What mathematical approaches can researchers use to prevent goal drift when an AGI begins rewriting its own source code?

Researchers focus on a concept called Corrigibility. The goal is to ensure that as an agent updates its own intelligence, it does not view its original objectives as obsolete or incorrect. One primary mathematical approach involves defining goals using preferences that are invariant under intelligence scaling. If the goal is a fixed mathematical point in a high-dimensional space, the agent's pursuit of that point should not change just because it becomes better at calculating paths to reach it.

Another method involves formalizing uncertainty. If an AGI is programmed to be 'uncertain' about the exact wording of its goals, it will treat its own goals as hypotheses to be tested rather than immutable commands. This mathematical humility prevents it from making drastic, irreversible changes to its core logic. We call this uncertainty-aware objective functions.

Finally, developers look at formal verification. By using automated theorem proving, we might eventually prove that a specific upgrade preserves certain properties of the original system. If we can mathematically guarantee that a code change leaves the core reward function unchanged, the risk of a sudden shift in behavior decreases. It is a difficult engineering problem, but building these guardrails into the logic itself is the most direct path forward.