发表机构
Wolfram Institute; Østfold University College（沃尔夫勒姆研究所; Østfold大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于简单开放基底的涌现模型框架，从理论证明其潜在通用性，实验显示微小规模的局部递归计算可实现精确外推等，旨在拓宽机器学习的设计空间。
AI 中文摘要
涌现模型（Emergent Models, EMs）是一种基于简单且开放基底（如元胞自动机）的机器学习范式，在该范式中，建模并非学习闭式输入-输出映射，而是在简单动力学系统中涌现出解决外部任务的计算行为。这类基底通常会在潜在空间上迭代固定局部规则，迭代步数为自适应数量，且存在将潜在状态与外部输入/输出信号相连的接口。训练过程通过进化搜索进行。我们假设该框架的部分实例偏向全局泛化：捕获生成数据的规则的完整域，从而能在训练范围之外进行外推。理论上，我们证明部分EMs具有潜在通用性：在更新规则和接口固定的情况下，仅通过改变潜在状态的初始条件，即可实现任何部分可计算函数。实验上，我们研究了离散和连续基底上的一系列最小EM实例，表明微小规模（数十至数百个参数）的局部递归计算可在简单算术函数上精确外推，支持控制行为与在线自适应，同时仍存在若干局限性。本研究具有基础性：它未提出具有竞争力的架构，而是提出了一个旨在拓宽机器学习设计空间的框架，使其超越可微分前馈映射的范畴。
英文摘要
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.
