# Emergent Models: Intelligence from Tiny Substrates

arXiv: https://arxiv.org/abs/2608.14019 · HTML: https://mlsanity.com/paper/2608.14019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad](https://mlsanity.com/paper/2406.06467/) (2024)
- [Towards self-organized control: Using neural cellular automata to robustly control a cart-pole agent](https://mlsanity.com/paper/2106.15240/) (2021)
- [Neural Cellular Automata for ARC-AGI](https://mlsanity.com/paper/2506.15746/) (2025)
- [Reservoir Computing using Cellular Automata](https://mlsanity.com/paper/1410.0162/) (2014)
- [Noncompact uniform universal approximation](https://mlsanity.com/paper/2308.03812/) (2023)
- [Disentangling Abstraction from Statistical Pattern Matching in Human and Machine Learning](https://mlsanity.com/paper/2204.01437/) (2022)
- [Deep Reservoir Computing Using Cellular Automata](https://mlsanity.com/paper/1703.02806/) (2017)

## Abstract (arXiv)

Emergent Models (EMs) are a machine learning paradigm based on simple yet open-ended substrates, such as cellular automata, in which modeling is treated not as the learning of a closed-form input-output map but as the emergence, within simple dynamical systems, of computational behaviors that solve external tasks. Such substrates typically iterate a fixed local rule over a latent space for an adaptive number of steps, with an interface linking the latent state to external input/output signals. Training proceeds by evolutionary search. We hypothesize that some instances of this framework are biased toward global generalization: capturing the rule generating the data over its full domain, and therefore extrapolating beyond the training range. Theoretically, we prove that some EMs are latent-universal: with the update rule and interface held fixed, they can realize any partial computable function by varying only the initial condition of the latent state. Empirically, we study a zoo of minimal EM instantiations across discrete and continuous substrates, showing that local-recursive computation at a tiny scale (tens to hundreds of parameters) can extrapolate exactly on simple arithmetic functions, can support control behaviour and online adaptation, while still exposing several limitations. This work is foundational: it does not propose a competitive architecture, but a framework meant to widen the design space of machine learning beyond differentiable feed-forward maps.