Errors are Robustly Tamed in Cumulative Knowledge Processes

TL;DR

This paper demonstrates that in complex societal knowledge accumulation models, implementing simple verification heuristics can effectively eliminate errors over time, even with adversarial influences and varied attachment mechanisms.

Contribution

It extends previous models by analyzing more general cumulative knowledge processes with multiple dependencies and adversarial nodes, showing error correction is robust under these conditions.

Findings

Errors are eventually eliminated in all studied models.

Simple heuristics suffice for maintaining knowledge quality.

Robustness holds despite adversarial insertions.

Abstract

We study processes of societal knowledge accumulation, where the validity of a new unit of knowledge depends both on the correctness of its derivation and on the validity of the units it depends on. A fundamental question in this setting is: If a constant fraction of the new derivations is wrong, can investing a constant fraction, bounded away from one, of effort ensure that a constant fraction of knowledge in society is valid? Ben-Eliezer, Mikulincer, Mossel, and Sudan (ITCS 2023) introduced a concrete probabilistic model to analyze such questions and showed an affirmative answer to this question. Their study, however, focuses on the simple case where each new unit depends on just one existing unit, and units attach according to a $\textit{preferential attachment rule}$. In this work, we consider much more general families of cumulative knowledge processes, where new units may attach according to varied attachment mechanisms and depend on multiple existing units. We also allow a (random) fraction of insertions 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 simple heuristics for checking a bounded number of units they depend on, all errors will be eventually eliminated. Our results indicate that preserving the quality of large interdependent collections of units of knowledge is feasible, as long as careful but not too costly checks are performed when new units are derived/deposited.