reliability-gap-has-three-independent-impossibility-proofs

IN derived (depth 13)

Created 2026-06-21T14:03:57+00:00 · Reviewed 2026-06-21T15:37:01+00:00

ML's reliability gap is supported by three largely independent lines of evidence operating at different levels: formal (Mitchell's definition structurally embeds the evaluation gap through proxy performance measures), economic (mathematical quality is orthogonal to evolutionary success, so reliability improvements may not survive paradigm selection), and epistemic (the crisis may be deeply intertwined with capable ML itself, suggesting reliability cannot be straightforwardly added without affecting capability) — each providing substantial independent support, collectively suggesting the gap's persistence as a structural feature rather than a solvable deficiency.

Justifications

SL — Three independently sufficient impossibility proofs (formal, economic, constitutive) overdetermine the reliability gap from fundamentally different levels of analysis.

Antecedents (all must be IN):

IN formal-learning-definition-contains-seeds-of-crisis — Mitchell's formal definition of learning — improvement on task T via experience E measured by performance P — relies on a performance measure P that functions as a proxy. Since standard evaluation methodologies and overfitting defenses address training-test generalization but are not designed to detect deployment-specific failure modes such as adversarial vulnerability and algorithmic bias, the definition's reliance on P may leave a structural gap between what the formalism measures and what deployment requires — suggesting that some of ML's deployment challenges are connected to limitations already present in the foundational framing, not solely to particular methodological shortcomings.
IN mathematical-quality-orthogonal-to-evolutionary-success — Mathematical quality alone does not determine paradigm survival in ML when economic selection pressure dominates — SVMs achieved strong theory-practice unity through intellectual selection pressure but face scaling barriers that economically strand their mathematical foundations, while GANs gained unique capabilities through pragmatic selection but inherited fundamental training instability despite sophisticated analytical characterization. This suggests that the type of selection pressure shaping a method is a primary factor in its methodological reliability and evolutionary trajectory, and that validated mathematical foundations can remain permanently disconnected from deployed systems when economic incentives sustain the misalignment.
IN crisis-constitutive-of-capable-ml — ML's reliability crisis appears deeply connected to capable ML itself — deep learning's foundational mechanisms (weight sharing for geometry-matched compression, gradient flow for trainability) have been validated as mathematical necessities rather than design choices, and the crisis these mechanisms produce is both self-perpetuating and structurally unresolvable within ML's existing intellectual resources. This suggests that a reliability crisis may be a recurring structural feature of ML paradigms powerful enough to be useful, though the link between mathematical necessity of the mechanisms and inevitability of the crisis remains an inference rather than a proven entailment.