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REVIEW 4 major objections 5 minor 42 references

RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Per-atom radii isolate the chemical bonds a 3D GNN relies on

desk verdict RISE's per-atom radius parameterization is a genuinely new and mostly effective way to explain 3D GNNs, producing clean bond-level subgraphs, but the paper overclaims 'exact' optimization, skips a same-group baseline (3DGraphX), and its radius-only search space cannot express angle-dependent motifs. read the letter →

arxiv 2505.02247 v1 pith:Q27KU3Q2 submitted 2025-05-04 cs.LG cs.AIq-bio.QM

Jingxiang Qu , Wenhan Gao , Jiaxing Zhang , Xufeng Liu , Hua Wei , Haibin Ling , Yi Liu This is my paper · ORCID
classification cs.LGcs.AIq-bio.QM
keywords 3DmoleculargraphsgraphneuralnetworkexplanationradiusofinfluencedirectedproximitysubgraphextractionchemicalinterpretabilityQM9GEOM
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

RISE is a proposal for explaining predictions made by 3D geometric graph neural networks on molecules. The paper argues that the right way to find the important substructure is not to mask edges one by one, but to shrink each atom's radius of influence until only decisive interactions remain. Because 3D GNNs build edges from distance cut-offs and learn distance-decaying interactions, the authors claim that per-atom radii give both better fidelity and chemically readable explanations, recovering actual chemical bonds under small budgets. In experiments on QM9 and GEOM across SchNet, DimeNet, and SEGNN, RISE reports lower prediction error than prior edge-mask and node-mask explainers at equal or smaller budgets.

What carries the argument

The load-bearing object is the directed proximity graph (DPG): a geometric graph on points in 3D space in which a directed edge $i \to j$ is present iff $d_{ij} < r_i$, with a radius $r_i$ attached to each source node. RISE optimizes these $n$ radii rather than edges, and the gate $M_{ij} = \sigma(k(M^r_i - d_{ij}))$ turns the hard radius rule into a differentiable mask whose $k\to\infty$ limit is exact, with the budget enforced by scaling the radii so that $\|M^r\|_1 \le B$ by construction. This single mechanism carries the whole argument: it makes the search space match the cut-off construction of 3D graphs, embeds distance decay directly into the explanation, removes the discrete-to-continuous relaxation gap that plagues soft edge masks, and is what lets the extracted subgraph be read as a set of atomic interaction spheres rather than a list of arbitrary edges.

What would settle it

Build a synthetic 3D regression task where the target is controlled by a three-atom angular interaction, such as a hydrogen bond whose strength depends on both distance and angle, so that keeping the decisive contact forces the radius to also include a distracting nearby atom. Train a 3D GNN, run RISE and an unconstrained edge-mask explainer at the same budget, and compare the MAE of predictions made from each extracted subgraph; if the edge-mask subgraph has strictly lower MAE than any radius-based subgraph, then RISE's directed-proximity search space cannot contain the optimal explanation.

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Extended reading notes

Core claim

The central claim is that an explanatory subgraph for a 3D molecular GNN should be defined as a directed proximity graph parameterized by one radius of influence per atom. In a directed proximity graph an edge from atom $i$ to atom $j$ exists exactly when the Euclidean distance $d_{ij}$ is below atom $i$'s radius $r_i$, so RISE replaces the dense $n\times n$ edge-mask optimization of GNNExplainer and PGExplainer with $n$ continuous radius variables, using a sigmoid gate $M_{ij}=1/(1+e^{-k(r_i-d_{ij})})$ to make the cut differentiable while preserving exactness at large $k$. The paper claims this reformulation is the only explanation pipeline that naturally accounts for both differences between 2D and 3D GNNs, namely that edges are cut-off-based rather than chemical bonds and that message importance decays with distance, and that it is therefore the only one that yields chemically interpretable substructures: under a small budget RISE keeps chemical bonds and only chemical bonds, as illustrated on ethane, while baseline explainers return scattered, chemically meaningless edges. Quantitatively, RISE is reported to consistently outperform GNNExplainer, PGExplainer, and LRI-Bernoulli across budgets on QM9 and GEOM with both invariant (SchNet, DimeNet) and equivariant (SEGNN) backbones, while preserving fewer edges than the baselines.

Load-bearing premise

RISE's whole argument rests on the assumption that the truly important part of a 3D molecule for the model's prediction can always be expressed by shrinking each atom's radius independently — every edge the explanation keeps must be inside its source atom's radius, and every edge it cuts must be outside it, so no decisive interaction can depend on direction, angle, or any nonlocal context.

Editorial extensions

If this is right

  • If RISE is right, explanation of 3D molecular GNNs can be done without ever constructing an edge-mask matrix: one radius per atom is enough.
  • At small budgets, the extracted subgraph should read as chemical bonds only, giving chemists a direct visual check of what the model used instead of a cloud of thresholded edge weights.
  • Because the radius gate is differentiable and no sparsity or discreteness penalties are needed, RISE avoids the thresholding gap that soft-mask explainers pay for in fidelity.
  • The same radius parameterization transfers across invariant and equivariant backbones and across datasets, so the method is a general replacement for edge-mask explainers in 3D molecular settings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the learned radii themselves could serve as a compact atom-level importance profile: an atom whose radius stays large under tight budgets is one whose entire local neighborhood is decisive, which could be compared across properties to expose which interaction ranges matter for dipole moment versus orbital energies.
  • One extension the paper leaves implicit: because radii shrink monotonically as the budget decreases, RISE naturally produces nested explanation subgraphs, so a single optimization run could animate how the model's reliance spreads from the nearest contacts outward.
  • A limitation the paper acknowledges is long-range context; a testable consequence is that for macromolecules the per-atom radius rule will need angular or directional corrections, such as hydrogen bonds that depend on both distance and angle, which the current directed-proximity formulation cannot express.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes RISE, an instance-level explanation method for 3D molecular GNNs. Instead of optimizing a dense binary edge mask, RISE assigns each atom a learnable radius of influence, so that a directed edge from atom i to atom j is retained when the interatomic distance is smaller than i's radius. The authors motivate this design by arguing that 3D GNNs differ from 2D GNNs both in representation (distance-cutoff dense edges) and in learning (distance-dependent message importance), and they provide annulus-removal experiments suggesting that closer edges are more important. RISE is evaluated on QM9 and GEOM with SchNet, DimeNet, and SEGNN backbones and is compared with GNNExplainer, PGExplainer, and LRI-Bernoulli; the reported fidelity, measured by prediction MAE on the retained subgraph, is generally better for RISE under comparable or more favorable edge budgets for the baselines. The paper also claims exact optimization without continuous-mask relaxation and claims that RISE is the only existing pipeline yielding chemically interpretable substructures.

Significance. If the central claims hold, RISE would be a useful and practical contribution to 3D molecular GNN interpretability: per-atom radii give a compact, chemically suggestive explanation format, the authors provide code, and the empirical comparison covers multiple backbones, datasets, and properties. The proximity-annulus analysis in Sec. 4.1 is a nice empirical probe of how 3D GNNs use distance. However, the paper's strongest advertised advantages--'exact optimization' and being 'the only' interpretable 3D explainer--are overstated relative to what is actually shown. The DPG search-space restriction is a real limitation that is not tested against angle-dependent interactions, which matters because the evaluation includes DimeNet and SEGNN. The core idea is defensible and the empirical results are promising, but the load-bearing theoretical and expressivity claims need to be corrected or substantiated before the paper can be accepted.

major comments (4)
  1. [§3.2, Eq. (7); contribution ③] The claim that RISE 'does not require the relaxation from binary masks to continuous masks' and 'allows exact optimization' is contradicted by Eq. (7). There, M_ij is defined as a sigmoid of k(M^r_i - d_ij), which is a continuous relaxation of the desired indicator function: it is never exactly binary, and the final discrete DPG must still be recovered by thresholding or by reading off the optimized radii. The consistency advantage over GNNExplainer-style soft masks is therefore a matter of degree, not an exact equivalence. Please remove the word 'exact' from the contribution and Sec. 3.3, or provide a formal argument that the sigmoid in Eq. (7) is not a relaxation and that the optimized solution is exactly the discrete DPG.
  2. [Definition 3.1, Eq. (7); Tables 3 and 7] The DPG search space makes edge retention depend only on the source-node radius and the pairwise distance, so it cannot express angle-dependent or other multi-body interactions. This is load-bearing because RISE is evaluated on DimeNet (Table 7) and SEGNN (Table 3), whose message passing uses bond angles and equivariant geometric features: an interaction that matters because of a specific angle cannot be isolated by any radius assignment, since enlarging a radius to include the angular partner also includes all shorter edges from that atom. The annulus-removal evidence in Table 1 is aggregate and monotone, but it does not establish that per-node radii can represent the optimal subgraph in individual molecules; the same table also shows that removing the outermost annulus (80-100%) roughly doubles SchNet's alpha MAE, indicating that long-range edges carry nontrivial signal. I request either a controlled synthetic experiment with an angle-dependent ground-truth subgraph that compares RISE with a full edge-mask explainer under the same budget, or a clear statement that RISE is intentionally restricted to distance-only interactions, with correspondingly weaker claims about angle-aware backbones.
  3. [§3.1.1, Eq. (3)] Eq. (3) is mathematically malformed. The left-hand side is an argmin, the first right-hand term is an objective value evaluated at the soft-masked graph, and the second right-hand term is a difference between predictions, but the inequality connecting them is never derived; the loss L is used with different argument structures and the second term does not show its target. Since this equation is the paper's only formal argument for the inconsistency of soft-mask optimization, it should be replaced by a precise statement (for example, a triangle-inequality bound relating the suboptimality of the thresholded mask to the soft-objective gap plus a prediction-difference term) or removed.
  4. [§3.3, contribution ④] The claim that RISE is 'the only explanation pipeline that can produce chemically interpretable explanatory subgraphs' is stronger than the evidence. Interpretability is assessed qualitatively on a small number of molecules (Fig. 4 and Appendix D), and the 'chemical bonds only' outcome is conditional on an unspecified 'appropriate small budget.' No quantitative interpretability metric, no comparison of interpretation quality across budgets, and no study of how often the bond-only behavior occurs are provided. The claim should be softened to what the experiments actually support, or supplemented with a quantitative evaluation.
minor comments (5)
  1. [Table 1, caption] The caption says values 'in most cells are strictly greater than the previous ones in the row,' but several adjacent cells are equal (e.g., SchNet alpha 0.373 vs. 0.373 and SchNet epsilon_HOMO 0.051 vs. 0.051). Rephrase to 'non-decreasing' or 'generally increasing.'
  2. [Eqs. (5) and (8)] The budget notation mixes normalized masks with physical radii: Eq. (5) forms the effective radius as M^r ⊙ R, while Eq. (8) constrains ||M^r||_1 ≤ B with B = ρ||R||_1. Since R has units of length and M^r is dimensionless, please clarify the normalization of R and the exact quantity being constrained.
  3. [Appendix H, Table 6] The hyperparameter search table contains malformed entries, including a duplicated 'λpred = 1, λpred ∈ {0.1, 0.5, 1.0}' for GNNExplainer and unexplained quantities 'Z ∈ [1, 10]' for PGExplainer and LRI-Bernoulli. Please correct the notation and define Z.
  4. [References and Related Work] The reference list includes Liu et al. (2025, 3DGraphX), but the main text does not discuss this prior 3D explanation work; given the paper's 'first to identify' claims, the distinction should be stated explicitly.
  5. [Abstract and Fig. 1] The abstract contains the grammar error 'an radius of influence'; also, the values quoted in Fig. 1 (C-H 1.171 > 1.095, C-C 1.532 > 1.530) would be clearer if the thresholding rule used to decide edge retention from the optimized radii were stated in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RISE's radius-based subgraph search is optimized against the same fidelity loss used for evaluation and all baselines, and its distance-dependence motivation is an independent empirical observation.

full rationale

I walked the claimed derivation chain from Eqs. (1)-(2) through Definition 3.1 and Eqs. (5)-(8). The DPG definition is a modeling choice, not a derived result: RISE restricts the search to edge sets of the form {i->j : d_ij < r_i} and optimizes r_i to minimize L(Y; Phi(P, M^r ⊙ R, X)) under the budget B = ρ||R||_1. Evaluation then reports the MAE of predictions made with the extracted subgraph, which is exactly the objective minimized. This is the standard post-hoc explanation fidelity protocol and is applied identically to GNNExplainer, PGExplainer, and LRI-Bernoulli, so it is a fair comparative benchmark rather than a fitted input being renamed as a prediction. The proximity analysis in Sec. 4.1 (annulus deletion and random intra-annulus masking) is a separate empirical study used to motivate the radius ansatz; it is not a fitted parameter of RISE and no result in Sec. 4.2 is forced by it. The claim that RISE is 'the only explanation pipeline that can produce chemically interpretable explanatory subgraphs' is a design-expressiveness and visualization claim, not a circular derivation. The self-citations in the reference list (e.g., 3DGraphX, SphereNet, ComENet) are not invoked as load-bearing justification for any step of the method or for the uniqueness claim. Concerns about angle-dependent interactions or the expressiveness of the DPG search space are limitations on scope and verifiability, not circular reasoning; the paper itself concedes long-range dependencies as future work. I find no step where an equation is equivalent to its inputs by construction or where a claim depends on an unverified self-citation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central inductive bias is the radial parameterization: edge importance is assumed to be a function of source-node radius and distance only. This is a domain assumption with only aggregate empirical support. The fitted parameters are the per-node radii; the sigmoid temperature is hand-chosen. No new physical entities are introduced.

free parameters (3)
  • Per-node radius parameters Theta_i, Omega_i (effective radii r_i) = not reported per graph
    Optimized per graph to minimize the fidelity loss; this is the core search variable of RISE (Eq. 8).
  • Sigmoid temperature k = not reported; described as 'typically large'
    Controls the sharpness of the mask in Eq. (7); the value is hand-chosen and affects the relaxation gap.
  • Budget ratio rho = 0.3 to 0.7 across experiments
    User-specified evaluation budget controlling the sum of radii; not fitted but directly determines the number of preserved edges.
assumptions (4)
  • domain assumption Edges in 3D molecular graphs are constructed from a distance cutoff, not from chemical bonds
    Used throughout (Sec. 3.1.1) and standard in SchNet, DimeNet, SEGNN; defines the graph structure that RISE explains.
  • domain assumption The importance of a message decays with the Euclidean distance between nodes
    Stated in Sec. 3.1.2 and empirically motivated in Sec. 4.1; this is the physical prior that justifies optimizing per-node radii.
  • standard math A sigmoid with large k approximates a step function and yields approximate binary masks
    Used in Eq. (7) to make the radius-based mask differentiable; a standard smooth relaxation.
  • domain assumption Minimizing prediction loss on the explanatory subgraph is the correct objective for explanation fidelity
    Adopted from Ying et al. (2019) and used both for optimization (Eq. 5) and evaluation (MAE in Sec. 4.2); this is the accepted criterion in graph explainability.

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Cite this review

Pith. "Pith review of RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation." pith.science (2026). https://pith.science/paper/Q27KU3Q2

@misc{pith2026250502247,
  author       = {Pith},
  title        = {Pith review of: RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q27KU3Q2}},
  note         = {Machine review of arXiv:2505.02247}
}
read the original abstract

3D Geometric Graph Neural Networks (GNNs) have emerged as transformative tools for modeling molecular data. Despite their predictive power, these models often suffer from limited interpretability, raising concerns for scientific applications that require reliable and transparent insights. While existing methods have primarily focused on explaining molecular substructures in 2D GNNs, the transition to 3D GNNs introduces unique challenges, such as handling the implicit dense edge structures created by a cut-off radius. To tackle this, we introduce a novel explanation method specifically designed for 3D GNNs, which localizes the explanation to the immediate neighborhood of each node within the 3D space. Each node is assigned an radius of influence, defining the localized region within which message passing captures spatial and structural interactions crucial for the model's predictions. This method leverages the spatial and geometric characteristics inherent in 3D graphs. By constraining the subgraph to a localized radius of influence, the approach not only enhances interpretability but also aligns with the physical and structural dependencies typical of 3D graph applications, such as molecular learning.

Figures

Figures reproduced from arXiv: 2505.02247 by the authors.

Figure 1
Figure 1. Comparison with existing approaches. Existing approaches require a relaxation from binary masks to soft continuous masks, leading to inconsistencies between the optimized masks and the explanatory binary masks. These inconsistencies not only compromise explanation fidelity quantitatively but also produce chemically uninterpretable results, making the model explanation itself a black-box. On the other hand, RISE intr… view at source ↗
Figure 2
Figure 2. (a): 2D representation of C8H18—Nodes are atoms, and edges are chemical bonds. No geometric information; typically a small number of edges. (b): 3D representation of C8H18—Nodes are atoms with spatial locations. Edges are constructed with a specified cut-off distance, resulting in a dense graph. (c): 3D representation of C8H18 with all non-bonding edges removed. 3.1.1. DIFFERENCE IN REPRESENTATION We find that the d… view at source ↗
Figure 3
Figure 3. (a): Original 3D graphs constructed based on a com￾mon cut-off distance; this is the approach taken in most 3D GNNs (Schutt et al. ¨ , 2017; Gasteiger et al., 2020; Liu et al., 2022; Brandstetter et al., 2022). The edges are bidirectional and dense. (b): Explanatory substructure identified by finding the radii of influence. The radii of influence are optimized (the circles shrink dynamically; see an illustration in … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Explanatory substructure produced from experiments by different explanation methods on the Ethane molecule (CH3CH3) in the QM9 dataset (Ramakrishnan et al., 2014). The same budget (number of edges) is used for different explainers. It is obvious that only RISE yields c…
Figure 5
Figure 5. Figure 5: The visualization of the quantitative results of α of the QM9 dataset on SEGNN when randomly masking 10% edges in different annuli. It shows that the influence of edge masking has a significant correlation with the distances, i.e., masking short edges will cause larger…
Figure 6
Figure 6. Figure 6: An animation of optimizing the radii of influence. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Comparison between node-masking methods (a) and RISE (b). (a): Node-masking methods fail to accurately capture important interactions because they do not consider spatial proximity. Two nodes with high mask values will always result in a high importance for their conne…
Figure 8
Figure 8. Figure 8: The visualized samples of molecules within the QM9 dataset. The explanatory results of GNNExplainer, PGExplainer, LRI￾Bernoulli, and RISE are inferred based on SchNet. The budgets are the same across different explanation methods; in other words, the same number of edg…
Figure 9
Figure 9. Figure 9: The visualization of MAE prediction on µ, α, ϵHOMO, and ϵLUMO with randomly mask 10% edges within the top 0 − 20%, 20 − 40%, 40 − 60%, 60 − 80%, and 80 − 100% distant range, respectively. The results on four properties jointly indicate the correlation between edge dist…

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.