function of the set of parameters $\{\mathbf{W}_l, \mathbf{R}_l\}$ at each layer. By optimizing the cross-entropy loss, we have the following problem formulation of node feature learning: $$\min_{\{\mathbf{W}_l,\mathbf{R}_l\}} 
-\sum_{i=1}^N \sum_{c=1}^C \mathbf{Y}_{ic} \log(\hat{\mathbf{Y}}_{ic}(\mathbf{W}_l, \mathbf{R}_l)), 
\label{eq:opt_node}$$ where $N$ is the number of input instances, $C$ is the number of classes, and $\mathbf{Y}$ denotes the ground truth label matrix.

Problem Formulation of Joint Learning
-------------------------------------

Integrating Eq. and Eq. , we pose the joint learning of underlying graphs and node features as minimizing both GLR and the cross entropy. The final problem formulation is $$\begin{split}
\min_{\{\mathbf{W}_l, \mathbf{R}_l\}} 
& -\sum_{i=1}^N \sum_{c=1}^C \mathbf{Y}_{ic} \log(\hat{\mathbf{Y}}_{ic}(\mathbf{W}_l, \mathbf{R}_l)) \\
& + \lambda \sum_l \sum_{\{i,j\}}\exp\left\{-\|\mathbf{R}^{\top}_l (\mathbf{f}^i_l - \mathbf{f}^j_l)\|_2^2 \right\} \, s_{i,j},
\end{split}
\label{eq:opt_R}$$ where $\lambda > 0$ is a hyper-parameter for the trade-off between the cross entropy and the GLR term.

Proposed Network Structure {#sec:network}
==========================

Having discussed the problem formulation of joint learning, we elaborate on the proposed network architecture to realize dynamic learning of graphs and node features, with focus on the JLGCN Layer.

JLGCN Layer
-----------

![Demonstration of a JLGCN layer. A graph is first learned from node features, and then employed to propagate node features via graph convolution.[]{data-label="fig:layer"}](figures/layer.pdf){width="2.6in"}

As illustrated in Fig. \[fig:layer\], the JLGCN layer 