The power of the Inverse Scaling Law lies in its cross-domain validation. When a single mathematical constraint consistently predicts behavior in unrelated fields, we are looking at a fundamental law of the kernel.
1. Biological Systems (Neural Efficiency)
Validation:
Recent studies in neural architecture show that as modular specialization increases in certain cortical regions, the energy cost per bit of information processed decreases monotonically.
2. Computational Systems (LEGO-MoE)
Validation: error rate.
Production-grade Mixture-of-Experts (MoE) architectures show that doubling the expert pool () reduces localized latency (
) precisely as predicted by the ISL efficiency curve.
3. Mathematical Systems (Riemann Framework)
The distribution of prime numbers exhibits what we term “Modular Smoothing”. As the scale increases, the “cost” (computational effort to verify structural gaps) follows an inverse scaling relationship relative to the density of zeroes on the critical line.
4. Economic Systems
Market efficiency is not a result of “perfect information,” but of modular participation. As more specialized actors (experts) enter a market structure, the transaction cost () per dollar of value-transfer decreases.
The ISL is the common denominator of efficiency.