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We study processes of societal knowledge accumulation, where the validity ofa new unit of knowledge depends both on the correctness of its derivation andon the validity of the units it depends on. A fundamental question in thissetting is: If a constant fraction of the new derivations is wrong, caninvesting a constant fraction, bounded away from one, of effort ensure that aconstant fraction of knowledge in society is valid? Ben-Eliezer, Mikulincer,Mossel, and Sudan (ITCS 2023) introduced a concrete probabilistic model toanalyze such questions and showed an affirmative answer to this question. Theirstudy, however, focuses on the simple case where each new unit depends on justone existing unit, and units attach according to a $\textit{preferentialattachment rule}$.  In this work, we consider much more general families of cumulative knowledgeprocesses, where new units may attach according to varied attachment mechanismsand depend on multiple existing units. We also allow a (random) fraction ofinsertions of adversarial nodes.  We give a robust affirmative answer to the above question by showing that for$\textit{all}$ of these models, as long as many of the units follow simpleheuristics for checking a bounded number of units they depend on, all errorswill be eventually eliminated. Our results indicate that preserving the qualityof large interdependent collections of units of knowledge is feasible, as longas careful but not too costly checks are performed when new units arederived/deposited.

Errors are Robustly Tamed in Cumulative Knowledge Processes