SuperMAN: Interpretable and Expressive Networks over Temporally Sparse Heterogeneous Data
Authors: Andrea Zerio
Maya Bechler-Speicher
Maor Huri
Marie Vibeke Vestergaard
Tine Jess
Ran Gilad-Bachrach
Samir Bhatt
Aleksejs Sazonovs
Venue: ICLR 2026 Poster (2026)
Keywords: Graph Deep Learning
Graph Neural Networks
Interpretability
Primary area: learning on graphs and other geometries & topologies
TL;DR: We present a novel SoTA interpretable model for learning over temporally sparse heterogeneous data

Abstract: Real-world temporal data often consists of multiple signal types recorded at irregular, asynchronous intervals. For instance, in the medical domain, different types of blood tests can be measured at different times and frequencies, resulting in fragmented and unevenly scattered temporal data. Similar issues of irregular sampling occur in other domains, such as the monitoring of large systems using event log files. Effectively learning from such data requires handling sets of temporal sparse and heterogeneous signals. In this work, we propose Super Mixing Additive Networks (SuperMAN), a novel and interpretable-by-design framework for learning directly from such heterogeneous signals, by modeling them as sets of implicit graphs. SuperMAN provides diverse interpretability capabilities, including node-level, graph-level, and subset-level importance, and enables practitioners to trade finer-grained interpretability for greater expressivity when domain priors are available. SuperMAN achieves state-of-the-art performance in real-world high-stakes tasks, including predicting Crohn’s disease onset and hospital length of stay from routine blood test measurements and detecting fake news. Furthermore, we demonstrate how SuperMAN’s interpretability properties assist in revealing disease development phase transitions and provide crucial insights in the healthcare domain.

Published as a conference paper at ICLR 2026
SUPERMAN: INTERPRETABLE AND EXPRESSIVE NET- WORKS OVER TEMPORALLY SPARSE HETEROGENEOUS DATA
Andrea Z Maya Bechler-Speicher':
Maor Huri',
Marie Vibeke Vestergaard",
Ran Baadd-Bachrach,, Tine Jess2.3, Samir Bhatt4.
Aleksejs Sazonovs
Mett
"Center of Excellence for Molecular Prediction of IBD (PREDICT).
Department of Clinical Medicine, Aalborg University
3 'Department of Gastroenterology & Hepatology, Aalborg University Hospital *University Copenhagen
'Imperial College London
6 "Department of Biomedical Engincering, Tel-Aviv University
7 "agoo School of Neuroscience, Tel-Aviv University
ABSTRACT
Real-world temporal data often consists multiple signal types recorded at ir- regular, asynchronous intervals. For instance, in the medical domain, different types of blood tests can be measured different times and frequencies, resulting in fragmented and unevenly scattered temporal data. Similar issues of irregular sampling occur in other domains, such as the monitoring of large systems using event log files. Effectively learning from such data requires handling sets of tem- porally sparse and heterogeneous signals. this work, we propose Super Mixing Additive Networks (SUPERMAN), novel and piterpettable-b--deee for learning directly from such heterogeneous signals, by modeling them as sets implicit graphs. SUPERMAN provides diverse interpretability capabilities, includ- ing node-level, graph-level, and subset-level importance, and enables practitioners trade finer-grained interpretability for greater expressivity when domain priors are available. SUPER M AN achieves state-of-the-ar performance in real-world high-stakes tasks, including predicting Crohn's disease onset and hospital length of stay from routine blood test measurements and detecting fake news. Furthermore, we demonstrate how SUPERMAN's interpretability properties assist in revealing disease development phase transitions and provide crucial insights in the healthcare domain.
framework
INTRODUCTION
Modern clinical data consist of diverse types of signals, often collected at irregular and asynchronous time intervals. For example, a patient's medical record may include a set of blood tests taken over their lifetime, where each type of test is performed its own frequency. As a result, the data can be viewed as set of sparse temporal signals, each with its own fragmented temporal structure. Similar patterns occur in other domains. For instance, the spread of news articles in social media networks often follow asynchronous tree-like patterns of dissemination. Another example is system event logs, which typically include different types of events occurring varying times and rates.
Thhee authors contributed equally this work.

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A common approach for learning from such data is to align the signals to fixed-size time grid, thereby enforeing a shared timeline. This is typically achieved by trimming or aggregating signals and filling in missing values through interpolation or learned imputation models (Cao et al. 2018: Tashiro et al. 202T Wu et al.] 2022 Du et al. 2023). However, these procedures can lead to substantial information loss and ignore the informative patterns in the irregularity itself, such the varying time intervals between different measurement types.
In this work, introduce Super Mixing Additive Networks (SUPERMAN), a novel framework designed to learn directly from heterogeneous, temporally sparse and irregular signals, without information loss or imputation. SUPERMAN models these signals as sets of implicit graphs by introducing a distance function between each pair of signals within each type of signal. For example, in blood test data, each biomarker type can be modeled as a directed graph whose nodes correspond to individual measurements, with the distance between each pair of measurements being the time delta between them. These implicit graphs may differ in structure, size, and feature space, reflecting the diversity of real-world heterogeneous signals.
SUPERMAN allows for multi-resolution interpretability capabilities, including node-level, graph- level, and subset-level importance. It also enables practitioners trade fine-grained interpretability for greater expressivity when domain priors are available. Specifically, sigmal graphs can be grouped into subsets, allowing for more expressive modeling of non-lime non-linear interactions within the subsets. This shifts interpretability from individual nodes or graphs to the subset level. SUPERMAN builds on Graph Neural Additive Networks (GNAN) (Bechler-Speicchr al.. 2024), interpretable class of GNNs that operate on individual nodes or graphs. In contrast, SUPERMAN is expressly designed for sets of implicit graphs and introduces a graph-grouping mechanism that aggregates signals within subsets of graphs while preserving an additive decomposition across subsets. Rather than applying GNAN directly, SUPERMAN employs an extended and more flexible variant, which we denote by EXIGNAN. Within each graph, EXIGNAN generalises GNAN's univariate feature-shape networks to multivariate feature groups, allowing non-linear dependencies among related features while retaining additive transparency at the group level. In analogy to signal grouping, EXIGNAN supports grouping features into subsets, thereby replacing feature-level interpretability with subset-level interpretability, such importance scores. We prove that grouping signals or features strictly increases expressivity, and that SUPERMAN is strictly more expressive than GNAN.
We demonstrate the effectiveness of SUPERMAN it achieves sfute-of-the-aae (SoTA) performance while also providing valuable clinical and biological insights through its interpretability.. In addition, we show that SUPERMAN attains SoTA performance in fake news detection, highlighting its flexibility in operating on sets of graphs with arbitrary structure. This contrasts with existing approaches, which are restricted sets of path-like signals and offer no interpretabilityy. Finally, we demonstrate how SUPERMAN's 's interpretability reveals phase transitions and provides crucial insights in healthcare.
real-world high-stakes medical datasets, where
Our main contributions are as follows:
1. We introduce SUPERMAN, novel framework for learning directly from sets of sparse, irregular temporal signals, without information loss or imputation.
2. We allow practitioners to integrate domain priors. when available, by grouping features or signal types into subsets. This shifts interpretability from fine-grained (node- or feature- level) to subset-level, while strictly improving expressivity. This capability is particularly valuable in the medical domain, where such priors are common.
3. We provide theoretical analysis proving that groupings of features and signals make SUPERMAN strictly more expressive.
4. We demonstrate the effectiveness of SUPERMAN on real-world high-stakes medical datasets and fake news detection, achieving state-of-the-art performance in both domains.
5. We show that SUPERMAN provides valuable interpretability capabilities, including node- level, graph-level, and subset-level importance, which yield meaningful clinical and biologi- cal insights.
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Graph Repeoserations
EHGGNN1
Subeet Reprosetations
Deepert
ODB
EXIGNAN
Rcpresontatiinn
Veeter Sun
Sum
$2
E
Figure I: In this example, the imput is a set of three graphs, G1, G2, G3. grouped into two subsets S and S2. Within each subset, the same EXIGNAN instance is applied to graphs to produce their graph-level representations. For subsets containing multiple graphs, DeepSets module aggregates these graph representations into a single subset representation. For subsets of size one, the subset representation is simply the graph representation itself. The final set representation is then obtained by summing the subset representations, and the final label prediction is produced by summing the entries of this set representation.
2 RELATED WORK
Graph Neural Additive Networks Graph Neural Networks (GNNs) (Kipf & Welling 2016
Gilmer al.) 2017: Velickovic et al. 2017 Xu al. 2018) have become the dominant framework for learning over graph-structured data, enabling flexible representation learning across diverse domains such healthcare (Paul al., [2024 Ochoa & Mustafa 2022. Peng al. (202)) chemistry (Reiser
et al. 2022 Jumper et al.) 2021) and social networks (Li et al. 2023] Sharma et al.. 2024). among
others. GNNs leverage both the graph topology and node features compute learned representations for individual nodes for entire graphs. Recently, |Bechler-Speicher et al. (2024) introduced Graph
Neural Additive Networks (GNANs), a novel interpretable-by-dest inspired by generalized additive models (GAMs) (Hastie & Tibshirani, 1986 1987). GNAN applies univariate neural networks to each feature of the nodes separately, and then linearly combines their outputs across nodes to produce node-level and graph-level representations. As features are not mixed non-linearly, GNAN is fully interpretable, and provides feature-level and node-level interpretability which shows exactly how each feature and each node contributes to the final target variable.
graph learning framework
Learning from sparse data In many real-world settings, data often presents missing values from irregular sampling and variable feature availability. Recurrent models (Cao et al. 2018) treat missing
data as latent variables, while attention- based methods (Du al. 2023 Wu al. 2022 Tipimeni
& Reddy, 2022 Labach et al.) 2023) reconstruct them via contextual masking and temporal blocks.
Diffusion models (Tashiro et al.] 2021 Alcaraz & Strodthoff] 2022 Senane et al. 2024 Dai et al.
2024) learn conditional distributions over missing values using score-based processes. Graph-based approaches use GNNs to model feature dependencies through bipartite graphs, adaptive message passing, opatio-fempont
attention (You et al., 2020 Cini et al. 2022 Marisca al. 2022 Ye et al. 302T:Cheer et al.] | (2024). These imputation methods often distort dynamics and may not improve prediction (Qian et al. 2025). An alternative is to model sparsity directly. Neural and Latent ODEs (Chen et al. 201 8 Rubanova et al,, 2019) address irregular gaps via continuous dynamics but are compute-intensive and rely on missingness encodings. Recent models (Zhang et al.) (02T) have used graph representations to capture sparsity without imputation. Importantly, none of the aforementioned methods offer built-in multi-grain interpretability in the way that SUPERMAN does.
3 SUPER MIXING ADDITIVE NETWORKS
In this section, we present SUPERMAN, an interpretable and flexible method for learning over sets of arbitrary graphs.
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Preliminaries SUPERMAN acts set of graphs S [G1,.... ....... Gm.. which can be directed or undirected. Each node v E G2 S & m is associated with a feature vector 2, E R and a time-stamp t., SUPERMAN utilizes the distances between each pair of nodes in each graph, denoted by Auv. where
tu tvs if there exists path from u to v
0,
otherwise.
Graphs may be provided directly through an explicit layout, e.g., the news propagation graphs evaluate SUPERMAN over in section 4 More commonly, however, sparse temporal heterogeneous data does not come with predefined graph structure. In such cases, we construct directed path- graphs for each signal type based on its measurement time stamps, as demonstrated for the medical dataset section 4 For instance, patient blood test records, each graph corresponds to a specific biomarker. Nodes in each graph represent individual measurements of that biomarker, annotated with the observed test value as a feature and the associated time stamp. We mark vectors with bold, and denote the entry of a vector h by [h]c. and the set of entries corresponding to set of features S by [h]s.
Signal Grouping To incorporate domain priors, the graphs in S can be partitioned into l disjoint subsets Si,..., with U S; S. If least one subset S' contains multiple graphs, the model's expressivity increases, as we prove in Theorem 3.2 at the cost of shifting interpretability from individual nodes and graphs in S' to the subset level. In practice, this means we can attribute importance to S' as whole, but not to its individual components. This trade-off-enhancee enhanced expressivity at reduced granularity
especially valuable in domains such as medicine, where priors often suggest natural groupings of signals and interpretability is only needed at the subset level. This is demonstrated in Section[4]
interpretability
SUPERMAN linearly aggregates representations of the subsets of S to form final set representation, and then assigns a single label to S.
First, SUPERMAN applies function o; to each subset S; to obtain a representation of the subset S., denoted as h, E R
h; = (S:):
Then, produces a representation for the whole set, hy by summing the subsets' hy Σx= hi. Finally, to produce the label, it sums over the d entries of hg. Overall:
SUPERMAN(S) = d k
>> p. (S,)le
(I)
Where (S,) hs, is representation of the subset S..
For subsets of size one, (S,)) applies an Extended GNAN (EXTGNAN), as described in Section 3.1 For subsets containing multiple graphs, a featuregroupgnan is applied each graph, followed by a DeepSet aggregation (Zaheer et al., 2018) over the resulting vectors. Importantly, each subset is assigned its own EXTGNAN, and all graphs within subset share the same one. A DeepSet first applies a neural network (NN) f TRd + Rd for each vector in the set (hiGaiss sums the results, and then applies another NN g : Rd
Rd
Σ s(h:) JES
g
Here, g and f are NNs arbitrary depth and width. A high-level visual overview SUPERMAN is presented in F We now turn to define EXTGNAN.
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3.1 EXTGNAN
In GNAN, univariate NNs are applied to each feature of each node in isolation, to learn a representation for a graph. This has the benefit of generating interpretable models features do not mix non- linearly. Nonetheless, when interactions between features are crucial for the task, or feature-level interpretability is required for all features, it may result in sub-par performance. Therefore. EXTGNAN extends GNAN by allowing multivariate NNs to operate on groups of features to gain accuracy at the cost of reducing the feature-level interpretability only for features that are grouped together, and obtaining interpretability for their subset as a whole instead.
Assume that the features are partitioned into K subsets {Fi For any subset of features greater than one, EXTGNAN applies a multivariate NN for all the features in the subset together, instead of a univariate NN for each one separately. To learn a representation of graph G, EXTGNAN first computes representations for the nodes of G as follows.
EXTGNAN learns distance function p(z;0) : IR + R and a set feature shape functions { JK ()(x;;;) RlAl + RI Each of these functions is a NN of arbitrary depth. For brevity, we omit the parameterization and 0g for the remainder of this section.
The entries of the representation node j corresponding to the indices of the features in F;, denoted as [hy] F is computed by summing the contributions of the features in the subset Fi from all nodes in the graph:
[hym = Σ p (()(w,)) t// (X JR)
WEV
where A(w,j) = t - t and [X,] Fi are the features of node w corresponding to the subset Fi- Overall, the full representation of node j can be written as:
h, = ([h,) [byle...... (,yFxx)
Then EXTGNAN produces a graph representation by summing the node representations,
hg Σ h
(2)
NEV
This concludes the description of EXTGNAN, which computes graph-level representations. We provide a complexity analysis of SUPERMAN in the appendix, where we also discuss how p can be masked to adapt to any complexity limitation, including a linear one. Next, we describe how SUPERMAN combines these representations across sets and enables multi-level interpretability.
3.2 NODE, GRAPH AND SUBSET IMPORTANCE.
SUPERMAN retains all interpretability properties of GNAN, including feature-level and node-level importance. However, extends beyond GNAN by operating on sets of graphs rather than single graphs, enabling additional forms of interpretability such graph-level and subset-level importance. Because SUPERMAN allows a flexible trade-off between interpretability and expressivity, permitting non-linear mixing within graph subsets, some adaptations are required obtain importance scores. A key property of SUPERMAN's interpretability is that its importance scores directly reflect the contribution of each node, graph, or subset to the predicted label, since these terms are combined additively to produce the final output. Dection[4illustrran how node-level importances yield insightful real-world insights.
We can extract the total contribution of each node to the prediction by summing the contributions of the node across all feature subsets. This only valid when the node belongs to graph that is not combined non- -ineiin with other graphs, i.e., it belongs to subset of size one.
Therefore, the contribution of node j
K
K
TotalContribution()) = LhyA Σ (A(W Σ
th ([xwli, / Fx).
(3)
WEV
The contribution of graph G is then
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TotalContribution
TotalContribution(())
PEG
For graphs that are mixed non-linearly, i.e., graphs that belong in subsets of size greater than one, we provide instead the total contribution of the set the final prediction
TotalContribution(()
3.3 EXPRESSIVITY PROPERTIES
In this section, we provide theoretical analysis the expressiveness of SUPERMAN. Proofs are provided in the Appendix
Theorem 3.1. SUPERMAN is strictly more expressive than GNAN.
The following theorem shows that a SUPERMAN which is applied to subsets of graphs of size at least two, is more expressive than SUPERMAN that is applied to only subsets of size one:
Theorem 3.2. Let S be set of graphs {Gx) Let S = J be a partition of S such that |S 1. Let S₂ {S.)== such that there exists & with [Sy] 1. with subset partition {S.) Then a SUPERMAN trained over S2 is strictly more expressive than a SUPERMAN trained over St-
4 EMPIRICAL EVALUATION
In this section, we evaluate SUPERMAN on real-world tasks, and demonstrate its interpretability properties
4.1 MEDICAL PREDICTIONS
We evaluate SUPERMAN two high-impact clinical prediction tasks: LoS of intensive care patients and onset of CD. both settings, each individual is represented as set of time-stamped biomarker trajectories, where each trajectory forms directed path graph with nodes corresponding to test results and edges encoding the time elapsed between measurements. This representation preserves the temporal structure of each biomarker independently while enabling joint reasoning across biomarkers during learning.
Data Next, we describe the two medical datasets used in our evaluation.
P12 (ICU Length of Stay): The PhysioNet2012 (P12) dataset, introduced by Goldberger et al. (000), contains records from 11,988 intensive-care unit (ICU) patients, following the exclusion T2 samples deemed inappropriate according to the criteria in Horn et al. (2020). For each patient, longitudinal measurements from 36 physiological signals were recorded over the initial 48 hours of ICU admission. Additionally, each patient has a static profile comprising 9 features, including demographic and clinical attributes such as age and gender. The dataset is labelled for binary classification task: predicting whether not the total LoS in the ICU exceeded 72 hours. The dataset is highly imbalanced, with ~93% positive samples. To balance the classes we perform batch minority class upsampling, following the example in Zhang al. (202T).
Crohn's 's Disease (CD Onset): The Danish health registries (DHR) are comprchensive, nationwide databases covering healthcare interactions for over 9.5 million individuals (Pedersen) 2011). A key resource is the Registry of Laboratory Results for Research (RLRR). which has collected laboratory test results from hospitals and general practitioners since 2015 (Arendt et al.) 2020). We first identify 8,567 individuals in the DHR who are later diagnosed with CD and use them as our patient class. We then construct control pool by randomly sampling individuals from the DHR and downsampling by age to match the expected frequency of blood tests in the prediagnostic period, reflecting that CD
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typically manifests in early adulthood (00-30 years). From this age-matched control pool, we sample 8,567 controls, yielding two balanced classes. For each person, we extracted temporal trajectories of 17 routinely measured biomarkers, reflecting key physiological processes. The complete list and descriptions of these biomarkers are provided in the Appendix. The task is binary classification: predicting future CD onset from pre-diagnostic medical histories.
Setup We compare SUPERMAN to 8 baselines from Zhang et al. (202T),
Table 1: Evaluation of SUPERMAN on two real-world
spanning both sequential and graph- based models, including: former (Vaswani et al.) 2017), vanilla self-attention model applied to irregu- lar time series; Trans-mean, which com- bines a Transformer with mean impu- tation of missing values; GRU-D (Che eet al. 2016). a gated recurrent model with decay terms that encode informa- tive missingness; SeFT (Horn et al.) 2020). which treats each record as a set of timestamped feature-value pairs and aggregates them with permutation- invariant encoders; mTAND (Shukla & Marlin] 2021), a multi-time attention architecture that outperforms broad range of RNN- and ODE-based models on irregular data; DGM (Wu et al. 2021 and MTGNN (Wu et al. 2020), graph- happh-bbaedddd methods originally proposed for multivariate time-series forecasting; and Raindrop (Zhang et al., 2021), a state-of-the-arr art graph model for sparse, irregular EHR time series. For the P12 we used the splits in (Zhang et al. 200T). For CD, randomly split the data into train (80%), validation (10%), and test (10%) sets. We conducted a grid search by training on the training set and evaluating on the validation set. We then selected the best-performing model over the validation set and report results over the test set. We define each individual biomarker as a unique signal type and group them according to coarse physiological categories. Importantly, these clinically- guiided groups are based on broad domain knowledge and do not rely on specialized expertise. We also examine data-driven grouping that does not rely on any priors, based on the insights presented in Subsection 1.1.1. 1. Due to space limitations in Tablee 44 App. F We tune the biomarker subsets over no grouping at all (i.e, full interpretabilityy, and 5 additional subset groupings motivated by public common clinical knowledge. To account for class imbalance, and as commonly done for these datasets, we report the average AUPRC score and standard-deviation of the selected configuration with 3 random seeds. Additional details on the datasets, experimental setup, sub- set groupings, and hyperparameter configurations are provided in the Appendix. We also present Calibration and robustness evaluations in Appendix G
medical tasks. The metric reported is the mean AUPRC
Trans-
with standard deviation, calculated over 3 random seeds.
Methods
LoS in ICU
CD onset
Transformer
96.06 0.32
75.60 0.52
Trans-mean
9..44
75.96 0.92
GRU-D
95.11
SeFT
71.22 2.30 9.08
mTANN
83.17 9.00
DGM2
9..0
MTGNN
0.78
75,26 + 3.04
RAINDROP
96.32 # 0.13
82.60 + 0.82
SUPERMAN
97.41 # 0.38
83.93 # 0.27
The results in Table I show that SUPERMAN achieves the highest AUPRC across both medical prediction tasks. On Length of Stay in ICU, it improves upon the best baseline with a relative uplift of about 0.41 points, while on Crohn's 's Disease onset, it outperforms the best baseline by 0.57 points. Notably, these improvements are achieved while SUPERMAN also provides interpretability properties, as shown in detail in the next subsection.
Results
4.1.1 CLINICAL INSIGHTS THROUGH INTERPRETABILITY
Beyond predictive performance, a central strength of SUPERMAN is that interpretability is built into the model by design, rather than added post hoc. This allows for fine-graine grained, temporally resolved explanations that go beyond global feature importance, enabling users to understand how and when specific biomarkers influence the model's predictions. In high-stakes domains such as healthcare, this level of transparency is crucial. Clinical decision-making often depends not only on the outcome of a prediction but on a clear understanding of the reasoning behind it. Models that can provide such insights are far more likely to be trusted, audited, and integrated into clinical workflows. To highlight the interpretability of SUPERMAN, we conduct attribution analyses on both the CD and P12 datasets, examining how the model assigns importance across time and signals.
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6w02
191
11y
-4
15y
by
b1
-2
(a) P12
(b) CD
Figure 2: Node-level importances for two individuals from (a) the P12 ICU LoS and (b) CD onset datasets. Node size indicates the exact node (measurement) contribution to the prediction.
Critical phase detection through node-level importance In the SUPERMAN framework, nodes represent individual signals within biomarker trajectory. As such, highly influential nodes can high- light critical phases where specific signals most strongly impact the prediction. We use Equation (3) to quantify node-level contributions across biomarkers in both the CD and P12 datasets. To comply with privacy and data protection legislation, CD data is anonymised via noise and temporal shifting. Figure displays node-level importance across biomarker trajectories for two randomly selected individuals from each dataset, with node size reflecting the magnitude of each node's ' contribution to the model's prediction. In both clinical tasks, the model's attributions appear consistent with established biomedical knowledge. For CD prediction, SUPERMAN AN highlights key inflammatory and immune markers, such as F-Cal, platelets, and lymphocytes, as primary contributors. All of these known to play central roles in discase onset (Vestergaard et al. 2023). In the P12 example, the model assigns high importance to markers of renal function, liver injury, cardiac stress, and metabolic imbalance, aligning well with clinical predictors of severity in intensive care settings.
Total biomarker contribution addition to node-level importance scores, SUPERMAN also provides subset-level scores, quantifying the contribution of entire biomarker groups to the model's prediction. This enables flexible, system-level interpretability, allowing users to assess the collective influence of physiologically related biomarkers the target variable. We conduct subset-level importance analysis on the CD dataset using two clinically motivated grouping strategies. In the first, assess individual biomarkers to determine whether the model prioritizes features known to be associated with CD onset, allowing us to verify its alignment with established biomedical knowledge. In the second, we group biomarkers into clinically coherent subsets based on physiological function, such as immune response; inflammation; oxygen transport; and liver function; to examine whether the model captures system-level patterns consistent with disease progression. Full details on the clinical significance of these groupings are provided in the Appendix.
For each grouping strategy, we trained a separate instance of SUPERMAN To quantify the importance of each biomarker subset, we use Equation 44) measuring how the model's prediction changes when increasing the noise added to the features of nodes within that subset. To introduce noise in structured way, we apply PCA (Abdi & Williams 2010) to the feature vectors of all nodes corresponding to biomarkers in the group, and progressively perturb the input along the 1st principal component. This procedure performed independently for each subset and allows us to assess the model's sensitivity to perturbations in biologically meaningful groupings, offering insight into the relative predictive weight of each group. Importantly, SUPERMAN is interpretable by design, which makes do not
perturbation analysis directly reflect its internal computation. Unlike post-hoe hoc attribution, estimate influence indirectly but observe how the additive contribution changes. Adding structured noise (via PCA) and measuring the resulting prediction shift faithfully traces the model's internal
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Whdt sooo
Inlurrartion
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Levslotapbe
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(a) Single-biomarker groups SUPERMAN
(b) Best-perforning SUPERMAN groups
Figure 3: Subset-level contribution curves for Crohn's Disease prediction. Each curve shows how the SUPERMAN's oulput changes as increasing noise is added to the latent representation of a biomarker group. (a) uses individual biomarkers; (b) uses physiologically coherent groups.
mechanism rather than relying on an external approximation. Thus, perturbation effects align exactly with feature importance, making the experiment both natural and principled. Figure 3 presents the results of the subset-level attribution analysis. In the single-biomarket setting (Figure 3a)). F-Cal, platelets, and lymphocytes show strong directional effects on model output. F-Cal and platelets are positively associated with CD risk, while lymphocytes have an inverse effect, findings that are both biologically grounded and consistent with prior work (Vestergaard et al., 2023). In the clinically- coherent group setting (Figure (())p, the inflammation subset emerges as the most influential, with pronounced non-linest moneri effect on predictions, aligning with established diagnostic relevance CD (Vestergaard et al. 2023). We note that the above also serves as quantitative measure of faithfulness, as in SUPER M N interpretability is not post-hoc but built into the model architecture by design. Specifically, the contributions of nodes, graphs, or subsets are explicitly and additively used in computing the final prediction. This means that importance scores correspond directly to the actual values that are summed to produce the output label, making them faithful by construction.
4.2 FAKE-NEWS DETECTION
Data GossipCop (GOS) is a dataset of news articles annotated by professional journalists and fact-checkers, containing both content- based labels and social context information verified through the GossipCop fact-checking platform. It is composed of 5,464 tree-structured graphs based on sharing information, where the news article is the root node and sharing users are subsequent nodes in the cascade, with edges signifying sharing relationships. Each node in these graphs is associated with 4 features: f68-dimensional embeddings generated using a pretrained BERT model on user historical posts, 300-dimensional embeddings from a pretrained word2vec (Mikolov al. 2013) the same historical posts, 10 10-dimensional fea- tures extracted from user profiles, and a 3 30-diieesiionll "content" feature that combines the 300-dimensional embedding of user comments with the 10- dimensional profile features. Each graph is labelled to indicate whether it originates from a fake news post or not. We decomposed the tree into set of directed graphs rooted at the origin, each representing a distinct path of news propagation.
Table 2: Evaluation of SUPERMAN on the Gossipeop (GOS) fake news detec- tion dataset.
Methods
Accuracy
GATv2
96.10 + 0.3
GraphCony
96.77 + 0.1
GraphSage
94.45 # 1.5
GCNEN
96.52 # 0.2
SUPERMAN
97.34 0.2
Setup While SUPERMAN can be applied to sets of graphs with any structure, the baselines used in the CD and P12 experiments are limited to path-like graphs and are unable to act on more complex graphs in this dataset. Therefore, we instead evaluate SUPERMAN against 4 GNNs, including GATv2 (Brody et al. 2022), GraphConv (Morris et al. 2021), GraphS (Hamilton et al. 2018) and GCNFN (Monti et al. 2019). We use random splits of train (80%). validation (10%), and test (10%) sets over the data and selected the best performing model over the validation set. We then report the average Accuracy score and std of the selected configuration with three seeds. Since many

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Figure 4: Node importance for fake-news spread graphs, over the GOS dataset. The node size corresponds to its importance learned by SUPERMAN, according to Equation (3). All graphs with a single node are grouped into subset. Therefore, the importance is provided on the subset level rather than the node level (green node).
subgraphs reduce to a single node after decomposition, we group all size-one graphs into shared subset and combine them non-linearly. For the remaining graphs, whose identities are not uniquely distinguishable, we apply a shared EXTGNAN. In total, we use two distinct EXTGNAN instances for this experiment.
Results and node-level importance Results are provided in Table SUPERMAN outperforms all baselines, with an uplift of 0.57 accuracy points. Figure 4 presents the node importance of random sample from the datasets, where the size of node corresponds to its importance score according to Equation 3
4.2.1 ABLATION STUDY
Finally, carry ablation study on the CD dataset, to isolate the impact of key com- ponents performance. Specifically, take the best best-performing configuration from
Table 3: Ablation study of SuperMAN components.
Ablation
AUPRC drop 19.98% .28 %
the training-data grid search and re-train
(i) DeepSet- pooling
it with individual components ablated to assess their effect on performance. We test:
(ii) p->1
12.39% 1.39%
(iii) EXIGNAN
11.00% 2.09 %
(i) replacing DeepSet with mean pooling
(iv) EXiGNAN Iddentity
-17.70% + 0.15%
to assess the value of learned non-linear aggregation; (ii) replacing the distance
ExiGNAN-
-4.38 % + 2.85%
function NN (p) with a constant value.
This tests the usefulness of structural information; (iii) substituting ExIGNAN with a node-wise MLP to test the importance of graph inductive bias; (iv) replacing ExIGNAN with an identity mapping lower bound without feature learning; and (v) using standard GNAN (no multivariate feature groups) evaluate the benefit of grouped feature processing. We report the performance degradation (AUPRC difference) in Table The ablation results demonstrate that the core components of SUPER MAN are critical its effectiveness, as their removal consistently leads to notable performance degradation.
CONCLUSION
We introduced Super Mixing Additive Networks (SUPERMAN), framework for learning from sets of graphs that represent irregular and asynchronous temporal signals. SUPERMAN was designed to handle real-world scenarios where multiple signal types are collected uneven intervals, such as medical records with heterogeneous blood tests or event logs in complex systems. The framework combined strong predictive performance with built-in interpretability, offering importance scores at the node, graph, and subset levels. SUPERMAN allows practitioners to integrate domain priors when available, trading fine-grained interpretability for greater expressivity. Across experiments on world high-stakes tasks, SUPERMAN achieved tfateoof-hee-at results. Beyond predictive accuracy, SUPERMANT interpretability capabilities proved particularly valuable in domains like healthcare, where uncovering phase transitions and providing actionable insights is critical.
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A
APPENDIX
B
THEORETICAL FRAMEWORK
B. PROOF OF THEOREM 3.1
We will prove that SUPERMAN is strictly more expressive than GNAN. To prove this, we use ground truth function that is feature-level XOR. Let single-node graph be endowed with binary features x (2) E {0, 1)² and define the target Sa (x) = Iι $ 22.
First we will show that GNAN cannot express fe. A GNAN scores the graph by 2 = a(o (xI) de (x2)), where each Φ; is univariate. Put a Φ1 (0), = Φ1 (1), = (2( d = Φ2(1). To match the XOR truth-table there exist threshold such that
a+c T, b+C a a+d> T, b d <.
Summing the first and last inequalities yields a + b-bc+ < 2r, while the middle pair gives + b + + d >> 2T-a contradiction. Thus no GNAN realises fa.
Now we will show that SUPERMAN can express fa- Place the two features in the same subset F = { and choose the subset-network
(1( = + 22 2r
For the four binary inputs this mapping returns (0, 1, 0), exactly fe. Hence SUPERMAN represents a function unattainable by GNAN, proving that SUPERMAN is strictly more expressive.
B.2 PROOF OF THEOREM 3.2
Let S be set of graphs [- Let S1 {S be a partition of such that |S&]| 1. Let S2 = ( such that there exists & with [Sp] > 1. with a subset partition {S We will prove that SUPERMAN trained over S2 is strictly more expressive than a SUPERMAN trained over S1.
To prove this, we use a ground truth function that is a set-level XOR. Let every graph G; carry a single binary feature x; E {0, } and let the EXIGNAN encoder return this feature unchanged, i.e. M(G;) = Iz. Denote a set containing two graphs by S = {G1, G2} and define the permutation- invariant target
Sa = @ x2-
Singleton partition (S1). If each graph is placed in its subset, SUPERMAN aggregates additively: the model output is
" ((x1) + d(x2),
because the final SUPERMAN wttpaaaiieeelnieeeoooooeeeeeeeee To realise fe via threshold 7 we would need
stage simply sums subset scores :contentRefer-
oaicite: Jindex=1. jinexee: Write x(0) and ((1).
a a T, b a a+b>r, b-bК-.
Adding the first and last inequalities yields +b < r, while the middle pair gives a + > 5 contradiction. Hence SUPERMANs, cannot represent fg.
Paired partition (Sz). Group the two graphs together and use a DeepSet P(S,) = f(r))
with (xx = x and g(s) = s(2 - 8). Then
(0 + x2) [0
(21, (0. 0) 11,
(x1, (0, (1,0),
exactly fa- The final SUPERMAN sum over feature channels leaves this value unchanged, so SUPERMANs, realises fe.
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Strict separation. Because fg is representable by SUPERMANS, but not by SUPERMAN,, the former is strictly more expressive.
B.3 FOUR-POINT CONDITION AND RECOVERABILITY
We now turn structural identifiability. We prove that when input graphs connected, acyclic, and positively weighted (i.e., trees), the pairwise distance matrix learned by SUPERMAN encodes the full structure of the graph, up to isomorphism. This provides theoretical justification for the model's ability to reason over temporal structure without needing explicit graph supervision.
The following theorem shows that if the graph satisfies the four-point condition (Buneman 1974). SUPERMAN can reconstruct the original graph from the transformed distance matrix that is fed to SUPERMAN as the graph input:
Theorem B.1. Let G be graph represented by an adjacency matrix A, and D be the transformed distance-matris for SUPERMAN. Then if D satisfies the four-point condition, SUPERMAN can learn p such that p(D) = AA.
Proof. Let = (V, E, a positively weighted path graph, i.e.
V {UI....; Up).
E = { u++1
i i= .....: n 1},
(((u,,0411) 0.
Define the pair-wise distance matrix D E R by
Duv Σ w(e),
eEPo(u.))
where Pa(u, u) the unique u-v path in G. Then:
(a) Tree-metric property. D satisfies the four-point condition of Buneman (Buneman 1974); hence (V, D) is tree metric.
(b) Uniqueness (no information loss). By Buneman's theorem the tree that realises is unique up to isomorphism. For path graph the only automorphism is the reversal (V1,..., Un) + (Un,.... 11), so determines G completely except for left-right orientation.
(c) Efficient reconstruction. G can be reconstructed from D On?)) time:
i. Choose endpoint arg max.ev max D Order the vertices U1 = 8, 1/2 U2,..., so that Den < Davg < ... < D Dea.- iii. Set edge weights wi( (U;, 0c+1 Devi+1 Dav, for 1,..., 1.
C COMPUTATIONAL COMPLEXITY AND EFFICIENT IMPLEMENTATION
In this section, we provide big-O analysis of the time complexity of SUPERMAN. We also provide an efficient approach to implement SUPERMAN.
Computational Complexity
The computational complexity of SUPERMAN is as follows:
Scales linearly with the number of graphs m: Each graph is processed independently in small subsets, so total cost is ((m) assuming fixed per-graph cost.
Scales quadratically with the number of nodes per graph Due the dense aggregation over all node pairs in EXIGNAN, the per-graph cost is O(n?).
Overall complexity for set of graphs
(mm n² d
where K is the number of feature groups and dæ is the cost of evaluating the multivariate neural networks.
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Adapting the complexity We note that while the per-graph complexity of ExIGNAN is O(n²) in the most general case, the distance function A can be masked to enforce any desired sparsity pattern between nodes, and therefore adapt to any complexity limitation, including linear one. For example, one can define the A to only be the distance between adjacent nodes in trajectory, and then will be both linear in memory and time.
Efficient Implementations In the main paper, present SUPERMAN with the objective of maximal clarity, c.g., by presenting vector entry-wise operations. Nonetheless, the operations of SUPERMAN be done in an optimized fashion for GPU, through tensor operations.
D DATASET DETAILS
D.1 PHYSIONET P12
We provide the full list of the 36 physiological signals and static patient features used our experiments.
Alkaline phosphatase (ALP): liver- and bone-derived enzyme; elevations suggest cholestasis, bone disease, or hepatic injury.
2. Alanine transaminase (ALT): Hepatocellular enzyme; increased values mark acute or chronic liver cell damage.
3. Aspartate transaminase (AST): Enzyme in liver, heart, and muscle; rises indicate hepatocellular or muscular injury.
4. Albumin: Major plasma protein maintaining oncotic pressure and transport; low levels reflect inflammation, malnutrition, or liver dysfunction.
5. Blood urea nitrogen (BUN): End-product of protein catabolism cleared by the kidneys; elevation signals renal impairment high catabolic state.
6. Bilirubin: Hemoglobin breakdown product processed by the liver; accumulation indicates hepatobiliary disease hemolysis.
7. Cholesterol: Circulating lipid essential for membranes and hormones; dysregulation is linked to cardiovascular risk.
8. Creatinine: Waste from muscle metabolism filtered by the kidneys; higher levels imply reduced glomerular filtration.
9. Invasive diastolic arterial blood pressure (DiasABP): Pressure during ventricular relaxation; low readings may reflect vasodilation or hypovolemia.
10. Fraction of inspired oxygen (FiO2): Proportion of oxygen delivered; values above ambient air denote supplemental therapy.
11. Glasgow Coma Score (GCS): Composite neurologic score for eye, verbal, and motor responses; scores < indicate severe impairment.
12. Glucose:
Principal blood sugar; hypo- hyper-glycemia cause neurologic compromise and metabolic instability.
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13. Serum bicarbonate (HCOs): Key extracellular buffer; low levels signal metabolic acidosis, high levels metabolic alkalosis or compensation.
14. Hematocrit (HCT): Percentage of blood volume occupied by red cells; reduced values denote anemia, elevated values hemoconcentration.
15. Heart rate (HR): Beats per minute reflecting cardiac demand; tachycardia indicates stress or shock, bradycardia conduction disorders.
16. Serum potassium (K): Crucial intracellular cation; deviations predispose dangerous arrhythmias.
17. Lactate: By-product of anaerobic metabolism; elevation marks tissue hypoxia and shock severity.
18. Invasive mean arterial blood pressure (MAP): Time-weighted average arterial pressure; low values threaten organ perfusion.
19. Mechanical ventilation flag (Mech Binary indicator of ventilatory support: presence denotes respiratory failure or peri-operative care.
20. Serum magnesium (Mg): Cofactor for numerous enzymatic reactions; abnormalities contribute to arrhythmias and neuromuscular instability.
21. Non-invasive diastolic arterial blood pressure (NIDiasABP): Cuff-derived diastolic pressure; trends mirror vascular tone without arterial line.
Non-invasive mean arterial blood pressure (NIMAP): Cuff-based mean pressure; used when invasive monitoring is unavailable.
23. Non-invasive systolic arterial blood pressure (NISysABP): Cuff-derived systolic pressure; elevations suggest hypertension or pain response.
24. Serum sodium (Na): Principal extracellular cation governing osmolality; dysnatremias cause neurologic symptoms and fluid shifts.
25. Partial pressure of arterial carbon dioxide (PaCO2): Indicator of ventilatory status; hypercapnia implies hypoventilation, hypocapnia hyperventilation.
26. Partial pressure of arterial oxygen (PaO2): Measure of oxygenation efficiency; low values denote hypoxemia.
27. Arterial pH: Measure of hydrogen-ion concentration; deviations from normal reflect systemic acse-base disorders.
28. Platelet count (Platelets): Thrombocyte concentration essential for hemostasis; low counts increase bleeding risk, high counts thrombosis risk.
29. Respiration rate (RespRate): Breaths per minute; tachypnea signals metabolic acidosis or hypoxia, bradypnea central depression.
30. Hemoglobin oxygen saturation (SaO2): Percentage of hemoglobin bound to oxygen; values below normal indicate significant hypoxemia.
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31. Invasive systolic arterial blood pressure (SysABP): Peak pressure during ventricular ejection; extremes compromise end-organ perfusion.
32. Body temperature: Core temperature; fever suggests infection, hypothermia exposure or metabolic dysfunction.
33. Troponin I: Cardiac-specific regulatory protein; elevation confirms myocardial injury.
34. Troponin T: Isoform of cardiac troponin complex; rise parallels Troponin in detecting myocardial necrosis.
35. Urine: Hourly urine volume gauge of renal perfusion; oliguria signals kidney hypoperfusion or failure.
36. White blood cell count (WBC): Reflects immune activity; leukocytosis suggests infection stress, leukopenia marrow suppression or severe sepsis.
Static patient features: Age; Gender; ICUType- categorical code for the admitting intensive care unit (1 Coronary Care, 2 = Cardiac Surgery Recovery, 3 = Medical ICU, 4 = Surgical ICU), capturing differences case mix and treatment environment.
D.2 CROHN'S s DISEASE PREDICTION
We detail the full list of the 17 biomarkers extracted from the Danish health registries.
1. C-reactive protein (CRP): A protein produced by the liver in response inflammation. Elevated CRP indicates active inflammation, often associated with inflammatory diseases like CD.
2. Faecal Calprotectin (F-Cal): A protein released from neutrophils into the intestinal lumen, detectable in stool samples. Elevated levels indicate gastrointestinal inflammation and commonly used to detect and monitor inflammatory bowel disease.
3. Leukocytes (White Blood Cells): Cells that central to the body's immune response. Elevated leukocyte counts typically suggest infection or inflammation, including flare-ups in CD.
4. Neutrophils: A type of leukocyte involved, among other things, in fighting bacterial infections. High neutrophil counts often indicate acute inflammation infection, including intestinal inflammation in CD.
5. Lymphocytes: A group of white blood cells that form the core of the adaptive immune system, including T cells, B cells, and natural killer (NK) cells. They are responsible for antigen-specific immune responses. Abnormal levels can signal immune dysregulation, often implicated in autoimmune and chronic inflammatory diseases such as CD.
6. Monocytes: type of white blood cell that circulates in the blood and differentiates into macrophages or dendritic cells upon entering tissues. These cells are essential for phagocytosis, antigen presentation, and regulation of inflammation. Elevated levels may reflect immune activation or tissue damage.
7. Eosinophils: Immune cells involved primarily in allergic reactions and parasitic infections. Elevated cosinophil counts might reflect allergic responses or gastrointestinal inflammation.
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8. Basophils:
The least common type of leukocyte, involved in allergic and inflammatory responses. Their elevation is uncommon but may accompany certain inflammatory or allergic conditions.
9. Platelets: Cell fragments critical for blood clotting and also involved in inflammatory responses. High platelet counts (thrombocytosis) are commonly seen during active inflammation in conditions like CD.
10. Hemoglobin (Hb): The protein in red blood cells responsible for oxygen transport. Low hemoglobin (anemia) is frequently observed in chronic inflammatory conditions such as CD due to blood loss or nutrient deficiencies.
11. Iron: essential mineral for red blood cell production. Low iron levels often indi- cate chronic blood loss or malabsorption, both common in CD due to intestinal inflammation.
12. Folate (Vitamin B9): vitamin necessary for red blood cell production and DNA synthesis. Deficiency may result from impaired absorption in inflamed intestinal tissue.
13. Vitamin B12 (Cobalamin): Required for red blood cell production and neurological function. Deficiencies are common in CD, especially when the ileum is affected.
14. Vitamin D2+D3 (Ergocalciferol Cholecalciferol): Vitamins essential for bone health and immune regulation. Low levels are often seen in CD due to malabsorption and systemic inflammation.
15. ALAT (Alanine Aminotransferase): An enzyme indicating liver function. Elevated levels may reflect liver inflammation, medication effects, or co-occurring autoimmune liver disease.
16. Albumin: protein produced by the liver that helps maintain blood volume and transport nutrients. Low albumin can reflect chronic inflammation, malnutrition, or protein loss in CD.
17. Bilirubin: A compound produced from red blood cell breakdown. It is filtered by the liver and excreted into the intestine via bile. Elevated levels may indicate liver dysfunction, bile duct obstruction, or hemolytic anemia.
D.2.1 CLINICAL CONTEXT AND RELATED WORK FOR PREDICTING CD ONSET
Research on predicting the onset of CD has explored a range of approaches, including the use of routinely measured blood-based biomarkers and more complex biological data derived from multi-omics technologies.
Several studies have assessed the predictive potential of standard clinical blood tests. For example, (Vestergaard et al.) (002)) analyzed six routine biomarkers from 18186 Danish patients eventually diagnosed with CD, achieving moderate predictive performance (AUROC of 0.74) approximately six months before clinical diagnosis. Larger-scale analyses, such as those using UK Biobank data, combined multiple standard biomarkers and basic demographic information, reporting similar predictive performances (AUROCs typically between 0.70-0.75). These analyses generally utilized methods like logistic regression, random forests, or gradient-boostee trees, favored for structured clinical datasets.
Other studies have integrated advanced biochemical data, known as multi-omics, including large-scale protein measurements (proteomics), metabolites (metabolomics), or genomic markers. (Garg et al.) 2024) for instance, combined 67 blood biomarkers with approximately 2,900 plasma proteins from the UK Biobank, achieving AUROC of 0. 7878.. (Woerner et al., (205)) combined genetic risk scores with extensive proteomic data, achieving an AUROC of 0.76 for CD prediction up to five years prior diagnosis. Similar multi-omics approaches employing mierobiome profiling, immune signaling
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molecules (cytokines), lipid molecules typically achieve AUROCs between 0.75 and 0.80 but often involve significant cost, specialized laboratory analyses, and reduced consistency across diverse patient cohorts.
Overall, routine blood tests provide meaningful predictive signals for CD onset, while integrating com- plex biochemical measurements can improve predictive accuracy, albeit at greater cost, complexity, and variability across clinical populations.
E
BIOMARKER SUBSET GROUPINGS
E.I
P12
In the PhysioNet P12 task, we grouped the 36 physiological signals into one multivariate subset and 29 singleton subsets. Domain knowledge showed that only the respiratory and gas-exchange variables shared sufficiently strong, coherent dynamics to benefit from joint modeling. All other signals were physiologically diverse, so they were left as singletons retain their unique predictive information.
Arterial blood gas profile
[pHI PaCO2, PaOz, SaO2, HCO3, FiO2]
This group captures systemic acid-base status (pH. HCOa), carbon dioxide clearance (PaCO2), oxygenation (PaO2, SaO2), and inspired oxygen fraction (FiO.).. Together they form the canonical arterial blood gas panel, enabling the model to detect respiratory de- rangements such hypoxemia, hypercapnia, metabolic compensation.
2. Complete blood count
[WBC, HCT, Platelets) This cluster summarizes hematologic composition by measuring leukocyte- muukocyte-meiiaee im- mune response (WBC), oxygen-carrying capacity (HCT), and clotting potential (Platelets). Joint modeling supports recognition of systemic inflammation, anemia, and coagulopathy.
3. Comprehensive metabolic panel [Glucose, Na, K, Mg. BUN, Creatinine] These biomarkers represent key substrates and electrolytes (Glucose, Na, K, Mg) and renal waste products (BUN, Creatinine). Grouping them provides a unified view of metabolic balance, electrolyte homeostasis, and kidney function.
4. Liver function tests
[ALT, AST, ALP, Albumin, Bilirubin]
These biomarkers assess hepatocellular injury (ALT, AST), cholestasis (ALP, Bilirubin), and hepatic synthetic function (Albumin). Their combined interpretation reflects multiple dimensions of liver health.
5. Lipid and cardiae markers [Cholesterol, Troponini, TroponinT, HR]
This group integrates lipid metabolism (Cholesterol), cardiac injury markers (Troponin I, Troponin T), and heart (HR). Together, they provide insight into cardiovascular stress, myocardial injury, and metabolic risk.
6. Blood pressure profiles
[SysABP, DiasABP, MAP. NISysABP, NIDiasABP, NIMAP] These variables capture invasive and non-invasive arterial blood pressures, reflecting sys- temic hemodynamics. Grouping them enables the model learn coherent pressure dynamics rather than treating each measurement in isolation.
7. Ventilation mechanics
Rats MechVent]
This group reflects mechanical and physiological components of ventilation. Their joint dynamics provide context for interpreting respiratory compensation and ventilatory support.
8. Tissue perfusion
[Lactate, Urine]
Elevated lactate indicates anaerobic metabolism. while urine output tracks renal perfusion. Together they provide complementary signals of global tissue perfusion and shock severity.
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9. Global status indicators /GCS, Temp]
These variables capture overall neurologic responsiveness (GCS) and systemic temperature regulation (Temp), providing global context on patient stability and severity of illness.
E.2 CD
In the Crohn's 's Disease prediction task, we grouped the 17 selected biomarkers into subsets based on shared physiological function, clinical relevance, and correlated patterns observed in exploratory analyses. This configuration produced the most robust and interpretable results, balancing domain knowledge with empirical performance. The grouping is as follows:
1. White blood cell subtypes
[Leukocytes, Neutrophils, Lymphocytes, Monocytes, Eosinophils, Basophils] These biomarkers all represent components of the immune system's 's cellular response. Grouping them enables the model to learn shared immune activation patterns, which are known to be dysregulated in inflammatory bowel diseases like CD. Combining them in multivariate subset captures both their relative proportions and total counts, which are clinically relevant for distinguishing inflammation subtypes.
2. Inflammation markers
/CRP, Faecal Calprotectin] These key indicators of systemic and intestinal inflammation, respectively. CRP reflects acute-phase liver response, while F-Cal is specific to intestinal neutrophilic activity. Though mechanistically distinct, both strongly correlated with inflammatory disease activity and complement each other in modeling CD-specific inflammation signatures.
3. Platelets
|Platelets]
Thrombocytosis (elevated platelet count) is a well-established marker chronic inflammation. As platelet behavior is relatively independent from other hematological and nutritional markers, we model it as its own trajectory.
4. Hemoglobin
[Hemoglobii]
Hemoglobin concentration is a direct measure of anemia, which is prevalent in CD patients due to chronic blood loss and inflammation illammatiooninduced induced iron sequestration. Its temporal dynamics often diverge from those of other blood components, warranting separate representation.
5. Iron status [Iron]
Iron metabolism is tightly linked to both hemoglobin levels and systemic inflammation but shows distinct dynamics. Modeling separately allows the model to learn delayed decoupled effects (e.g.. iron deficiency preceding hemoglobin drop).
6. Vitamin and folate status
[Folate Vitamin B12, Vitamin D2+D3}
These nutrients are absorbed different regions of the gastrointestinal tract (e.g., B12 in ileum, folate in the jejunum), and their deficiency profiles can be informative of CD location and severity. Grouping them allows the model to detect joint patterns of malabsorption and systemic nutrient depletion.
7. Liver function markers [ALAT, Bilirubin, Albumin]
These biomarkers reflect hepatic function and protein synthesis. Abnormal liver enzymes and hypoalbuminemia are frequently observed CD due to medication effects, chronic inflamma- tion, or comorbid autoimmune liver disease. Combining them supports learning of systemic inflammatory effects beyond the gut.
This grouping reflects known biological relationships, enhances the interpretability of the model's subset-level attributions. and improves performance compared to unstructured or purely univari- ate representations. enables SUPERMAN to exploit interactions among related features while maintaining modular structure that aligns with clinical reasoning.
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F EXPERIMENTAL SETUP, HYPERPARAMETEE CHOICES AND GROUPING CONFIGURATIONS
This section outlines key implementation choices and model settings used in experiments, includ- ing the manually tuned biomarker grouping configurations that served as an important hyperparameter for performance and interpretability.
F.1 PHEER--ARMMEERS
We trained all models with 100 epochs using the Adam optimizer with weight decay 1e-5, We used a CeduueeLROnPlateur scheduler with max learning rate in the le-2, le-4 range, min learning rate in the 1e-7, 1c-8 range, factor in the 0.2-0.9 range, and patience=100
We trained all models with batch size of range (16, 32), dropout rate (0.1, 0.2), number of layers in the (3, 4, 5 range, hidden channels in the {32, 64) range.
Random seeds were fixed for reproducibility, and results are reported across three independent runs. All models were trained on a single NVIDIA Tesla V100-PCIE- 16GB GPU.
F.2 GROUPING CONFIGURATIONS FOR CLINICAL TASKS
In both clinical tasks, the configuration of input feature subsets (i.e., how we grouped input biomarkers into multivariate trajectories) was treated as manually tuned hyperparameter. These groupings determine how SUPERMAN combines individual graph representations prior to final prediction, and they affect both the expressivity and interpretability of the model.
In-Hospital Mortality (P12). We compared SUPERMAN's performance under the following grouping strategies:
No grouping: Each biomarker its own size one subset.
Respiratory- one group of the biomarkers: [FiO2, PaOz, PaCO2, SaO RespRate, pH, MechVent] and the rest are singletons.
Metabolic Electrolytes one group of the biomarkers: (Na, K, Mg, HC03, Lactate,
Glucose] and the rest are singletons.
Liver Panel one group of the biomarkers: [ALT, AST, ALP, Alhumin, Bilirubin, Choles- terol] and the rest singletons.
Pathway-Based Grouping: Biomarkers are organised based on their molecular or mech- anistic roles, grouping them by their function metabolism, homeostasis, or cellular composition: Energy metabolism [Glucose, Cholesterol, Lactate]; nitrogen waste clearance [BUN, Creatinine, Urine]; protein synthesis and enzymes [Albumin, ALT, AST]; liver function and cholestasis [ALP, Bilirubin]: acid-base balance [pH, HCO3]; gas transport [PaO2, PaCO2, SaO FiO2]: mineral homeostasis [Na, K, Mgl: hematologic composition [HCT, Platelets, WBCJ; cardiovascular dynamics [SysABP, DiasABP, MAP, NISysABP, NIDiasABP, NIMAP, HR]; respiratory mechanics [RespRate, Mech Vent]; and cardiac injury [TroponinI, TroponinT].. Global status indicators grouped separately [Temp, GCS).
Organ-System Grouping Biomarkers are organized around organ systems and clinical monitoring domains (respiratory support, cardiovascular dynamics etc: oxygenation support [SaO2, PaO,, FiOz, Mech Vent]; ventilation and acid-base balance [PaCOz, RespRate, pH. HCO3]: cardiovascular dynamics [HR, MAP, SysABP, DiasABP, NIMAP, NISysABP, NIDiasABPJ; perfusion and renal function [Urine. Lactate, Creatinine. BUNJ; hepatobil- iary function [Bilirubin, ALT, AST, ALP, Albumin]; inflammation and coagulation [WBC, Platelets]; electrolyte and oxygen-carrying capacity [Na, K, Mg. HCT]; metabolic reserve [Glucose, Cholesterol]: myocardial injury [TroponinI, TroponinT]: and global status indica- [Temp, GCS).
Crohn's Disease Onset. We evaluated several grouping configurations:
No grouping: Each biomarker is in its own size subset.
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1.0
Empirical frequency (positives)
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Predicted probability
Figure 5: Q-Q calibration plot (reliability diagram) for SUPERMAN on the CD task.
Biologically driven grouping (see Appendix E.2 Biomarkers are grouped into 7 clinically coherent subsets (e.g., inflammation markers, immune cell subtypes, liver function).
Diagnostic Panel Grouping: clinically motivated grouping that mirrors standard blood test panels used in routine diagnostics.
Data-driven grouping:
Groupings are derived from clustering biomarkers based on the complementary signal their attribution curves (see Section 4.1.1)
Merged coarse groupings: Broad categories such inflammation, haematology, and micronutrients.
Minimal Pairwise Interaction Emphasizes minimal yet informative combinations that capture key axes of immune, inflammatory, and metabolic variational proximity.
We report the AUPRC of different biomarker groupings for predicting the onset of CD Table
G CALIBRATION AND ROBUSTNESS ANALYSES
Here report additional evidence the reliability (calibration) and robustness of SUPERMAN the Crohn's Disease (CD) task.
G.1 CALIBRATION
We compute Expected Calibration Error (ECE) for SUPERMAN and all baselines on the CD task. ECE is reported mean + std over three data splits. Lower values indicate better agreement between predicted probabilities and observed outcome frequencies. As shown Table SUPERMAN attains the lowest ECE among the compared methods.
To complement ECE, we provide Q-Q calibration plot for SUPERMANin Fig. The plot compares binned predicted probabilities against empirical outcome frequencies. Close alignment with the diagonal indicates good calibration. The ncar-diagonal trend is consistent with SUPERMAN's 's low ECE.
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G.2 NOISE ROBUSTNESS UNNDER CONTROLLED DISTRIBUTION SHIFT
We evaluate robustness under controlled distribution shifts by training all models on clean data and injecting noise only at test time. For each noise level, we re-compute AUROC and AUPRC and report the relative performance drop ő (percentage change) from the clean-test baseline.
Additive value noise. For each biomarker trajectory graph, we perturb the primary biomarker feature (feature index 0 corresponding to the observed biomarker value) at every node by adding zero-mean Gaussian noise with fixed standard deviation value independent of the feature's 's magnitude. If is the original biomarker value, sample \O0 1) and use v absolute mcasurement variability with a uniform noise scale. The results are shown in Table 6
v This models
Multiplicative value noise.
Using the same feature, we instead add zero-mean Gaussian noise whose scale is proportional to the absolute feature value. If v is the original value, we set the noise scale |o| value and sample o' + |o] dvalus v (1 + o This models relative measurement/umits variability, where larger measurements incur larger absolute perturbations. The results are shown in Table 7
Temporal noise. with standard deviation Time (in days). This perturbs pairwise time gaps between visits while keeping biomarker values and graph structure unchanged. The results shown in Table g
We inject zero-mean Gaussian noise into the temporal distance matrix at test time,
H
LLM USAGE
We relied on Large Language Models solely for grammar and spelling checks, without using them to generate or modify the scientific content.
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Table Performance using different biomarker subsets for CD prediction.
Grouping Strategy
Biomarker Groups
AUPRC
Flal grouping
Each bismarker is modeled independenily: CRP F-Cal, Leukocyles, Neutrophils, I ymphhoyytes, Monocytes, Fosinaphils, Rasophils, Platelets, Hemoglohin, Iron, Folate, Vitamin B12, Vitamin D2+D3, ALAT, Albomin, Bilirubin.
79.66 + 0.96
Biologically driven grouping
83.93
White blood cell subtypes: Leukocytes. Neutrophils, Lymphocytes, Monocytes. Eosinophils, Basophils
Inflammatory markers: CRP, F-Cal
Platelets
Haemoglobin
Iron
Vitamin and folate status: Folate, Vitamin B12, Vitamin D2 D3
Liver function markers: ALAT, Albumin, Bilirubin
Diagnostic Panel Grouping
Inflammatory markers: CRP, F-Cal
count Leukocytes, Neutrophils, Lymphocytes
WBC subtypes: Monocytes, Eosinophils, Basophils
Platelets Hemoglobin: Platelets, Hemoglobin
Nutrient panel: Iron, Folate, Vitamin B12, Vitamin D2+D3
Liver function test panel: ALAT, Albumin, Bilirubin
Data-driven grouping
79.04
Acute Inflammation CRP, F-Cal,
Immune-Iron
Lymphocytes, Iron
Neutrophils
Monocyles
Fasinophils
Basophils
Hemoglobin
Folate
Vitamin
ALAT'
Bilirubin
Albumin
Total Lukoccytes
Merged groupings
7..21
(local inflarmation))
Systemic inmuncinfanmmatin: CRP, Leukocytes, Neutrophils, Lymphocytes, Monocytes
Allergy-linked cosinophils/bsophiis
Hematological status: Platelets, Hemoogloii
Nutritional status: Iron, Folate, Vitamin Vitamin
Hopatic ALAT, Albumin, Bilirobin
Minimal Pairwise Interaction
81,50 a: 1.3
CRP F-Cal
Leukocytes Neutrophlls
Lymphocytes Monocytes
Eosinophils + Basophils
Hemoglobin
Iron Folate
Vitamin B12 Vitamin D2+DD3
ALAT + Albumin
Bilirubin
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Model
ECE (mean + std)
SUPERMAN
0.028 + 0.004
Raindrop
0.040 + 0.070
DGM2
0.035 = 0.001
mTAAN
2.16 0.54
Transformer
3.32 = 1.08
Trans-mean
3.30 + 1.03
SEFT
2.40 + 0.71
Table 5: Expected Calibration Error (ECE) on the CD task, reported as mean + std over three splits.
SUPERMAN
Raindrop
mTAND
AAUROC
AAUPRC
AAUROC
AAUPRC
AAUROC
AAUPRC
0.0
0.00 1.001:00000 0.00%
0.00%
0.00 1: 0.00%
1.00::0.009:
0.00 0.00
0.00 1.00::000 1.00%% 0.00%
0.1
-0.07 =
0.007
-26.20 = 1.97%
-28.72 2.54%
0.811
-0.71 0.64%
0.2
-0.10 0.15%
0.52%
-32.82 0.96%
-36.70 1.49%
-2.98 1.23%
-2.88 0.98%
0.3
-0.18 0.34%
0..7%%
-34.74 1.36%
-38.69 1.78%
-5.38
-5.16 1.06%
0.51 + 0.35%
-.117
-36.35
1.54%
-40.60 + 1.79%
+
-10.84 0.73%
0.8
-1.32 + 0.97%
+.850
-37.25 + 1.59%
-41.41 1.68%
-17.13
-17.97 + 2.58%
1.5
-1.87 2.48%
-1.31
-37.73 + 1.34%
-12.27 + 1.33%
-26.67 1.44%
-29.26 14.26+22
2.05% +..5%%
3.0
337.70 + 1.52%
-42.39
1.49%
-34.00 1.34%
-36.41 + 2.36%
5.5
7.35
5.45%
-7.48
7.05%
-3.007
1.45%
-42.34
1.73%
338.56
1.21%
-41.31
1.88%
7.0
9.39
1 5.22%
9.82 1 7.54%
37.55 1 1.60%
-42.37
1.72%
38.44 1 1.67%
-41.40 1 1.63%
Table 6: AAUROC and AAURRC under additive value noise (o,t).
SUPERMAN
Raindrop
mTAND
AAUROC
AAUPRC
AAUROC
AAUPRC
AAUROC
AAUPRC
0.0
0.00 0.00%
0.00%
0.00 0.00%
0.00 0.00%
0.00 0.00%
0.00 0.00%
0.1
-0.04 0.02%
0.00 0.04%
1.11%
0.02 - 0.65%
-0.35
-0.35 1..33%
0.2
+.244%
0.26
-0221
-0.27 + 0.64%
-1.36
-1.36 0.29%
0.3
0.48%
0.54%
-0.40 1.200
+..19%
-3.18 -.118
0.5
0
-0.39
-1.28
-1.26
-7.61
-7.79 1.08%
0.8
0.66%
1.70%
-
2.444:0:47%
-13.79
-13.25 1 1.11%
1.5
-182 + 1.98%
3..1%
1.18%
-24.22 1 1.96%
-22.58 + 1.45%
3,0
4.63
+ 3.22%
4.8995
-4.56 1: 1.18%
0.51%%
-31.53 1 1.61%
-29.08 1 1.56%
5.5
4.91
4.85%
55.31
5.82%
6.41 1.51%
-6.20
0.84%
33..16 1 1.09%
-32.07 1 1.10%
7.0
7.45
5.28%
-8.15 6.59%
-7.23 1.80%
-7.37 + 0.65%
-36.74 1.82%
-33.55
+ 2.34%
Table 7: AAUROC and AAUPRC under multiplicative value noise (o )
SUPERMAN
Raindrop
mTAND
Tt (days)
AAUROC
AAUPRC
AAUROC
AAUPRC
AAUROC
AAUPRC
0.0
0.00 = 0.00%
0.00 +: 0.00%
0.00 + 0.00%
0.00 +: 0.00%
0.00 + 0.00%
0.00 + 0.00%
10.0
0.02 0.17%
0.03 + 0.16%
-0.54 1.17%
-0.72 0.44%
-2.17
-2.16
30.0
0.05%
0.04%
-0.82
-1.44 0.53%
-1.94
-1.89 0.80%
90.0
-..3%
0.39
-1.58
-2.20
-1.99
-2,02 1 0.56%
150.0
-0.22 + 0.09%
-0.32 0.08%
-2.75 - 0.63%
-2.24
-2.28 1 0.71%
300.0
-0.45 + 0.42%
-0.87 0.78%
-2.41 + 1.21%
-3.26 + 0.47%
-1.85 +.99%%
-1.81 + 0.74%
500.0
0..74 0.04%
-1.12 0.29%
-2.63 1.24%
-3.73 0.90%
-2.14
-2.11 + 0.70%
Table 8: Relative change (A) in AUROC and AUPRC under temporal noise.
26


Reviews:
[{"review_id": "AYd4HNnIbk", "reviewer": "Reviewer_efJq", "summary": "This paper introduces Graph Mixing Additive Networks (GMAN), a novel, interpretable framework for learning from sets of sparse, irregular temporal graph signals. Using Extended Graph Neural Additive Networks (ExtGNAN), GMAN models nonlinear interactions within signal groups while preserving additive interpretability at the node, graph, or subset level. This approach balances expressiveness and interpretability, allowing user-defined signal grouping (domain knowledge) to enhance representational power. GMAN is theoretically proven more expressive than prior models like GNAN. It achieves state-of-the-art performance on high-stakes tasks (e.g., Crohn’s disease prediction, fake news detection), delivering meaningful insights via built-in attributions.", "questions": "The proofs demonstrate that grouping signals increases expressivity (Theorems 3.1–3.2). Could the authors clarify what classes of real-world functions this additional expressivity enables beyond XOR-type examples, perhaps with a more domain-relevant illustration (e.g., nonlinear biomarker interactions)?\n\nThe model’s flexibility depends on user-defined graph/feature grouping. Could the authors discuss automatic or data-driven methods for learning optimal groupings, and whether improper grouping choices can significantly degrade performance?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. It handles irregular, heterogeneous data: GMAN introduces a novel way to learn from sets of sparse, irregular time-series signals without any resampling or imputation. By converting each signal into a graph (e.g. linking events by time), the model preserves timing gaps and irregular patterns that other methods might obscure. This design avoids the information loss incurred by aligning or filling in missing data, enabling the model to exploit the full richness of the raw data (e.g. varying intervals between events can inform the prediction).\n\n2. Interpretable at Multiple Granularities: A key strength of GMAN is its inherently interpretable architecture. The additive structure means one can decompose the prediction into contributions from individual nodes, entire graphs, or subsets of graphs. It retains the feature-level and node-level interpretability of GNAN for those parts of the model that remain ungrouped, and additionally provides graph-level and subset-level importance scores for grouped components. These transparent contributions are directly linked to the final output (since GMAN sums them linearly), making it straightforward to explain what drove a prediction. This multi-level interpretability is especially valuable in domains like healthcare, where practitioners might ask which biomarkers (or groups of biomarkers) were most influential in a diagnosis.\n\n3. Flexible Expressiveness via Grouping: GMAN offers a trade-off between model complexity and interpretability. By grouping features or signals, domain experts can inject prior knowledge about which inputs actually interact, enabling the model to capture nonlinear interactions within those groups. The theory guarantees that any such grouping strictly increases the model’s expressive power compared to keeping everything separate. Practically, this flexibility led to state-of-the-art performance in diverse tasks – from clinical predictions to fake news detection – indicating that GMAN can adapt to different data structures and learn complex patterns when needed. Notably, its success across domains (time-series medicine and graph-structured social data) showcases the approach’s generality and robustness. Additionally, the use of a learned time-distance function ρ in ExtGNAN means GMAN can flexibly model temporal influence (e.g. decaying or long-range effects) rather than relying on fixed time windows, which is a powerful design for temporal graphs.", "weaknesses": "1. While GMAN’s grouping mechanism is powerful, it requires a priori decisions about how to partition features or signals. The model’s performance can depend on choosing sensible groups – a process that may need domain expertise or extensive tuning. In the experiments, the authors manually tried several grouping schemes (including no grouping vs. clinically guided groupings) and selected the best performing one. This indicates an added complexity: users must either have prior knowledge to guide grouping or resort to hyperparameter search to find an optimal grouping strategy. In scenarios with little known domain structure, finding the right grouping could be challenging. Moreover, if signals that truly interact are mistakenly kept separate (or vice versa), the additive structure of GMAN might fail to capture those cross-signal effects, potentially hurting performance in such cases.\n\n2. GMAN cannot maximize expressiveness and maintain full fine-grain interpretability at the same time – there is an inherent trade-off. When features are grouped or signals are combined into a subset, the model loses the ability to attribute importance to each individual feature or each individual graph within that group. Interpretability is then only available at the aggregate subset level. In practice this means, for example, one might know a collection of biomarkers as a whole was important, but not the exact contribution of each single biomarker in that group. If a use case demands insight at the most granular level for every feature/signal, GMAN would need to forego grouping – but then it essentially reduces to GNAN, which might yield weaker accuracy if important interactions exist. Thus, in scenarios where every individual feature’s impact needs to be distinctly understood, GMAN’s strength (grouped nonlinear modeling) becomes limited unless one is willing to sacrifice some clarity.\n\n3. The GMAN architecture introduces more components than a standard model, which could raise computational complexity. Each subset of graphs has its own ExtGNAN (each with multiple neural networks for feature groups) and possibly a DeepSets aggregator, and each node in a graph aggregates messages from all other nodes (weighted by ρ). This additive all-pairs message passing can be costly for large graphs, potentially $O(n^2)$ per graph in the worst case. In their experiments, this was manageable (e.g. path graphs or moderate-sized biomedical time series), but for very large graphs or very large numbers of signals, training and inference might slow down. Additionally, representing certain data as a set of many graphs could inflate memory or computation: for instance, breaking a big tree into hundreds of path graphs means running many small GNN instances. There is also a risk of model complexity in terms of parameters – with separate neural networks for each feature group and each subset, the number of parameters grows, which might require careful regularization and ample data to avoid overfitting. While not reported as an issue in the paper, these factors suggest that GMAN could be less sample-efficient or slower to train compared to simpler architectures, especially if used naively on very large-scale problems.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "m0odp4ORGX", "reviewer": "Reviewer_PX2M", "summary": "This paper proposes GMAN, a model for learning from a set of graphs that represent irregular, asynchronous signals (e.g., per-biomarker paths in EHR; propagation trees in social media). The key idea is to (i) encode each graph with an Extended GNAN (ExtGNAN) that allows grouped (multivariate) feature functions to trade fine-grained feature-level interpretability for higher expressivity, and then (ii) mix multiple graphs via a DeepSets aggregator at the subset level, yielding additive scores at the node/graph/subset levels and thus transparent importance attributions. The paper proves GMAN is strictly more expressive than GNAN and that grouping multiple graphs into subsets further strictly increases expressivity; it also gives a recoverability result (four-point condition) and a complexity analysis. Empirically, GMAN is evaluated on ICU length-of-stay (PhysioNet 2012), Crohn’s disease onset, and GossipCop fake-news detection, reporting competitive performance with built-in interpretability; ablations show non-trivial drops when removing the DeepSets mixer, the distance kernel ρ, or replacing ExtGNAN.", "questions": "* Can you report calibration (ECE/Reliability) and robustness (noise stress tests, temporal shift) on P12/CD?\n* How does performance/interpretability scale beyond 48-hour P12 windows—can GMAN handle much denser ICU streams without subsampling given the O(n²) component? Any sparse kernel or Nyström-like approximation?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* Well-motivated representation of irregular, multi-signal data: Modeling each signal trajectory as a path graph and learning over a set of such graphs avoids time-gridding/imputation artifacts; the paper also justifies recoverability of structure under a tree-metric condition and gives a clear O($m·K·n²·d\\psi$) complexity with GPU-friendly implementation notes.\n* Theory for interpretability–expressivity trade-off: ExtGNAN enables multivariate within-graph feature grouping; the authors prove GMAN > GNAN in expressivity and that subset-mixing of multiple graphs (DeepSets) is strictly more expressive than singleton mixing, aligning with additive-model literature and permutation-invariant set learning.\n* Built-in, multi-grain interpretability that surfaces plausible clinical signals: Node-, graph-, and subset-level importances are direct contributions (not post-hoc), and qualitative analyses on P12/CD highlight clinically coherent markers (e.g., F-Cal/CRP; renal and hepatic panels) and meaningful subset curves.\n* Ablations substantiate design choices: Replacing DeepSets with mean pooling, removing ρ, or downgrading ExtGNAN causes notable AUPRC drops (e.g., −20% with mean pooling; −12% without ρ), supporting the necessity of the proposed components.\n* Experiments span clinical time-series and social-media propagation graphs (GossipCop) with appropriate baselines per structure family (sequence-like vs. general graphs), and GMAN outperforms strong GNN baselines on GossipCop.", "weaknesses": "* Novelty relative to GNAN could be made crisper in the writing: While theorems show strict expressivity gains, the narrative at times reads like an incremental extension of GNAN; emphasize the two-level mixing (within-graph feature grouping and across-graph subset mixing) and the new recoverability/complexity results as core contributions.\n\n* Scalability: ExtGNAN performs dense pairwise aggregation across nodes, giving per-graph O(n²) cost and overall O(m·K·n²·dψ); this may limit very long trajectories (ICU with minute-level vitals) unless optimized kernels or sparsification are used. Benchmarks on long sequences would strengthen the case.\n\n* Limited evidence of robustness & calibration: Results focus on discrimination (e.g., AUPRC/accuracy). Reliability (calibration curves/ECE), OOD generalization (e.g., cross-hospital or temporal drift), and fairness stratifications are missing; these are common asks in clinical ML.\n\n* Codes are not avaialble at this stage, limiting its reproducibility", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jYOKjZS4xY", "reviewer": "Reviewer_TSAx", "summary": "GMAN extends Graph Neural Additive Networks by operating on sets of graphs representing irregular, heterogeneous temporal signals.", "questions": "1. For the \"interpretability-expressivity trade-off,\" the biological grouping of biomarkers shows the best performance, but it’s unclear if data-driven grouping (e.g., clustering) can achieve similar results without domain priors. Please add experiments to validate this and discuss when domain knowledge is indispensable.\n2. GMAN is applied to path graphs (medical data) and tree graphs (fake news), but it’s unclear how it performs on cyclic or disconnected graph, please add experiments on such graph types to verify generalizability beyond the tested structures.\n3. The paper uses AUPRC for imbalanced medical tasks but doesn’t discuss how class imbalance is handled during training (e.g., sampling strategies, loss functions), please clarify this and provide additional metrics (e.g., AUROC) for comprehensive evaluation.\n4. The ablation replaces ExtGNAN with MLPs/identity mappings, but it doesn’t test if simpler additive GNN variants (e.g., GNAN with minor modifications) can achieve comparable performance, please add such baselines to highlight GMAN’s unique value.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Addresses an under-explored irregular-sampling problem.\n2. Good design combining additive interpretability with graph-set flexibility.\n3. Compelling real-world demonstrations (Crohn’s disease, LOS prediction).", "weaknesses": "1. Evaluation section briefly described; lacks detailed baselines beyond GNAN.\n2. Interpretability examples are qualitative; quantitative faithfulness metrics missing.\n3. Computational efficiency compared with standard GNNs unclear.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pOsenV6C4g", "reviewer": "Reviewer_B9RD", "summary": "This paper presents GMAN (Graph additive mixing network) for learning on graphs that represent irregularly sampled time signals. Results show good empirical performance on different datasets.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- GMAN provides good empirical predictive performance and interpretability\n- Domain prior can be incorporated into method\n- Some theoretical analysis is included", "weaknesses": "- In the table 1 for example, GMAN is shown to beat other baselines, but the authors state that signals are grouped based on common biomarker domain knowledge, and tuning biomarker sets are also performed. My concern is that the benefit of GMAN is incremental in accuracy, and other methods do not use such specific domain knowledge, thus are more widely applicable and performant.\n- Novelty is limited, and contribution seems incremental. Prior methods Raindrop uses GNNs and SeFT uses deep sets, and heavily relies on GNAN which also uses node level and graph level representations.\n- Theoretical analysis is not extensive, seems elementary, and does not capture major elements of learning with temporal irregular signals", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)