  We propose a new framework that generalizes the parameters of neural network
models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the
space of complex numbers. A typical example is the space of continuous
functions on a compact space. This generalization enables us to combine
multiple models continuously and use tools for functions such as regression and
integration. Consequently, we can learn features of data efficiently and adapt
the models to problems continuously. We apply our framework to practical
problems such as density estimation and few-shot learning and show that our
framework enables us to learn features of data even with a limited number of
samples. Our new framework highlights the potential possibility of applying the
theory of $C^*$-algebra to general neural network models.
