Brandenberger Anna, Marcussen Cassandra, Mossel Elchanan, Sudan Madhu
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Computer Science, School of Engineering and Applied Sciences, Harvard University, Boston, MA 02134.
Proc Natl Acad Sci U S A. 2025 Feb 4;122(5):e2416866122. doi: 10.1073/pnas.2416866122. Epub 2025 Jan 30.
As knowledge accumulates in science and society in a distributed fashion, erroneous derivations can be introduced into the corpus of knowledge. Such derivations can compromise the validity of any units of knowledge that rely on them in the future. Can societal knowledge maintain some level of integrity given simple distributed error-checking mechanisms? In this paper, we investigate the following formulation of the question: assuming that a constant fraction of the new derivations is wrong, is it possible for simple error-checking mechanisms that apply when a new unit of knowledge is derived to maintain the integrity of the corpus of knowledge? This question was introduced by Ben-Eliezer et al. ["Is this correct? Let's check!" (ITCS, 2023)], who gave a robust affirmative answer in a specific probabilistic model for knowledge accumulation. Namely, this model required that new units depend on just one existing unit and join the process according to a preferential attachment rule. In this work, we consider much more general families of processes of knowledge accumulation, where new units may depend on multiple existing units and join according to varied attachment mechanisms. We also consider models with a (random) fraction of insertions of adversarial nodes. We give a robust affirmative answer to the above question by showing that for all of these models, as long as many of the units follow simple local heuristics for checking a bounded number of units they depend on, all errors will be eventually eliminated.
随着知识以分布式的方式在科学和社会中积累，错误的推导可能会被引入知识体系。这样的推导可能会在未来损害任何依赖它们的知识单元的有效性。在简单的分布式错误检查机制下，社会知识能否保持一定程度的完整性？在本文中，我们研究这个问题的如下表述：假设新推导中有固定比例是错误的，当一个新的知识单元被推导出来时应用的简单错误检查机制是否有可能保持知识体系的完整性？这个问题由本 - 埃利泽等人提出[《这正确吗？让我们检查一下！》（2023年计算理论创新会议）]，他们在一个特定的知识积累概率模型中给出了有力的肯定答案。具体来说，这个模型要求新单元仅依赖一个现有单元，并根据优先连接规则加入这个过程。在这项工作中，我们考虑了更一般的知识积累过程族，其中新单元可能依赖多个现有单元，并根据不同的连接机制加入。我们还考虑了带有（随机）比例的对抗节点插入的模型。我们通过表明对于所有这些模型，只要许多单元遵循简单的局部启发式方法来检查它们依赖的有限数量的单元，所有错误最终都会被消除，从而对上述问题给出了有力的肯定答案。
