Self-supervised learning is the backbone of state of the art language
modeling. It has been argued that training with predictive loss on a
self-supervised dataset causes simulators: entities that internally represent
possible configurations of real-world systems. Under this assumption, a
mathematical model for simulators is built based in the Cartesian frames model
of embedded agents, which is extended to multi-agent worlds through scaling a
two-dimensional frame to arbitrary dimensions, where literature prior chooses
to instead use operations on frames. This variant leveraging scaling
dimensionality is named the Cartesian object, and is used to represent
simulations (where individual simulacra are the agents and devices in that
object). Around the Cartesian object, functions like token selection and
simulation complexity are accounted for in formalizing the behavior of a
simulator, and used to show (through the L\"obian obstacle) that a proof of
alignment between simulacra by inspection of design is impossible in the
simulator context. Following this, a scheme is proposed and termed Partial
Simulation Extrapolation aimed at circumventing the L\"obian obstacle through
the evaluation of low-complexity simulations.

自我监督学习是最先进的语言建模的基础。本文利用嵌入式智能体的笛卡尔框架模型，将单智能体世界扩展至多智能体世界，提出了一种名为 Cartesian object 的变体用于表示模拟，其中函数如令牌选择和模拟复杂性在模拟器的行为中进行了形式化，并通过 L"obian 障碍证明了通过设计检查模拟之间的一致性是不可能的。接着，提出了一种名为 Partial Simulation Extrapolation 的方案，旨在通过评估低复杂度的模拟来规避 L"obian 障碍。