Structural Prognostic Event Modeling for Multimodal Cancer Survival Analysis
Authors: Yilan Zhang
Li Nanbo
Changchun Yang
Jürgen Schmidhuber
Xin Gao
Venue: ICLR 2026 Poster (2026)
Keywords: Computational Pathology
Multimodal Learning
Cancer Survival Prediction
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: The integration of histology images and gene profiles has shown great promise for improving survival prediction in cancer. However, current approaches often struggle to model intra- and inter-modal interactions efficiently and effectively due to the high dimensionality and complexity of the inputs. A major challenge is capturing critical prognostic events that, though few, underlie the complexity of the observed inputs and largely determine patient outcomes. These events---manifested as high-level structural signals such as spatial histologic patterns or pathway co-activations---are typically sparse, patient-specific, and unannotated, making them inherently difficult to uncover. To address this, we propose SlotSPE, a slot-based framework for structural prognostic event modeling. Specifically, inspired by the principle of factorial coding, we compress each patient’s multimodal inputs into compact, modality-specific sets of mutually distinctive slots using slot attention. By leveraging these slot representations as encodings for prognostic events, our framework enables both efficient and effective modeling of complex intra- and inter-modal interactions, while also facilitating seamless incorporation of biological priors that enhance prognostic relevance. Extensive experiments on ten cancer benchmarks show that SlotSPE outperforms existing methods in 8 out of 10 cohorts, achieving an overall improvement of 2.9%. It remains robust under missing genomic data and delivers markedly improved interpretability through structured event decomposition.

Published as a conference paper at ICLR 2026
STRUCTURAL PROGNOSTIC EVENT MODELING FOR MULTIMODAL CANCER SURVIVAL ANALYSIS
Yilan Zhangi, Li Nanbo', Changchun Yang, Jürgen Schmidhuber, Xin Gao"
TBqual contribution, "Corresponding author {yilan. zhang, nanbo.. 1i,, changchun yang, juergen. aecemnsschiioo chhme, xin. gao) kaust...... @ edu. sa
King Abdullah University of Science and Technology (KAUST)
Thuwal, Saudi Arabia
ABSTRACT
The integration of histology images and gene profiles has shown great promise for improving survival prediction in cancer. However, current approaches often struggle to model intra- and inter-modal interactions efficiently and effectively due to the high dimensionality and complexity of the inputs. A major challenge is capturing critical prognostic events that, though few, underlie the complexity of the observed inputs and largely determine patient outcomes. These events- manifested as high-level structural signals such as spatial histologie patterns or pathway co-activations- typically sparse, patient-specific, and unannotated, making them inherently difficult to uncover. To address this, we propose Slot- SPE, slot-based framework for structural prognostic event modeling. Specif- ically, inspired by the principle of factorial coding, we compress each patient's 's multimodal inputs into compact, modality-specifff sets of mutually distinctive slots using slot attention. By leveraging these slot representations as encodings for prognostic events, our framework enables both efficient and effective model- ing of complex intra- and inter-modal interactions, while also facilitating seam- less incorporation of biological priors that enhance prognostic relevance. Exten- sive experiments on ten cancer benchmarks show that SlotSPE outperforms exist- ing methods in out of 10 cohorts, achieving an overall improvement of 2.9%. It remains robust under missing genomic data and delivers markedly improved interpretability through structured event decomposition. Code available at ( https: // /ttp://ggtttb/tt/ com/ www.o///wwwwteeee/eeeeeeeeeeeeee venvet/Slotts.
INTRODUCTION
Cancer survival analysis aims to estimate patient mortality risk survival time, serving as key tool for personalized prognosis and precision oncology, as it helps quantify outcomes, identify prog- nostic factors, and guide individualized treatment decisions (Cox & Reid, 2004; [Jnkins 20055 Wiegrebe et al. 2024). Whole-slide images (WSIs) and genomics are two widely-used tools in cancer survival analysis, as they capture complementary prognostic signals: WSIs reveal how can- cer manifests morphologically in tissue, while genomics uncovers its underlying molecular drivers. Their integration offers the opportunity for more accurate, robust, and biologically grounded sur- vival prediction, which has in turn sparked growing interest in multimodal learning approaches for survival analysis (Chen al., 20216 Xu & Chen 2023 (123)aJum Jaume al. 2024 Zhou al. 2025).
Effective and efficient multimodal learning for survival analysis faces a fundamental challenge: al- though patient outcomes are often driven by small number of critical events (Vogelstein et al. 2013 Hosseini et al. (024). WSI and genomic signals are rather complex and high-dimensional. High-resolution WSIs can exceed 10 x 10 pixels (Song et al. 2023) and genomics involve thou- sands of genes (Györffy 1021 These events manifest as meaningful structural associations within WSI and genomic signals e.g., in histopathology, immune activity and tumor aggressiveness (Chan) et al. 2024: Liang et al. 2025) reflected in the density and proximity of the pixel organizations of tumor- infiorrn lymphocytes and cancer nests, while in genomics, the tumor promotino effects emerge from the co-activation of РЕ3K/АKT and MAPK pathways (Glaviano et al. 2023). How-

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ever, learning to uncover such event-related patterns structures from the input signals is difficult for machines: these high-level associations are typically sparse, speciffc,, and unannotated. Compounding the challenge, the enormous scale of input units-millions of WSI pixels and thou- sands of genomie reatures-createe massive self-interactions within each modality, further amplified by the need for cross-modal alignment, rendering direct modeling prohibitively expensive.
Existing attempts, e.g., (Ilse et al. 2018 Shao et al.] 2021 Chen et al. b021b Xu & Chen 2023
Jaume et al. 2024). fall short of capturing high-level prognostic associations.
The most rele- 2024 Song et al. 2024). which employ fixed prototype representations and therefore lack adaptability to individual patients. For example, PIBD (Zhang et al., (2024) approximates prototypical distribution for each risk group via infor- mation bottleneck TTihby et al.) 2000) Alemi et al. 2016). Yet, these prototypes are static-once trained, the same set is applied to all patients. MMP (Song et al., 2024) takes a different route by adopting Gaussian mixture model (GMM) (Bishop & Nasrabadi, (006) to define prototypes for each WSI. However, the image-wise prototypes are unlearnable (i.e., fixed) during training, making end-to-end optimization suboptimal.
vant studies are prototype-basee
methods (Zhag et al.)
In this paper, we introduce SlotSPE, a slot-based framework for structural prognostic event model- ing. Inspired by factorial coding (Schmidhuber 1992] Higgins et al., 2017 Greff et al., 2020), our method compresses high- high-dimensional multimodal inputs into compact set of semantic slots using a slot attention module (Locatello et al. 2020), where each slot corresponds to a latent prognostic event. Unlike fixed prototypes, these slots are dynamically instantiated for each patient, allowing the model to capture individualized prognostic patterns while preserving a concise representation. To reduce slot redundancy and encourage slots to capture distinct prognostic events, we introduce selective slot activation through a Mixture-of--ippers-ssyy decoder (Hampshire & Waibell 1989]
Jacobs et al., 1991: Jordan & Jacobs 1994; Shazeer et al. 2017), which activates only the most predictive slots for each patient.
Beyond compression, we further model cross-modal interactions by incorporating a biological prior: histopathological phenotypes often reflect underlying molecular events, revealing molecular- morphology mappings (Wang et al., [022]] [Lu et al., 20256). Guided by this insight, we design a cross-modal reconstruction task where omics-derived slots are encouraged to predict gene expres- sion from histology image. This alignment not only enforces biologically meaningful interactions across modalities but also improves robustness in missing genomic data.
The key contributions are: (1) A structural prognostic event modeling framework for multimodal survival prediction that effectively and efficiently extracts patient-specific events; (2) A cross-modal reconstruction that encodes biological priors to enhance alignment and robustness; (3) Extensive evaluation ten cancer cohorts demonstrating the superiority and robustness; and (4) Enhanced interpretability through the structured decoupling ability of the proposed representation.
2 RELATED WORKS
Single Modality. The advent of deep learning marks a paradigm shift in cancer progmosis, where artificial neural networks (NN) can uncover prognostic patterns from radiological (Aerts et al. 2014 Lou et al. 2019 Xu et al. 2019 Yao et al.) 2021), pathological (Ciresan et al. 2
al.
2013), and molecular data (Chaudhary et al. 2018 Ching et al. 2018)) that were previously inac- cessible conventional methods. In histopathology. whole-slide images (WSIs) under the multiple instance learning (MIL) (Dietterich et al., 1997; Maron & Lozano-Pérez 1997) waradigm-where slide represented as bag of patches with only slide- or patient-level survival labels have
become standard (Hou et al., 2016: Isse et al., 2018 Shao et al. 2021] Lu et al. (021). Recent MII. approaches address the challenge of abundant patches by using clustering (e.g. k-means) Yao
et al. 2020 Vu et al.) 2023) Yang et al. 2024 Zhou et al. (024). graph models (Li et al.) 2018 Chen et al. 202 a)), and hierarchical WSI representations (Shao et al., (002).. Meanwhile, genomic methods moved from simple MLP or shallow nets high-dimensional gene profiles (Haykin 1998
Klambauer et al. 2017) to sathway-based representations that group genes into biologically mean- ingful sets for better interpretability (Zhao et al. 2021 Hou et al. 2023 Wang al. 2024). Building on these advances, our method preserves the MIL standard for histopathology. adopts pathway-level
genomic features.
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Multiple Modality. Multimodal approaches, especially the integration of histopathology and ge-
nomics, have attracted increasing attention because combining morphological and molecular infor-
mation often yields better prognostic performance than either modality alone (Chen et all, 2020
2021b Yuan et al.] 2.25). Typical strategies include late fusion (e.g., concatenation or Kronecker
product) (Chen et al. |020 Ding et al., [023 Volinsky-Fremond al. 2024 Zhao al. 2025
Luo
itt al. 2025). ) and early fusion via co-attention mechanisms operating at the patch-gene level Chen
al. b02 Xu & Chen 2023 Zhou & Chen 2023 Jaume et al. 2024 Yuan et al. 2025
Wang
et al. 2025| Zhou et al. (025). Since inputs are complex and high-diman -igh-dimessional, recent work has
adopted adaptive token selection (Zhang et al.) 2025) or compact latent representations by com-
pressing WSI and pathway data via prototypes (Liu et al., 2025a Song et al.) 2024; Zhang et al.)
2024). The former, however, lacks modeling of interpretable structural associations; the latter fails to address sparsity and patient-specific event variation, relying instead on fixed prototypes.
Structural Event Modeling. A key challenge in multimodal survival analysis lies in handling the high-dimensional histology and omics inputs, which not only incurs substantial computational costs but also complicates modeling of intricate intra-finter-modal interactions. An important insight is that patient outcomes are often driven by small number of critical events (Vogelstein et al. 2013)- This motivates approaches that aim to uncover the underlying event-related structures withi com- plex inputs. For examples, PIBD (Zhang al. 2024) and MMP (Song et al. 2024) attempt derive structured representations from complex multimodal data. However, relying on fixed prototypes, these methods cannot dynamically capture the sparse and patient-specific structural events that of- ten determine outcomes. From the perspective of machine learning, this challenge can be framed as a problem of factorial coding, well-established paradigm concerned with decomposing and compressing high-dimensional data into disentangled latent factors (Schmidhuber 1992 Tipping & Bishop 1999
| Higgins et al., [011 Kim & Mnih 2018). Building on this connection, our tramework advances beyond static prototypes by introducing learnable slots through slot attention (Locatello al. 2020), modeling prognostic events that are selectively activated per patient and aligned via biologically guided cross mooal reconstruction. This design enables structured decomposition of survival-related events, binding multimodal prognostic signals to interpretable representations.
3 METHOD
Survival prediction is the task of estimating a patient risk of an event (e.g., death) given the patho- logical observations (e.g. WSIs and genomic) of the patient. In this paper, we tackle the prob- lem of learning such hazard predictor from the multi-modal data. Formally, let the hazard pre- diction function be denoted he, representing the probability of death occurring at time t (i.e., survival up to time t). The model is trained using the negative log-likelihood (NIL.) loss (Zadeh) & Schmid 2020), denoted as Leurv (see Appendix B.I for details). Each patient sample is rep- resented as
(4) x g 260) c(()) where indexes the patient, x denotes the pathology data,
x denotes the genomic profile, ((0) E (1,...,Ny, and cli) E {00, 1} is the censoring indicator (c0) = O for an observed event, c(i)) = for right-censoring). Operationally, following standard practices in computational pathology (Chen al. 2021b) Jaume et al. 2024), WSI and genomic in- puts are pre-processed by dedicated image and gene encoders and represented as hags of instances: Mr
x N. CRd دبر and X {x(()
(1)
9.j أ where Mj. and M,, denote the numbers of
Rdd M,
WSI patches and biological pathways, respectively, and d is the feature dimension. When modeled with state-of-the-art transformers like prior works (Xu & Chen 2023: Zhou & Chen, 2023 Jaume
ct al. 2024), the resulting intra- and moder-modal interactions scale quadratically as O( (M, Mg) creating major challenge for both efficacy and efficiency.
In this section, we present SlotSPE, a novel Slot-based Sturctual Prognostic Event modeling frame- work for multimodal cancer survival analysis (Figure. Tp.
3.1 SLOT-BASED INFORMATION COMPRESSION
Inspired by factorial coding (Schmidhuber 1992 Higgins et al. 2017). which aims disentangle data into independent latent factors, we perform structural decomposition for two bags of histology
and genomic instances, i.e., x(9) and x(() using a slot attention module (Locatello et al. 2020
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Moxd
Selective Slot Activation
Patching
Patch Encoder
Slot Attention
Self Attention
XT
Whole Image
Iterative Cross Attention
Predictor
Image Paches
recon
JC,
Inter-
Tokenizzng nizing
Gene Encoder
Slot Attention
Self Attention
CD44
Mean Pooling
Patch Token
AFC
Intra-
Pothway Taken
Slots
Genes
Selective Slot Activation
Masks
Pathways
Figure 1: Framework of SlotSPE. Histology and gene features are extracted into bag structures, then compressed into slots via slot attention. Selective slot activation enforces sparsity and mutual competition, while a biologically guided cross-modal reconstruction aligns modalities. Finally, slot interactions are modeled using self- and cross-attention predict survival.
This allows us to compress the large input sets into much smaller slot-based representations, signif- icantly reducing computational overhead. These slots are then decoded using a MoE-style decoder that selectively activates patient-specific slots, promoting both sparsity and competition among them.
Slot Attention. Slot attention (Locatello al. 2020) learns to encode distinct structural patterns present in the input into finite set of latent vectors, i.e., the "slots". Since WSI and genomic data inherently contain massive redundancy (Zhang et al. 2024 Song et al.] 2024), it desirable to aggregate them into smaller set of compact representations while preserving their semantic content. This makes slot attention particularly well-suited for our task, where the resulting compact representations can be interpreted as latent prognostic events modeled by slots.
We re-organize the input features both modalities as matrices, X E Raxd With a set of slots, organized as (()) E Sxdaa, initialized from some learnable distributions, the slot attention compresses X into S slots through 7 iterations of cross-attention-basse routing. At each iteration E (0...., T - 1}. the slots S(F) attend to the input X to produce updated representations, which are then refindd using multilayer perceptron (MLP). Slot updates across iterations are applied recurrently using a recurrent neural network (RNNs) (Hochreiter & Schmidhuber 1997] Cho et al.) 2014) to preserve temporal consistency and iterative refinement. Mathematically, each slot Sę is obtained by:
softmax ((((+)))((x))) Vdstor
E R.S.
Σ
(r) oij
V(x));
S(n)
j=1
(++1) = RNN(S uf()) 8
s (r+1)
- s/
(7+1)
MLP(s
where 2(-), KC(-), and V(-) are linear projections into query, key, and value spaces. Note that the softmax is applied over (slots) for each j. enforcing competition among slots and enabling structured decomposition. Through iterative updates, the learnable bottleneck maps I Mxd + g with S & M. yielding S(T) as the final set of slots (simply as S). The complexity of slot attentions for both histology and genomic instances will be O(S,, x M, + SA * Mn).
Selective Slot Activation. In our task, to avoid slots redundantly attend to similar structures or collapse onto spurious and prognostic irrelevant patterns, we propose selective slot activation (Myle-style decoder with learnable gating mechanism that
(Figure ((guree(()): Mfxture-of--xxpee sparsely activates the most predictive slots per patient, encouraging specialization and improving discriminative performance across the cohort.
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Risk Logits
Omics-derived Slots
Predictor
L recon
Ssrrv
Slot Attention
Reconstruction Head
Slots
(())
Gate
Top
X X
Reconstructed
Patch Token
Pathway Token
Masks
(a) Selective Slots Activation
(b) Cross-modal Reconstruction
Figure 2: Detailed component structure of SlotSPE. (a) Selective slot activation: a Mixture-of- Experts(MoE) decoder sparsely activates only the most predictive slots. (b) Cross-modal construction: guided by biological priors, omics-derived slots are aligned with histology by predict- ing pathway-level gene expression from WSIs.
Conceptually, each slot is treated From the slot set S, we derive per-slot predictions by projecting them into class logits Es E IR via an MLP predictor, obtaining S candidate predictions. A lightweight gating function predict retention score for each slot Sy:
"expert" potentially encoding a critical prognostic event.
Fk ((Sk),
R -
Then the top-K slots are selected using the Gumbel-Top-K trick (Gumbel, 1954 Maddison et al., 2014 Kool 2019) with Straight-Through Estimation (ST) (Jang (016)), producing
differentiable K-hot mask G E {0, 1) (see Appendix B.2 for details). The selected slots
reweighted by masking and renormalizing the softmax weights:
ih Gk
Wk
W softmax(r) R
(3)
==1 U. G.
Finally, patient-level predictions obtained gated mixture of slot logits:
wp lu N.
(4)
Thus, each patient is represented by a compact, patient-specific subset of slots, yielding sparse mixture of prognostic events. The entire decoder is trained end-to-end with the survival loss Laures which supervises the gating mechanism to prioritize cetcome-relevane slots.
Slots Regularization. While selective slot activation encourages sparsity, it also lead to the emergence null slots-slots that fail to attend to any input teareres- weakening the com- petition enforced by the gating mechanism. In information compression, the entropy of the in- formation bottleneck is upper-bounded by the input features X, non-activated slots-though less predictive than activated ones-are leveraged capture residual information for input reconstruc- tion, thereby mitigating potential information loss and ensuring completeness. To mitigate this po- tential loss of information during slot-based compression, we introduce a reconstruction objective. Specifically, we decode the slots using a reconstruction head, and minimize the reconstruction loss Ciecon X, X), where X denotes the reconstructed features (see Appendix B.3 for details).
3.2 MULTIMODAL SLOTS INTERACTION WITH BILOGICAL GUIDANCE
Cross-modal Reconstruction using Biological Prior. To ensure effective cross- modal interaction, introduce cross-modal reconstruction (Figure b)) uncover molecular-morpholgg mappings

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reflecting the fact that molecular events give rise to histopathological phenotypes (Wang al. 2021 Liu et al. 2025b).
Given the omics-derived initialization slots Sg. i.c. initialization learned from the training omics data, we perform slot attention (Eq. D with histopathology patch features X,, (for a better inter- pretability original WSIs, choose Xn, instead of using Sn,) to obtain cross-modal slot repre- sentations Sy-h, which capture gene-related events expressed in histopathological morphology. Thus, the cross-modal interaction this step is OSS, MR) with Sg < Mn. These slots are then decoded by a reconstruction head R. recover the original genomic features, with position embeddings Qg E IR M, Xd;
(5) Since the input pathway features are arranged in a fixed index order, corresponds to a specific path- way index, providing a positional prior that anchors reconstruction to the correct genomic coordi- nate. The reconstructed features are obtained as:
(0, Mg 1])-
X
(6)
with reconstruction loss Lrecon Xg. x)). Here, histology serves the morphological manifesta-
tion of underlying molecular events, guiding omics-derived slots toward biologically meaningful alignment. Notably, because genomic profiling is substantially more costly than histopathology and often unavailable at test time (Payne et al., 2018). this cross-modal reconstruction enhances robust- ness: the reconstruction head can impute genomic features directly from histology images, enabling inference even when omics data are missing.
Slots Interactions. To capture multimodal dependencies, model slot interactions at both intra- and model levels handled in parallel. Intra-modal interactions are captured using masked self-attention using only the top-K most self-predictive slots within each modality. For inter-modal interactions, we use all slots without masking to fully capture inter-modal synergies, including those arising from slots that are originally less self predictive within their own modality. Instead of relying on one-shot co-attention (Chen et al. 202 Xu & Chen 2023] Jaume et al. (024], we design an iterative cross-attention scheme that tollows the recurrent update slot attention module. At each iteration, slots from one modality attend to those of the other: histology queries attend to omics keys/values, and vice versa (see Appendix [B.4 for details). Finally, the output of three branches are concatenated and passed into risk classification head for risk prediction. The computational complexity of slots interactions O((S, + )2) Overall, instead of the original O(MM, + M,))). our model requires OSS, Mg + Sn MA + Sy M,, + (Sg + S,)?). Since Sy. Sp. & Mg. M, in practice and the (Sg + 8% term is negligible, this expression can be upper-bounded by O(S,, + Sx) (M, + Mn)).
3.3 TRAINING AND INFERENCE
Overall Loss. The total training objective of SlotSPE
Caurv + XCrscoo
where balances the survival and reconstruction components. Laure includes both the survival prediction loss and the survival prediction losses w.r.t. each single modalities, while Lrecon combines the slots regularization and cross-modal reconstruction objectives (refer to Appendix B.5 for more details).
Inference. At test time, neither slots regularization reconstruction nor cross-modal reconstruction required when both modalities are available. Cross-modal reconstruction only invoked when genomic data are missing, serving an imputation mechanism.
4 EXPERIMENTS
4.1 DATASETS AND IMPLEMENTATIONS
We perform comprehensive evaluations across ten publicly available cancer cohorts from TCGA Case counts for each dataset are listed in Table 1. Following (Jaume al. 2024), we predict disease-
https://portal] gde. cancer.gov/

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Table 1: Comparison of mean C-index values across cancer datasets. g. and h. refer to genomic modality and histological modality, respectively. The best results and the second-bess results are highlighted in bold and in underline. (See Table for the completed table with standard deviation.)
BRCA
COADREAD
KIRC
UCEC
LUAD
LUSC
HNSC
SKCM
BLCA
STAD
Model
Modality
Overall
(N-1046)
(N-573)
(N-488)
(N-488)
(N-467)
(N-450)
(N-458)
(N-40)
(N-383)
(N-366)
MLP &
0.64
0.611
0.750
0.731
0.634
0.584
0.584
0662
0.67
0.615
SNN
0.645
0.754
0.753
0673
0.666
SNNTrams
0,657
0,710
0.747
0.724
0.48
0.555
0.605
0.684
0.699
0.593
0,662
ShoSPE
0.088
0.733
0.774
0.752
0.646
0.616
0691
0.678
0.701
0.5%6
0.681
ABMIL
h. 0.656
0.715
0.782
0.779
0.645
0.593
0.664
0.068
0.663
0.642
0.681
TransMIL
h.
0.647
0.723
0.267
0.759
0.655
0.582
0.644
0.632
0.647
0.656
0.671
CLAM-SB
0.696
0.742
0.784
0.757
0.639
0.581
0.619
0.613
0.645
0.637
0.678
CLAM MB
0.715
0.782
0.788
0.632
0.636
0.610
0.657
0.641
0.682
SloiSPE
0.728
0.729
0.790
0.779
0.656
0.635
0.689
0.642
0.676
0.690
Porpoise
0.681
0.788
0.788
0.647
0.599
0.682
0.090
0.619
0.676
MCAT
p.+h
0.700
0.737
0.795
00:002
04699
0.583
0.622
0.667
0.688
0.639
0.690
MOTCal
4.+h.
0.717
0.742
0.799
0.773
0.663
0.573
0.627
0.688
0,700
0.642
0.692
CMTA
g++b.
0.731
0.720
0.794
0.764
0.662
0.599
0.619
0.681
0.202
0.639
0.091
SurvParh
B-+h.
0.728
0.787
0.751
0.661
0.577
0.611
0.666
0.666
0.647
PIBD
g-+h.
0.662
0.772
0.783
0.634
0.627
0.619
0.693
0.676
MMP
g-+b.
0.714
0.686
0.720
0.755
0.634
0.580
0.590
0.682
0
0.602
0.669
LI&CVAE
g.+h.
0,705
0.753
0.792
0.788
0.651
0.630
0.635
0.682
0.635
0.683
0.692
ShdSPR
p.+b
0.779
0.773
0,815
0.813
0.683
0.634
0.642
0.688
0.708
0.671
0,721
specific survival (DSS) with histological data including all diagnostic WSIs and transcriptomic pro- files with DSS labels are obtained from cBioPorta?) Pathway gene sets are curated from Hallmarks
(Subramanian al. 2005 Liberzon et al., (2155) and Reactome (Gillespie al.. 2022), with genes absent in cBioPortal removed. We use 5-fold cross-validation and report the concordance index (C-
index) (Harrell Jr et al. 1996) with standard deviation (std) and visualize the Kaplan-Meier (KM) Kaplan & Meier (1958) survival curves for stratified risk groups, perform the log-rank test Man- tel et al. (1966) and restricted mean survival time (RMST) (Irwin) 1949. Karrison 1986) to assess
differences between them. Further information can be found in Appendix
4.2 COMPARISONS WITH SOTAS
We benchmark our approach against three categories of state-of-thheart (SOTA) methods: (1) Tran- scriptomics. We consider a feed-forward neural network (MLP) (Haykin 1998). pathway-specific
baseline (SNNs) (Klambauer et al., 2017). and SNNTrans, which integrates SNNs with transform-
ers (Klambauer et 2017 et al.] [22TT] (2) Histology. We compare with leading MaLeb
models, including ABMIL (Ise et al. 2018). TransMIL (Shao et al. [20TT, and CLAM (Lu et al.)
2021 (3) Multimodal. We evaluate against eight multimodal SOTA methods including Porpoise
(Chen et al. 2022). MCAT (Chen et al. 2021b), MOTCat (Xu & Chen 2023), CMTA (Zhou &
Chen 2023). ). SurvPath (Jaume et al. (2024) PIBD (Zhang et al.] 2024). MMP Sonng et al. (2024),
and LD-CVAE (Zhou et al. 2025). Among them, the first five methods adopt instance-level interac-
tions for histology and omies integration, PIBD and MMP employ prototype- based modeling, while
LD-CVAE is specifically designed to handle missing genomic data.
From Table D we observe that most multimodal approaches (except Porpoise, PIBD, and MMP) outperform unimodal ones, confirming the complementary value of integrating histology and ge- nomics. Although prototype-based methods (PIBD and MMP) use prototypes to represent complex inputs, their limited adaptability in capturing patient-specific events leads to unsatisfactory results on certain datasets, reducing overall effectiveness. In contrast, SlotSPE consistently achieves supe- rior results, ranking first or second in nearly all cohorts and outperforming the second-best method by 2.9% in overall C-index across ten cancer types. Notably, this advantage also holds in single- modality settings: gene-only variant surpasses the next best model by 1.9%, while WSI-only variant improves by 0.8% in overall C-index. These results highlight the generalizability and flexibility of SlotSPE on cancer types and modalities. By dynamically capturing structured prognostic events and enabling cross- modal event-level alignment, SlotSPE establishes itself as a strong and reliable framework for survival prediction.
/org/
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Table 2: C-index across ten cancer datasets under missing-genomies settings. The column Missing
indicates whether the genomic is missing (V= missing), (See T for the complete table.)
Model
Missing
BRCA
COADREAD
KIRC
UCEC
LUAD
LUSC
HNSC
SKCM
BLCA
STAD
Overall
LD-CVAE
0.705
0.753
0.792
0.788
0,651
0.620
0.635
0.682
0.635
0.653
0.692
LD-CVAE
0.715
0.775
0.638
0.596
0.676
0.644
0.688
SIoSPE
0.779
0.773
0.815
0.813
0.683
0.634
0.642
0.688
0.708
0.671
0.721
SloSPE
0.734
0.741
0.789
0,802
0.663
0.634
0.649
0.678
0.678
0.677
0,704
BRCA
COADREAD
KIRC Kadde sneier 336-14)
UCEC
LUAD
1pn3 75640)
inder Meud0)
34
Parted 36
eogs 23
LD-CVAE
Explas
stede
Roukse kaeerr
Kaulee Eieeia
Ours
(Missin
150
Figure 3: Haplan-Meies curves of predicted high-risk and low-risk groups. A p-value 0.05 the top indicates statistically significant separation between groups. The restricted mean survival time (RMST) up to 60 months is also reported, with values shown as A (High-Low), and ratio (High/Low). (Zoom in to view details.)
4.3 ROBUSTNESS
Since collecting genomic data is substantially more costly than acquiring histology images (Payne) jet al.) 2018). clinical deployment often faces performance degradation when genomic features are unavailable. To evaluate the robustness of our approach, we test SlotSPE under the missing- genomic-modalin setting (Table 2). SlotSPE maintains strong performance, and in several cohorts (e.g.. HNSC, STAD) its missing-modality variant matches sion, demonstrating resilience to incomplete omics data. This robustness stems from the cross- modal reconstruction task, which enables the model to infer pathway representations from histology through omics-derived slots. Compared with LD-CVAE (Zhou et al., 2025)-a method explicitly designed for missing genomic SlotSS shows a somewhat larger drop relative to its full- modality variant, yet still achieves superior or comparable performance across most datasets. No- tably, its overall performance even exceeds that of full-modality LD- DVEE. These findings highlight that SlotSPE not only integrates multimodal features effectively but also delivers robust predictions the absence of genomic data.
surpasses the full-modalig ver-
4.4 RISK STRATIFICATION
We further evaluate our model using standard survival analysis techniques. Figure shows Ka- -lan-Meier (KM) curves, where patients are stratified into high- and low-risk groups based on pre- dicted risk scores, with validation-set median as cut-off. Group separation is assessed using the log-rank test, and the corresponding p-values are reported. Across cohorts, our method achieves significantly greater separation between risk groups than the second-best method (LD-CVAE). For instance, in UCEC, LD-CVAE yields a non non-significam p-value (> 0.05), while our model demon- strates significant separation (p 1.33 10 7). For more intuitive quantitative view, our method attains a larger absolute RMST difference (High-Low) and a smaller RMST ratio (High/Low), together indicating robust prognostic stratification--rnt under modaltyy condition.
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Table 3: Ablation of model components reported as mean C-index across ten cancer datasets. (See
Table 8 for the complete table.)
Variant
BRCA
COADREAD
KIRC
UCEC
LUAD
LUSC
HNSC
SKCM
BLCA
STAD
Overall
Baseline (Vanilla Slots)
0.711
0.734
0.784
0.779
0.661
0.592
0.610
0.668
0.686
0.644
0.687
wro Sclcetive Slot Attention
0.728
0.755
0.787
0.800
0.659
0.620
0.615
0.685
0.688
0.650
0.699
w/o Slots Regularization
0.734
0.763
0.794
0.811
0.662
0.611
0.621
0.679
0.693
0.667
0.701
w/o Cross Cress-modal modall Reconsmmction
0.710
0.758
0.787
0.794
0.663
0.619
0.611
0.671
0.698
0.645
0.696
wio Iterative Cross-atiention
0.727
0.761
0.803
0.794
0.653
0.602
0.624
0.676
0,702
0.648
0.699
StotSE
0.779
0.773
0.815
0.813
0.683
0.634
0.642
0.688
0.708
0.671
0.721
Performance vs (Inference) Memory Trade-off
Performance vs (Inference) Runtime Trade-off
PUOSPE (burs)
S Touns)
3755
1O COA
0.122
0.759
1:40
0:44
CNT
8.42
LOLOME
9.43
MOTEOT
MCKT
CMTI
exttr (O.r)
2299
3ite
4239
GPU Memory (MB)
Wal-CC ock Time (sec)
Figure 4: Performance (Inference) Memory/Runtine Trade-off
4.5
ABLATION STUDY
Table summarizze the ablation results for each component of SlotSPE. We construct strong base- line by retaining the vanilla slot attention and multimodal fusion modules while removing selective slot attention and reconstructions, and replacing the ilerative cross-attention in multimodal fusion with standard dual branch cross-attention. As shown in the first and the last rows, SlotSPE yields substantial improvement over this baseline. Moreover, removing any of the four key components of SlotSPE results in consistent performance drop across most datasets (Rows 2-6), indicating that each module contributes critically to the framework. Specifically, excluding selective slot attention reduces the model's 's ability to focus discriminative prognostic patterns; removing cross-modal reconstruction with biological priors weakens the alignment between histology and genomics; and dropping iterative cross-attention impairs the iterative refinement needed capture complex cross- modal dependencies. Slots regularization reconstruction further helps prevent null slots. Overall, the full SlotSPE achieves the best performance, with an average C-index of 0.721, demonstrating that all four modules act synergistically to enable effective multimodal survival prediction.
4.6 EFFICIENCY
In this section, we assess the inference efficiency of our model by comparing it against the four strongest baselines listed in Table Because all methods share the same WSI and omics encoders, we exclude these components and evaluate only the model-specific modules to ensure a fair and meaningful comparison. We measure peak inference memory and wall-clock time on the COAD- READ dataset, using all WSI patches during inference and configuring SlotSPE with 16 slots and 3 iterations. As shown in Figure 4. SlotSPE achieves the highest C-index while maintaining low run- time and memory usage. MCAT and MOTCAT achieve shorter runtime primarily because they omit self-attention computations within WSI patches; however, this design choice leads to a consider- able drop in predictive performance. CMTA improves upon these baselines by employing Nyström attention (Xiong et al. 202I) as an approximation to full self-attention, but its capacity remains in- sufficient to capture the sparse, patient-specific structural prognostic signals. LD-CVAE attains the second-bes best performance, yet its reliance on a variational autoencoder introduces substantial mem- ory and runtime overhead. Overall, SlotSPE offers the most favorable balance between efficiency and predictive performance, with minimal memory usage and the recond-fastes. runtime among all compared methods. Additional analysis is provided in the Appendix G
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A
Patient ID: TCGA-A1-AOSP (BRCA)
Whole Slide
Histology Assignment Map
Genomic Slot Assignment Map
B
Histology
Genomic
Set
Sket
Figure 5: Interpretability of slots. (A) Original WSI, assignment map of histology- slots, and assignment map of omics-derived slots. (B) Attention maps for each slot with the top-5 most relevant patches highlighted. (C) Top-3 relevant and irrelevant pathways identified per slot.
4.7 INTERPRETABILITY
Cross-modality Alignment. Visualization of slot assignments (Figure 5AA shows that histology- and genomics-derived slots often align to structurally similar tissue regions in WSIs, reflecting event-level cross-modal consistency. Subtle differences remain, which can be attributed to modality- specific information: morphology-driven slots emphasize structural patterns, whereas genomics- driven slots highlight regions linked molecular features. Intra- and Inter-modal Interactions. For intra-modal analysis, we visualize attention maps of histology-derived slots (first three plots in Figure 5) and report the top-3 most relevant and irrelevant pathways per omics-derived slot (Fig- ure 5C). For inter-modal analysis, we link pathway-level attention scores with the corresponding genomic-slot attention maps WSIs (last three plots in Figure ()). For instance, in Slot 2, highly attended pathways correspond to uumorenniched regions, consistent with prior studies on breast cancer prognosis (Wang DuBois) 2010, Neman et al., 2014:) Chen et al. 2019) Ta et al. [00T]] Xie et al. 2023). In general, these interpretability analyzes demonstrate the ability of SlotSPE to establish event-level alignment across modalities and reveal moophooyy correspondences, offering the potential for biologically plausible explanations and new hypotheses for further valida- tion. Additional examples are provided in the Appendix]]
5 CONCLUSION
In this work, we introduced SlotSPE, a blot-based framework for structural prognostic event mod- cling in multimodal cancer survival analysis. By compressing high-dimensional histology and omics data into interpretable slots, selectively activating the most predictive ones, and aligning them through biologically guided cross-modal reconstruction, SlotSPE effectively captures sparse, patient-specific prognostic events and effectively reduces the computational complexity of multi- modal interactions. Our extensive evaluation across ten TCGA cohorts demonstrates that Slot- SPE not only achieves state-of- -f-the-rrt predictive performance but also maintains robustness under missing-modality
missing- modality conditions. Moreover, the interpretability analyses highlight its ability to uncover event-level -molccll correspondences. These results underscore the potential of Slot- SPE a powerful and interpretable framework for multimodal precision oncology.
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ACKNOWLEDGMENT
We gratefully acknowledge Dr. Juan He from the Department Pathology. the First Affiliated Hos- pital of Guangxi Medical University, for her assistance in providing the patch annotations for our visualizations. This work was supported by the King Abdullah University of Science and Tech- nology (KAUST) Office of Research Administration (ORA) under Award Nos. REI/1/5234-01-01, REI/1/5414-01--11 REI/1/5289 11899900--00 01-01, REI/1/5404-01 0001000044-0 REI/1/5992-01-00 and URF/1/4663-01 01. Additional support was provided by the Center of Excellence for Smart Health (KCSH) under Award No. 5932, and the Center of Excellence on Generative Al under Award No. 5940.
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APPENDIX TABLE OF CONTENTS
The Use of Large Language Models (LLMs)
19
Method Details
19
B,
Problem Formulation
19
Details of Selective Slot Activation
19
Details of Reconstructions
20
4 Details of Multimodal Interactions
20
B.5
Details of Overall Loss
20
Datasets and Implementations
21
Comparisons with SOTAS
22
Robustness and Risk Stratification
23
Ablation Study
25
Component Validation
25
F2
Histology Encoder ablations
................................
25
Hyperparameters Ablations in Slot Attention
26
F3.1
Slot Numbers Ablations
26
E3,2
Slot Attention Iterations Ablations.
28
F.4
H Hyperparameters Ablations in Selective Slot Activation
29
F4.1
Top-K Slot Selection Ablations
29
F4.2
Softmax Temperature Ablations
29
Efficiency Analysis
30
Inference Runtime and Memory
30
G.2
Training Runtime and Memory
30
G.3
Module-level Cost Breakdown
30
H
Clinical Utility
32
Multivariable Survival Analysis
32
H.2
Calibration, Decision Analysis, and Risk Stratification
32
Interpretability
33
Patient-level Interpretability
33
1.2
Cohort-level Interpretability
36
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A THE USE OF LARGE LANGUAGE MODELS (LLMs)
In this work, we use Large Language Models (LLMs) to correct grammar mistakes and polish the writing.
B
METHOD DETAILS
B.1 PROBLEM FORMULATION
(8) x (00) ,c()) where X (i) denotes the Given the i-th patient with multimodal inputs I (x()
pathology data, x denotes the genomic profile, 100 E (1,..., [i) is the discretized survival time interval (risk band), and cl)) E {0, 1} the censoring indicator (c(1)
for observed event, (( for right-censoring) Following the multiple instance learning (MIL) paradigm (Chen al. 2021b Jaume et al. 2024). features extracted from the WSI patch encoder and gene encoder are Ms Rd دزر and X { TR
M, رسر where Mr and My denote the numbers of WSI patches and biological pathways, respectively, and d is the feature dimension. The objective is to learn FB Nr x X, + R mapping (x)") xx')) + z(1) for
organized bags of instances: (
(5) hJ
s.j
survival prediction. We denote by (0) the predicted hazard probability at a discrete time interval I, ie., the probability of event occurring at given survival up to t. The survival funetion is s. With Np patients in the training set, the hazard, survival, and the negative log-likelihood (NLL) loss Zadeh Schmid 2020) are:
( = T S
II
1 - (1)
1i) Lourrv (earr((2/))) (1x10) (1)
log s/t + (1 - ) ) log ((t)
((0 + (1 (1) log h ( p(0)
|i=1
(8)
B.2 DETAILS OF SELECTIVE SLOT ACTIVATION
To achieve sparse yet differentiable slot selection, we adopt the Gumbel-Top-K (Gubell, 1954
Maddison et al.] 2014 Kool et al. 2019) trick combined with a Thrighh (ST) estima-
tor (Jang et al. 2016).
Given slot scores r E S.S add i.i.d. Gumbel noise 9k Gumbel(O, 1):
Fs Fk + gk.
This perturbation transforms deterministic scores into a stochastic sampling process where larger Tkk values are more likely be selected. To obtain differentiable relaxation, then apply softmax to the perturbed scores:
softmax(F).
(10)
In practice, we use an ST estimator that combines hard mask for the forward pass with soft relaxation for the backward pass:
G + onehot.topk(a) + (a stopgrad(at)).
(11)
where onehot_topk()) produces discrete K-hot mask in the forward pass, while gradients flow through the soft assignment a.
Finally, the selected slots are reweighted by masking and renormalizing the softmax weights in Eq, which ensures that only the top-K slots contribute, while their relative importance is adaptively normalized. The resulting G E [0, 1 acts as a differentiable K-hot mask, enforcing sparse slot selection while preserving end-to-end trainability.
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B.3 DETAILS OF RECONSTRUCTIONS
Slots Regularization as Reconstruction. Within each modality, slots S are required to reconstruct the original mopelity-specific features address the emergence of null slots. We Transformer decoder (Vaswani et al. 2017) as the reconstruction head. For genomics, slot embeddings S, are decoded to approximate the original pathway embeddings Xg. guided by the positional embeddings Qg (Eg. 5). with reconstruction optimized via MSE loss:
X R(Qq Sy),
Le |X X
(12)
For histopathology, reconstructing entire WSIs is infeal sible due to their scale and random patch sampling. Instead, we employ a fixed MLP to map the original patch features X₁, to query em- beddings Qu. The WSI slots S₁, are then decoded back to patch-level embeddings, with cosine similarity enforcing feature-level consistency:
M
X, = =,, Sp),
L C =
Σ
cos Xh.j).
(13)
M,
Cross-modal Reconstruction. To capture molecular molccular-morpholee morphological mappings, we introduce a cross-modal reconstruction task in which omics-derived slots are guided to predict pathway embed- dings from histopathology. Specifically, WSI patch features are re-encoded through omics-derived slots Sg and decoded to approximate Xg with MSE loss:
X R(Qg: Sggg))
recon
| x,1
(14)
B.4 DETAILS MULTIMODAL INTERACTIONS
In contrast to one-shot co-attention methods (Chen et al. 202 Xu & Chen 2023 Jaume et al,, 2024]. we employ an iterative cross-attention scheme that reuses a single fusion layer for L iter- ations of bidirectional updates. At each iteration I, omics- and histology-derivee
slots alternately attend to one another, absorbing complementary information while preserving their own context recurrent updates, akin to slot attention. This iterative design supports multi-step fusion, progres- sively aligning molecular and morphological evidence that may require hierarchical inference (c.g.. molecular dysregulation propagating through cellular morphology to tissue-level structure (Huang jet al. 22255). Concretely, iteration the update of histology slots attending to omics slots is defined as
A ( h = softmax 2(S ) (T
SAXS, E E
U = A hog V(S
va
(15)
$(+1) RNN(S "
S((+T)
s + ( MLP(S
with symmetric update for omics slots attending to histology slots. Repeating for / = (0. T.-
}} yields progressively aligned multimodal slot representations.
In parallel with cross-attention, each modality undergoes intra-modal self-attention, yielding refined representations S, and Sy. To form the final multimodal representation, we compute pooled sum- maries (mean slots) and concatenate three branches outputs:
z = (o)l((S..($,)) || Pool(S..)
|| (So))( E 3d
(16)
where || denotes concatenation along the slot dimension and Pool(-) indicates mean pooling over slots. Finally, a prediction head maps to discrete risk classes, with training jointly optimizing the survival loss and the auxiliary reconstruction losses described above.
B.5 DETAILS OF OVERALL LOss
The total training objective of SlotSPE is
L Ceurv + XCrecon-
(17)
where À balances the survival and reconstruction components. The survival loss Leary consists the survival prediction loss together with each single-modal modal survival losses. The single-modal survival
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predictions, i.., M/ (histology) and By (genomics) in Eq. 18| obtained by applying their modal- specific MoE decoders to the corresponding slot representations. S₁, and Sy. These single-modal survival losses incorporate task supervision for the gated slot logits yh and yy-
Laury = Su, (,) + C (yn, 1, c) + Laur t,)
(18)
while Lrecon combines the slots regularization and cross-mos modal reconstruction objectives:
Lrecom = L + Crocon + Laocon
(19)
C DATASETS AND IMPLEMENTATIONS
Dataset, We perform comprehensive evaluations across ten publicly available cancer cohorts from TCGA including Breast Invasive Carcinoma (BRCA), Bladder Urothelial Carcinoma (BLCA), Colon and Rectum Adenocarcinoma (COADREAD), Stomach Adenocarcinoma (STAD), Head and Neck Squamous Cell Carcinoma (HNSC), well Lung Adenocarcinoma (LUAD), Lung Squa- mous Cell Carcinoma (LUSC), Kidney Renal Clear Cell Carcinoma (KIRC), and Skin Cutaneous Melanoma (SKCM). Case counts for each dataset are listed in Table [ Following (Jaume al.) 2024). we predict disease-specific survival (DSS), more precise indicator of patient status than overall survival. Histological data include all diagnostic WSIs, while transcriptomic profiles with DSS labels are obtained from cBioPortaf"] Pathway gene sets are curated from Hallmarks (Subra- maanian et al. 2005 Liberzon et af., 5015) and Reactome (Gillespie et al. 2022). with genes absent in cBiooortal removed, yielding 330 pathways.
Evaluation. We adopt 5-fold cross-validation and report the concordance index (C-index) (Har- rell Jr et al. 1996) together with the standard deviation (std) across folds. To further assess clinical relevance, we visualize Kaplan-Meier (KM) survival curves (Kaplan Meier 1958) for stratified risk groups and apply the log-rank test (Mantel et al. 1966) to evaluate global differences in sur- vival distributions. In addition, we compute the restricted mean survival time (RMST) (Irwin 1949) Karrison (986). RMST,, defined as the area under the estimated survival curve up clinically meaningful truncation time (60 months in our experiments), provides an interpretable summary of the average survival time within the specified horizon and does not rely on the proportional haz- ards assumption. We report: (a) the RMST values for both high- and low-risk groups, (b) the RMST difference (A = High-Low) with a 95% bootstrap confidence interval (CI) and a two-sided p-value testing whether the difference is significantly different from zero, and (c) the RMST ratio (High/Low) with a log-transformed 95% bootstrap CI scale-free measure of group separation. To ensure robust inference, both CI and p-values are estimated from 1000 bootstrap replicates (Tib-) shirani& Efron 1993). These statistics are annotated on the KM plots, providing an interpretable and robust evaluation of prognostic stratification.
Taken together, the three metrics are complementary: the C-index measures overall ranking con- cordance of predicted risks, the log-rank test evaluates survival curve separation under proportional hazards, and RMST provides a clinically grounded and assumption- light measure of absolute and relative survival differences.
Implementation. Tissue regions are segmented from WSIs, and non-overlapping 256 x 256 patches extracted 20x magnification. We adopt UNI (Chen et al. 2024) as the patch encoder and SNNs as the pathway encoder. The method is implemented in Python using PyTorch and executed on only one NVIDIA A100 GPU. For survival prediction, disease-speciff survival (DSS) time is discretized into four intervals. Bag features are embedded via an MLP with a 512-dimensional hidden layer and 256-dimensional output, thus d and dstot all set to 256. The number of iterations for slot attention is set to T = 10. and for iterative aross-attention to L = 3. The top-K in selective slot activation decoder is set to 25% slot numbers since patients are divided into 4 risk groups. We report the best performance by ablating the slot numbers in Appendix F.3. Pathway tokens are reconstructed using MSE loss, while histopathology tokens are optimized with cosine similarity loss using hyperparameter À = 0.1 (searched from [0.01, 0.1, 1.0).. To support batch training, 4096 patches are randomly sampled per WSI, whereas all patches are used during inference. Optimization is carried out with Adam (Kingma & Ba 2014) at a learning rate of 5 x 10 All models are trained for 30 epochs with a batch size of 32.
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Table Comparison of C-index (mean + std) across ten cancer datasets using biological pathways. Best and second-bes's results are in bold and underline.
BRCA
COADREAD
KIRC
UCEC
LUAD
Model
Modality
Overall
(N=1046)
(N=573)
(N=488)
(N=488)
(N=467)
MLP
R-
0.6444 0.097
0 0.053
0.750+ 0.035
0.731 0.071
0.6344 0.069
SNN
R.
0.645=0.086
0.664+0.021
0.754+ 0.038
0.753+ 0.071
0.652# 0.063
SNNTrans
R.
0.657=00000
0.710=0.053
0,747:00035
0.724:0.061
0.648=0.059
SlotSPE
0.698=0.046
0,733=00,05
0.774++0.02
0,752=+0.06
0.646=0.064
ABMIL
0.65610.037
0.71510.029
0.782:10.026
0.779.10.057
0.645:0.006
TransMIL
b.
0.647=0.082
0.723++0.022
0,767+40.05
0.759+400099
0.655=0.052
CLAM-SB
b.
0.696=0.049
0,742=000046
0,784+00033
0.757=00,072
0.639=0.059
CLAM-MB
b.
0.715=0.034
0.701
0.782:40.014
0.788=0.074
0.632=0.070
SlotSPE
0.738=0.019
0.729=0.038
0.790=200023
0.779=00057
0.656=0.038
Porpoise
g.th.
0.651 100046
0..0000.050
0.788.10.028
0.788
0.647_10.01
MCAT
g.th.
0.709
0.737.00033
0.795110.018
0.80210.060
0.659L0.054
MOTCal
g.th.
0.717..0.04
0.742.10.02
0.79910.013
0.773.10.060
0.663.1..022
CMTA
g.+b.
0.701
0,720= 008
0.794=0.018
0.764:0.069
0,662=0.053
SurvPach
g.+b.
0.728=0.040
0.727=0.024
0.787=0.025
0.751=0.084
0,661=0.050
PIBD
g-+b.
0.662=0.054
0.716#0.054
0.772+00007
0.783=20003
0.634=0.065
MMP
g.
0.714 = 0.050
0.686 + 0.016
0.770 =0.011
0.755 +0.073
0.634 = 0.048
LD-CVAE
g.
0.705=0.050
0.753=0.029
0.792:10.025
0.788:00068
0.651=0.055
SlotSPE (8 slots/mechality)
g-th.
0.748 0.052
0.759
0.802:10.009
0.807.10.06
0.653:00.56
SlotSPE (T 3)
g.+b.
0.752=0.056
0.763+0.031
0.817:10.000
0.788:0.067
0.672=0.056
SlotSPE
g.+b.
0.779
0.773:20042
0.81540.017
0.813:100099
0.683=0.058
LUSC
HNSC
SKCM
BLCA
STAD
Model
Modality
Overall
(N=460)
(N=438)
(N=409)
(N=381)
(N=366)
MLP
g.
0.584=0.072
0.584=0.061
0.652-0:038
0.677:40003
0.615=00.033
0.653
SNN
0.548_00.04
0.5979
0.603_.0.21
0.69410..00
0..058
0.656
SNNTranS
g.
0.555 0.042
0.605
0.684_..029
0.69910.033
0.0033
0.662
SlotSPE
g.
0.056
0.6011
0.678_0.025
0.701
0.50610..33
ABMIL
h.
0.593=0.055
0.664:20043
0.668=0.042
0.603:20.072
0.64220.044
0.681
TransMIL
h.
0.582=0.039
0.644=0.020
0,632=0.050
0.647=t0.032
0.656=0.038
0.671
CLAM-SB
h.
0.584=0.065
0.649=0.042
0.643=0.049
0.645:20.022
0.637=0.022
0.678
CLAM-MB
h.
0.608=0.056
0.636:0.038
0.640=0.032
0.657:00.09
0.641=0.032
0.682
SlotSPE
b.
0.598=0.054
0.635=0.038
0.659=0.063
0.642:20.035
0.67620.033
0.690
Porpoise
g.
0.597 0.050
0.099
0.682-0.021
0.690
0.619:00022
0.676
MCAT
g.
0.583=0.051
0.622:1.049
0.667=0.049
0.688:0.024
0.63920.032
0.690
MOTCat
g.
0.573=0.026
0.627:0.049
0.688=0.054
0.700100010
0.642:0.019
0.692
CMIA
g.
0.599000071
0.619:10051
0.681=0.036
0.702:20003
0.63920.038
0.691
SurvPath
g.+h.
0.577=0.024
0.611:0.024
0.666=0.054
0.666:10.034
0.64710.027
0.682
g.
0.575=0.098
0.627:0.069
0.649_0.048
0.693:100022
0.64420.038
MMP
g.
0.580 0.043
0.580 1: 0.049
0.682 = 0.029
0.686 1 0.004
0.602 : 0.020
0.669
LD-CVVE
g.
0.020-0.045
0.635:10.051
0.682_00037
0.635:10.037
0.65310.036
0.692
SlotSPE (8 slots/modality)
g.
0.620-0.055
0.642+0..35
0.688-0.051
0.705+00.037
0.637+0.018
0. 0.706
SlotSPE (T 3)
g.+h.
0.610-00644
0.624+0.052
0.676=0.056
0.703+40.03
0.657=0.048
0.704
SlotSPE
g.+h.
0.079
0.642400.35
0.688-00011
0.708=00.025
0.671+00028
0.721
D COMPARISONS WITH SOTAS
The complete results with standard deviations (std) for Table using the biological pathway format for gene data, are provided in Table In addition, we also report results using slots per modality and T 3 iterations in slot attention, with further ablations the number of slots provided in Appendix F and on the number of iterations in Appendix FF3.2. The results demonstrate that even with very small number of slots for both histopathology and genomics, SlotSPE maintains strong performance, indicating that the slots effectively capture structured prognostic events through highly compressed representations.
To further assess the generalization ability of our approach, we compare SlotSPE with other multi- modal methods under a higher-level grouping of genes into six functional categories (Subramanian
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Table 5: Comparison of C-index (mean + std) across ten cancer datasets using six gene functional groups. Best and second-bes results are in bold and underline.
BRCA
COADREAD
KIRC
UCEC
LUAD
Model
Modality
Overall
(N=1046)
(N=573)
(N=488)
(N=188)
(N=167)
Porpoise
g.+h.
0.681+00075
0.742+00038
0.778+-0.023
0.798
0.655+0.006
MCAT
g+th.
0.706:00.038
0.736=0..22
0.797:2.0188
0.800=0.065
0.641=0.062
MOTCat
g.th.
0.683:10.031
0.759=0.039
0.7911000110
0.808=0.041
0.683=0.057
CMTA
g.+h.
0.670=+0.031
0.751=+0.00
0.729-00.12
0.779=0.059
0.644=0.031
SurvPath
g-th.
0.707:+0.049
0.751
0.7001
0.764=0.072
0.663=#0.000
PIBD
g.+h.
0.683::00016
0.733=00030
0.791110.019
0.774=0.054
0.649=0.077
MMP
g.+h.
0.684 1:0.081
0.699 0.032
0.767:100017
0.772=0.056
0.643=0.041
LD-CVAE
g.+h.
0.695:000033
0.736=00029
0.797+40.025
0,792=0.052
0.677=0.050
SlotSPE
g.th.
0.735:00.011
0.780=10044
0.804:10.020
0.824:0.062
0.669=0.063
LUSC
HNSC
SKCM
BLCA
STAD
Model
Modality
Overall
(N=460)
(N=438)
(N=109)
(N=381)
(N=366)
Porpoise
g.+h.
0.585=0.065
0.617=0.058
0.674=0.035
0.683:10.040
0.620:10.036
0.683
MCAT
g.+h.
0.571=0.056
0.658=0.025
0.679=0.041
0.682:10.029
0.630=10.011
0.690
MOTCat
g.+h.
0.578:00053
0.634:0.036
0.688=0.049
0.689:10.045
0.657:000007
0.692
CMTA
g.+h.
0.582=00.048
0.651
0.667=0.031
0.682:40.039
0.627=10.045
0.684
SurvPuth
g.+h.
0.564=0.033
0.636=20.36
0.658=0.064
0.707:10.049
0.637:40.22
0.686
PIBD
g.+h.
0.595=00.100
0.626=0.029
0.649=0.037
0.676::0.058
0.648:10.04
0.682
MMP
g.+h.
0.584:0.048
0.588=00054
0.667=0.034
0.680+1.051
0.597:10.029
0.668
LD-CVAE
g.+h.
0.613-40.051
0.633-20.035
0.645=00.00
0.68440.043
0.663-40.041
0.693
SlotSPE
g.+h.
0.616:00.099
0.645=0.030
0.679=00035
0.70144.0026
0.667-10.017
0.712
et al. 2005 Liberzon et al., 2015 Chen et al. 2021b Xu & Chen 2023 Zhou & Chen 2023):
tumor supression, oncogenesis, protein kinases, cellular differentiation, transcription, and cytokines and growth. In this setting, the number of gene slots is fixed to six, while the number of histopathol- ogy slots is varied and the best performance is reported. Results in Table 5 show that SlotSPE achieves the best overall performance, ranking first or second in 8 out of 10 cohorts, and outper- forming the second-best method (LD-CVAE) by 1.9% on average. This indicates that even when genes are grouped into higher-level functional categories, our SlotSPE is able to maintain strong predictive performance across different granularities of gene input.
E ROBUSTNESS AND RISK STRATIFICATION
The complete results with standard deviations for Table 2 using the biological pathway representa- tion for gene data, are reported in T While most baselines are not explicitly designed to handle missing modalities, they can still be evaluated under coissing-genonee
settings by supplying a neu- tral placeholder input in place of genomic features (Zhang et al. (205)). For completeness, we also include two strong methods (MOTCAT and CMTA). The results show that when these approaches rely solely on histology histology-withutt modeling reconstructing genomic information-tie tic performance drops substantially. Moreover, under missing- geesinngeenomcs conditions, their limited worse than strong single-modal baselines (e.g., ABMIL).
prognos-
robustness leads performance
Kaplan-Meies curves for all ten datasets are shown in Figure 6 For clarity, Table 7 summarizes four complementary statistics: (a) log-rank p-values across all cancer types, (b) RMST values for both high- and low-risk groups, (c) the RMST difference (A = High-Loow) with 95% confidence intervals, and (d) the RMST ratio (High/L Low) with 95% confidence intervals. Across most datasets, SlotSPE consistently achieves larger RMST differences (Because A is typically negative, a "larger" separation corresponds
more negative value, i.e. smaller numerically but larger magnitude) and smaller RMST ratios than competing methods, demonstrating clearer prognostic separation. Even in datasets where performance is comparable (e.g., KIRC, LUSC, HNSC), SlotSPE generally maintains equal or better significance with tighter confidence intervals.
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COADREAD
UCEC
LD-CWAE
LD-CVAE
(Missing))
Ours (Missing)
LUSC
HNSC
SKCM
BLCA
STAD (-A
LD-CVAE
LD-OVAE
(Missing)
Ours (Misiing)
Figure 6: -eplen-Meier curves of predicted high-risk and low-risk groups. A p-value < 0.05 at the top indicates statistically significant separation between groups. The restricted mean survival time (RMST) up to 60 months is also reported, with values shown as A (High-Low), and RMST ratio (High/Low). (Zoom in view details.)
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Table 6: C-index (mean + std) across ten cancer datasets under missing-genomies settings. The column Missing indicates whether the genomic modality is missing (V missing), Best and second- best results are highlighted in bold and underline.
BRCA
COADREAD
KIRC
UCEC
LUAD
Model
Missing
Overall
(N=1046)
(N=573)
(N=488)
(N=488)
(N=467)
MOTCAT
0.600=0.077
0.645+0..028
0.738:0.034
0.659
0.643++0.03
CMTA
0.604=0.112
0.683+0.005
0.662:t0.045
0.676:0.122 124
0.593=#0.051
LD-CVAE
0.705=0.050
0.75340.029
0.792:10.025
0.788=10.068
0.651=200055
LD-CVAE
0.715=000066
0.736:10.042
0.798::0.014
0.775=:0.073
0,638:100116
SlotSPE
0.779=10061
0.773-10.042
0.815:10.018
0.813-10.099
0.683:10.057
SlotSPE
0.734=0.056
0.741=10004
0.789=100299
0.802=0.047
0.663:10.044
LUUCC
HNSC
SKCM
BLCA
STAD
Model
Missing
Overall
(N=460)
(N=438)
(N=409)
(N=381)
(N=366)
MOTCAT
V
0.540=0..04
0,578:10.030
0.642=0.050
0.565:20.098
0.385=0.071
0.619
CMTA
0.541=0.045
0.564:10.074
0.541:0.048
0.538:0.054
0.608:0.065
0.603
LD-CVAE
0.620=000055
0.635:H0.051
0.682:00.037
0.635-+0.037
0.653=#0.036
0.692
LD&CVAE
0.596#0.002
0.649:10.049
0.676#0.038
0.644440.048
0.647:0.049
SlotSPE
0.634
0.642:10.035
0.688=0.051
0.708:10025
0.671=0.028
0.721
SlotSPE
0.634:10.022
0.649:10.031
0.678=0.068
0.678:10041
0.677=00029
0.704
Table 7: Summary of log-rank p-values and RMST-based statisties (RMST values, differences, and ratios) for group separation across ten cancer datasets in Figure 6
Dataset
Method
Log-rank p-value
RMST (Low)
RMST (High)
(High-Low) (95% CII
Ratio (High/Low) 195% CI)
LD-CVAE
3.75
55.0
1.50 -188
0.94 [0.91, 0.97]
BRCA
SIatSPE
6,84 10-8
59.2
53.9
-5.3 (-6.9.-3.8)
0.91 (0.88,0.94)
LD-CVAE
9.48 10-6
$5.0
46.1
-8.9 (-1.444,,
0.84 [0.78, 0.900
SleSPPE
10-7
55.1
45.3
.9.8 [-1.6,,,,
0.82 [0.76, 0.89)
I.D.VAEE
4.13 10
(-16,
[0.71,
KIRC
S1atPE
3.08
57.3
44.1
-13.2 1-16.4-10.1
0.77 [0.72, 0.82)
LD-CVAE
1.76 x 10
53.6
53.6
-2.11-5.0, 0.81
0.96 [0.91, 1.00]
UCBC
SloSPE
1.33 10-7
58.5
51.1
-7.40-1000, -4.9]
0.87 [0.83, 0.92]
LD-CVAE
10-2
46.5
42.0
[-.4 10.1]
0.90 [0.82, 1.00)
LUAD
SlaSPE
-11.91-16.3 -7.6
0.84]
LD CV-E
7.70 10
42.9
1-12,,11,,3.61
0.85 [0.77, 0.93)
LUSC
SlotPE
1.07 x 10
50.0
42.9
-7.1 (-11,,5,,
0.86 (0.78, 0.95)
LD-CVAB
2.83 10-"
48.2
39.6
-8.7 (-12,9-19
0.82 [0.74, 0.91]
SletSPE
10
(-.94-12.4.-3.4)
0.83 [0.75, 0.93]
LDDCVAE
(.9..
[0.82, 0.96]
SKCM
SloSSP
1.03 x 10
54.1
43.8
-10.3 [-1388 -6.7]
0.81 (0.75, 0.87)
LD-CVAE
2.74 10-4
44.8
35.1
.9.7 [-15.3, -4.4]
0.78 [0.68, 0.90)
SiaSPE
5.37 10
46.3
33.9
-12.4 1-17.6, -7.11
0.73 [0.63, 0.84
LD-CVAE
-9.6
0.79
STAD
SloeSPE
-12.3 (-18
[0.63, 0.85]
ABLATION STUDY
F.1 COMPONENT VALIDATION
The complete results with standard deviations for Table using the biological pathway representa- tion for gene data, are reported in Table
F.2 HISTOLOGY ENCODER ABLATIONS
To assess the robustness of SlotSPE to the choice of visual encoder, first replace the histology coder with a ResNet50 (Srivastava et al. 20133 He et al.) 2016) pretrained only on ImageNet (Deng et al. 2009), rather than a pathology-specifi foundation model. This setting tests whether SlotSPF:
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Table 8: Ablation of model components reported C-index (mean + std) across ten cancer datasets. Best and second- best results are in bold and underline.
BRCA
COADREAD
KIRC
UCBC
LUAD
Variants
Overall
(N=1046)
(N=573)
(N=488)
(N=488)
(N=467)
Baseline
0.71110.052
0.734110021
0.784=0.010
0.779=00081
0.661=0.059
w/o Selective Slot Attention
0.728=00057
0.755+0.030
0.787=0.011
0.800=0.064
0.659=000667
w/o Slots Regularization
0.734=0.065
0.763++0.029
0.794=0.017
0.811=0.069
0.663=000053
w/o Cross-modal Reconstruction
0.710:10.067
0.758:10.027
0.787=00008
0.794-10.056
0.663-10.062
w/o Iterative Cross-atention
0.727:40.331
0.761:10.033
0.003
0.794:10.056
0.653+:0.022
SlotSPE
0.779-10.011
0.773:10.042
0.015
0,813:10.059
0.683-10.057
LUSC
HNSC
SKCM
BLCA
STAD
Variants
Overall
(N=460)
(N=138)
(N=109)
(N=381)
(N=366)
Baseline
0.592+00.04
0.610-0.056
0.668+00.043
0.686+0.030
0.644+-0.001
0.687
w/o Selective Slot Attention
0.620+0.071
0.615=0.045
0.685++0.052
0.688+0.042
0.650++0..06
0.699
Slots Regularization
0.61110.060
0.621=0.061
0.679:10.053
0.6931100388
0.667.10.018
0.704
w/o Cross-model Reconstruction
0.619110,90
0.611=0.058
0.671
0.698
0.645.10.017
0.696
w/o Itcrative Cross-attention
0.602:0.071
0.624=0.048
0.676::0.039
0.702=00024
0.648:100.017
0.699
SlotSPE
0.634:10.079
0.642-0.035
0.688:10.051
0.708=00025
0.671=0.028
0.721
Table 9: Comparison of C-index (mean + std) across five datasets using ResNer50 as histology encoder. Best and second-best results are in bold and underline.
BRCA
COADREAD
KIRC
UCEC
LUAD
Methods
Modality
Overall
(N-1046)
(N=573)
(N=488)
(N=488)
(N=467)
TransMIL.
g-
0.008
0.641
0.661+400036
0.690+00088
0.5954
0.640
CLAM MB
0.57340.035
0.616:0.081
0.637::0076
0.655:100092
0,50010.006
0.620
MCAT
g.+h.
0.694:0.074
0.712=00034
0.75440.023 023
0.7711:0002
0.633:100058
0.713
MOTCAT
g.+h.
0. 0.706:00002
0.674=0.034
0.752:10.026
0.790:10.053
0.637:10.054
0.711
SurvPath
g.
0.650=00.038
0.674::0.05
0.743:10.037
0.761:10.022
0.643::0.046
0.694
LD-CVAE
g.+h.
0.656:00.01
0.676:10.055
0.714:10001
0.733:10008
0.620110.037
0.680
SlotSPE
g-+h.
0.730:00002
0.030
0.769:10.024
0.775:10.052
0.645:10.064
0.730
can still achieve strong performance when the visual backbone lacks domain -spccffc pretraining. For this experiment, we evaluate representative unimodal and multimodal baselines listed in Ta- [ As summarized in Table D SlotSPE continues to outperform all baselines under this weaker configuration, suggesting that its performance is not tightly coupled to specialized encoder. We further extend this analysis by examining SlotSPE with recent pathology foundation models, includ- ing CONCH (Lu al. 2024), CONCH v1.5 (used in TITAN (Ding et al.) (025)), and UNI (Chen) et al. 2024). The results in Figure 7 show that performance varies across different encoders: while recent pathology foundation models generally improve results compared to ImageNet- preetrrind encoder. the best performance is obtained with UNI. These results indicate that SlotSPE is both ro- bust to weaker, non-specialized encoders and compatible with strong sethology-speciffe foundation models.
F.3 HYPERPARRMETTRR ABLATIONS SLOT ATTENTION
F
SLOT NUMBERS ABLATIONS
Figure illustrates how the number of slots for histology (Sr) and genomics (S,) affects perfor- mance across six TCGA cohorts. In most cases, increasing the number of slots usually improves performance compared to the minimal baseline (red line), suggesting that additional slots enable the model to capture broader set of prognostic events. However, beyond moderate slot size (e.g., 16-32 slots), further increases often yield little to no gain, and in some cases even slight declines, indicating that excessive slots may introduce redundancy or prognostic irrelevant patterns.
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Mode Performunce sovvss Offorent Houndaiinn Hucds
Madel Pertrmmnc acrves Ontoreed hourdittonn Hoddts
Vedel Ps flemmncc scos Officer Foundation Models
0813
0.17
8.811
1,4e
6204
DONGH
71/49
AtsRe150
CONCH
11:AM
Asskend
CONTO
11AW
UMM
BRCA
COADREAD
KIRC
Figure 7: Effect of different foundation models used as histology encoders. Performance (C-index) shown for three cohorts (BRCA, COADREAD, KIRC) using four backbone encoders: ResNet50, CONCH, TITAN, and UNI. Bars represent mean across five folds, with error bars indicating standard deviation. Higher values indicate better performance.
BRCA
COADREAD
KIRC
0.35
0.225
Grouped by Sy.
0.00
0.735
0.33
0.99
0475
30
126
0332
120
120
122
120
Grouped by Sg
020
0.93
0323
6.755
0.79
6.73
0.70
0.0
am
420 160
144
023
UCEC
LUAD
LUCC
0.95
Grouped by Sh
0.00
0.99
Clncea
0.53
609
0.2
0.30
59
120
10
20
407
8
100
140
126
110
15
126
110
02
120
100
126
120
Grouped by S
124
031
91
40
10
10
27
15 20
67
84
d4
144
1208
161
08
100
40
m0
R.60
60
Figure 8: Ablation on slot numbers. Boxplots show C-index across cohorts as the number of histol- ogy slots (Sr, top) and genomic slots (S,, bottom) varies, with the x-axis indicating the pair (S₁. S2). The red line denotes the baseline with the minimum slot setting. Increasing the number of slots generally improves performance, though gains plateau once saturation reached.
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Model www.oreeeoooeooooooooo Drraar (7)
Hod WwMe/atomaaassecoo Deilored festice
Hol Nwlormano Roster
6.13
0,90
BRCA
COADREAD
KIRC
(a) Effect of Different Iteration Number in Slot Attention
C.
0,14
0.12
Ng- 190 2290) 1r 10-90
184--307 207AL (099)) 1pp6-
133 VAL tes---22200 Iep-fi 4PMNI Hest-KONM
BRCA
COADREAD
KIRC
(b) Effect Tap-K Stat Selection Selective Slot Activation
rifermmanc acnea Othere. (e
Model tefommane scone 2eturen fampantaore
Vodel Perommnnce acrm fumpertur (Temp)
8.214
lamp
91
3.0
tamp +01
BRCA
COADREAD
KIRC
(c) Effect of softmax Temperature in Selective Stot Activation
Figure 9: Ablation study of hyperparameters, (a) Effect of different iteration number T in the slot attention. (b) Effect of different top- Vop-K(n K (percentage of slots) in selective slot activation (slot number fixed 8). (c) Effect of so aoftmar temperature on in selective slot activation. Bars represent mean across five folds, with error bars indicating standard deviation. Higher values indicate better performance.
F.3.2 SLOT ATTENTION ITERATIONS ABLATIONS.
We ablate the number of iterations T' in slot attention to examine its impact performance shown in Fa). With small number of iterations (T 1), slots are updated only once, limiting their ability to refine representations and capture complex prognostic patterns, which results in lower C-index values (e.g., 0.720 on BRCA). As T increases, slot updates stabilize, enabling better infor- mation bindings and improved outcomes (best at T 10 on BRCA with 0.779). In datasets such as KIRC, performance saturates around = 3-5, suggesting diminishing returns after sufficient updates. Although larger T enhances stability and accuracy, it also increases training time. Over- all, our results indicate that moderate values provide a favorable trade-off between performance and efficiency. For consistency, also report main results under the T 3 setting in Table 4
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F.4 HYPERPARAMETERS ABLATIONS SELECTIVE SLOT ACTIVATION
F.4.1 TOP-K SLOT SELECTION ABLATIONS
We analyze the effect of top-K selection by fixing the slot number to 8 for both modalities and evaluate four settings: top-1 (12.5% all slots), top-2 (25% all slots), top-4 (50% slots), and top- 6 (75% all slots), shown in Figure 9 (b). Using only top-1 results in the weakest performance, which is expected, because patients are divided into four risk groups, activating only a single slot per patient causes several slots to be rarely activated during training. Conversely, when top-K becomes too large (c.g.. top-6), some slots that are not discriminative for a given patient are still forced to activate. While the 25% and 50% settings perform similarly across datasets, we adopt the 25% configuration because it aligns naturally with our design: with four risk groups, selecting roughly one-quarter of the slots provides trade-off between sparsity and coverage.
F.4.2 SOFTMAX TEMPERATURE ABLATIONS
We further evaluate the effect of softmar temperature (denoted temp) in selective slot activation as shown Figure 9 (c). higher temperature (e.g.. temp = 1) produces soft, diffuse gating and results in weaker performance. Lowering the temperature sharpens the gating distribution and leads to more discriminative slot selection, generally improving results. The setting lemp = 0.01 achieves the best C-index across three datasets, and therefore adopt in experiments.
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G EFFICIENCY ANALYSIS
In this section, we analyze the efficiency of our model by comparing it with the four strongest baselines in Table without missing modality setting on identical hardware (An NVIDIA RTX A6000, 48GB). Since all methods use the same WSI and omics encoders, we omit these components and focus our comparison solely on the remaining model modules for more meaningful efficiency assessment.
G.1 INFERENCE RUNTIME AND MEMORY
We compare inference (where all patches are used) peak memory and wall-clock time against model performance the COADREAD dataset. In this comparison, as 16 and iteration as 3. As shown in Figure a) SlotSPE achieves the highest C-index while maintaining low runtime and memory usage. MCAT and MOTCAT achieve shorter runtime primar- ily because they omit self-attention computations within WSI patches; however, this design choice leads considerable drop predictive performance. CMTA improves upon these baselines by employing Nyström attention (Xiong et al. 2021) as an approximation to full self-attention, but its capacity remains insufficient to capture the sparse, patient-specifie prognostic signals. LD-CVAE attains the second- best performance, yet its reliance on a variational autoencoder introduces sub- stantial memory and runtime overhead.
model with slot number
G.2 TRAINING RUNTIME AND MEMORY
We also compare training- time runtime and memory usage. Since the official implementations of MCAT, MOTCAT, and LD-CVAE don't support batch training, we set the batch size to for all methods and randomly sample 4,096 patches ensure fair comparison. For SlotSPE, retain the same configuration of 16 slots and iterations. As shown in Figure [ojb), SlotSPE exhibits moderately higher memory usage and training time compared with its inference cost, primarily due to the additional reconstruction component that is active during training. Nonetheless, its overall training resource footprint remains well balanced and sits near the middle all evaluated methods.
G.3 MODULE-LEVER COST BREAKDOWN
To identify the main computational bottlenecks, Figure [0 reports the module-level breakdown of GPU memory consumption and runtime within SlotSPE. The reconstruction component dominates both memory (45.0%) and runtime (55.4%), accounting for the largest share of training cost. Slot attention ranks second, contributing 26.2% of memory usage and 36.9% of runtime. The remain- ing modules-inchuding the MoE-style decoder, slot interaction, and the final predictor-togetherr account for a relatively small proportion of the overall cost. The heavier cost of the reconstruction branch arises from the inclusion of two slot regularizations for both modalities and one cross-mode modall reconstruction. These reconstruction components are used only during training and are disabled at inference unless the omics modality is missing, in which case the gross-moda reconstruction head is activated.
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Performance vs (Inference) Memory Trade-off
Performance ve (Inference) Runtime Trade-off
0iorre [Dam)
Bac
C Codee
MOTEAY
6,748
NOTGAT
case
11.00
sISRt 1Ound
Susse yound
1000
6/6
0.00
0.55
0.0
0.55
(a) Performance (Inference) Memory//untime Trade-off
Training Memory Comparison
Training Time Comparison
4715.010
3.2
Peek Mernory Ubage (M00)
Voll cook Time (sccggdd sto0)
2:22
0:35
0:1
1048.660
0.028
264.209
012
MCAT
MOTCAT
LD CAKE
CMTA
SlotSPE (Ours)
MCAT
MOTCAT
LD ČVAE
CMTA
Slot5PÉ (Ours)
(b) Training Memory/Runtime Comparison
(Training) GPU Memory Proportions vs. Modules
(Training) Runtime Proportions va. Modules
26.2%
36.9%
45.0%
9.6%
14.5%
6. 2%
4.8%
Reconstruction
Slot Attention
MoE-style Decoder
Slot Interaction
Predictor
(c) Training Memory/Runtime Proportions vs. Modules
Figure 10: Efficiency analysis. (a) Performance vs. inference memory/runtine trade-off across compared models. (b) Training memory/runtime comparison under a unified batch-size setting. (c) Module-level breakdown of training GPU memory/runtime proportions.
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Table 10: Multivariable Cox analysis with clinical variables and SlotSPE predictions. Comparison of clinical-only vs. clinical + model configurations using AUC, IBS, C-index, and AC-index across five cohorts. The clinical variables of the TCGA cohort were downloaded from cBioPortal.
ACC1
IBS
C-index
Cohort
in-index
clinical
elinical-model
clinical
clinical+model
clinical
clinical-model
BRCA
0.731-+0.081
0.782:00006
0.134#00022
0.133+0.022
0.768-+0.058
0.81==0.071
0.053=0.064
COADREAD
0.778++0.053
0. 0.782:0.062
0.138=00017
0,140:10.300
0.780-00072
0.819=0.058
0.040=0.022
KIRC
0.858:10.049
0 0.88910.039
0.137:00.200
0.110:10.021
0.844:10.013
0.868
0.023=00.144
LUAD
0.722:40.114
0.726==0.085
0.176=#0.008
0.174:00001
0.683-0.080
0.739=0.061
0.054=0.044
LUSC
0.6811:0.084
0.747=0.111
0.185:100018
0.166:10.030
0.652:10.059
0.699=0.077
0.047=0.057
Seouteed
030
Deteaated survivel Set
Ratio=0.77
0.6
0.4
0.
High
20
5.1
06
10
Threande Probubility
(4) Calibration Curve (60 months)
(b) Dacision Curve (Positivn Not Banofit Region)
(c) Kaplan-Maier (KM) Curoo 3.08x 11))
Figure 11: Calibration curve, decision curve analysis, and Kaplan Kaplan-Meier Meier risk stratification for KIRC.
H CLINICAL UTILITY
H.1 MULTIVARIABLE SURVIVAL ANALYSIS
To assess whether SlotSP provides prognostic value beyond clinical variables (age, sex, stage, and neoadjuvant treatment), which are empirically shown as crucial prognostic factors (Xu et al. 2019
Tomasello et al. 2017 Edge & Compton, 2010; Yu et al. 2022), we performed multivariable Cox regression (Cox 1972) using both clinical covariates and our model's predicted risk scores. For each cohort, we merged the risk prediction of SlotSPE with these clinical variables on a per-patient basis. Importantly, the risk scores were obtained from the validation folds, ensuring that the model had no access to these samples during training. We then fitted Cox models across the five validation folds to quantify the incremental prognostic contribution of SPotSPE. In Table [00] we report the time- dependent AUC (Heagerty al. 2000) Heagerty & Zheng 2005). integrated brier score (IBS) (Gral) et al. 1999 Gerds Schumacher (2066), C-index for two configurations: (i) clinical-only, using only the clinical covariates, and (i) clinical model, where the predicted risk score of SlotSPE is in- cluded as an additional covariate. We also report the corresponding improvement AC-index. Across all five cohorts, adding the risk score of SlotSPE to the clinical covariates consistently improves the C-index, with AC-index ranging from 0.023 (KIRC) to 0.054 (LUAD). Time-dependent AUC likewise increases or remains comparable when including the model, while IBS is generally stable or reduced (e.g., substantial IBS reduction for KIRC and LUSC). These results indicate that Slot- SPE captures complementary prognostic information that is not fully explained by routine clinical variables, showing the clinical utility potential to incorporate our model's prediction as a clinically useful prognostic factor when combined with established clinical factors.
H.2 CALIBRATION, DECISION ANALYSIS, AND RISK STRATIFICATION
To further evaluate the clinical utility of SlotSPE, we examine calibration and decision curve analysis (DCA) on the KIRC cohort. As shown in Figure a), the 60-month calibration curve demonstrates strong agreement between predicted and observed survival probabilities, indicating that SlotSPE provides well-calibrated risk estimates. The decision curve in Figure b) shows that SlotSPE yields positive net benefit across a clinically meaningful range of threshold probabilities. Within this range, SlotSPE consistently yields higher net benefit than both the "treat-all" and "treat-none"
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Intra- and Inter-modal Interactions. For the histological modality (Figure 123. first row), we display the attention map for its assigned slot, and further show the top-5 patches with the highest attention. An experienced pathologist provided expert annotations for each of these patches. These attention maps provide insight into which tissue regions the model identifies the most prognos- tically informative. For the pathway modality, we visualize the assignment maps of pathways for omics-derived slots and also report the top-3 most relevant and irrelevant pathways per slot, reveal- ing how the model differentiates biologically meaningful signals (Figure T2C). Then, to analyze cross-modal interactions, we connect pathway-level attention scores with the corresponding atten- Published as a conference paper at ICLR 2026
strategies, demonstrating potential practical value for supporting clinical decision decision-making. making. Finally, the KM analysis in Figure (Tje) shows a clear and statistically significant separation between high- and low-risk groups, confirming that SlotSPE offers meaningful prognostic stratification.
I INTERPRETABILITY
1.1 PATIENT-LEVEL INTERPRETABILITY
Cross-modality Alignment. We visualize slot assignment maps for both histological and genomic slots (Figure 12A). Slots from both modalities consistently segment similar cellular and tissue re- gions within the WSI, indicating that SlotSPE captures event-level alignment across modalities. At the same time, differences emerge: morphology-drive slots emphasize structural tissue patterns, whereas genomics-driven slots highlight regions reflecting underlying molecular features.
tion map of genomic slot on WSIs (Figure 12B, second row). Another case in UCEC shown in Figure 13
Overall, the interpretability analysis highlights the ability of the model to establish event-level align- ment across modalities, well showing the potential make novel hypotheses by identifying unexpected patwway-morphlogy correspondences for further biological validation.
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Published as a conference paper at ICLR 2026
A
Patient ID: TCGA-A1-AOSP (BRCA)
Whole Image
Histology Slot Assignment Map
Genomic Slot Assignment Map
B
Histology Slot
Genomic Slot
Slat 0
Sict
Sloc
Figure 12:
Case study of patient-level interpretability in BRCA. (A) From left to right: original WSI, assignment map of distology-derivee slots, and assignment map of omics-derived slots. (B) Attention maps for each slot highlighting the top-5 most relevant patches. (C) Assignment maps of pathways for omics-derived slots with corresponding attentions, showing the top-3 relevant and inrelevant pathways per slot.
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Published as a conference paper at ICLR 2026
A
Patient (UCEC)
Whole Slide Image
Histology Slot Assignment Map
Genomic Slot Assignment Map
B
Histology Slot
imoure
Genomic Slot
Siet
Sko
Figure 13: Case study of patient-level interpretability in UCEC. (A) From left right: original WSI, assignment map of histology-derive slots, and assignment map of omics-derived slots. (B) Attention maps for each slot highlighting the top-5 most relevant patches. (C) Assignment maps of pathways for omics-derived slots with corresponding attentions, showing the top-3 relevant and irrelevant pathways per slot.
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Published as a conference paper at ICLR 2026
Top10 Pathways across bins
Top10 Pathways across bins
1.7
1199
AHALAAA L0 sasiia LAV
1312
3373
390
(a) BRCA
(b) UCEC
Figure 14: Cohort-level pathway analysis for BRCA and UCEC. Patients are stratified into four risk groups, and top-10 pathways are identified per group based on slot attentions. Distinct patterns emerge across bins, highlighting biologically meaningful differences between high- and low-risk groups.
1.2 COHORT-LEVEL INTERPRETABILITY
To extend interpretability beyond individual patients, analyze cohort-level pathway attention patterns in the genomic modality. For each patient, we identify the slot with the highest retention score from the MoE decoder and extract its pathway-level attentions. Patients then stratified into four risk groups (bins) based on their survival time. Within each group, pathway attentions are averaged to obtain group-level profiles, and the top- 10 pathways per bin are reported (Figure [4).
In BRCA, for example, high-risk patients (binl) are enriched in fatty acid and xenobiotic metabolism pathways, reflecting the metabolic reprogramming characteristic of aggressive tumors (Pavlova &
Thompson| 2016; Röhrig & Schulze (0166). In contrast, low-risk patients (bin4) exhibit stronger
DNA repair and immune-related pathways, consistent with improved prognosis (Nolan et al. [017]]
Denkert et al. 20188. Such cohort-level analyses illustrate the potential of SlotSPE to uncover pathway-risk associations and generate hypotheses for further biological validation.
36


Reviews:
[{"review_id": "C2Rnryx12y", "reviewer": "Reviewer_kV7i", "summary": "This paper proposes a structural prognostic event modeling framework for multimodal survival prediction. The proposed method identifies the patient-specific prognostic events through slot-based representation learning, integrates a cross-modal reconstruction mechanism embedded with biological priors to enhance modal alignment and robustness, and delivers superior and stable performance on ten cancer cohorts. Moreover, the framework demonstrates improved interpretability through the structured decoupling ability of the proposed representation.", "questions": "Please refer to the **Weaknesses**.", "limitations": "", "rating": 2, "confidence": 5, "soundness": 3, "presentation": 1, "contribution": 2, "strengths": "1. This paper adopts a slot-attention module to survival analysis task and further introduces a Mixture-of-Experts (MoE) mechanism for selective slot activation.\n\n\n2. Incorporating reconstruction regularizations preserves the information in input features and enhances the model’s robustness under missing-modality scenarios.\n\n\n3. The proposed framework exhibits the generalization across ten cancer survival datasets, offers good interpretability.", "weaknesses": "1. The novelty of this work is limited, as both the Slot Attention and MoE modules have been widely used across various tasks, including survival analysis.\n\n2. The overall writing and structural organization of the paper are quite unclear:\n\n    (1) In the Selective Slot Activation section, the text notes “Conceptually, each slot is treated... A lightweight gating function $\\phi$ predicts a retention score for each slot.” The description claims that the output is of dimension $N_t$, while according to the accompanying formula, it should be a scalar score—which is inconsistent.\n\n    (2) In the paragraph “Then the top-K slots are selected using the Gumbel-Top-K...”, the variable $\\widetilde{w}$ is of dimension $S$, where $S$ denotes the number of slots before selection. It is unclear whether the softmax is applied to the selected slots or to all slots.\n\n    (3) Throughout the paper, many variables—especially those with subscripts—lack clear definitions, which seriously hinders readability.\n    \n    (4) Figure 2 is not introduced or referenced in the main text, making its purpose and relevance unclear.\n    \n    (5) In the paragraph “Given the omics-derived slots $S_g$,...”, the specific role of $S_g$ is not clarified—does it serve as initialization weights or as fixed guidance for new slot generation?\n\n    (6) Section 3.2 as a whole lacks appropriate references to figures, leading to poor readability.\n\n    (7) The paper’s organization is confusing; for instance, to understand the “reconstruction” part, the reader must jump to Appendix B.3, which in turn refers to Equation (5) that appears in the following section—this disrupts the logical reading flow.\n   \n    (8) In Section 3.2 (Slots Interactions), the description of self-interaction and cross-attention mechanisms is vague—it is not specified whether these operations are performed on all slots or only on the selected ones.\n\n    (9) In Section 3.3 (Training and Inference), the reader is directed to Appendix B.5 for the total loss, yet the survival loss is not clearly defined. What exactly constitutes the “standard survival prediction loss”? Moreover, without Equation (18), it is impossible to infer the last two terms of $L_{\\mathrm{surv}}$ from the main text, which indicates significant ambiguity in the writing.\n\n3. The authors are encouraged to clarify the unique aspects and improvements of the MoE mechanism used in this work in comparison to the previously published paper such as [1], in order to emphasize the genuine novelty of the proposed approach.\n\n    [1] From Single-Cancer to Pan-Cancer Prognosis: A Multi-Modal Deep Learning Framework for Survival Analysis with Robust Generalization Capability.", "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": "JfVTVpxpN3", "reviewer": "Reviewer_7qhV", "summary": "The paper proposes a slot-based, patient-specific representation for multimodal prognosis: whole-slide images and pathway-level transcriptomics are compressed into a few sparsely gated “prognostic event” slots; cross-modal reconstruction guided by biological priors aligns morphology and omics and enables imputation when omics is missing. Across multiple TCGA cohorts, the method shows consistent C-index gains and argues lower computational complexity by interacting at the slot level rather than instance level. While promising for interpretability and robustness, the work lacks empirical evidence for its efficiency claims (runtime/throughput/memory/scaling) and does not integrate clinical covariates or report multivariable analyses, calibration, or decision utility.", "questions": "1. Efficiency & scaling\n  - Please report training/inference time, throughput, and peak GPU memory for your method and strong baselines on the same hardware and batch size.\n  - Provide scaling curves for time/memory as functions of #slots (S), Top-K, and #WSI patches, and discuss speed/accuracy and memory/accuracy trade-offs.\n  - Break down module-level costs (WSI encoder, omics encoder, slot interactions, reconstruction) to identify bottlenecks.\n\n2. Clinical utility\n  - Incorporate clinical covariates (age, sex, stage, treatment, etc.) and report multivariable Cox/discrete-time results for: (i) clinical-only, (ii) model-only, and (iii) clinical + model, with ΔC-index, time-dependent AUC, and IBS.\n  - Add calibration plots and decision curve analysis (DCA), and propose a concrete high/medium/low-risk stratification to illustrate potential clinical use.", "limitations": "", "rating": 6, "confidence": 1, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Patient-specific slot representation with sparse gating focuses on a small set of salient prognostic factors, improving interpretability.\n\n- Cross-modal reconstruction with pathway priors aligns WSI and transcriptomics and supports missing-omics scenarios.\n\n- Consistent performance gains over baselines across multiple TCGA cohorts, with competitive single-modality ablations.\n\n- Architecture and losses are clearly specified, facilitating ablations and reproduction.", "weaknesses": "- Efficiency evidence missing: No wall-clock time, throughput (slides/s), peak GPU memory, or scaling curves vs. #slots/Top-K/#patches under identical hardware/batch settings.\n\n- Clinical variables omitted: No inclusion of age/stage/treatment etc., and no multivariable survival analysis, calibration, or decision-curve analysis to establish clinical utility.", "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": "1OjDI14dCk", "reviewer": "Reviewer_xj7Z", "summary": "This paper focuses on the problem of modeling intra- and inter-modal interactions effectively and efficiently. The authors proposed SlotSPE, a Slot-based Structural Prognostic Event modeling method. SlotSPE compress each patient’s multimodal inputs into compact, modality-specific sets of mutually distinctive slots using slot attention. By using the slots representations as encoding s for prognostic events, the method enables both efficient and effective modeling of complex intra- and inter-modal interactions, while also facilitating seamless incorporation of biological priors that enhance prognostic relevance.", "questions": "1. How sensitive is SlotSPE to the number of slots and gating hyperparameters?\n2. Have the authors examined whether the reconstructed genomic features can be used directly for downstream biological interpretation?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The evaluation experiments is comprehensive and convincing.\n2. The paper is overall well-written and easy to follow.\n3. The experimental results shows that the value of most evaluation metrics of the proposed method obviously outperform the baseline methods.\n4. The proposed selective slot is simple but effective and novel.", "weaknesses": "1. The ablation study, though detailed, could be extended to include comparisons with more recent foundation models.", "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": "3pjxlSghO1", "reviewer": "Reviewer_HWAP", "summary": "This paper introduces SlotSPE, a novel framework for multimodal cancer survival analysis that integrates histology images (WSIs) and genomic data. The core innovation is to model sparse, patient-specific \"prognostic events\" by compressing high-dimensional inputs into a compact set of dynamic \"slots\" using slot attention. The model selectively activates the most predictive slots for each patient via a Mixture-of-Experts (MoE) style decoder, enhancing personalization and sparsity. A key feature is a biologically-guided cross-modal reconstruction task, where the model learns to predict gene expression from histology images, thereby enforcing meaningful alignment and enabling robust performance even with missing genomic data. Extensive experiments on ten TCGA cancer cohorts demonstrate that SlotSPE significantly outperforms existing state-of-the-art methods in predictive accuracy, robustness, and interpretability.", "questions": "1. Your method is somewhat similar to AdaMHF[1], both consider efficient and input sparse. Please explain the difference and compare and cite it.\n[1] Zhang S, Lin X, Zhang R, et al. AdaMHF: Adaptive Multimodal Hierarchical Fusion for Survival Prediction[J]. arXiv preprint arXiv:2503.21124, 2025.\n2. The article does not provide a detailed analysis of training time or computational resource usage compared to other methods (e.g. flops), which makes it difficult to assess its practical scalability.\n3. There are a few baselines for comparison under missing modalities. Although some baselines do not take into account the actual modality, you can manually modify the code for testing.\n4. Hyperparameter Sensitivity: The model has numerous hyperparameters, including the number of slots for each modality, the number of selected top-K. Are there any results of ablation of these hyperparameters?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Strong Empirical Evidence: The claims are well-supported by extensive experiments across ten TCGA cancer cohorts. \n2. Enhanced Interpretability: The model provides a structured way to interpret its predictions. \n3. This model can better capture the sparse and individualized nature of cancer drivers.\n4. Biologically Guided Alignment: A key strength is the cross-modal reconstruction task, where omics-derived slots are used to predict gene expression from histology images.", "weaknesses": "1. The article does not provide a detailed analysis of training time or computational resource usage compared to other methods (e.g. flops), which makes it difficult to assess its practical scalability.\n2. There are a few baselines for comparison under missing modalities. Although some baselines do not take into account the actual modality, you can manually modify the code for testing.\n3. Hyperparameter Sensitivity: The model has numerous hyperparameters, including the number of slots for each modality, the number of selected top-K. Are there any results of ablation of these hyperparameters?", "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)