# Informal Safety Guarantees for Simulated Optimizers Through Extrapolation from Partial Simulations


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.

[Read Full Article](https://arxiv.org/abs/2401.16426)