Neurobiology eJournal | 2019
Self-referential Boltzmann Machine
Abstract
We recently reported that the income structure of the low and middle class (about 95% of populations) in a well-functioning free-market country would follow a Boltzmann-like distribution that has self-referential entropy [Physica A 502, 436-446 (2018)]. The empirical evidences cover 66 free-market countries and the Hong Kong SAR. By contrast, the entropy of a physical system is not self-referential. This finding implies that the self-reference may be a potential difference between biological and lifeless-physical systems. In this paper, we employ such a Boltzmann-like distribution to construct a self-referential Boltzmann machine (SRBM). Due to the self-reference of the entropy, we show that the SRBM always has a positive energy even if all neurons are inactive. This singular feature leads to that the SRBM is a self-motivated system, which makes the SRBM somewhat biologically plausible. As a simple application, we apply the self-motive of the SRBM to perform the task of searching images.