Thermodynamics proof of sensory learning and implication of mammal homeostasis

While Oja et al. have derived a Hebbian learning neural net algorithm of PCA reproducing Petland´s eigenfaces for examples, Bell-Sejnowski and Amari have improved an unsupervised maximum output entropy learning algorithm for ICA sensory pre-processing reproducing the Hubel-Wiesel edge maps, among others. This paper unifies proofs of the convergence of both supervised and unsupervised learning artificial neural networks in the Lyapunov sense. It implies the effortless division of labor such as the cocktail party effect of supervised word spotting under the unsupervised rejection of severe clutter noise. The proof is based on the minimization of Helmholtz thermodynamic free energy: A=U -TS; Hopfield dynamics: du_i/dt=-∂U(v_i )/∂v_i; v_i=σo(u_i); and Bell-Sejnowski dynamics: du_i/dt=+∂S(w_ij)/∂w_ij for arbitrary brain-like open systems which suggests homeostasis constant body temperature T reservoir. This is characteristic of all mammals, as opposed to cold-blooded reptiles. Other than the known cocktail party effect, applications are given to unsupervised image de-noise generalization of PCA eigenfaces and the supervised recognition of ICA faces