Preprint Derives Logarithmic Value Measure from Resource-to-Goal Rate and Ergodicity, Validated on 30 LLM-Domain Pairs
The preprint formalizes value as a structural, logarithmic quantity governing goal-directed agency under constraints, bridging ergodicity economics and information theory. Empirical checks on language models support the I(X;Y) bound. It supplies a control-theoretic route to alignment without invoking external norms.
The evidence rests on two pre-registered LLM experiments (n=30 and n=42) with shape-invariant slope 0.953. Stronger tests would require closed-loop resource allocation in deployed agents rather than static capability probes. The main limitation is restriction to single-frame stationary tasks; non-stationary multi-agent settings remain untested.
Independent labs: MI-capability Spearman correlation falls below 0.85 on non-stationary tasks within 18 months
Sources (3)
- [1]Primary Source(https://arxiv.org/abs/2606.12502)
- [2]Supporting Source(https://arxiv.org/abs/1906.04652)
- [3]Supporting Source(https://arxiv.org/abs/1811.07216)