Abstract
We propose a Boltzmann machine formulated as a probabilistic model where every random variable takes bounded continuous values, and we derive the Thouless–Anderson–Palmer equation for the model. The proposed model includes the non-negative Boltzmann machine and the Sherrington–Kirkpatrick model with spin-S at S !1 as a special case. It is known that the Sherrington–Kirkpatrick model with spin-S has a spin glass phase. Thus, the proposed Boltzmann machine is expected to be able to learn practical complex data.
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