A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints
Researchers have developed a new mathematical framework to quantify value, defining it as the rate at which goal-directed agents convert resources into progress relative to their objectives. This theory, drawing parallels with information theory, proposes a logarithmic measure for value and establishes a coding theorem that links value creation to mutual information. The framework was empirically tested on language models, showing that perceptual mutual information correlates with capability rather than parameter count, and that realized value aligns with theoretical predictions. AI
IMPACT This framework could provide a new lens for understanding and optimizing AI agent behavior and alignment.