On Explaining Equivariant Graph Networks via Improved Relevance Propagation

W1. Interpretability does not seem to be an invariant scalar.

It seems that the interpretability of nodes should be an invariant scalar, but Hadamard division and Hadamard multiplication are used in the calculation process, which does not seem to be an invariant scalar? If this property is not an invariant scalar, the analysis of equivariant neural networks seems meaningless, and it seems that it is not as good as studying traditional graph neural networks.

W2. The practical significance of node interpretability.

In actual scenarios, many interactions involve a subgraph, such as a benzene ring or a sulfonic acid group. Discussing the interpretability of a single node seems more like a toy and has no practical significance.

W3. Is EquiGX generalizable to other models?

The article claims to "extend the layer-wise relevance propagation rules tailored for spherical equivariant GNNs". I am curious whether it can be extended to other common high-degree steerable models (e.g. SEGNN [a], Cormorant [b], NequIP [c], Allegro [d], MACE [e]). In addition, can the models using high-degree steerable features based on scalarization methods (e.g. SO3KRATES [f], HEGNN [g]) be explained? I am not asking the authors to discuss all of them. Can authors analyze one or two and make simple analogies for the rest?

W4. Will the symmetrical structure of the synthetic experiment cause potential problems?

Some literature [h, g] points out that symmetric structures can cause the degradation of equivariant graph neural networks of a certain order. Will this affect the experimental results? Are there any potential errors?

W5. Explanation of Fig. 3-4.

This graph looks very interesting. Does it have any specific meaning? Also, is this graph specially selected? Can other data results have such a sharp contrast?

W6. More baselines and dynamic datasets.

Is it possible to add more baselines [a-g] to these experiments? And can EquiGX be tested on dynamic datasets (e.g. CMU Motion Capture dataset [i], Adk equilibrium trajectory dataset[j])?

W-Others. Typos and suggestions.

• [Line 104] $\mathcal{C}\_{(\ell\_1, m\_1),(\ell\_2, m\_1)}^{(\ell\_3, m\_3)}$should be $\mathcal{C}\_{(\ell\_1, m\_1),(\ell\_2, m\_2)}^{(\ell\_3, m\_3)}$.
• [Line 212] $d\_ij$ should be $d\_{ij}$.
• It is recommended not to mix degree and order, as the latter is generally used to represent multi-body interactions. In addition, the Taylor decomposition in this article also has order, which can easily cause confusion.

[a] Cormorant: Covariant molecular neural networks.

[b] Geometric and physical quantities improve e(3) equivariant message passing.

[c] E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.

[d] Learning local equivariant representations for large-scale atomistic dynamics

[e] Mace: Higher order equivariant message passing neural networks for fast and accurate force fields.

[f] A Euclidean transformer for fast and stable machine learned force fields

[g] Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?

[h] On the expressive power of geometric graph neural networks

[i] Carnegie-mellon motion capture database

[j] Molecular dynamics trajectory for benchmarking mdanalysis.

1. The method seems to be a straightforward implementation of layer-wise relevance propagation.

2. Lacking experiments on more backbones that are widely adopted in equivariant graph neural networks literature. Please see Q1.

3. Some experiment settings lack sufficient justification compared with previous works and the results seem troublesome. Please see Q2.

The paper lacks a robust foundation for its motivation, asserting that existing explanation approaches for 2D graphs are inadequate for 3D graphs without providing comprehensive discussion or evidence to support this claim. It fails to specify the characteristics of current methods detailed in Section 2.2 that render them unsuitable for geometric graphs, leaving unclear what specific aspects of these approaches are overly tailored to 2D structures. Additionally, the authors do not explore how these methods could be naively extended to 3D contexts and, more importantly, why such adaptations would be ineffective; including a clear example of a naïve extension along with an analysis of its shortcomings would significantly strengthen the argument.

2.The statement in lines 123-225, which claims that "despite significant advances in XAI for 2D GNNs, these methods primarily focus on evaluating the importance of edges, nodes, and subgraphs, struggling to incorporate positional information effectively and fully evaluate the importance of geometric features," lacks clarity and soundness. The authors should elaborate on the reasons behind this struggle; for instance, why can't coordinates be effectively treated as features, and what limitations do existing methods for highlighting features present? Additionally, the challenges associated with emphasizing edges and nodes require further explanation, especially since Section 4 later employs these very techniques to assess the method against existing approaches. Similarly, the subsequent assertion that applying these techniques to 3D geometric graphs, particularly in the context of equivariant GNNs, poses significant challenges is vague. It would greatly enhance the paper if the authors provided a detailed discussion of the specific challenges encountered in this area.

3. The paper lacks citations for several key feature-based explanation methods in neural networks, such as integrated gradients, which are also applicable to graph neural networks (GNNs), e.g. [1]. The authors should consider expanding the discussion to include interpretable GNNs in addition to focusing solely on post-hoc explanation techniques, e.g. [2].

[1] Axiomatic Attribution for Deep Networks, Sundararajan et al., 2017. [2]The Intelligible and Effective Graph Neural Additive Networks, Bechler-Speciher et al., NeurIPS 2024.

• My concerns in experiments stem from the backbone model and datasets. It seems the authors use only the TFN to conduct experiments. Can the proposed method be applied to other geometric GNNs like EGNN or SE(3)-Transformer? If so, it is recommended to include these backbones to strengthen the experiments. I also found the recent baseline LRI, showing higher scores in the ActsTrack dataset from the original paper than it is reported in this paper. The deviation should be explained. In addition, compared with synthetic datasets, I am more interested in seeing the comparison in other datasets used in LRI but not included in this paper.

• I think the proposed method is reminiscent of previous gradient-based methods via propagation. In addition, the taylor decomposition also requires the computation of gradients. However, previous gradient-based methods are known to be sensitive to the model randomization [1]. I am concerned if this is also an issue to the proposed method given that the variance in table 3 is high in most datasets. Also, how this variance is computed is not mentioned in the paper.

[1] Adebayo, Julius, et al. "Sanity checks for saliency maps." Advances in neural information processing systems 31 (2018).