{"id":"055d61f7-786a-43fe-bd9c-8b218a1882f4","arxiv_id":"2505.02247","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"RISE explains 3D GNN predictions by optimizing per-atom radii of influence, extracting subgraphs that preserve chemical bonds and improve prediction fidelity over prior explainers.","lead":"This paper introduces RISE, a method that explains 3D molecular graph neural networks by learning a per-atom radius of influence and extracting the subgraph of atoms within those radii. It reports improved prediction fidelity over existing explainers and argues that the resulting subgraphs are more chemically interpretable.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"DPG search space cannot express angle-dependent interactions, yet RISE is evaluated on DimeNet/SEGNN; a synthetic angle-controlled test would settle whether this limits fidelity.","rationale":"The stress-test pass focuses on the weakest link in the central claim: the directed-proximity-graph representation (Definition 3.1, Eq. 7) that makes edge importance a function of distance alone. This is load-bearing because the paper claims RISE is the only pipeline producing chemically interpretable subgraphs and consistently outperforms all baselines. The reader identified the same assumption, and my analysis adds two concrete points. First, DimeNet and SEGNN use angular or equivariant message passing, but RISE's search space ignores angles; a molecule whose prediction depends on a specific bond angle cannot be faithfully explained by any DPG. Second, the paper's own Table 1 shows that removing the outermost annulus (80-100%, distances 4.4-10 A for SchNet) raises alpha MAE from 0.118 to 0.248, so long-range edges carry considerable signal; DPG under a small radius budget cannot retain a single important long edge without also retaining all shorter edges from that atom. The aggregate Sec. 4.1 experiments show a monotone distance-importance trend but do not establish that per-node radii can carve out arbitrary important edge sets. The Sec. 5 limitation about macromolecules is a partial admission, but the angle issue applies even to small molecules with DimeNet and SEGNN. These are addressable with targeted experiments, so the reader's CONDITIONAL verdict is appropriate; the concern reinforces, but does not overturn, the conditional acceptance.","tokens_in":19724,"tokens_out":6262,"duration_ms":77588,"concrete_test":"Construct a synthetic 3D dataset with a known ground-truth motif: the target depends exclusively on a two-edge angle motif A-B-C with angle ABC near 90 degrees, and all other interatomic distances are shorter than AB and BC. Train DimeNet and SEGNN on this data, then run RISE with a budget that preserves roughly two edges per molecule. If RISE cannot recover the motif without including extra short edges (or if prediction fidelity on the explained subgraph is substantially worse than an edge-mask baseline such as GNNExplainer), the DPG search space is too restrictive for angle-aware backbones. Also run a control where the target depends on one long edge at 3.5 A; if RISE fails to retain it under any reasonable budget, the distance-only assumption is further weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Definition 3.1 and Eq. (7) restrict explained subgraphs to directed edges i->j iff d_ij < r_i, making edge importance depend only on pairwise distance and the source node's radius. However, the paper evaluates RISE on DimeNet (Appendix I, Table 7) and SEGNN (Sec. 4.2, Table 3), whose message passing uses bond angles and equivariant features. An interaction that matters because of a specific bond angle (e.g., a two-edge motif with a 90-degree angle) cannot be isolated by any DPG: setting r_i large enough to include the angular partner also includes all shorter edges from that atom. The paper's support for the distance-only premise (Sec. 4.1, Table 1) is aggregate annulus removal, which shows a monotone trend but not that per-node radii can express the optimal subgraph in individual molecules. Notably, Table 1 shows that removing the outermost annulus (80-100%, distances 4.4-10 A for SchNet) raises SchNet alpha MAE from 0.118 to 0.248, so long-range edges carry substantial signal; a small radius budget would drop them. The authors themselves note long-range dependencies as a limitation (Sec. 5), but the angle issue affects even small molecules when the backbone is DimeNet or SEGNN. Thus the central claim that RISE's search space suffices is not established for angle-aware backbones.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":19975,"tokens_out":5957,"duration_ms":80357,"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":[{"comment":"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.","section":"§3.2, Eq. (7); contribution ③"},{"comment":"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.","section":"Definition 3.1, Eq. (7); Tables 3 and 7"},{"comment":"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.","section":"§3.1.1, Eq. (3)"},{"comment":"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.","section":"§3.3, contribution ④"}],"minor_comments":[{"comment":"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.'","section":"Table 1, caption"},{"comment":"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.","section":"Eqs. (5) and (8)"},{"comment":"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.","section":"Appendix H, Table 6"},{"comment":"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.","section":"References and Related Work"},{"comment":"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.","section":"Abstract and Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"This is a promising empirical contribution with a clean central idea and reproducible code, but the advertised exactness and uniqueness claims do not survive close reading, and the DPG expressivity issue is relevant to the chosen backbones. The proposed synthetic angle-controlled experiment would be the cleanest way to resolve the expressivity concern. I would not reject the paper: the core method is coherent and the empirical comparison is substantial. However, the authors should be asked to revise the theoretical framing and to temper the 'only' and 'exact' claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"RISE is a genuinely new parameterization, not a repackaging: it explains a 3D GNN by giving each atom a radius of influence and keeping edge i→j iff d_ij < r_i, so the explanatory subgraph is a directed proximity graph. On QM9 and GEOM with SchNet, DimeNet, and SEGNN backbones, it generally beats GNNExplainer, PGExplainer, and LRI-Bernoulli on fidelity at similar or smaller edge budgets, and the qualitative advantage is real—the ethane example (C radius 1.532 Å, H radius 1.171 Å, bonds and only bonds) is exactly what a chemist wants from an explainer. The motivation study in Sec. 4.1 (removing nearer annuli hurts predictions more than removing farther ones) is well designed and supports the distance-based design. Code link is provided.\n\nThe central method holds up. The soft spots are overclaims and omissions, not a broken core.\n\nModerate: the paper cites 3DGraphX, a directly relevant 3D explainer from the same group, yet says only LRI exists and never compares against it. That inconsistency, plus the \"only explanation pipeline\" claim, will not survive contact with a referee.\n\nModerate: the \"exact optimization\" claim is overstated. Eq. (7) is a sigmoid relaxation of the hard threshold d_ij < r_i, so RISE still has a continuous-to-discrete gap; it is just pushed into the temperature k. The consistency argument is directionally right, but the wording needs fixing.\n\nModerate: the directed-proximity-graph search space cannot express angle-dependent interactions. On angle-aware backbones like DimeNet or SEGNN, a two-edge motif that matters because of its bond angle cannot be isolated by any radius assignment—raising r_i to include the angular partner also includes every shorter edge from that atom. The Sec. 4.1 evidence is aggregate annulus removal, not per-molecule support. I don't think this is fatal, since RISE still mostly wins against unrestricted edge-mask baselines on those backbones, but the paper should acknowledge the limit and ideally run a synthetic angle-controlled test.\n\nMinor-to-moderate: no error bars anywhere, and the appendix reports best-performing hyperparameter settings, so some of the closer wins could be noise.\n\nMinor: the results summaries overreach. \"Consistently outperforms all baselines across various budgets\" carries its own stated exceptions, and \"consistently achieves the best performance across all configurations on the GEOM dataset\" is contradicted by Table 8 (SchNet at budget 0.4, where PGExplainer reports lower MAE than RISE).\n\nMinor: Eq. (3) is mathematically malformed—an arg min written inside an inequality with a sum of losses—and the \"first to identify these two overlooked differences\" claim is generous, since dense cut-off edges and distance-decaying interactions are standard knowledge in geometric deep learning.\n\nWho this is for: anyone benchmarking 3D GNN explainers or auditing molecular property models. The flaws are addressable. Send it to a serious referee.","headline":"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.","tokens_in":20582,"tokens_out":8219,"would_cite":true,"duration_ms":89037,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Per-atom radii isolate the chemical bonds a 3D GNN relies on","keywords":["3D molecular graphs","graph neural network explanation","radius of influence","directed proximity graph","subgraph extraction","chemical interpretability","QM9","GEOM"],"falsifier":"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.","tokens_in":19489,"feed_emoji":"🧪","tokens_out":8311,"duration_ms":90387,"temperature":0.7,"pith_summary":"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.","feed_headline":"Per-atom radii isolate the chemical bonds a 3D GNN relies on","feed_subtitle":"RISE replaces fuzzy edge masks with one learned distance threshold per atom, yielding bond-level explanations.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the instance-level subgraph explanation objective, Eq. (1), that RISE reformulates from edge masks to radii.","marker":"(Ying et al., 2019)"},{"why":"PGExplainer is the inductive edge-mask baseline RISE must beat in fidelity comparisons.","marker":"(Luo et al., 2020)"},{"why":"LRI is the only prior 3D-specific explanation method and a main baseline; RISE claims to account for the learning difference LRI misses.","marker":"(Miao et al., 2023)"},{"why":"SchNet is the invariant backbone whose cut-off graph construction motivates dense 3D edges and is used in experiments.","marker":"(Schütt et al., 2017)"},{"why":"DimeNet is the second invariant backbone; RISE's experiments use it on QM9 and GEOM.","marker":"(Gasteiger et al., 2020)"},{"why":"SEGNN is the equivariant backbone used to show RISE transfers beyond invariant models.","marker":"(Brandstetter et al., 2022)"},{"why":"QM9 provides the molecular regression testbed and the properties μ, α, εHOMO, and εLUMO.","marker":"(Ramakrishnan et al., 2014)"},{"why":"GEOM supplies the conformer-energy dataset used to test generalization beyond QM9.","marker":"(Axelrod & Gomez-Bombarelli, 2022)"}],"fun_headline_variants":["Per-atom radii isolate bonds in 3D GNN explanations","RISE: one distance threshold per atom for clearer molecular explanations","Radius of influence slices 3D graphs into bond-relevant subgraphs","Learned radii replace edge masks for truly chemical explanations","RISE pinpoints chemical bonds with per-atom influence radii"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Per-atom radii isolate bonds in 3D GNN explanations","RISE: one distance threshold per atom for clearer molecular explanations","Radius of influence slices 3D graphs into bond-relevant subgraphs","Learned radii replace edge masks for truly chemical explanations","RISE pinpoints chemical bonds with per-atom influence radii"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000199,"raw_usage":{"total_tokens":1420,"prompt_tokens":1040,"completion_tokens":380,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":656,"completion_tokens_details":{"reasoning_tokens":293}},"tokens_in":656,"tokens_out":380,"duration_ms":5066,"temperature":1.0,"reasoning_tokens":293,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:58:04.187087+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Gnnexplainer: Generating explanations for graph neural networks","cited_arxiv_id":null,"evidence_quote":"Defines the instance-level subgraph explanation objective, Eq. (1), that RISE reformulates from edge masks to radii."},{"cited_title":"Parameterized explainer for graph neural network","cited_arxiv_id":null,"evidence_quote":"PGExplainer is the inductive edge-mask baseline RISE must beat in fidelity comparisons."},{"cited_title":"Interpretable geometric deep learning via learnable randomness injection","cited_arxiv_id":null,"evidence_quote":"LRI is the only prior 3D-specific explanation method and a main baseline; RISE claims to account for the learning difference LRI misses."},{"cited_title":"Directional message passing for molecular graphs","cited_arxiv_id":null,"evidence_quote":"DimeNet is the second invariant backbone; RISE's experiments use it on QM9 and GEOM."},{"cited_title":"J., and Welling, M","cited_arxiv_id":null,"evidence_quote":"SEGNN is the equivariant backbone used to show RISE transfers beyond invariant models."}],"review_version":1}