Leonie Kayser (she/her)

A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition.

Yuan et al. claim their proposed method SubgraphX achieves (i) higher fidelity in explaining models for graph- and node classification tasks compared to other explanation techniques, namely GNNExplainer. Additionally, (ii) the computational effort of SubgraphX is at a ’reasonable level’, which is not further specified by the original authors. We define this as at most ten times slower than GNNExplainer. We reimplemented the proposed algorithm in PyTorch. Then, we replicated the experiments performed by the authors on a smaller scale due to resource constraints. Additionally, we checked the performance on a new dataset and investigated the influence of hyperparameters. Lastly, we improved SubgraphX using greedy initialization and utilizing fidelity as a score function.