论文标题
$ c^*$ - 代数网络：一种将神经网络参数推广到$ c^*$ - 代数的新方法
$C^*$-algebra Net: A New Approach Generalizing Neural Network Parameters to $C^*$-algebra
论文作者
论文摘要
我们提出了一个新框架，将神经网络模型的参数推广到$ c^*$ - 代数值。 $ c^*$ - 代数是对复数空间的概括。一个典型的例子是在紧凑空间上连续函数的空间。这种概括使我们能够连续组合多个模型，并使用工具来进行回归和集成等功能。因此，我们可以有效地学习数据的功能，并将模型不断地适应问题。我们将框架应用于实际问题，例如密度估算和很少的学习学习，并表明我们的框架使我们能够学习数据的功能，即使使用有限的样本。我们的新框架突出了将$ C^*$ - 代数理论应用于一般神经网络模型的潜在可能性。
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.
