USC's Zeta Law paper uses Riemann zeta function to predict when data is enough for discovery

PTenigma · x · 2026-11-05

Paul Thompson (USC) published "The Zeta Law of Discoverability in Biomedical Data," tackling the core question of how much data is enough for reliable scientific discovery.

Argues existing scaling laws and sample complexity theory fail to explain the highly variable gains seen across domains, especially biomedical settings with high-dimensional signals aligned across heterogeneous data
Proposes a unified cross-modal discoverability framework based on the spectral structure of data, signals, and their alignment: metrics like AUC can be expressed via an effective signal-to-noise parameter
Addresses when you need better models vs. better input variables, and how much data suffices for clinically useful diagnostic models, invoking the Riemann zeta function
The surrounding thread discusses modal analysis of non-normal matrices and the author's use of Davis-Kahan, Weyl's inequality, and Vershynin's law in prior data scaling-law work

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USC's Zeta Law paper uses Riemann zeta function to predict when data is enough for discovery

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