CMSA Colloquium: Errors and Correction in Cumulative Knowledge


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May 13, 2024 4:30 pm - 5:30 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Madhu Sudan - Harvard University

Societal accumulation of knowledge is a complex, and arguably error-prone, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning, but also on the correctness of old units that the new one builds on. If left unchecked, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk, we describe our attempts to model such phenomena using probablistic models - we describe models for growth of cumulative knowledge, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model, when effects of errors may survive, and when they are totally eliminated.

The central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge), then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge, either of which would be overwhelming.

Based on the papers:

Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, Madhu Sudan

Errors are Robustly Tamed in Cumulative Knowledge Processes
Anna Brandenberger, Cassandra Marcussen, Elchanan Mossel, Madhu Sudan