Semi-supervised semantic segmentation requires the model to effectively propagate the label information from limited annotated images to unlabeled ones. A challenge for such a per-pixel prediction task is the large intra-class variation, i.e., regions belonging to the same class may exhibit a very different appearance even in the same

In the following, we review related work from graph kernels, GNNs, and theory. More recently, graph kernels' developments have emphasized scalability, focusing on Notable instances of this architecture include, e.g., [ Sato et al. studied the limits of GNNs when applied to combinatorial problems. Finally, there exists a new line of work focusing on extending GNNs to hypergraphs, see, e.g., [ We briefly describe the Weisfeiler-Leman algorithm and, along the way, introduce our notation. Let k be a fixed positive integer. The successive refinement steps are also called rounds or iterations .

Hence, the running time of each iteration does not take the sparsity of a given graph into account.

The comparisons of AHGP with the GPU-based baselines are presented in Figure 1 and Table 8, 9, 10. Results are similar to comparisons with the CPU-based baselines in the main section.

There are also very recent works that address the dynamic pricing problem with consumer reference effects under uncertain demand. Nevertheless, these two lines of works are oblivious to consumer reference effects. In contrast to these two papers, our work studies price competitions over an infinite time horizon where reference prices adjust over time, and provides theoretical guarantees for the convergence of pricing strategies under the partial information setting. In their setting, the subgradient for each bidder's objective is a function of all bidders' decisions as well as its budget rate (i.e. total fixed budget divided by a given time horizon), which can be B.1 Proof of Theorem 3.1 (i) By first order conditions, we know that arg max We now follow a similar proof to that of Tarski's fixed point theorem: consider the set Note that convergence is monotonic because U () is nondecreasing. This implies that under Assumption 1, the interior SNE is unique.

We will comment on this in the discussion section.