Journal article
Algorithms of the Möbius function by random forests and neural networks
Journal of big data, Vol.11(1), 31
02/21/2024
DOI: 10.1186/s40537-024-00889-7
Abstract
The Möbius function μ (n) is known for containing limited information on the prime factorization of n. Its known algorithms, however, are all based on factorization and hence are exponentially slow on log n. Consequently, a faster algorithm of μ(n) could potentially lead to a fast algorithm of prime factorization which in turn would throw doubt upon the security of most public-key cryptosystems. This research introduces novel approaches to compute μ (n) using random forests and neural networks, harnessing the additive properties of μ (n). The machine learning models are trained on a substantial dataset with 317,284 observations (80%), comprising five feature variables, including values of n within the range of 4 × 10 9.. We implement the Random Forest with Random Inputs (RFRI) and Feedforward Neural Network (FNN) architectures. The RFRI model achieves a predictive accuracy of 0.9493, a recall of 0.5865, and a precision of 0.6626. On the other hand, the FNN model attains a predictive accuracy of 0.7871, a recall of 0.9477, and a precision of 0.2784. These results strongly support the effectiveness and validity of the proposed algorithms.
Details
- Title: Subtitle
- Algorithms of the Möbius function by random forests and neural networks
- Creators
- Huan Qin - San Diego State University, Imperial Valley CampusYangbo Ye - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of big data, Vol.11(1), 31
- DOI
- 10.1186/s40537-024-00889-7
- eISSN
- 2196-1115
- Publisher
- Springer International Publishing
- Language
- English
- Date published
- 02/21/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984560420402771
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