涌现模型（Emergent Models, EMs）是一种基于简单但开放性基质（如元胞自动机）的机器学习范式，其中建模不被视为学习一个封闭形式的输入-输出映射，而是视为在简单动力系统中涌现出可求解外部任务的计算行为。此类基质通常在隐状态空间上迭代一个固定的局部规则，并自适应地执行若干步，同时通过一个接口将隐状态与外部输入/输出信号相连接。训练过程采用进化搜索。我们假设该框架的某些实例具有朝向全局泛化的偏差：即能够捕获生成数据的规则在其整个定义域上的行为，从而实现对训练范围之外的外推。理论上，我们证明了某些EM具有隐状态通用性（latent-universal）：在更新规则与接口固定的前提下，仅通过改变隐状态的初始条件，即可实现任意偏可计算函数。实验上，我们在离散与连续基质上研究了一系列极简EM实例，结果表明，在极小规模（数十至数百参数）下实现的局部递归计算，可对简单算术函数实现精确外推，支持控制行为与在线适应，同时也暴露出若干局限性。本工作具有基础性意义：它并未提出一种具备竞争力的架构，而是旨在拓展机器学习的设计空间，使之超越可微分前馈映射。

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.