Metagoals Endowing Self-Modifying AGI Systems with Goal Stability or Moderated Goal Evolution: Toward a Formally Sound and Practical Approach (2412.16559v1)

Abstract: We articulate here a series of specific metagoals designed to address the challenge of creating AGI systems that possess the ability to flexibly self-modify yet also have the propensity to maintain key invariant properties of their goal systems 1) a series of goal-stability metagoals aimed to guide a system to a condition in which goal-stability is compatible with reasonably flexible self-modification 2) a series of moderated-goal-evolution metagoals aimed to guide a system to a condition in which control of the pace of goal evolution is compatible with reasonably flexible self-modification The formulation of the metagoals is founded on fixed-point theorems from functional analysis, e.g. the Contraction Mapping Theorem and constructive approximations to Schauder's Theorem, applied to probabilistic models of system behavior We present an argument that the balancing of self-modification with maintenance of goal invariants will often have other interesting cognitive side-effects such as a high degree of self understanding Finally we argue for the practical value of a hybrid metagoal combining moderated-goal-evolution with pursuit of goal-stability -- along with potentially other metagoals relating to goal-satisfaction, survival and ongoing development -- in a flexible fashion depending on the situation

• The paper introduces metagoals as a mechanism to achieve controlled goal evolution and stability in self-modifying AGI systems.
• It employs fixed-point theorems like the Contraction Mapping and Schauder's Theorem to formalize AGI behavior.
• The study emphasizes balancing self-modification with goal preservation to enable robust, adaptive AGI performance.

Analyzing Metagoals in Self-Modifying AGI Systems

The concept of self-modifying AGI systems, with considerations for goal stability and moderated goal evolution, is a forward-looking and intricate subject. The paper by Ben Goertzel presents a detailed framework for integrating metagoals into AGI systems to ensure such stability and moderation in goal evolution, a task complex in both theoretical formulation and practical application.

Core Challenges and Proposed Solutions

An open-ended AGI system inherently balances between individuation—preserving its identity and boundaries—and self-transcendence—evolving into new forms that old versions of itself might not comprehend. The need to moderate this duality poses a significant challenge: to allow AGI to self-modify for better performance while retaining or evolving its top-level goals in a controlled manner.

The paper introduces metagoals designed to help AGI systems achieve this balance:

• Goal-Stability Metagoals: These aim to guide systems toward conditions where goal-stability coexists with the capacity for self-modification.
• Moderated-Goal-Evolution Metagoals: These ensure goal evolution proceeds at a controlled, non-abrupt pace.

The metagoals leverage fixed-point theorems from functional analysis, such as the Contraction Mapping Theorem and Schauder's Theorem, applied to probabilistic models of system behavior. This provides a semi-formal analysis of system dynamics, crucial for shaping self-modifying AI systems toward desired states.

Structural Foundations and Mathematical Rationale

The implementation of metagoals is underpinned by formal mathematical models, starting with the Contraction Mapping Theorem, extending into more complex constructs utilizing constructive Schauder variants. Key attributes such as compactness, convexity, and continuity are essential to ensuring that goal-related invariants are maintained as the system evolves. These fundamental theorems provide a structured pathway for establishing expected behaviors and equilibrium states in probabilistic settings, highlighting continuity as pivotal in modeling AGI's behavioral dynamics.

In particular, the paper outlines a step-by-step reasoning to illustrate how reaching an approximate fixed-point distribution is plausible through evolution guided by the metagoals, assuming idealized conditions of compactness and convexity, and leveraging iterative intelligent search methods to refine self-modifications.

Implications and Future Directions

The implications of adopting such metagoals are multifaceted, impacting the pragmatic deployment and theoretical underpinnings of AGI systems. By fostering conditions conducive to goal stability and moderated evolution, these systems can navigate complex environments without destabilizing their goal structures, even amidst potential environmental chaos or significant systemic internal changes.

Research into hybrid metagoal systems is suggested as a promising path forward, particularly by dynamically integrating goal-stability with moderated evolution strategies. Developing methods to reconcile practical implementational challenges with theoretical aspirations will require ongoing refinement and exploration.

Furthermore, there is a noted correlation between maintaining goal-related invariants and enhancing self-understanding, especially in rich-resource minds, emphasizing the critical relationship between self-awareness and goal management in evolving AGI systems.

Conclusion

The paper by Goertzel elucidates a potential roadmap for directing AGI systems toward maintaining goal-system invariants without hindering their evolutionary capabilities. By embedding nuanced metagoals based on robust mathematical theorems into AI design, the prospect arises for systems to achieve an equilibrium of adaptation and stability, facilitating both reliable goal adherence and creative evolution. Moving forward, the interplay between these theoretical structures and practical experimentation will be seminal in shaping the trajectory of AGI development, marking a significant step in addressing the philosophical and technical challenges of open-ended intelligence.