Paper deep dive

VINCENT: Validated Interaction Network for Cross-drug Explanation of Therapeutics

Fan-Sheng Chuang, Xuchen Li, Yujing Bian, Kaixiong Zhou

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 93

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%

Last extracted: 8/29/2026, 3:31:04 AM

Summary

The paper introduces VINCENT, a post-training framework for explaining drug synergy predictions by identifying validated cross-drug motif pairs. VINCENT extracts atom-pair evidence from attention and gradient signals, groups atoms into chemically coherent motifs, and validates these pairs through repeated local perturbations. The validated evidence is fed back to refine motif assignments, ensuring chemical coherence, perturbation stability, and alignment with the predictor's behavior. VINCENT outperforms baselines in recovering literature-supported molecular regions.

Entities (10)

VINCENT · method · 98%Drug Synergy Prediction · task · 95%Motif-pair synergy explanation · task · 92%Chemical structure coherence · property · 90%Integrated Gradients · technique · 90%Perturbation stability · property · 90%Predictor-explainer alignment · property · 90%Bliss independence · concept · 85%ComboNet · model · 85%GNNExplainer · model · 80%

Relation Signals (7)

VINCENT → solves → Drug Synergy Prediction

confidence 95% · VINCENT is a post-training framework for a fixed interaction-aware synergy predictor.

VINCENT → ensures → Chemical structure coherence

confidence 92% · yielding explanations that satisfy these three criteria... chemical structure coherence

VINCENT → ensures → Perturbation stability

confidence 92% · yielding explanations that satisfy these three criteria... perturbation-stable

VINCENT → ensures → Predictor-explainer alignment

confidence 92% · yielding explanations that satisfy these three criteria... aligned with predictor behavior

VINCENT → uses → Integrated Gradients

confidence 90% · We therefore also compute pairwise Integrated Gradients... yielding IG

VINCENT → outperforms → GNNExplainer

confidence 85% · These results show that closed-loop perturbation validation recovers literature-supported molecular regions more accurately than existing alternatives

ComboNet → inspires → VINCENT

confidence 80% · Our experimental predictor builds on the multi-task training and Bliss-based formulation of ComboNet

Cypher Suggestions (0)

No Cypher suggestions yet.

Abstract

Abstract:Drug synergy prediction estimates whether two drugs produce a stronger joint effect than expected from their individual activities. For drug combination discovery, a single synergy score is often not enough: researchers also need to know which molecular regions jointly drive the prediction. We study motif-pair synergy explanation, which identifies pairs of chemically coherent regions, one from each drug, that jointly contribute to predicted synergy. Existing interpretable synergy models expose atom- or substructure-level signals, but their explanations are built into the predictor architecture, and none validates cross-drug region scores under repeated perturbations or feeds that evidence back to refine the explanation. A reliable motif-pair explanation should instead be chemically coherent, perturbation-stable, and aligned with predictor behavior. We introduce VINCENT (Validated Interaction Network for Cross-drug Explanation of Therapeutics), a post-training framework for a fixed interaction-aware synergy predictor. VINCENT extracts atom-pair evidence from attention and gradient signals, groups atoms into chemically coherent motifs, and validates candidate motif pairs through repeated local perturbations. The validated evidence is fed back to refine motif assignments, yielding explanations that satisfy these three criteria. On a 25-pair literature-annotated subset, VINCENT achieves a mean motif recall of 0.826 (95% CI: 0.78-0.87), compared with 0.49-0.66 for baselines. Across all 71 test pairs, its validated interaction scores yield a TP/TN separation of 3.36. These results show that closed-loop perturbation validation recovers literature-supported molecular regions more accurately than existing alternatives while producing cross-drug interaction scores that better reflect predictor behavior.

PDF

Open source PDF →Open local PDF →

Trouble viewing inline? Open PDF directly →

Full Text

89,511 characters extracted from source content.

Expand or collapse full text

VINCENT: Validated Interaction Network for Cross-drug Explanation of Therapeutics Fan-Sheng Chuang Affiliation: North Carolina State University, Computer Science, Raleigh, USA email: fchuang2@ncsu.edu , Xuchen Li Affiliation: North Carolina State University, Electrical and Computer Engineering, Raleigh, USA email: xli263@ncsu.edu , Yujing Bian Affiliation: North Carolina State University, Electrical and Computer Engineering, Raleigh, USA email: ybian3@ncsu.edu and Kaixiong Zhou Affiliation: North Carolina State University, Electrical and Computer Engineering, Raleigh, USA email: kzhou22@ncsu.edu © none Abstract. Drug synergy prediction estimates whether two drugs produce a stronger joint effect than expected from their individual activities. For such predictions to support drug combination discovery, a single synergy score is often not enough: researchers also need to know which molecular regions of the two drugs jointly drive the predicted effect. We study motif-pair synergy explanation, whose goal is to identify which pairs of chemically coherent regions, one from each drug, jointly contribute to the predicted synergy. Recent interpretable synergy models expose atom- or substructure-level signals, but their explanation mechanisms are typically built into the predictor architecture, and none validates its cross-drug region scores under repeated perturbation or feeds that evidence back to refine the explanation. A reliable motif-pair explanation should instead be chemically coherent, so its regions are connected motif pairs across the two drugs; perturbation-stable, so scores reproduce across repeated perturbations rather than a single noisy forward pass; and aligned with predictor behavior. We introduce VINCENT (Validated Interaction Network for Cross-drug Explanation of Therapeutics), a post-training framework that explains a fixed interaction-aware synergy predictor. VINCENT extracts atom-pair evidence from the predictor’s attention and gradient signals, groups atoms into chemically coherent motifs, and validates candidate motif pairs through repeated local perturbation. The validated evidence is fed back to refine the motif assignments, yielding explanations that are chemically coherent, perturbation-stable, and aligned with predictor behavior. On the 25-pair literature-annotated subset, VINCENT achieves mean motif recall of 0.826 (95% CI: 0.78–0.87), compared with 0.49–0.66 for baselines. Across all 71 test pairs, its validated interaction scores yield a TP/TN separation of 3.36. These results show that closed-loop perturbation validation recovers literature-supported molecular regions more accurately than existing alternatives while producing cross-drug interaction scores that better reflect predictor behavior. Keywords: Drug synergy prediction, motif-pair synergy explanation, graph neural networks, motif substructure learning. 1. Introduction Drug-pair synergy prediction asks whether two drugs act together more effectively than expected from their individual effects. It is central to drug combination discovery across drug repurposing, lead optimization, and antiviral combination screening, including COVID-19 settings (Bobrowski et al., 2021; Wagoner et al., 2022). Deep learning models predict drug-pair synergy scores (Preuer et al., 2018; Jin et al., 2021; Wang et al., 2022; Liu and Xie, 2021), but most work targets the accuracy of a single scalar score, which does not reveal which molecular regions drive the predicted synergy. We study motif-pair synergy explanation: identifying which pairs of chemically coherent regions (motifs), one from each drug, jointly contribute to the predicted synergistic effect. This matters in practice because a medicinal chemist needs trustworthy interaction evidence, not only a numerical prediction. We argue that a useful synergy explanation should be a validated cross-drug motif-pair interaction matrix satisfying three requirements. First, chemical structure coherence (R1): each motif is a connected region of the molecular graph, and the explanation encodes cross-drug motif pairs rather than isolated atom scores. Second, motif-pair perturbation stability (R2): the explanatory effect assigned to a motif pair should be supported by consistent predictor responses across repeated local perturbations of that pair, rather than by a single forward-pass attribution that may be noisy or unrepeatable. Third, predictor-explainer alignment (R3): across drug pairs, the aggregate validated motif-pair evidence should be positively associated with the predictor’s synergy output, so the explanation reflects the predictor’s decision behavior. Existing work does not fully address this task. Existing drug-synergy models (Preuer et al., 2018; Jin et al., 2021; Wang et al., 2022; Liu and Xie, 2021) primarily optimize combination prediction; although some provide pathway- or substructure-level interpretability, they do not produce perturbation-validated cross-drug molecular-region-pair explanations. General GNN explainers (Ying et al., 2019; Yuan et al., 2021; Luo et al., 2020; Lucic et al., 2022) identify important nodes, edges, or subgraphs for an individual input graph, but are not designed for pair-conditioned cross-drug interactions. Recent interpretable synergy models provide richer structural or biological explanations, including molecular substructures (Liu et al., 2024; Guo et al., 2024; Xia et al., 2026), cross-drug structural attention (Xin et al., 2026), biological or causal subnetworks (Li et al., 2025; Dong et al., 2021; Dong et al., 2023), and multi-scale structural representations (Huang et al., 2026). However, these explanation mechanisms are typically integrated into their respective predictor architectures rather than designed for post-training analysis of a separately trained model. Moreover, to our knowledge, no existing method closes the loop between explanation and validation by repeatedly estimating the stability of cross-drug region-pair effects under local perturbation and feeding those scores back to update the region partition itself. Table 1 summarizes these distinctions. We propose VINCENT (Validated Interaction Network for Cross-drug Explanation of Therapeutics), a post-training framework for extracting validated cross-drug motif-pair explanations from a fixed interaction-aware drug synergy predictor. The predictor supplies atom-level representations, cross-drug signals, and the predicted synergy score; predictor design itself is not a contribution of this work. VINCENT uses these internal signals to construct chemically coherent motifs, screens candidate motif pairs, and validates the retained pairs through repeated local perturbation. The validated evidence is fed back to refine the motif assignments, closing the loop between explanation and validation. To our knowledge, this is the first drug-synergy explanation framework in which perturbation-derived validation is part of the explanation-generation loop itself, actively reshaping the learned molecular regions rather than serving only as a post-hoc check. We make four contributions. (1) Problem formulation. We formulate post-training drug synergy explanation as the recovery of a validated cross-drug motif-pair interaction matrix, operationalized through three testable requirements: chemical coherence, perturbation stability, and predictor alignment (R1–R3), formalized in Section 3.1. (2) Closed-loop explanation method. We propose VINCENT, which combines predictor-derived cross-drug evidence, motif construction, repeated local perturbation validation, and feedback refinement in a closed explanation–validation loop. Validated motif-pair evidence is used not only to score the explanation but also to refine the explanatory regions themselves. (3) Literature-grounded evaluation protocol. We construct a literature-grounded reference set of 111 pharmacophore-level molecular-region annotations across 25 literature-supported drug pairs, and use it to evaluate whether explanation methods recover pharmacologically relevant regions. All annotations are traceable to their supporting sources, as documented in Appendix A. (4) Results and significance. On the literature-annotated subset of 25 pairs, VINCENT substantially improves the recovery of literature-supported molecular regions, achieving mean motif recall of 0.826 compared with 0.49–0.66 for the evaluated explanation baselines. Across the full 71-pair test set, its validated interaction scores also show stronger predictor alignment, including a TP/TN separation of 3.36. 2. Related Work Drug synergy prediction. Drug-synergy models span descriptor- and fingerprint-based neural networks (Preuer et al., 2018), graph-based architectures (Wang et al., 2022; Yang et al., 2021), and more recent dual-view, mechanism-informed, similarity-network, knowledge-graph, and multimodal formulations (Liu and Xie, 2021; Li et al., 2024; Lai et al., 2026; Li et al., 2023; Yan et al., 2026; Saeed et al., 2026). Large-scale combination databases such as DrugComb (Zagidullin et al., 2019) and DrugCombDB (Liu et al., 2020) have further accelerated model development; see Abbasi and Rousu (Abbasi and Rousu, 2024) for a recent survey. Our experimental predictor builds on the multi-task training and Bliss-based formulation of ComboNet (Jin et al., 2021) and serves solely as the fixed model to be explained. Predictor architecture and training details are described in Section 3.2 and Appendix H. GNN explainability. Attribution methods such as Integrated Gradients (Sundararajan et al., 2017) estimate input-component contributions by path integration, while attention weights alone are not necessarily faithful explanations (Jain and Wallace, 2019). Mask-learning approaches such as GNNExplainer (Ying et al., 2019) and PGExplainer (Luo et al., 2020), and subgraph search methods such as SubgraphX (Yuan et al., 2021), provide complementary strategies for explaining graph predictions. Counterfactual approaches such as CF-GNNExplainer (Lucic et al., 2022) and cooperative explanation methods (Fang et al., 2023) address the same task from different angles; broader surveys appear in (Jiménez-Luna et al., 2020; Vo et al., 2022; Ding et al., 2025). These methods typically identify important nodes, edges, or subgraphs for an individual input graph, whereas our task requires pair-conditioned explanations over molecular regions from both drugs. CF-GNNExplainer, for example, searches for minimal graph perturbations that change a prediction; VINCENT instead uses repeated local feature perturbations to estimate the magnitude and stability of a cross-drug region-pair effect, without requiring the prediction to flip. Substructure-level synergy explanation. Recent interpretable synergy models provide structural and biological interpretations at several levels. SDDSynergy (Liu et al., 2024) learns adaptive molecular substructures, while SynergyX (Guo et al., 2024) uses predefined substructures within a mutual-attention architecture. GraFSyn (Xia et al., 2026) uses connected graphlets, while DeepSTFSynergy (Huang et al., 2026) models atomic, substructural, and global structure. DeepDrugs (Xin et al., 2026) maps cross-drug attention signals to pharmacophoric regions, whereas SDCInterpreter (Wang et al., 2026), IDSP (Dong et al., 2021), SANEPool (Dong et al., 2023), and CASynergy (Li et al., 2025) provide mechanism-path or biological-network interpretations. Outside synergy-specific models, Wu et al. (Wu et al., 2023) use molecular fragmentation and masking for post-hoc single-molecule explanation. These works establish the value of substructure- and mechanism-level interpretation, but synergy-specific approaches are typically integrated into their predictor architectures, while generic post-hoc methods do not repeatedly validate cross-drug region pairs or feed the resulting evidence back into region construction. VINCENT instead combines post-training motif construction with repeated cross-drug perturbation validation and feedback refinement in a closed explanation–validation loop. Table 1 summarizes these distinctions. Table 1. Comparison of interpretable and post-hoc approaches relevant to cross-drug motif-pair explanation. Post-hoc: applicable to an independently trained, fixed predictor. Rep. valid.: the same cross-drug region pair is repeatedly perturbed to estimate a stable interaction effect. Feedback: validated evidence is used to update the explanatory regions. ✓/– denote yes/no. Method Expl. unit Post-hoc Rep. valid. Feedback SDDSynergy (Liu et al., 2024) Learned substruct. – – – SynergyX (Guo et al., 2024) Predef. substruct. – – – GraFSyn (Xia et al., 2026) Graphlet substruct. – – – DeepSTFSynergy (Huang et al., 2026) Multi-scale struct. – – – DeepDrugs (Xin et al., 2026) Cross-drug attn. – – – SDCInterpreter (Wang et al., 2026) Mechanism paths – – – CASynergy (Li et al., 2025) Causal / gene net. – – – IDSP (Dong et al., 2021) Signaling net. – – – SANEPool (Dong et al., 2023) Gene subnetwork – – – Wu et al. (Wu et al., 2023) Predef. fragments ✓ – – PGExplainer (Luo et al., 2020) Learned edge mask ✓ – – CF-GNNExplainer (Lucic et al., 2022) CF edges ✓ – – VINCENT (ours) Multi-view motifs ✓ ✓ ✓ 3. Preliminaries 3.1. Problem Setting Drug synergy prediction. Consider a drug pair (A,B)(A,B) with NAN_A and NBN_B atoms, respectively. Each drug is represented as a molecular graph whose nodes are atoms and whose edges are chemical bonds. A structure learning model obtains atom-level representations from this molecular input, for example using a graph neural network (GNN) operating directly on the drug graph. We denote the resulting atom-level representations by HA∈ℝNA×dhH_A ^N_A× d_h and HB∈ℝNB×dhH_B ^N_B× d_h. The single-drug activities PAP_A and PBP_B are inferred by feeding each drug representation into a prediction head, while the combination activity PABP_AB is inferred by feeding the pair-conditioned representations into a combination head. Following ComboNet (Jin et al., 2021), the Bliss independence baseline is Pbliss=PA+PB−PAPBP_bliss=P_A+P_B-P_AP_B, and the predicted synergy score is (1) sAB=PAB−Pbliss.s_AB=P_AB-P_bliss. PblissP_bliss is the combined activity expected if the two drugs acted independently under Bliss independence. Subtracting this baseline from the predicted combination activity PABP_AB measures the gain beyond independent action. Thus, sAB>0s_AB>0 indicates positive excess above the Bliss baseline; in our predictor, a pair is classified as synergistic when this excess exceeds 0.5, i.e., sAB>0.5s_AB>0.5. Motif-pair synergy explanation. Given a fixed synergy predictor f and a drug pair (A,B)(A,B), the synergy explanation is to produce a validated interaction strength matrix R=[rkl]∈ℝKA×KBR=[r_kl] ^K_A× K_B over learned motif pairs, where KAK_A and KBK_B denote the numbers of motifs identified in the two drugs. Here a motif is a chemically coherent molecular region, and rklr_kl is the validated interaction score between the k-th motif of drug A and the l-th motif of drug B, quantifying their joint contribution to the predictor’s synergy output. Unlike the scalar sABs_AB, R localizes the cross-drug evidence to specific molecular regions. The explanation must satisfy: (R1) Chemical structure coherence: each motif is a connected region of the molecular graph, and R encodes cross-drug motif pairs rather than isolated atom scores. (R2) Motif-pair perturbation stability: each score rklr_kl should be supported by consistent predictor responses across repeated perturbations of the motif pair, rather than by a potentially noisy or unrepeatable single forward pass. (R3) Predictor-explainer alignment: across drug pairs, the aggregate interaction strength ∑k,lrkl _k,lr_kl should be positively associated with the predicted synergy score sABs_AB, so the explanation tracks the predictor’s own decision behavior. 3.2. Fixed Predictor Interface VINCENT operates on a separately trained interaction-aware predictor that exposes atom-level representations and cross-drug association signals. In our implementation, molecular representations combine a 2D message-passing encoder with geometry-aware 3D representations. The fused representations are then conditioned through a bidirectional atom-level cross-attention module, which exposes an atom-pair association matrix A^∈ℝNA×NB A ^N_A× N_B, where A^ij A_ij captures the predictor’s learned association between atom i of drug A and atom j of drug B. Separate prediction heads estimate PAP_A, PBP_B, and PABP_AB; the synergy score sABs_AB is computed via Eq. (1). Exact encoder, 2D/3D fusion, and training details are provided in Appendix H. The predictor is trained using the drug-target interaction, single-agent activity, and combination objectives adopted from ComboNet. After training, all predictor parameters are frozen. Before explanation, we perform a one-time mask-aware calibration in which only the neutral mask embedding and local reconditioning operator are learned, so that the local feature masking used during perturbation-based validation does not introduce an unfamiliar input pattern. The calibrated perturbation components are then frozen as well; no predictor parameter is updated during calibration or VINCENT explanation. Calibration details are provided in Appendix H. 4. Method VINCENT uses the fixed predictor only as a source of atom-level evidence and prediction outputs, and explains its synergy score by identifying cross-drug molecular-region pairs whose effects remain stable under repeated perturbation. The framework proceeds in four phases. Phases 1–2 extract and organize predictor evidence for motif discovery, while Phases 3–4 form an iterative assignment–validation loop: motifs are constructed, candidate motif pairs are perturbation-validated, and the validated evidence is fed back to refine the next assignment. The evidence map and two base affinity views remain fixed; only motif assignments, validated scores, and feedback affinity evolve across iterations. Figure 1. Overview of VINCENT: the fixed predictor (left) provides atom-level representations and cross-drug signals. Phases 1–2 prepare the loop’s inputs; Phases 3–4 form the assignment–validation loop with iterative feedback, yielding the top-ranked cross-drug motif pairs (right). Matrices and molecular fragments are illustrative. 4.1. Phase 1: Cross-drug Signal Extraction The goal of Phase 1 is to extract atom-pair evidence from the fixed predictor of where the two drugs jointly contribute to the predicted synergy. We start from the cross-drug association matrix A^∈ℝNA×NB A ^N_A× N_B, where A^ij A_ij is the predictor’s learned association between atom i of drug A and atom j of drug B. This matrix identifies where the predictor establishes cross-drug associations at the atom level, but association alone does not guarantee relevance to the synergy score. We therefore also compute pairwise Integrated Gradients (Sundararajan et al., 2017), yielding IG∈ℝNA×NBIG ^N_A× N_B, where IGijIG_ij measures the contribution of atom pair (i,j)(i,j) to sABs_AB. Integrated Gradients are directly tied to the prediction target but can be noisy in isolation. We define the atom-pair evidence map as the positive intersection of these two signals: (2) M=ReLU⁡(A^)⊙ReLU⁡(IG),M=ReLU( A) (IG), where ⊙ denotes element-wise multiplication. The ReLUReLU operations retain only positive values; the product suppresses atom pairs supported by only one signal. A large MijM_ij indicates that atom pair (i,j)(i,j) is both associated by the predictor and positively involved in increasing sABs_AB. The matrix M is computed once and remains fixed throughout the explanation process. 4.2. Phase 2: Within-drug Affinity Construction The matrix M∈ℝNA×NBM ^N_A× N_B identifies important atom pairs across the two drugs, but motif discovery requires a within-molecule relation: which atoms should be grouped together. Phase 2 therefore constructs three complementary affinity matrices for each drug. For drug A, each WAV∈ℝNA×NAW_A^V ^N_A× N_A, where WAV[i,j]W_A^V[i,j] measures how strongly atoms i and j should share a motif under view V; drug B is treated analogously. The three views encode distinct grouping cues: chemical locality, partner-conditioned predictor behavior, and perturbation-validated feedback. The structural view WAstructW_A^struct uses a Gaussian decay of shortest-path distance in the molecular graph, providing a chemical-locality prior for coherent regions. The interaction-pattern view WApatternW_A^pattern favors nearby, sufficiently active atoms with similar evidence profiles M[i,:]M[i,:] toward drug B. Thus, structural affinity asks whether two atoms are plausible local motif members, whereas pattern affinity asks whether the fixed predictor uses them similarly with respect to the partner drug. These two base views are computed once—the former from molecular structure and the latter from M—and remain fixed. The feedback view WAfbW_A^fb supplies information unavailable before validation. It is initialized to zero; after Phase 4 produces validated motif-pair scores, that evidence is projected back to atoms so that nearby atoms with similar validated interaction profiles receive higher affinity. This is the only dynamic view, allowing perturbation-stable evidence to reshape the next motif assignment without modifying the original evidence map M. Before Phase 3, each affinity is converted into a normalized Laplacian. Exact operators are given in Appendix D. No single view provides all three cues: structural affinity is chemically grounded but partner-agnostic, whereas interaction-pattern affinity is partner-conditioned but still derived from the unvalidated evidence map M. The feedback view supplies the missing post-validation signal, so the three views respectively capture structure, initial predictor evidence, and validated interaction evidence. 4.3. Phase 3: Constrained Motif Assignment Phase 3 groups each drug’s atoms into chemically coherent motifs by learning a soft assignment matrix SA∈ℝNA×KAS_A ^N_A× K_A, where SA[i,k]≥0S_A[i,k]≥ 0 denotes the soft membership of atom i in motif k and each row sums to one. The same process applies to drug B. The assignment is obtained by minimizing: (3) ℒ⁡(SA)=∑V∈struct,pattern,fbλVTr(SA⊤LAVSA)+ℛ⁡(SA),L(S_A)= _V∈\struct,\,pattern,\,fb\ _V\,Tr\! (S_A L_A^VS_A )+R(S_A), where LAVL_A^V is the normalized Laplacian of affinity view V. The three smoothness terms encourage atoms to share a motif when they are chemically local, exhibit similar partner-conditioned interaction patterns, or receive similar validated feedback. The regularizer ℛR combines entropy regularization, which prevents premature collapse of the soft assignment, with a minimum-mass penalty that discourages tiny clusters. After optimization, each atom is assigned to its highest-weight motif: k^(i)=arg⁡maxkSA[i,k] k(i)= _kS_A[i,k]. We then enforce graph connectivity on the hard assignment so that each resulting motif forms a connected molecular region. A ring-completion step subsequently absorbs remaining ring atoms when a motif already contains at least half of a ring system, preventing chemically indivisible rings from being split. The resulting motifs provide the candidate regions tested in Phase 4. 4.4. Phase 4: Perturbation-Based Validation and Feedback The goal of Phase 4 is to validate whether candidate motif pairs from the two drugs induce stable joint effects in the fixed predictor, and to feed the validated evidence back to improve the next motif assignment. We describe the four steps of this phase in order: screening, perturbation, scoring, and feedback. Candidate screening. We first screen motif pairs by aggregating the fixed evidence M over the current soft assignments SA,SBS_A,S_B from Phase 3. The coarse score between motif k of drug A and motif l of drug B is: (4) akl=SA[:,k]⊤MSB[:,l].a_kl=S_A[:,k] \,M\,S_B[:,l]. This score aggregates atom-pair evidence weighted by motif membership and is used only to rank candidate pairs; it is not the final interaction score. Only the highest-ranked candidates proceed to perturbation validation. Repeated local perturbation. For each retained motif pair (k,l)(k,l), we perform T local perturbation trials. Each trial masks a different local subset and fraction of the atoms in the two motifs, producing multiple nearby perturbed realizations of the same motif pair. Masked atom features are replaced by a learned neutral embedding, after which nearby representations are locally reconditioned while the molecular topology remains unchanged. This neutral intervention is supported by the one-time mask-aware calibration described in Section 3.2, which reduces distribution shift during perturbation evaluation. Details of the masking and reconditioning operators are in Appendix E. Pairwise interaction effect. For trial t, let s11(t)s_11^(t), s10(t)s_10^(t), s01(t)s_01^(t), and s00(t)s_00^(t) denote the predictor’s synergy output when both sampled regions are retained, only the region from drug A is retained, only the region from drug B is retained, or both are masked, respectively. The pairwise interaction effect is the second-order finite difference: (5) Ikl(t)=(s11(t)−s10(t))−(s01(t)−s00(t)).I_kl^(t)= (s_11^(t)-s_10^(t) )- (s_01^(t)-s_00^(t) ). A positive Ikl(t)I_kl^(t) indicates a joint effect that cannot be explained by the two local perturbations independently. Stable interaction score. Across the T trials, we summarize the interaction-effect distribution by its mean μkl _kl, variability σkl _kl, activation frequency qklq_kl, and positive-effect frequency pkl+p_kl^+. The validated interaction score is: (6) rkl=softplus⁡(μklσkl+ϵ)⋅max⁡(0, 2pkl+−1)⋅qkl,r_kl=softplus\! ( _kl _kl+ε )· (0,\,2p_kl^+-1)· q_kl, which is high only when the effect is large relative to its variability, directionally consistent, and repeatedly activated. The matrix R=[rkl]R=[r_kl] is the validated interaction matrix at this outer-loop state. Feedback refinement. The validated matrix R completes one half of the closed loop; the other half projects this evidence back into the motif assignment for the next iteration. The feedback operator Φfb _fb connects nearby atoms within the same drug when their validated interaction profiles toward the partner drug are similar. Atoms that repeatedly participate in the same validated cross-drug effects are thereby encouraged to form a common motif in the next iteration. The feedback affinity is smoothed across iterations via exponential moving average to avoid abrupt assignment oscillations: (7) Wfb(t+1)=EMA⁡(Wfb(t),Φfb(S(t),R(t))).W_fb^(t+1)=EMA\! (W_fb^(t),\; _fb\! (S^(t),R^(t) ) ). Starting from Wfb(0)=0W_fb^(0)=0, each outer-loop iteration alternates between motif assignment (Phase 3), perturbation validation, and feedback update. We use three outer-loop iterations by default; longer runs are used only for convergence analysis (Appendix F). The original evidence map M is never modified by feedback; validation therefore reshapes how the fixed predictor evidence is grouped into motifs, rather than creating new evidence. Table 2. Key hyperparameter settings. Parameter Default Role Target motif size c 6 Motif granularity Perturbation trials T 16 Perturbation stability Outer-loop iterations 3 Refinement depth Candidate screening top 30%, min 3, max 20 Pair-selection scope 5. Experiments We evaluate VINCENT through motif coverage against independently annotated pharmacophore regions, predictor alignment with synergy behavior, and ablation and sensitivity analyses of individual components. 5.1. Experimental Setup Dataset. We use the SARS-CoV-2 drug-combination benchmark released with ComboNet (Jin et al., 2021), which pairs antiviral compounds and measures their combination activity. After canonicalizing molecular representations and deduplicating unordered pairs, the final splits contain 88 training, 19 validation, and 71 test pairs. We adopt the same auxiliary training data (drug–target interaction, single-agent activity, and HIV combination data) as in the original work; all explanation experiments are conducted exclusively on the SARS-CoV-2 combination pairs. VINCENT is run on all 71 test pairs. Literature-supported reference set. Evaluating motif coverage requires knowing which molecular regions are pharmacologically relevant for each drug pair. Starting from the 71 test pairs, we retain 25 for which published pharmacological sources provide sufficient mechanistic detail to identify specific molecular regions in each drug. For each retained pair, we manually map literature-identified regions to atom indices, producing 111 pharmacophore-level motif annotations in total (averaging 4.4 annotated regions per drug pair, counting both drugs). All annotations are constructed independently of model output; the full construction procedure and source traceability are described in Appendix A. Implementation details. The predictor parameters are frozen after training and remain fixed during the one-time mask-aware calibration described in Section 3.2; only the perturbation-interface components are calibrated. Unless otherwise specified, VINCENT uses a target motif size of c=6c=6 atoms, T=16T=16 perturbation trials per retained motif pair, top-30% candidate screening (minimum 3, maximum 20 pairs), and 3 outer-loop iterations. The outer-loop depth was selected on validation/pilot data before test-set evaluation. Baselines. We compare VINCENT against four groups under the same fixed predictor and evaluation protocol. Attribution baselines use Integrated Gradients or cross-drug attention to score individual atoms without motif grouping. External single-graph explainers—GNNExplainer (Ying et al., 2019), SubgraphX (Yuan et al., 2021), PGExplainer (Luo et al., 2020), and CF-GNNExplainer (Lucic et al., 2022)—explain each drug separately, with scores converted to candidate regions under the common matching protocol. Controlled baselines cluster atoms using either signal and apply the same perturbation-based validation without iterative feedback, isolating the grouping step. The lower bound is a random connected substructure of matched size. To keep the comparison controlled, all methods explain the same frozen predictor, and their outputs are converted into molecular regions before evaluation under the same region-matching protocol and size constraints. Thus, differences in coverage reflect the explanation strategy rather than changes in the prediction model or evaluation rule. Adaptation details appear in Appendix C. 5.2. Predictor Adequacy and Evaluation Protocol Predictor adequacy. Because post-training explanation is meaningful only for an informative prediction target, we first verify the fixed predictor’s predictive adequacy. It achieves a test ROC-AUC of 0.85, compared with 0.82 for the original ComboNet, 0.80 for DeepDDS, 0.68 for DeepSynergy, and 0.62 for a random forest baseline. Full predictor comparison details appear in Appendix H. Motif-coverage evaluation. We run each explanation method on the 25 annotated test pairs and compare predicted molecular regions against the 111 literature-supported pharmacophore annotations. The evaluation is per reference motif: for each annotated region, we select the best-matching predicted region from a single cluster or a union of at most two bond-adjacent clusters, subject to the size cap |P|≤max⁡(|L|+3,⌈1.4|L|⌉)|P|≤ (|L|+3, 1.4|L| ) to prevent inflated scores. We report recall, precision, Jaccard overlap, and hit rate at recall ≥0.7≥ 0.7 (the fraction of the 111 reference motifs for which the best-matching predicted region achieves recall of at least 0.7). All confidence intervals are from pair-level bootstrap (2,000 resamples). Robustness analyses appear in Appendix G. Predictor-alignment evaluation. We additionally assess whether the validated interaction scores reflect the predictor’s synergy behavior. This evaluation uses all 71 test pairs, not only the annotated subset. For each pair, Phase 4 produces a validated interaction matrix R; we sum the validated interaction scores over all motif pairs into a total explanation strength ∑k,lrkl _k,lr_kl and compute the Pearson correlation with the predicted synergy score sABs_AB. We also report the TP/TN separation ratio: the mean of the highest single validated interaction score maxk,l⁡rkl _k,lr_kl for predictor true positives (pairs correctly predicted as synergistic by the fixed predictor) divided by that for predictor true negatives (pairs correctly predicted as non-synergistic), testing whether the explanation scores discriminate the two groups. 5.3. Motif Coverage Results Table 3. Main explanation results. Recall, precision, Jaccard, and HR≥ 0.7 are evaluated on the 25-pair literature-annotated subset (111 reference motifs). Predictor-alignment metrics ρ⁡(sAB,∑r)ρ(s_AB,Σ r) and TP/TN separation are evaluated on all 71 test pairs. Coverage confidence intervals are from pair-level bootstrap with 2,000 resamples. Method Recall Precision Jaccard HR≥ 0.7 ρ⁡(sAB,∑r)ρ(s_AB,Σ r) TP/TN Sep. Attribution Integrated Gradients Saliency 0.498 0.344 0.288 28.8% — — Cross-Drug Attention Saliency 0.488 0.338 0.287 30.6% — — External GNNExplainer 0.581 0.476 0.394 39.2% — — SubgraphX 0.661 0.536 0.443 48.9% — — PGExplainer 0.552 0.451 0.371 40.8% — — CF-GNNExplainer 0.486 0.397 0.311 26.7% — — Lower bound Random Substructure 0.347 0.263 0.184 14.3% — — Controlled IG Clust.+Pert. 0.586 0.539 0.392 18.0% 0.043 1.49 ATT Clust.+Pert. 0.646 0.599 0.458 38.7% −-0.238 0.48 Ours No Feedback 0.724 0.681 0.568 54.9% 0.352 1.95 VINCENT (Full) 0.826 0.790 0.689 76.6% 0.423 3.36 We test whether VINCENT’s learned motifs overlap with independently annotated pharmacophore regions, indicating pharmacologically meaningful structure. Table 3 and Figure 2 present the comparison. VINCENT achieves the strongest literature motif coverage among all evaluated methods, with mean recall of 0.826 (95% CI: 0.782–0.868), precision of 0.790, Jaccard of 0.689, and a 76.6% hit rate at recall ≥0.7≥ 0.7. Atom-level attribution baselines reach only about 0.49 recall, consistent with their lack of motif construction. External single-graph explainers improve to 0.49–0.66 by producing connected subgraphs, but explain each drug independently of its partner. The controlled single-signal clustering baselines further reach 0.586 and 0.646 under the same perturbation validation. The remaining improvement to 0.826 supports the benefit of combining multi-view assignment with iterative feedback. Figure 2. Literature motif coverage: (a) coverage metrics across methods; (b) distribution of best-region recall across motifs. 5.4. Synergy Discrimination Motif coverage asks whether the right molecular regions are recovered; predictor alignment asks the complementary question of whether their validated interaction scores track the fixed predictor’s synergy behavior. We evaluate this across all 71 test pairs using the aggregate and top-interaction measures defined in Section 5.2. VINCENT’s validated interaction scores align with the predictor’s synergy behavior. The Pearson correlation between sABs_AB and total validated interaction strength ∑k,lrkl _k,lr_kl is 0.423. The mean top interaction score is 4.82 for predictor true positives and 1.43 for true negatives, yielding a TP/TN separation of 3.36. In contrast, IG Clust.+Pert. yields correlation 0.043 and separation 1.49, while ATT Clust.+Pert. yields −-0.238 and 0.48. Thus, VINCENT’s validated scores are substantially more associated with the fixed predictor’s decision behavior than those of the controlled baselines. 5.5. Ablation and Sensitivity Analysis The full method combines two ingredients beyond standard single-signal clustering: multi-view affinities for grouping, and iterative feedback from validation back into assignment. We isolate each contribution using Table 3. Iterative feedback is the largest contributor to the improvement beyond the initial multi-view assignment. Removing the feedback loop while keeping the multi-view assignment (the “No Feedback” variant) reduces recall from 0.826 to 0.724 and TP/TN separation from 3.36 to 1.95, with the synergy correlation dropping from 0.423 to 0.352. This shows that feeding perturbation-validated evidence back into motif assignment materially changes the recovered regions and improves their alignment with predictor behavior. Multi-view assignment improves motif recovery even without feedback. Even without feedback, the multi-view variant achieves 0.724 recall, compared with 0.586 for IG Clust.+Pert. and 0.646 for ATT Clust.+Pert. Because all three variants use the same perturbation-based validation, this comparison directly isolates the grouping step: combining partner-conditioned interaction patterns with molecular locality produces better initial motif candidates than either signal alone. Hyperparameter sensitivity. Table 4 reports the effect of varying one parameter at a time. Target motif size is stable between five and eight atoms per motif; substantially coarser clusters reduce coverage. Increasing perturbation trials from 16 to 32 changes recall by only 0.002 and TP/TN separation by 0.08, indicating that the aggregate metrics are stable beyond the default setting. Performance rises rapidly through the first three outer-loop iterations and then stabilizes; complete results for the five hyperparameter sweeps and the early outer-loop convergence analysis appear in Appendix F. Table 4. Sensitivity to target motif size c, perturbation trials T, and outer-loop refinement. Bold marks the default c and T; the default outer-loop depth is 3. ρ: Pearson correlation between predicted synergy and total validated interaction strength. Parameter Setting Recall Precision Jaccard HR≥ 0.7 ρ TP/TN Target size c 4 .791 .766 .641 .69 .404 3.05 5 .823 .788 .686 .75 .418 3.28 6 .826 .790 .689 .77 .423 3.36 8 .802 .741 .632 .71 .409 3.14 10 .768 .699 .582 .63 .392 2.88 Perturbation trials T 4 .812 .777 .668 .73 .331 2.38 8 .821 .785 .681 .75 .401 3.02 16 .826 .790 .689 .77 .423 3.36 32 .824 .791 .690 .77 .431 3.44 Outer-loop state 0 .724 .681 .568 .55 .352 1.95 1 .796 .758 .648 .70 .399 2.78 2 .821 .782 .678 .75 .417 3.19 3 .826 .790 .689 .77 .423 3.36 4 .828 .789 .690 .76 .419 3.29 5.6. Diagnostic Case Study Because VINCENT reads the fixed predictor’s internal representations rather than its final binary output, it can surface cross-drug interaction evidence even when the predictor misclassifies a pair. We illustrate this with Nitazoxanide + Remdesivir, a pair with literature-reported synergy (Bobrowski et al., 2021) that the predictor classifies as non-synergistic (sAB=0.487s_AB=0.487, below the 0.5 classification threshold defined in Section 3.1). Figure 3. Diagnostic case study: Nitazoxanide + Remdesivir (sAB=0.487s_AB=0.487, false negative). (a,b) Motif clusters for each drug. (c) Validated interaction matrix R. VINCENT recovers strong interaction evidence in this misclassified pair. For correctly classified synergistic pairs, the mean top validated interaction score is 4.82; for predictor true negatives it is 1.43. In this false-negative pair, the top score reaches 5.9 (between the nitrothiazole region of Nitazoxanide and the adenine ring of Remdesivir; Figure 3), placing it above the synergistic group mean despite the incorrect negative label. This suggests that synergy-relevant cross-drug evidence remains present in the predictor’s internal representations despite not being reflected in the final binary decision. A researcher reviewing VINCENT’s outputs could flag this pair for further investigation. An additional true-positive case study (Amodiaquine + Nitazoxanide) is provided in Appendix B. 6. Limitations and Ethical Considerations VINCENT is a post-training explanation framework and therefore inherits the behavior and assumptions of the fixed predictor it explains. Its region-pair scores characterize predictor-level evidence and should not be interpreted as direct evidence of biological causality or clinical efficacy. Our literature-grounded evaluation covers 25 benchmark entries for which published evidence supports region-level annotation, and its conclusions remain conditioned on the compounds and assay settings in the underlying benchmark. Extending evaluation to larger combination screens and experimentally characterized molecular interactions is an important direction for future work. If the predictor has learned spurious correlations, VINCENT’s explanation will reflect those correlations rather than true pharmacological signals; pairing explanation with predictive uncertainty estimates (Wollschläger et al., 2023; Garain et al., 2026) could help identify such cases. The framework currently requires a compatible interaction-aware predictor that exposes atom-level representations and cross-drug signals; applicability to predictors without these interfaces would require architectural adaptation. This study, which uses publicly available molecular and drug-combination data, involves no identifiable personal data or human-subject intervention. VINCENT is intended to support mechanistic inspection and experimental prioritization; its outputs should be interpreted together with domain expertise and experimental evidence rather than used directly for treatment selection or clinical decision making. 7. Generative AI Usage Generative AI tools were used to assist with code generation and debugging, language revision, organization, and literature and citation cross-checking. All methodological decisions, experimental design, analyses, reported results, and final claims were determined and verified by the authors, who take full responsibility for the content of the paper. 8. Conclusion We set out to answer a specific question: given a fixed drug synergy predictor, how can we identify which cross-drug motif pairs jointly contribute to its synergy decision, in a way that is learned and perturbation-validated rather than predefined or read from a single forward pass? VINCENT addresses this through a closed explanation–validation loop that constructs chemically coherent motifs, validates retained motif pairs through repeated local perturbations, and feeds the validated evidence back to refine the motifs. On the 25-pair literature-annotated subset, VINCENT achieves a mean motif recall of 0.826, compared with 0.49–0.66 for baselines. Across the full 71-pair test set, its validated interaction scores yield a TP/TN separation of 3.36, compared with 0.48–1.49 for the controlled baselines. These results show that closed-loop perturbation-based validation improves recovery of literature-supported molecular regions while producing interaction scores that better reflect the fixed predictor’s behavior. References Abbasi and Rousu (2024) F. Abbasi and J. Rousu New methods for drug synergy prediction: a mini-review. Current Opinion in Structural Biology 86, p. 102827. External Links: Document, Link Cited by: §2. Bobrowski et al. (2021) T. Bobrowski, L. Chen, R. T. Eastman, Z. Itkin, P. Shinn, C. Z. Chen, H. Guo, W. Zheng, S. Michael, A. Simeonov, M. D. Hall, A. V. Zakharov, and E. N. Muratov Synergistic and antagonistic drug combinations against SARS-CoV-2. Molecular Therapy 29 (2), p. 873–885. External Links: Document Cited by: §1, §5.6. Ding et al. (2025) Q. Ding, R. Yao, Y. Bai, L. Da, Y. Wang, R. Xiang, X. Jiang, and F. Zhai Explainable artificial intelligence in the field of drug research. Drug Design, Development and Therapy 19, p. 4501–4516. External Links: Document, Link Cited by: §2. Dong et al. (2021) Z. Dong, H. Zhang, Y. Chen, and F. Li Interpretable drug synergy prediction with graph neural networks for human-ai collaboration in healthcare. External Links: 2105.07082, Link Cited by: §1, §2, Table 1. Dong et al. (2023) Z. Dong, H. Zhang, Y. Chen, P. R. O. Payne, and F. Li Interpreting the mechanism of synergism for drug combinations using attention-based hierarchical graph pooling. Cancers 15 (17), p. 4210. External Links: Document, Link Cited by: §1, §2, Table 1. Fang et al. (2023) J. Fang, X. Wang, A. Zhang, Z. Liu, X. He, and T. Chua Cooperative explanations of graph neural networks. In Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, p. 616–624. External Links: Document, Link Cited by: §2. Garain et al. (2026) B. C. Garain, M. Pinheiro, M. de Oliveira Bispo, and M. Barbatti Uncertainty calibration in molecular machine learning: comparing evidential and ensemble approaches. Chemistry – A European Journal 32 (15), p. e03299. External Links: Document, Link Cited by: §6. Guo et al. (2024) Y. Guo, H. Hu, W. Chen, H. Yin, J. Wu, C. Hsieh, Q. He, and J. Cao SynergyX: a multi-modality mutual attention network for interpretable drug synergy prediction. Briefings in Bioinformatics 25 (2), p. bbae015. External Links: Document, Link Cited by: §1, §2, Table 1. Huang et al. (2026) Y. Huang, L. Guo, C. Huang, W. Lan, and C. Zhong DeepSTFSynergy: a multi-scale structural information fusion method for personalized drug combination prediction. Journal of Biomedical Informatics 178, p. 105033. External Links: Document, Link Cited by: §1, §2, Table 1. Jain and Wallace (2019) S. Jain and B. C. Wallace Attention is not explanation. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), p. 3543–3556. External Links: Document, Link Cited by: §2. Jiménez-Luna et al. (2020) J. Jiménez-Luna, F. Grisoni, and G. Schneider Drug discovery with explainable artificial intelligence. Nature Machine Intelligence 2 (10), p. 573–584. External Links: Document, Link Cited by: §2. Jin et al. (2021) W. Jin, J. M. Stokes, R. T. Eastman, Z. Itkin, A. V. Zakharov, J. J. Collins, T. S. Jaakkola, and R. Barzilay Deep learning identifies synergistic drug combinations for treating COVID-19. Proceedings of the National Academy of Sciences 118 (39), p. e2105070118. External Links: Document, Link Cited by: §H.2, §1, §1, §2, §3.1, §5.1. Lai et al. (2026) J. Lai, J. Wu, Y. He, Y. Zhang, B. Li, T. Shi, and J. Han Interpretable graph deep learning framework for drug synergy prediction by integrating functional and clinical similarities. npj Digital Medicine. External Links: Document, Link Cited by: §2. Li et al. (2025) H. Li, L. Zheng, L. Li, Y. Chen, J. Li, C. Zheng, and Y. Su CASynergy: a causal attention model for interpretable prediction of cancer drug synergy. PLOS Computational Biology 21 (10), p. e1013567. External Links: Document, Link Cited by: §1, §2, Table 1. Li et al. (2023) H. Li, L. Zou, J. A. H. Kowah, D. He, L. Wang, M. Yuan, and X. Liu Predicting drug synergy and discovering new drug combinations based on a graph autoencoder and convolutional neural network. Interdisciplinary Sciences: Computational Life Sciences 15 (2), p. 316–330. External Links: Document, Link Cited by: §2. Li et al. (2024) X. Li, B. Shen, F. Feng, K. Li, Z. Tang, L. Ma, and H. Li Dual-view jointly learning improves personalized drug synergy prediction. Bioinformatics 40 (10), p. btae604. External Links: Document, Link Cited by: §2. Liu et al. (2020) H. Liu, W. Zhang, B. Zou, J. Wang, Y. Deng, and L. Deng DrugCombDB: a comprehensive database of drug combinations toward the discovery of combinatorial therapy. Nucleic Acids Research 48 (D1), p. D871–D881. External Links: Document, Link Cited by: §2. Liu and Xie (2021) Q. Liu and L. Xie TranSynergy: mechanism-driven interpretable deep neural network for the synergistic prediction and pathway deconvolution of drug combinations. PLOS Computational Biology 17 (2), p. e1008653. External Links: Document, Link Cited by: §1, §1, §2. Liu et al. (2024) Y. Liu, P. Zhang, C. Che, and Z. Wei SDDSynergy: learning important molecular substructures for explainable anticancer drug synergy prediction. Journal of Chemical Information and Modeling 64 (24), p. 9551–9562. External Links: Document, Link Cited by: §1, §2, Table 1. Lucic et al. (2022) A. Lucic, M. A. Ter Hoeve, G. Tolomei, M. De Rijke, and F. Silvestri CF-gnnexplainer: counterfactual explanations for graph neural networks. In Proceedings of the 25th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research, Vol. 151, p. 4499–4511. External Links: Link Cited by: §1, §2, Table 1, §5.1. Luo et al. (2020) D. Luo, W. Cheng, D. Xu, W. Yu, B. Zong, H. Chen, and X. Zhang Parameterized explainer for graph neural network. In Advances in Neural Information Processing Systems, Vol. 33, p. 19620–19631. External Links: Link Cited by: §1, §2, Table 1, §5.1. Preuer et al. (2018) K. Preuer, R. P. I. Lewis, S. Hochreiter, A. Bender, K. C. Bulusu, and G. Klambauer DeepSynergy: predicting anti-cancer drug synergy with deep learning. Bioinformatics 34 (9), p. 1538–1546. External Links: Document, Link Cited by: §1, §1, §2. Saeed et al. (2026) D. Saeed, H. Xing, and L. Feng A scalable multimodal graph neural network for drug combination response prediction. Molecular Diversity 30, p. 1695–1708. External Links: Document, Link Cited by: §2. Sundararajan et al. (2017) M. Sundararajan, A. Taly, and Q. Yan Axiomatic attribution for deep networks. In Proceedings of the 34th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 70, p. 3319–3328. External Links: Link Cited by: §2, §4.1. Vo et al. (2022) T. H. Vo, N. T. K. Nguyen, Q. H. Kha, and N. Q. K. Le On the road to explainable AI in drug-drug interactions prediction: a systematic review. Computational and Structural Biotechnology Journal 20, p. 2112–2123. External Links: Document, Link Cited by: §2. Wagoner et al. (2022) J. Wagoner, S. Herring, T. Hsiang, A. Ianevski, S. B. Biering, S. Xu, M. Hoffmann, S. Pöhlmann, M. Gale, T. Aittokallio, J. T. Schiffer, J. M. White, and S. J. Polyak Combinations of host- and virus-targeting antiviral drugs confer synergistic suppression of SARS-CoV-2. Microbiology Spectrum 10 (5), p. e03331–22. External Links: Document, Link Cited by: §1. Wang et al. (2022) J. Wang, X. Liu, S. Shen, L. Deng, and H. Liu DeepDDS: deep graph neural network with attention mechanism to predict synergistic drug combinations. Briefings in Bioinformatics 23 (1), p. bbab390. External Links: Document, Link Cited by: §1, §1, §2. Wang et al. (2026) S. Wang, H. Yuan, Z. Hong, X. Chen, and X. Yang Path-based graph neural network for drug synergy prediction and interpretation. Journal of Chemical Information and Modeling 66 (1), p. 337–348. External Links: Document, Link Cited by: §2, Table 1. Wollschläger et al. (2023) T. Wollschläger, N. Gao, B. Charpentier, M. A. Ketata, and S. Günnemann Uncertainty estimation for molecules: desiderata and methods. In Proceedings of the 40th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 202, p. 37133–37156. External Links: Link Cited by: §6. Wu et al. (2023) Z. Wu, J. Wang, H. Du, D. Jiang, Y. Kang, D. Li, P. Pan, Y. Deng, D. Cao, C. Hsieh, and T. Hou Chemistry-intuitive explanation of graph neural networks for molecular property prediction with substructure masking. Nature Communications 14 (1), p. 2585. External Links: Document, Link Cited by: §2, Table 1. Xia et al. (2026) W. Xia, Y. Tian, S. Zhou, H. Du, M. Xiao, Z. Ge, and X. He GraFSyn: an interpretable deep learning framework for anticancer drug synergy via graphlet fingerprints. Journal of Chemical Information and Modeling 66 (12), p. 7252–7263. External Links: Document Cited by: §1, §2, Table 1. Xin et al. (2026) G. Xin, Y. Zhu, Q. Li, J. Han, Z. Xu, H. Wang, and J. Liu DeepDrugs: a mechanism-aware tri-linear attention framework for synergistic drug-combination prediction. Briefings in Bioinformatics 27 (2), p. bbag205. External Links: Document, Link Cited by: §1, §2, Table 1. Yan et al. (2026) C. Yan, M. Chu, G. Zhang, C. Fang, N. Liu, and H. Luo KGLGANSynergy: knowledge graph-based local and global attention network for drug synergy prediction. Journal of Translational Medicine 24, p. 208. External Links: Document, Link Cited by: §2. Yang et al. (2021) J. Yang, Z. Xu, W. K. K. Wu, Q. Chu, and Q. Zhang GraphSynergy: a network-inspired deep learning model for anticancer drug combination prediction. Journal of the American Medical Informatics Association 28 (11), p. 2336–2345. External Links: Document, Link Cited by: §2. Yang et al. (2019) K. Yang, K. Swanson, W. Jin, C. Coley, P. Eiden, H. Gao, A. Guzman-Perez, T. Hopper, B. Kelley, M. Mathea, A. Palmer, V. Settels, T. Jaakkola, K. Jensen, and R. Barzilay Analyzing learned molecular representations for property prediction. Journal of Chemical Information and Modeling 59 (8), p. 3370–3388. External Links: Document, Link Cited by: §H.1. Ying et al. (2019) Z. Ying, D. Bourgeois, J. You, M. Zitnik, and J. Leskovec GNNExplainer: generating explanations for graph neural networks. In Advances in Neural Information Processing Systems, Vol. 32, p. 9240–9251. External Links: Link Cited by: §1, §2, §5.1. Yuan et al. (2021) H. Yuan, H. Yu, J. Wang, K. Li, and S. Ji On explainability of graph neural networks via subgraph explorations. In Proceedings of the 38th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 139, p. 12241–12252. External Links: Link Cited by: §1, §2, §5.1. Zagidullin et al. (2019) B. Zagidullin, J. Aldahdooh, S. Zheng, W. Wang, Y. Wang, J. Saad, A. Malyutina, M. Jafari, Z. Tanoli, A. Pessia, and J. Tang DrugComb: an integrative cancer drug combination data portal. Nucleic Acids Research 47 (W1), p. W43–W51. External Links: Document, Link Cited by: §2. Appendix A Literature-Grounded Evaluation Protocol: Detailed Construction This appendix details the construction of the literature-supported molecular-region reference used in Section 5.2. The reference is designed to evaluate whether an explanation method localizes pharmacologically relevant regions of the two component drugs in the SARS-CoV-2 combination benchmark. Starting from the 71 test entries, we applied a common literature screening and annotation procedure and retained 25 entries for which published evidence provided sufficient molecular specificity for region-level annotation. The resulting reference contains 111 drug-specific molecular-region annotations. The annotations were constructed independently of explanation outputs and fixed before method comparison. We organize the supporting evidence into three provenance tiers. T1 denotes direct experimental combination-response evidence for the specific drug combination; T2 denotes mechanistic characterization of the component drugs together with an explicit combination rationale; and T3m denotes mechanism-supported pharmacological context sufficient to identify molecular regions relevant to the component drugs. The final set contains 10 T1 entries, 3 T2 entries, and 12 T3m entries. The construction follows four levels: published evidence evidence →pair-level mechanistic context -level mechanistic context →drug-specific molecular region -specific molecular region →atom-index reference set. -index reference set. This organization separates pair-level pharmacological context from region-level localization. The literature reference is used for molecular-region coverage evaluation, while cross-drug region-pair scores are assessed by the perturbation-based validation procedure described in the method. A.1. Level 1: Literature Evidence and Provenance We use published combination studies, antiviral screens, mechanistic studies, and structure–activity analyses to establish the evidence chain for each annotated entry. Direct combination-response studies provide experimental context for specific drug combinations, whereas drug-level mechanism and structure–activity studies identify pharmacologically meaningful regions that can be mapped to molecular structures. Table 5 lists key primary and mechanistic sources used to anchor the construction and the representative examples shown below. Identifiers are reported directly to make the evidence traceable to the corresponding publications. Table 5. Key literature evidence used in the reference construction. Combination-response sources establish drug-pair behavior, whereas mechanistic and structure–activity sources support drug-specific molecular-region annotation. Evidence Role Identifier Publication Combination response PMID:33333292; DOI:10.1016/j.ymthe.2020.12.016 Bobrowski et al., Synergistic and Antagonistic Drug Combinations against SARS-CoV-2 (2021). Combination response PMID:32251767; DOI:10.1016/j.antiviral.2020.104786 Choy et al., Remdesivir, lopinavir, emetine, and homoharringtonine inhibit SARS-CoV-2 replication in vitro (2020). Combination response PMID:34572416; DOI:10.3390/biomedicines9091230 Kongsomros et al., Anti-SARS-CoV-2 Activity of Extracellular Vesicle Inhibitors: Screening, Validation, and Combination with Remdesivir (2021). Combination response PMID:36190406; DOI:10.1128/spectrum.03331-22 Wagoner et al., Combinations of Host- and Virus-Targeting Antiviral Drugs Confer Synergistic Suppression of SARS-CoV-2 (2022). Drug mechanism PMID:33711336; DOI:10.1016/j.antiviral.2021.105056 Kumar et al., Emetine suppresses SARS-CoV-2 replication by inhibiting interaction of viral mRNA with eIF4E (2021). Combination response / mechanism PMID:35215969; DOI:10.3390/v14020374 Sacramento et al., Unlike Chloroquine, Mefloquine Inhibits SARS-CoV-2 Infection in Physiologically Relevant Cells (2022). Drug mechanism PMID:33465165; DOI:10.1371/journal.ppat.1009212 Ou et al., Hydroxychloroquine-mediated inhibition of SARS-CoV-2 entry is attenuated by TMPRSS2 (2021). Drug mechanism PMID:33676899; DOI:10.1016/j.ebiom.2021.103255 Hoffmann et al., Camostat mesylate inhibits SARS-CoV-2 activation by TMPRSS2-related proteases and its metabolite GBPA exerts antiviral activity (2021). Structure–activity PMID:34898207; DOI:10.1021/acs.jcim.1c01061 Freidel and Armen, Modeling the Structure–Activity Relationship of Arbidol Derivatives and Other SARS-CoV-2 Fusion Inhibitors Targeting the S2 Segment of the Spike Protein (2021). Drug mechanism PMID:32284326; DOI:10.1074/jbc.RA120.013679 Gordon et al., Remdesivir is a direct-acting antiviral that inhibits RNA-dependent RNA polymerase from severe acute respiratory syndrome coronavirus 2 with high potency (2020). A.2. Level 2: Pair-Level Mechanistic Context For each retained benchmark entry, the literature is first summarized at the drug-pair level. This step records the experimentally observed combination behavior when direct combination data are available and relates the pharmacological mechanisms of the two component drugs. The purpose of this level is to establish the biological context from which drug-specific regions are subsequently localized. Table 6 gives representative examples. The examples span direct combination evidence and complementary mechanistic evidence, illustrating how the same annotation procedure is applied across the evidence hierarchy. Table 6. Representative pair-level mechanistic context used to guide drug-specific region annotation. Pair ID Drugs Literature-Grounded Context pair_000 Amodiaquine + Nitazoxanide Experimental combination screening reports synergy for nitazoxanide with amodiaquine. The two drugs contribute distinct antiviral pharmacological scaffolds, motivating localization of the chloroquinoline/basic-amine regions of amodiaquine and the thiazolide regions of nitazoxanide. pair_002 Nitazoxanide + Remdesivir Direct combination screening reports significant synergy between nitazoxanide and remdesivir. Nitazoxanide contributes a thiazolide antiviral scaffold, whereas remdesivir acts through its nucleotide-analog/RdRp axis. These mechanisms define complementary drug-specific regions for localization analysis. pair_023 Emetine + Remdesivir In vitro experiments report synergistic inhibition of SARS-CoV-2 by emetine and remdesivir. Emetine suppresses viral protein synthesis and has been linked to inhibition of viral mRNA interaction with eIF4E, whereas remdesivir directly inhibits viral RdRp. The two mechanisms provide distinct post-entry pharmacological contexts for molecular region annotation. pair_061 Camostat + Remdesivir Camostat inhibits SARS-CoV-2 entry through TMPRSS2-related serine proteases, whereas remdesivir targets viral RNA synthesis through RdRp. The entry-versus-replication distinction provides a mechanistically complementary basis for localizing relevant regions on the two component drugs. pair_067 Mefloquine + Remdesivir Mefloquine has been shown to reduce SARS-CoV-2 entry in physiologically relevant cells and to enhance the antiviral activity of remdesivir. Remdesivir provides the complementary nucleotide-analog/RdRp mechanism, motivating region annotations on both drug structures. A.3. Level 3: Drug-Specific Literature-Supported Regions Pair-level mechanistic context is next resolved into drug-specific molecular regions. A region corresponds to a chemically coherent functional group, scaffold component, or pharmacophore-level locus that can be associated with the published pharmacology of the drug. This provides a common structural unit against which explanation methods can be evaluated. The annotation is intentionally region-based rather than restricted to individual atoms: many pharmacological determinants span aromatic systems, basic side chains, modified nucleosides, or prodrug moieties. Table 7 shows representative region definitions. Table 7. Representative drug-specific literature-supported molecular regions used in the localization evaluation. Pair ID Drug Region Chemical Type Annotation Role pair_000 A Chloroquinoline core Heterocyclic aromatic Principal heteroaromatic scaffold of amodiaquine pair_000 A Diethylamino sidechain Basic amine Basic side-chain region associated with the drug’s physicochemical and lysosomotropic behavior pair_000 B Nitrothiazole region Heteroaromatic motif Characteristic thiazolide heteroaromatic region of nitazoxanide pair_000 B Salicylamide core Aromatic amide Aromatic salicylamide scaffold region pair_002 A Nitrothiazole region Heteroaromatic motif Characteristic thiazolide heteroaromatic region of nitazoxanide pair_002 A Salicylamide core Aromatic amide Aromatic salicylamide scaffold region pair_002 B Adenine-like nucleobase Nucleobase Nucleobase-recognition region of the remdesivir nucleotide analog pair_002 B Sugar–nitrile core Modified ribose Modified ribose region contributing to the nucleotide-analog scaffold pair_002 B Phosphoramidate aryl head Prodrug motif ProTide region associated with intracellular formation of the active nucleotide analog pair_061 A Guanidinium benzoate region Serine-protease inhibitor motif Recognition region associated with camostat’s serine-protease inhibitory pharmacology pair_061 A Dimethylcarbamoyl ester tail Ester-containing region Peripheral ester-containing region of the camostat scaffold pair_061 B Adenine-like nucleobase Nucleobase Nucleobase-recognition region of the remdesivir nucleotide analog pair_061 B Phosphoramidate aryl head Prodrug motif ProTide region associated with intracellular activation A.4. Level 4: Atom-Index Reference Mapping Each literature-supported molecular region is finally converted to an atom-index reference set on the canonicalized molecular graph. Indices follow zero-based RDKit atom indexing. The mapping preserves the functional-group or scaffold boundary represented by the region; numerical indices therefore need not be consecutive when a chemically coherent region spans multiple branches of the molecular graph. For a reference region L and a predicted region P, coverage is evaluated through their atom-set overlap. Table 8 shows representative mappings together with the corresponding region-aware matching results. A.5. Region-Aware Matching Protocol Because learned cluster boundaries need not coincide exactly with literature-defined functional-group boundaries, we use a constrained region-aware matching rule. For each reference region L, candidate predictions are restricted to regions from the same benchmark entry and the same drug. We consider either a single predicted cluster or a union of at most two clusters. For a candidate union P, its size is restricted by (8) |P|≤max⁡(|L|+3,⌈1.4|L|⌉).|P|≤ (|L|+3,\; 1.4|L| ). Among admissible candidates, the best matching region is selected under the same rule for all compared methods. Region recall, precision, and Jaccard overlap are (9) Recall⁡(L,P)=|L∩P||L|,Precision⁡(L,P)=|L∩P||P|,Recall(L,P)= |L∩ P||L|, (L,P)= |L∩ P||P|, (10) Jaccard⁡(L,P)=|L∩P||L∪P|.Jaccard(L,P)= |L∩ P||L∪ P|. We additionally report the fraction of reference regions reaching recall ≥0.7≥ 0.7. The same reference atom sets and matching constraints are used for every explanation method. Table 8. Representative atom-level reference mappings and region-aware matching results. Atom indices are zero-based RDKit indices. |ref||ref| and |pred||pred| denote the reference and matched predicted region sizes, respectively. Pair Drug Region Atom Indices |ref||ref| |pred||pred| Recall Precision Jaccard pair_000 A Chloroquinoline core 10–20 11 11 1.000 1.000 1.000 pair_000 A Diethylamino sidechain 0–5 6 8 1.000 0.750 0.750 pair_000 B Nitrothiazole region 13–20 8 8 0.875 0.875 0.778 pair_000 B Salicylamide core 4–12 9 13 0.889 0.615 0.571 pair_002 A Nitrothiazole region 13–20 8 7 0.875 1.000 0.875 pair_002 A Salicylamide core 4–12 9 9 0.889 0.889 0.800 pair_002 B Adenine-like nucleobase 21–30 10 7 0.600 0.857 0.545 pair_002 B Phosphoramidate aryl head 11–15,35–41 12 12 0.917 0.917 0.846 pair_002 B Sugar–nitrile core 16–20,31–34 9 12 0.889 0.667 0.615 pair_023 A Amine polycyclic core 2–6,17–24 13 18 0.923 0.667 0.632 pair_023 A Dimethoxy aromatic face A 7–16 10 10 0.900 0.900 0.818 pair_023 A Dimethoxy aromatic face B 25–34 10 13 1.000 0.769 0.769 pair_023 B Adenine-like nucleobase 21–30 10 9 0.900 1.000 0.900 pair_023 B Phosphoramidate aryl head 11–15,35–41 12 16 0.917 0.688 0.647 pair_061 A Guanidinium benzoate region 14–26 13 17 1.000 0.765 0.765 pair_061 A Dimethylcarbamoyl ester tail 0–9 10 12 0.900 0.750 0.692 pair_061 B Adenine-like nucleobase 21–30 10 14 1.000 0.714 0.714 pair_061 B Phosphoramidate aryl head 11–15,35–41 12 16 1.000 0.750 0.750 A.6. Reference-Set Statistics Table 9 summarizes the final reference used for literature-region coverage evaluation. Across the 25 annotated benchmark entries, the reference contains 111 molecular regions, or 4.44 regions per entry on average. Table 9. Summary statistics of the literature-supported molecular-region reference. Statistic Value Annotated benchmark entries 25 Literature-supported reference regions 111 Mean reference regions per entry 4.44 Reference regions on Drug A 57 Reference regions on Drug B 54 T1 entries: direct combination-response evidence 10 T2 entries: mechanism + combination rationale 3 T3m entries: mechanism-supported context 12 Appendix B Case Study We provide a true-positive case study to illustrate how VINCENT connects molecular segmentation, cross-drug interaction scoring, and literature-supported region localization. Figure 4 shows Amodiaquine + Nitazoxanide, a true-positive pair with a predicted synergy score of 0.690. Drug A (Amodiaquine) is segmented into five predicted substructures (panel a). These include an ethyl-containing region (C0), a chlorinated-quinoline region (C1), a phenol-containing region (C2), a quinoline region (C3), and the diethylamino sidechain (C4). In particular, C1 and C3 together cover the broader chloroquinoline-containing scaffold, while C4 captures the diethylamino sidechain. Drug B (Nitazoxanide) is segmented into three predicted substructures (panel b): the nitrothiazole-containing region (C0), an acetyl-salicylate-containing region (C1), and the salicylamide-bridge region (C2). The resulting segmentation separates the major heteroaromatic and aromatic-amide components of the molecule into distinct regions for cross-drug interaction analysis. The region-pair interaction matrix R (panel c) shows that the strongest effect after local perturbation validation occurs between the phenol-containing region of Amodiaquine (C2) and the corresponding salicylamide-bridge region of Nitazoxanide (C2), with rkl=3.8r_kl=3.8. Other prominent interactions are also concentrated among a small number of region pairs, including C2×C1 (rkl=2.6r_kl=2.6), C1×C1 (rkl=2.5r_kl=2.5; chlorinated quinoline), and C3×C1 (rkl=1.9r_kl=1.9; quinoline). Together, these scores show that the validated interaction signal is concentrated on a small subset of cross-drug region pairs rather than being distributed uniformly across the two molecules. The high-scoring interaction pattern is also consistent with the literature-region evaluation. On Amodiaquine, the predicted segmentation recovers the literature-supported chloroquinoline core and diethylamino sidechain. On Nitazoxanide, the predicted regions overlap the annotated nitrothiazole and salicylamide regions. Across the four literature-supported reference regions for this benchmark entry, VINCENT achieves a mean recall of 0.941, including recall of 1.0 for both the chloroquinoline core and the diethylamino sidechain. This example illustrates how VINCENT jointly provides chemically localized molecular regions and cross-drug interaction scores supported by local perturbation validation. Figure 4. Case study of Amodiaquine + Nitazoxanide (true positive; predicted synergy score 0.690). (a) Predicted substructure segmentation of Amodiaquine. (b) Predicted substructure segmentation of Nitazoxanide. (c) Region-pair interaction matrix R after local perturbation validation, where rklr_kl denotes the validated interaction score between predicted regions k and l. Appendix C External Baseline Adaptation All external baselines explain the same fixed predictor. Because these methods are designed for single-graph predictions, each drug in a pair is explained separately. Atom-level importance scores are converted into candidate regions via two strategies: connected components of top-k atoms, and spectral clustering on the importance-weighted induced subgraph. For each baseline, k is swept globally and the configuration with highest mean recall is reported. PGExplainer is trained on all available drug molecules. SubgraphX returns ranked connected subgraphs; the top-3 are used for union selection. CF-GNNExplainer sweeps sparsity threshold (0.3–0.8) and regularization weight (λ∈0.01,0.05,0.1,0.5λ∈\0.01,0.05,0.1,0.5\). The random substructure baseline samples size-matched connected subgraphs via BFS (200 trials per molecule). All baselines use the same region-aware matching protocol as VINCENT: a reference motif may match a single predicted region or a union of at most two adjacent regions sharing at least one bond, subject to the same size cap. Appendix D Method Implementation Details This appendix provides the exact definitions of the operators abstracted in the main text. All notation follows Section 4. The constructions below are described for drug A; drug B is treated identically. D.1. Structural Affinity The structural view encodes molecular locality via a Gaussian decay on shortest-path graph distance: (11) WAstruct[i,j]=[dA(i,j)≤ds]⋅exp(−dA(i,j)22σs2),W_A^struct[i,j]=1[d_A(i,j)≤ d_s]· \! (- d_A(i,j)^22 _s^2 ), where dA(i,j)d_A(i,j) is the shortest-path distance between atoms i and j in the molecular graph of drug A, dsd_s controls the neighborhood radius, and σs _s controls the decay rate. D.2. Interaction-Pattern Affinity The interaction-pattern view connects nearby atoms whose cross-drug evidence profiles are both sufficiently active and similar. We first define, for each atom i, its cross-drug evidence magnitude and normalized profile: (12) ai=∥M[i,:]∥2,pi=M[i,:]max(∥M[i,:]∥2,ϵ).a_i=\|M[i,:]\|_2, p_i= M[i,:] (\|M[i,:]\|_2,\,ε). An activity gate suppresses misleading similarities between nearly inactive profiles: (13) m⁡(ai)=σ⁡(β⁡(ai−τact)),m(a_i)=σ\! (β\,(a_i- _act) ), where σ is the logistic sigmoid, β controls gate sharpness, and τact _act is the activity threshold (set to the 60th percentile of ai\a_i\). The interaction-pattern affinity is: (14) WApattern[i,j]=[dA(i,j)≤dp]⋅exp(−dA(i,j)22σp2)⋅m(ai)m(aj)⋅pi⊤pj.W_A^pattern[i,j]=1[d_A(i,j)≤ d_p]· \! (- d_A(i,j)^22 _p^2 )· m(a_i)\,m(a_j)· p_i p_j. Profile similarity captures whether two atoms interact with the partner drug in a similar way, while the activity gate ensures that this similarity is meaningful rather than driven by near-zero profiles. D.3. Normalized Laplacian Before motif assignment, each affinity matrix W is converted into a self-looped symmetric normalized Laplacian: (15) W^=W+I,Lnorm=I−D^−1/2W^D^−1/2, W=W+I, L_norm=I- D^-1/2\, W\, D^-1/2, where D D is the diagonal degree matrix of W W. D.4. Assignment Regularization The regularizer ℛ⁡(S)R(S) in Eq. (3) combines two terms: (16) ℛ⁡(S)=−λHℛent(S)+ρmassℛmass(S).R(S)=- _H\,R_ent(S)+ _mass\,R_mass(S). The entropy term ℛent(S)=−∑i,kS[i,k]log(S[i,k]+ϵ)R_ent(S)=- _i,kS[i,k] (S[i,k]+ε) prevents premature collapse of the soft assignment into hard one-hot vectors. The minimum-mass term ℛmass(S)=∑ksoftplus⁡(mmin−∑iS⁡[i,k])R_mass(S)= _ksoftplus(m_ - _iS[i,k]) penalizes clusters whose total soft mass falls below a threshold mminm_ , discouraging pathologically small motifs. D.5. Ring Completion After hard assignment k^(i)=arg⁡maxk⁡S⁡[i,k] k(i)= _kS[i,k], graph connectivity is enforced so that every resulting motif induces a connected subgraph of the molecular graph. Partially assigned ring systems are then completed: if a motif already contains at least half the atoms of a ring (identified via RDKit GetRingInfo), the remaining ring atoms are absorbed into that motif. This prevents chemically indivisible ring systems from being split across motifs. D.6. Feedback Operator For each atom i in drug A, the validated interaction profile summarizes its connection to drug B’s motifs through the current validated scores: (17) vA(t)(i,:)=∑kSA(t)[i,k]⋅R(t)[k,:].v_A^(t)(i,:)= _kS_A^(t)[i,k]· R^(t)[k,:]. The feedback affinity between atoms i and j combines graph locality with safe cosine similarity of their validated profiles: (18) W~Afb,(t+1)[i,j]=[dA(i,j)≤dfb]⋅exp(−dA(i,j)22σfb2)⋅vi⊤vjmax⁡(‖vi‖2‖vj‖2,ϵ). W_A^fb,(t+1)[i,j]=1[d_A(i,j)≤ d_fb]· \! (- d_A(i,j)^22 _fb^2 )· v_i v_j (\|v_i\|_2\,\|v_j\|_2,\,ε). The feedback view is then smoothed via exponential moving average: (19) WAfb,(t+1)=(1−αfb)WAfb,(t)+αfbW~Afb,(t+1).W_A^fb,(t+1)=(1- _fb)\,W_A^fb,(t)+ _fb\, W_A^fb,(t+1). D.7. Complete Hyperparameter Table Table 10 lists all hyperparameters of the explanation framework. Table 10. Complete hyperparameter settings for the explanation framework. Parameter Default Role Target motif size c 6 Atoms per motif (determines Kd=clip⁡(⌊Nd/c⌉,2,8)K_d=clip( N_d/c ,2,8)) Perturbation trials T 16 Trials per retained motif pair Outer-loop iterations 3 Default refinement depth Candidate screening θscreen _screen top 30%, min 3, max 20 Pair-selection scope (λstruct,λpattern,λfb)( _struct, _pattern, _fb) (1.0, 0.7, 0.3)(1.0,\;0.7,\;0.3) Affinity-view weights λH _H 0.03 Entropy regularization weight ρmass _mass 0.10 Minimum-mass penalty weight αfb _fb 0.5 Feedback EMA rate τact _act 60th percentile Interaction-pattern activity gate (ds,σs)(d_s, _s) (5.0, 1.5)(5.0,\;1.5) Structural affinity parameters (dp,σp)(d_p, _p) (4.0, 1.25)(4.0,\;1.25) Pattern affinity parameters (dfb,σfb)(d_fb, _fb) (5.0, 2.0)(5.0,\;2.0) Feedback affinity parameters Appendix E Perturbation-Based Validation Details This appendix provides the exact perturbation procedure abstracted in Section 4.4. E.1. Local Subset Sampling For each retained motif pair (k,l)(k,l) and trial t, we independently sample local subsets of atoms from the two motifs: (20) ℳA,k(t)⊆A(k),ℳB,l(t)⊆B(l),M_A,k^(t) _A^(k), _B,l^(t) _B^(l), where A(k)G_A^(k) denotes the set of atoms assigned to motif k in drug A. Each trial uses a different subset and masking fraction, so the T=16T=16 trials produce a distribution of local perturbations for the same motif pair rather than repeating an identical intervention. E.2. Feature Substitution For each selected atom i∈ℳA,k(t)i _A,k^(t), the atom-level representation is replaced by a learned neutral mask embedding: (21) HApert[i,:]=emask,emask∈ℝdh.H_A^pert[i,:]=e_mask, e_mask ^d_h. Drug B is treated identically. No nodes or edges are removed: the molecular topology remains unchanged throughout. E.3. Local Reconditioning After feature substitution, the representations in the 2-hop neighborhood of the masked motif are locally reconditioned: (22) A(k)=i:dA(i,A(k))≤2.N_A^(k)=\i:d_A(i,G_A^(k))≤ 2\. A 2-layer local message-passing network operates on A(k)N_A^(k) to allow nearby atom representations to adjust to the masked features, producing a locally consistent perturbed state without propagating the perturbation signal through the entire molecular graph. Its parameters are learned only during the one-time mask-aware calibration and remain frozen during explanation. E.4. Perturbation States and Interaction Effect For each trial t, four perturbation configurations yield four predictor outputs s11(t),s10(t),s01(t),s00(t)s_11^(t),s_10^(t),s_01^(t),s_00^(t) (both regions retained, only drug A’s region retained, only drug B’s region retained, both masked). The perturbation-derived interaction effect is the second-order finite difference given in Eq. (5). E.5. Stable Interaction Score Across T trials, the effect distribution is summarized by: (23) μkl _kl =1T∑tIkl(t),σkl=std⁡(Ikl(t)t), = 1T _tI_kl^(t), _kl=std(\I_kl^(t)\_t), (24) pkl+ p_kl^+ =1T∑t[Ikl(t)>0],qkl=1T∑t[|Ikl(t)|>τI]. = 1T _t1[I_kl^(t)>0], q_kl= 1T _t1[|I_kl^(t)|> _I]. The validated interaction score combines these four statistics: (25) rkl=softplus⁡(μklσkl+ϵ)⋅max⁡(0, 2pkl+−1)⋅qkl.r_kl=softplus\! ( _kl _kl+ε )· (0,\,2p_kl^+-1)· q_kl. Appendix F Hyperparameter Sensitivity Analysis This appendix reports the full sensitivity analysis summarized in Section 5.5. Each hyperparameter is varied individually with all others held at their defaults (Table 10). We report the same six evaluation metrics used throughout the main text. Table 11. Complete sensitivity results across five hyperparameter sweeps and an early outer-loop convergence analysis. Bold rows indicate defaults for the five swept hyperparameters and the preselected outer-loop depth of 3. The iteration-10 row is included only to characterize convergence beyond the default. Parameter Setting Recall Precision Jaccard HR≥0.7 ρ TP/TN KdK_d (c) 4 0.791 0.766 0.641 0.69 0.404 3.05 5 0.823 0.788 0.686 0.75 0.418 3.28 6 0.826 0.790 0.689 0.77 0.423 3.36 8 0.802 0.741 0.632 0.71 0.409 3.14 10 0.768 0.699 0.582 0.63 0.392 2.88 T 4 0.812 0.777 0.668 0.73 0.331 2.38 8 0.821 0.785 0.681 0.75 0.401 3.02 16 0.826 0.790 0.689 0.77 0.423 3.36 32 0.824 0.791 0.690 0.77 0.431 3.44 Outer-loop state 0 0.724 0.681 0.568 0.55 0.352 1.95 1 0.796 0.758 0.648 0.70 0.399 2.78 2 0.821 0.782 0.678 0.75 0.417 3.19 3 0.826 0.790 0.689 0.77 0.423 3.36 4 0.828 0.789 0.690 0.76 0.419 3.29 10 0.823 0.787 0.681 0.75 0.418 3.20 θscreen _screen top 10% 0.815 0.781 0.669 0.73 0.361 2.71 top 20% 0.823 0.787 0.684 0.75 0.414 3.24 top 30% 0.826 0.790 0.689 0.77 0.423 3.36 top 50% 0.827 0.788 0.689 0.76 0.425 3.31 top 100% 0.822 0.782 0.683 0.75 0.415 3.22 λpattern _pattern 0.3 0.799 0.770 0.648 0.70 0.394 2.98 0.5 0.824 0.789 0.687 0.76 0.419 3.30 0.7 0.826 0.790 0.689 0.77 0.423 3.36 1.0 0.814 0.758 0.652 0.71 0.421 3.29 λfb _fb 0.0 0.726 0.683 0.570 0.55 0.354 1.97 0.1 0.789 0.751 0.641 0.69 0.397 2.81 0.3 0.826 0.790 0.689 0.77 0.423 3.36 0.5 0.827 0.786 0.686 0.76 0.424 3.33 0.7 0.811 0.765 0.655 0.72 0.412 3.14 Across the five hyperparameter sweeps and the early outer-loop convergence analysis, the framework shows graceful degradation rather than cliff-edge sensitivity. The strongest effects come from feedback-related parameters (λfb _fb and the outer-loop depth): disabling feedback (λfb=0 _fb=0) reduces recall by approximately 0.10 and TP/TN separation by 1.4, consistent with the ablation findings in Section 5.5. Segmentation granularity has a moderate effect, with cluster sizes from 5 to 8 atoms yielding recall above 0.80. Perturbation trials primarily affect discrimination metrics rather than coverage: recall varies by only 0.014 across T∈4,8,16,32T∈\4,8,16,32\, while TP/TN separation ranges from 2.38 to 3.44. The screening threshold has minimal impact on motif coverage: validating all candidate pairs (top 100%) yields nearly identical recall to the default (top 30%). The interaction-pattern weight λpattern _pattern shows a mild optimum at 0.7; setting it to 1.0 slightly reduces precision, suggesting that over-weighting interaction-pattern similarity can override the structural prior. Appendix G Evaluation Robustness Analysis This appendix reports evidence-tier stratification and pair-selection stability analyses summarized in Section 5.2. Evidence-tier stratification. Table reports motif coverage metrics stratified by the evidence tier assigned during reference-set construction (Section 5.2 and Appendix A). Tier-1 pairs, supported by direct experimental synergy evidence, achieve the highest recall (0.842) and hit rate (85.8%), consistent with the expectation that pharmacophore annotations derived from primary screening data align most closely with the predictor’s learned motif boundaries. Tier-2 pairs show slightly lower recall (0.809) but higher precision (0.830), reflecting tighter but less complete motif recovery. Tier-3m pairs achieve recall of 0.824, with the widest variance, as expected given that their annotations are derived from mechanism-level rationale rather than direct combination evidence. Table 12. Motif coverage stratified by evidence tier. 95% CIs from pair-level bootstrap (2,000 resamples within each tier). The “All” row reports pair-level means; the motif-level mean in Section 5.3 (0.826) weights each motif equally regardless of pair. Tier #Pairs Recall Precision HR≥ 0.7 T1 10 0.842 [0.767–0.898] 0.814 [0.749–0.868] 0.858 [0.738–0.958] T2 3 0.809 [0.753–0.838] 0.830 [0.709–0.906] 0.700 [0.500–0.800] T3m 12 0.824 [0.757–0.890] 0.768 [0.709–0.829] 0.718 [0.546–0.875] All 25 0.829 [0.785–0.871] 0.794 [0.751–0.835] 0.771 [0.672–0.861] Pair-selection stability. To verify that the aggregate results are not driven by a small number of favorable pairs, we perform leave-k-out analysis for k∈1,2,3,5k∈\1,2,3,5\. For each k, we randomly remove k pairs from the 25-pair set and recompute mean recall over the remaining pairs, repeating 2,000 times. Table 13 reports the resulting stability ranges. Even at k=5k=5 (removing 20% of pairs), the 95% range of mean recall is 0.810–0.852, indicating that no small subset dominates the aggregate. The most influential single pair is pair_003 (Nitazoxanide + Remdesivir, recall 0.553): removing it raises the mean by +0.012; the most favorable pair is pair_061 (Camostat + Remdesivir, recall 0.975): removing it lowers the mean by −-0.006. No individual pair shifts the mean by more than 1.5 percentage points. Table 13. Pair-selection stability of mean recall under leave-k-out resampling (2,000 random subsets per k). k removed Pairs remaining 95% range of mean recall 1 24 [0.823–0.841] 2 23 [0.819–0.843] 3 22 [0.815–0.847] 5 20 [0.809–0.852] Appendix H Predictor Implementation and Adequacy H.1. Architecture The predictor combines two molecular encoding branches. A 2D branch based on a directed message-passing neural network (D-MPNN) (Yang et al., 2019) operates on the molecular graph and produces atom-level representations from bond-level messages. A 3D branch based on an equivariant graph neural network (EGNN) operates on a molecular conformer and provides geometry-aware atom representations. The 2D and 3D representations are fused before entering the interaction module. A bidirectional atom-level cross-attention module then conditions each drug’s representation on its partner, producing pair-conditioned atom representations and exposing the cross-drug association matrix A^∈ℝNA×NB A ^N_A× N_B used by VINCENT. Separate prediction heads produce the single-drug activities PAP_A, PBP_B and the combination activity PABP_AB; the synergy score is sAB=PAB−Pblisss_AB=P_AB-P_bliss (Eq. (1)), and a pair is classified as synergistic when sAB>0.5s_AB>0.5. H.2. Training The predictor follows the multi-task training setting of ComboNet (Jin et al., 2021), jointly optimizing three objectives: drug–target interaction prediction, single-agent antiviral activity prediction, and drug-combination synergy prediction. These auxiliary objectives help address the limited number of SARS-CoV-2 combination training pairs (88 pairs after deduplication) by sharing molecular representations across related tasks. H.3. Mask-Aware Calibration After predictor training, all pretrained predictor parameters are frozen. A one-time mask-aware calibration then learns only the neutral mask embedding emask∈ℝdhe_mask ^d_h and the local reconditioning operator used during perturbation-based validation; the predictor weights remain unchanged throughout. During calibration, randomly sampled connected molecular regions are replaced by emaske_mask and the original prediction objectives are used to calibrate these perturbation-interface components. This step reduces the distribution shift that would otherwise occur when motif atoms are masked. After calibration, emaske_mask and the reconditioning operator are frozen together with the predictor for all VINCENT explanations. H.4. Predictive Adequacy Table 14 compares the fixed predictor against published baselines on the SARS-CoV-2 test set. The predictor achieves a test ROC-AUC of 0.85, providing a sufficiently informative fixed target for post-training explanation. Predictor accuracy is not a contribution of this work; the comparison is included solely to verify that the explanation target is meaningful. Table 14. Predictor adequacy: test ROC-AUC on the SARS-CoV-2 combination benchmark. Model Test ROC-AUC Random Forest 0.62 DeepSynergy 0.68 DeepDDS 0.80 ComboNet (original) 0.82 Our predictor (fixed target) 0.85

Instant research discovery