular, we introduce a computationally-embedded perspective that represents an embedded agent as an automaton simulated within a universal (formal) computer. Such an automaton is always constrained; we prove that it is equivalent to an agent that interacts with a partially observable Markov decision process over a countably infinite state-space. We propose an objective for this setting, which we call interactivity, that measures an agent's ability to continually adapt its behaviour by learning new predictions. We then develop a model-based reinforcement learning algorithm for interactivity-seeking, and use it to construct a synthetic problem to evaluate continual learning capability. Our results show that deep nonlinear networks struggle to sustain interactivity, whereas deep linear networks sustain higher interactivity as capacity increases.