b6089408f4893289296ad0499783b3a6-Supplemental-Conference.pdf

Algorithm 2 shows how to prune k percentage edges from PC C following heuristic h . In this section, we provide detailed proofs of Theorem 1 (Section B.1) and Theorem 2 (Section B.2). Similar to the proof of Lemma 1, we prove Theorem 2 by induction. Equation 6. 17 Inductive case #1: suppose for all children of a product unit Finally, we prove the approximation step in Equation 3. Let Hardware specifications All experiments are performed on a server with 32 CPUs, 126G Memory, and NVIDIA RTX A5000 GPUs with 26G Memory. For MNIST -family datasets, we split 5% of training set as validation set for early stopping. Tree Bank dataset, we follow the setting in Mikolov et al.