Informal Safety Guarantees for Simulated Optimizers Through
  Extrapolation from Partial Simulations
Luke Marks
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.