{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:55:54Z","timestamp":1767084954898},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"Supp02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:p> Benford\u2019s Law is an interesting and unexpected empirical phenomenon\u00a0\u2014 that if we take a large list of number from real data, the first digits of these numbers follow a certain non-uniform distribution. This law is actively used in economics and finance to check that the data in financial reports are real \u2014 and not improperly modified by the reporting company. The first challenge is that the cheaters know about it, and make sure that their modified data satisfies Benford\u2019s law. The second challenge related to this law is that lately, another application of this law has been discovered \u2014 namely, an application to deep learning, one of the most effective and most promising machine learning techniques. It turned out that the neurons\u2019 weights obey this law only at the difficult-to-detect stage when the fitting is optimal \u2013 and when further attempts attempt to fit will lead to the undesirable over-fitting. In this paper, we provide a possible solution to both challenges: we show how to use this law to make financial cheating practically impossible, and we provide qualitative explanation for the effectiveness of Benford\u2019s Law in machine learning. <\/jats:p>","DOI":"10.1142\/s0218488523400111","type":"journal-article","created":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T07:38:56Z","timestamp":1707205136000},"page":"197-207","source":"Crossref","is-referenced-by-count":2,"title":["Economic and Financial Applications of Benford\u2019s Law: from Traditional Use in Audits to Help in Deep Learning"],"prefix":"10.1142","volume":"31","author":[{"given":"Phuoc Nguyen","family":"Kim","sequence":"first","affiliation":[{"name":"Ho Chi Minh City Open University, 97 Vo Van Tan, District 3, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonatan","family":"Contreras","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martine","family":"Ceberio","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nguyen Ngoc","family":"Thach","sequence":"additional","affiliation":[{"name":"Ho Chi Minh University of Banking, 36 Ton That Dam, District 1, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"S0218488523400111BIB001","first-page":"551","volume":"78","author":"Benford F.","year":"1938","journal-title":"Proceedings of the American Philosophical Society"},{"key":"S0218488523400111BIB002","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop C. 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