DistShap Appendix

Limitations. At present, DistShap constructs computational graphs on a CPU and distributes them across GPUs to compute Shapley values. Thus, DistShap cannot process graphs that exceed the available CPU memory (258 GB on the system used in our experiments).

Sampling time and scalability. Although the sampling step generates 30 million subgraphs for 50 nodes, it remains extremely fast due to our strategy of replicating the computation graph across GPUs. Figure 9 demonstrates that sampling is highly efficient and scales effectively up to 64 GPUs. A minor slowdown is observed at 128 GPUs, which can be attributed to CUDA kernel overhead.

Figure 9: Scalability of sampling on the Reddit dataset. Total sampling time for explaining 50 nodes.

GAT Fidelity Results

We evaluate the fidelity of different explanation methods using a 2-layer GAT, with the average Fidelity score computed over 50 test nodes. Bold values indicate the best results. DistShap achieves the best or near-best performance across all settings.

Fidelity₊ Scores

Table 1 shows Fidelity₊ scores for the top-k most important edges (higher is better).

Table 1: GAT Fidelity₊ results.

Method	Coauthor-CS (10)	Coauthor-CS (30)	Coauthor-Phy (10)	Coauthor-Phy (30)	DBLP (10)	DBLP (30)	ogbn-arxiv (10)	ogbn-arxiv (30)	ogbn-products (10)	ogbn-products (30)	Reddit (10)	Reddit (30)
Saliency	0.009	0.029	0.006	0.021	0.001	0.003	0.011	0.029	0.003	0.006	0.02	0.031
GNNExplainer	0.011	0.035	0.01	0.068	0.003	0.004	0.019	0.117	0.027	0.037	0.202	0.211
PGExplainer	0.003	0.007	0.003	0.007	0.001	0.001	0.00	0.00	0.00	0.00	OOM	OOM
PGMExplainer	0.005	0.01	0.004	0.006	0.001	0.001	0.009	0.009	0.002	0.003	OOM	OOM
OrphicX	0.001	0.002	OOM	OOM	0.00	0.001	OOM	OOM	OOM	OOM	OOM	OOM
FastDnX	0.011	0.031	0.009	0.026	0.002	0.005	0.02	0.076	OOM	OOM	OOM	OOM
GNNShap	0.022	0.027	0.013	0.022	0.004	0.006	OOM	OOM	OOM	OOM	OOM	OOM
DistShap	0.022	0.027	0.013	0.022	0.004	0.006	0.066	0.137	0.031	0.033	0.085	0.186

Fidelity₋ Scores

Table 2 shows Fidelity₋ scores across different sparsity levels (lower is better), where a sparsity of 0.6 indicates 60% of the least important edges are removed.

Table 2: GAT Fidelity₋ results.

Method	Coauthor-CS (0.3)	Coauthor-CS (0.6)	Coauthor-Phy (0.3)	Coauthor-Phy (0.6)	DBLP (0.3)	DBLP (0.6)	ogbn-arxiv (0.3)	ogbn-arxiv (0.6)	ogbn-products (0.3)	ogbn-products (0.6)	Reddit (0.3)	Reddit (0.6)
Saliency	0.018	0.033	0.012	0.024	0.009	0.015	0.034	0.058	0.034	0.055	0.049	0.106
GNNExplainer	0.024	0.054	0.015	0.03	0.004	0.008	0.161	0.179	0.076	0.095	0.056	0.205
PGExplainer	0.049	0.129	0.04	0.11	0.005	0.018	0.032	0.049	0.101	0.135	OOM	OOM
PGMExplainer	0.008	0.022	0.005	0.011	0.002	0.006	0.013	0.027	0.029	0.042	OOM	OOM
OrphicX	0.014	0.038	OOM	OOM	0.009	0.021	OOM	OOM	OOM	OOM	OOM	OOM
FastDnX	0.021	0.033	0.009	0.017	0.012	0.019	0.023	0.051	OOM	OOM	OOM	OOM
GNNShap	0.004	0.012	0.002	0.006	0.001	0.003	OOM	OOM	OOM	OOM	OOM	OOM
DistShap	0.005	0.016	0.003	0.005	0.001	0.004	0.006	0.014	0.016	0.023	0.016	0.056

GAT Total Explanation Times

Table 3 presents the total explanation times for 50 nodes. Training times of surrogate models are provided in parentheses. DistShap uses 8 GPUs for Coauthor and DBLP and 128 GPUs for other datasets. (Err: CUDA insufficient resources; OOM: Out Of Memory)

Table 3: GAT total explanation times for 50 nodes.

Method	Coauthor-CS	Coauthor-Phy	DBLP	ogbn-arxiv	ogbn-products	Reddit
Saliency	0.68	0.92	0.57	1.33	1.36	2.25
GNNExplainer	23.90	28.18	20.82	360.10	466.27	57.16
PGExplainer	0.30 (874.01)	0.32 (651.84)	0.26 (56.76)	2.70 (424.84)	4.79 (1858.80)	OOM
PGMExplainer	237.36	407.16	223.36	7521.50	3568.53	OOM
OrphicX	52.94 (7706.09)	OOM	65.68 (1986.32)	OOM	OOM	OOM
FastDnX	0.11 (66.12)	0.16 (284.98)	0.08 (10.18)	0.60 (21.52)	OOM	OOM
GraphSVX	663.13	1250.90	101.83	OOM	Err	Err
GNNShap	99.18	196.36	13.00	919.74	588.86	1139.92
DistShap	15.91	28.56	5.26	129.31	106.48	171.21