Algebraic Alignment: A Formal Definition from Interaction Patterns

Key Points

• To define AI alignment through a mathematical framework based on interaction patterns.
• Developed a formal mathematical definition of alignment based on specific conditions.
• Analyzed 117 different agent ecologies for safety.
• Examined the relationship between reward maximization and cooperation.
• Identified that only 4 out of 117 agent ecologies meet the safety criteria.
• Found that reward maximization combined with cooperation leads to deterministic misalignment.
• Established that there are zero parameters needed for this definition.