Yet another zeta function and learning

2001/07/25 by Igor Rivin, Rivin, Igor
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.3 #I.2.6 #Machine Learning (cs.LG) #Machine Learning and Algorithms #Neural Networks and Applications #Probability (math.PR) #cs.DM #cs.LG #math.PR

paper · pdf · doi:10.48550/arxiv.cs/0107033

arxiv created 2001/07/25 · openalex publication_date 2001/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the convergence speed of the batch learning algorithm, and compare its speed to that of the memoryless learning algorithm and of learning with memory (as analyzed in joint work with N. Komarova). We obtain precise results and show in particular that the batch learning algorithm is never worse than the memoryless learning algorithm (at least asymptotically). Its performance vis-a-vis learning with full memory is less clearcut, and depends on certainprobabilistic assumptions. These results necessitate theintroduction of the moment zeta function of a probability distribution and the study of some of its properties.

Citations

• Harmonic mean, random polynomials and stochastic matrices

Cited by

• Mathematics of learning

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