Bayesian polynomial neural networks and polynomial neural ordinary differential equations
Fig 2
For the univariate cubic polynomial f(x) = 1 + x + 2x2 + 4x3, a third order Bayesian polynomial neural network was trained with the No-U-Turn-Sampler (NUTS) algorithm.
The kernel density estimates for the posterior distributions of the weights and biases of the polynomial neural network are shown. The panes are sequentially ordered (left-to-right, top-to-bottom) from the first layer to the last layer in the neural network. There is no legend associated with the colors in the figure. The colors are only used to distinguish between posterior distributions of the parameters.