The World Is Bigger: Embedded Agents and Continual Learning

Paper: The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis (2512.23419) Published: 29 Dec 2025. Learn more on Emergent Mind: https://www.emergentmind.com/papers/2512.23419 arXiv: https://arxiv.org/abs/2512.23419 Sign up for our free trending papers email digest: https://www.emergentmind.com/subscribe Follow us on X: https://x.com/EmergentMind Join our Discord: https://discord.gg/BhfTC4mTXq This presentation explores a rigorous formalization of continual learning through the 'big world hypothesis,' where agents are modeled as finite automata embedded within computationally universal environments. The work introduces interactivity, a capacity-relative measure derived from algorithmic complexity, to quantify the necessity of continual adaptation. Through formal proofs and empirical evaluation, the authors demonstrate that agents who cease learning are provably suboptimal and reveal surprising differences in how deep linear versus nonlinear networks sustain adaptive behavior.