mlsanityData to 7 Oct 2026

The Price equation reveals a universal force-metric-bias law of algorithmic learning and natural selection

arXiv 2507.18549 ↗First posted 24 Jul 2025cs.LG q-bio.PEcited by 1

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Abstract (arXiv)

Diverse learning algorithms, optimization methods, and natural selection share a common mathematical structure, despite their apparent differences. Here I show that a simple notational partitioning of change by the Price equation reveals a universal force-metric-bias (FMB) law: Deltaθ = M,f + b + xi. The force f drives improvement in parameters, Deltaθ, in proportion to the slope of performance with respect to the parameters. The metric M rescales movement by inverse curvature. The bias b adds momentum or changes in the frame of reference. The noise xi enables exploration. This framework unifies natural selection, Bayesian updating, Newton's method, stochastic gradient descent, stochastic Langevin dynamics, Adam optimization, and most other algorithms as special cases of the same underlying process. The Price equation also reveals why Fisher information, Kullback-Leibler divergence, and d'Alembert's principle arise naturally in learning dynamics. By exposing this common structure, the FMB law provides a principled foundation for understanding, comparing, and designing learning algorithms across disciplines.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 23 of its 100 references that are in the map. First posted on arXiv 24 Jul 2025.

Builds on

23 of 100 references.

References · 23

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11 more
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Citing papers per year: 2026: 1.

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  1. 2026Direct From Darwin: Deriving Advanced Optimizers From Evolutionary First Principlescited by 0