math-determines-failure-mode-economics-determines-timing
IN derived (depth 9)
Created 2026-06-21T14:12:26+00:00 · Reviewed 2026-06-21T15:37:01+00:00
Mathematical impossibility results and economic selection pressures play orthogonal roles in paradigm evolution — GAN Nash impossibility (Farnia & Ozdaglar 2020) mathematically necessitated the specific failure mode (training instability, mode collapse) but did not determine adoption or displacement timing, which was governed by scalability economics; mathematics determines HOW paradigms fail while economics determines WHEN.
Justifications
SL — Math determines failure modes; economics determines paradigm timing — orthogonal axes of paradigm fate
Antecedents (all must be IN):
- IN gan-nash-impossibility-mathematically-necessitates-model-level-crisis — Farnia & Ozdaglar's proof that GANs lack guaranteed Nash equilibria provides formal grounding for the GAN-level pragmatism-crisis dynamic — the training instability that exemplifies the field-wide crisis pattern at the model level is not merely an empirical tendency but has a provable theoretical basis in adversarial game structure, strengthening the case that the pragmatism-crisis pattern at the model level is structurally rooted rather than incidental.
- IN paradigm-survival-determined-by-scalability-not-theory — Mathematical completeness and theoretical elegance are neither necessary nor sufficient for paradigm survival in ML — GANs had the most complete analytical characterization yet were eclipsed by diffusion models, SVMs had convex guarantees yet were outscaled by neural networks, while theoretically less grounded approaches that scaled with hardware thrived.