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New Mathematical Theory Quantifies Value in Goal-Directed Agents

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.

RANK_REASON The cluster contains an academic paper proposing a new theoretical framework for value in goal-directed agents, supported by empirical testing on language models. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.AI →

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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Cheng Qian ·

    A Mathematical Theory of Value: a synthesis on goal-directed agency under resource constraints

    arXiv:2606.12502v1 Announce Type: cross Abstract: We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information. Following Shannon's method, we make one ruthless abstraction: value i…