Sequential Information Bottleneck Fusion: Towards Robust and Generalizable Multi-Modal Brain Tumor Segmentation
Authors: TIANYI LIU
Xi Yang
Wei Wang
Anh Nguyen
Haochuan Jiang
Kaizhu Huang
Venue: ICLR 2026 Poster (2026)
Keywords: Brain Tumor Segmentation
Missing Modality
Generalization
Robustness
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: Using information bottleneck fusion to improve the generalization and robustness in brain tumor segmentation with missing modalities.

Abstract: Brain tumor segmentation in multi-modal MRIs poses significant challenges when one or more modalities are missing. Recent approaches commonly employ parallel fusion strategies; however, these methods often risk losing crucial shared information across modalities, which can degrade segmentation performance. In this paper, we advocate leveraging sequential information bottleneck fusion to effectively preserve shared information across modalities. From an information-theoretic perspective, sequential fusion not only produces more robust fused representations in missing-data scenarios but also achieves a tighter generalization upper bound compared to parallel fusion approaches. Building on this principle, we propose the Sequential Multi-modal Segmentation Network (SMSN), which integrates an Information-Bottleneck Fusion Module (IBFM). The IBFM sequentially extracts modality-common features while reconstructing modality-specific features through a dedicated feature extraction module. Extensive experiments on the BRATS18 and BRATS20 glioma datasets demonstrate that SMSN consistently outperforms traditional parallel fusion-based baselines, achieving exceptional robustness in diverse missing-modality settings. Furthermore, SMSN exhibits superior cross-domain generalization, as evidenced by its ability to transfer a trained model from BRATS20 to a brain metastasis dataset without fine-tuning. To ensure reproducibility, the code of the SMSN is provided in the supplementary file.

Published as a conference paper at ICLR 2026
SEQUENTIAL INFORMATION BOTTLENECK FUSION: TOWARDS ROBUST AND GENERALIZABLE MULTI- MODAL BRAIN TUMOR SEGMENTATION
Tianyi Liu', Xi Yang', Wei Wang", Anh Nguyen", Haochuan Jiang".1, Kaizhu Huang Xi' an Waotong-LLiverponn University University of Liverpool Duke Kunshan University Cooresponndig author: h.jiang @ xjtlu.edu.cn
ABSTRACT
Brain tumor segmentation in multi-modal MRIs poses significant challenges when one or more modalities are missing. Recent approaches commonly employ par- allel fusion strategies; however, these methods often risk losing crucial shared information across modalities, which can degrade segmentation performance. this paper, we advocate leveraging sequential information bottleneck fusion effectively preserve shared information across modalities. From an information- theoretic perspective, sequential fusion not only produces more robust fused rep- resentations in missing- data scenarios but also achieves a tighter generalization upper bound compared parallel fusion approaches. Building this principle, we propose the Sequential Multi-modal Segmentation Network (SMSN), which integrates an informnation-Botteennt tially extracts modality-common features while reconstructing modality-specific features through dedicated feature extraction module. Extensive experiments on the BRATS 18 and BRATS20 glioma datasets demonstrate that SMSN consistently outperforms traditional parallel iusion-based baselines, achieving exceptional ro- bustness in diverse moddlitty settings. Furthermore, SMSN exhibits supe- rior cross- donsin generalization, as evidenced by ability to transfer a trained model from BRATS20 to a brain metastasis dataset without fine-tuning.
Fusion Module (IBFM). The IBFM sequen-
INTRODUCTION
Brain tumors pose a significant threat to human health, Accurate brain tumor segmentation plays pivotal role treatment planning by precisely identifying tumor boundaries in multi-modal Mag- netic Resonance Imaging (MRI) modalities (Yan et al. 2020 Bakas et al.) 2017). ). It is essential to provide all the relevant modalities to achieve proper segmentation performance (Shaker al., 2024).
However, in real-wor world clinical practice, it is commonly seen that one more MRI modalities
unavailable due to various practical defects (Liu et al. 2023; Tran et al. 2017).
(X1, Xa.....
X1, X2
5162
Z1,
20 Zg.
fel.) Z.
Parallel Fusion
Sequential Fusion
Table 1: Illustration of parallel and sequential fusion strategies. X denotes the modality input, f()) or fe(-) are fusion functions, and Z is the latent representation.
Recently, the missing- modality challenge has been widely addressed through unified multi-modal feature learning, where joint fusion representations are constructed from available modalities (Zhang cet al., 2022. Shi et al., 2023). These methods aim to disentangle modality- common and modality- specific information (Zhao al. 2023 Liu et al. 2025a). Typically, modalities are fused in parallel via simple concatenation (Zhang et al. 2022) or attention mechanisms (Shi et al. 2023) Wang et al. 2025), where all modalities combined and mapped into shared latent representation, shown in Table T However, when certain modalities are absent, the common information may not be adequately preserved, resulting in degraded segmentation performance, illustrated in Figure [

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Seguential Irseee
P.R. P.K. K.
Hyt ?j
PCA Visualization
Grad-Cam Viunaitzation
Figure I: Comparison of parallel fusion (top) and sequential fusion (bottom). (a) PCA Visualization. Large distribution variation when an informative modality is missing indicates weaker robustness, while compact and consistent embeddings with preserved color gradients indicate better information preservation. Modalities 1-3 contain decreasing task-relevant information. Different points repre- sent different samples. (b) Grad-cam Visualization. Sequential fusion (I(X; Z,)) preserves more information when some modalities are missing, while parallel fusion (T(X; Zp)) preserves less.
Given the aforementioned disadvantage parallel fusion paradigms, we advocate that modalities should be considered by the sequential information bottleneck fusion, where modalities in- corporated step by step through recursive updates of the latent state, as shown in [ It could properly preserve
modality commonality. As illustrated in Figure [ when are missing. it will not heavily influence the mutual information between the joint inputs and la- tent fusion distribution. Importantly, series of theoretical analysis (see See. 3 shows that our sequential strategy offers a Lipschitz-continmuus lower bound. Compared with parallel fusion, it certifies more stable fused representations in loss landscapes (Figure[4) further reveal smoother and flatter optimization surfaces, thus supporting this advantage. Additionally, our proposed method can yield a provably tighter generalization upper bound, vs. parallel fusion, thus confirming again the advantages of our sequential fusion strategy.
modalities
scenarios. On the empirical front,
Building on these findings, in this paper, we develop the Sequential Multi-modal Segmentation Network (SMSN). Inspired by the ITHP (Xiao al. 2024), we introduce Sequential Fusion Mod- ule based on the Information Bottleneck objective (IBFM) in the SMSN to facilitate the extraction of modality-common information regardless of whether modalities are fully available partially missing. To further disentangle modality-specific representations, we employ Transformer based Feature Extraction Module, coupled with a series of task-specific losses (Ronneberger et al. 2015).
We validate SMSN on two benchmark datasets, BRATS18 and BRATS20 (Menze et al. 2014). where improved robustness generalize a trained SMSN on the BRATS20 glioma dataset directly to an unseen brain metastases dataset (Ramakrishnan et al. 2024) without any fine-tuning performed, where superior generaliza- tion performance can be observed comparing with other baselines. Major contributions of this paper are summarized as follows:
state-of-the-art fusion-based baselines be observed. We further
We propose novel Sequential Multi-modal Segmentation Network (SMSN) to decompose the modality-common information with the information bottleneck based fusion module (IBFM) in missing modality segmentation task.
We theoretically evidence the generalization and robustness of the sequential IBMF, demonstrating its superiority to parallel fusion.
We empirically verify the robustness and generalization of the proposed SMSN on various brain tumor segmentation datasets.
2 RELATED WORK
2.1
MULTI-MODAL BRAIN TUMOR SEGMENTATION
Multi modal MRI provides complementary information for brain tumor segmentation (Shaker et al.]
2024 Fang et al. 2025). but handling missing modalities remains major challenge in clinical prac-
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tice (Liu et al. 2025b). Non-fusion methods, such modality reconstruction (Liu al. 2023 or shared-speciff feature modeling (Wang et al.] 2023), have been explored, but their computa- tional overhead and limited scalability hinder wide adoption. Consequently, most existing works are fusion-based, typically following parallel fusion paradigm. for example, mmFormer (Zhang et al. 2022). F2Farans (Shi et al. 2023), MMMViT Qiu et al. (2024). and IMS2 Zhang al. (2024). through concatenation or attention. However, parallel fusion may fail to preserve modality- common information when some modalities are missing, leading to performance degradation. In this paper, we propose a sequential fusion framework that explicitly addresses this limitation and enhances robustness under missing missing-modality scenarios.
2.2 MULTI-MODAL INFORMATION BOTTLENECK
The Information Bottleneck (IB) models the trade-off between information compression and task relevance. It has been proven to be effective in speech and text classification tasks (Slonim & Tishby 2000 Tishby Zaslavsky 2015 Fang et al.] 2026). Recently, IB-based techniques have witnessed achievement for improving representation quality for multi-modal learning. The ITHP (Xiao et al.) 2.24), for example, employs an IB-driven hierarchical framework to distill information from aux- iliary modalities into compact, task-relevant representation. Building these insights, adopt the IB to address missing modality challenges multi multi-modal learning.
3 THEORETIC MOTIVATION
Theorem 1 (Optimality of the Information Bottleneck Representation for Multi- Multi-Modal Inputs). Let Y be a target variable and X2,, be N input modalities that are jointly dis- tributed with Y. Assume that the modalities can be modeled jointly composite random variable x= (X,, ,,,..., NN), with a joint distribution p(æ1.-. ,.,...,,,N... ,NN.y). Let be a stochastic represen- tation of X, learned via encoder p(2|æ1.... .NN), ) by optimizing the Information Bottleneck (IB) objective:
2 arg max p(a m))
-
3I(X;
where 3 > O controls the trade-off between prediction I(Z;Y) and compression I(X; Z). I(.)
represents the mutual information. Then, for any alternative representation such that 1(X; Z) S 1X; holds that:
1(2" Y) 2 I(Z
(2)
That is, under a fixed information constrain [X;; 2), the optimal representation Z maximally preserves the predictive information about the target variable Y, even when X is composed of multiple modalities.
Proof. Information bottleneck objective (Tihbyy et al. 1999). presented L I(Z:Y) (I; X), is initially introduced to compress the information with single modality input X. Here, Z is stochastic representation of X, and Y is the target. We assume that the multi-modal inputs Xi,...,X, can be jointly modeled as a single random vector = (Xi,..., XN), with a joint distribution p( ...,.,.... .NNy) u) Wu & Goodman 2018). Hence, this assumption allows the mutual information terms I [Z; Y') and X2;X) of multi modtl input to be defined in the same way as in the Information Bottleneck objective of single modal input. Given this, the objective of multi-moda modal in- formation bottleneck is structurally identical to the IB objective defined for single-modal data. Thus, the optimal representation Z" satisfies the same optimality condition Eq. _ Hence, the optimality result from the single modality IB theorem carries over directly to the multi-modal cases.
Remark 1 (Dominant and Non- Non-Dominant Modalities in Multimodal Learning). In multimodal rep- resentation learning, modalities contribute differently to predicting the target variable Y. A dom- inant modality Xa identified when it possesses higher mutual information with Y, denoted as I(Xa; Y), iee, Xa = arg max; I(X;; Y). Otherwise, modalities with lower mutual information are considered supportive since it provides less useful information to the prediction.
In the brain tumor segmentation, for instance, MRI sequences such as Flair are often more domi- nant for whole tumor segmentation, whereas Tlce is crucial for enhancing tumor details. Recent
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empirical results illustrate that dominant modalities consistently outprform non-dominant modali- ties across key tumor subregion segmentation tasks (Ding et al. 2021
Existing parallel fusion strategies process modalities independently and fuse them a specific layer; However, they may rely heavily on dominant modalities. As such, prediction performance degrades sharply when the dominant modality is absent, the fused representation lacks the most informative source. In contrast, Information Bottleneck (bBs-d sequential fusion strategies compress infor- mation from multiple modalities into a shared latent representation. Since it preserves musk-relevant representation, the fused feature will not rely on the availability of any single dominant input.
Theorem 2 (Generalization Bound with Complexity Measures). (Shaley-Shwartz & Ben-David 2014 Xu Raginsky ( Let H be a hypothesis class, and h E H. be a learned hypoth- esis (possibly based on an intermediate representation of the input X.. Given a training set S {( V:)) drawn ii.dd from distribution 'D where is the number of samples, in classical learning theory (Shalev-hwarrz Shwartz & Ben- Ben-David 2014), the generalization error satisfies.
(VC(H)
(T(h) S <s(h) + O
where the complexity term C(H) denotes hypothesis class complexity measure such VC dimen- sion or Rademacher complexity. In cnermaationthhoreee learning frameworks, when a learned representation from function f(). CHH. Z) can be bounded by the mutual information between Z and the input X, i.e., I(Z; X) Xu & Raginsky 20.7). The generalization ervor satisfies,
(V
[(2,X)
x) 12
er (h) S cs(h +
Z = f(X).
The generalization bound is adapted from classical learning theory Shalev-Shwartz & Ben- 2014) and its nnermatiin-theorede extension (Xu & Raginsky] 2017). In the following Proposition, the mutual information based bound is used for comparison since different kinds of fusion appears at the intermediate representation Z.
Proposition 1 (Tighter Generalization Bound via IB Fusion). Let ZIB PIB(2(x) be the repre- sentation produced by an Information Bottleneck (IB)-based fusion model, and Zp ~ Py(2(x) be the representation from a parallel fusion model (e.g., concatenation multi-head attention without bottleneck). Define the empirical risk gap A & (g(hIB) eg Ehpp)) and the mutual information [[ZIBi X). Assume that the IB model compresses task-irrelevant informa- tion such that g > 0 (i.e., I(Z]B; X) < I(Zp X)), and that the mutual- infoommatoonnnnn general- ization inequality in Theorem holds with the same sample size and hidden constant >> 0:
gap g I(Zp;
(h) S (s( + ov I12:X) Then the difference in generalization bounds satisfies
(V
T(Zpi:)) X)
T(ZIB; X)
(T(B)) (1p) S SA
n
72
In particular, the IB model achieves strictly tighter upper bound the test error whenever the threshold condition
A<c ((((pix)
[(ZIB:X)
n
is satisfied. It is typically seen since IB compresses mainly task-irrelevant information. Meanwhile,
A can be a small value when T(Zp; X) - T(ZIB; X) is positive.
This proposition is proved in Appendix Sec. A
The above proof holds under the assumption that the modalities independent. However, our analysis can be extended to the case where the modalities are not independent, i.e., when they follow a joint distribution. If the following assumption hold:
Assumption (Relaxed Cross-Modal Conditional Information Assumption). The aggregated cross- cross- modal conditional information preserved by the fusion satisfies
I(ZpiXes X1) 2
(2I(ZiB: I(ZIB; |xx)))
(3)
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where Zy denotes the latent representation obtained by ordered fusion, with X representing all modalities before the i-th modality, and ZıB denotes the latent representation obtained by random fusion, with X representing all modalities except the i-th one.
formal justification of this assumption is provided Appendix Sec. Based on this assumption, we have the new relaxed theory:
Proposition Under the relaxed cross-modal conditional information assumption, the following inequality holds for the aggregated mutual information:
[Zei ; 2 I1Er:: Xn),
where Zp is the latent representation obtained by parallel fusion, and ZIB is the latent representa- tion obtained by the information bottleneck (IB) fusion.
This proposition is proved in Appendix Sec. C
Please note that the Proposition [ and Proposition 2 still holds when some of the modalities are missing, In the following, we will draw remarks based on the different influences 1 [(;; brought by missing modalities.
Case 1: Xg is missing, Parallel fusion directly maps Zp = f(Xa) without controlling irrelevant features, leading to relatively high [ZZp; Sequential IB-based fusion compresses X, but leaves Xa unaltered. When X, is absent, the learned representation Zin retains only the clean signal from Xd. yielding I X) < T(Zp; X)-
Case 2: X is missing. Parallel fusion maps Zp = fX,) without any regularization. As remaining X, might be less informative to the prediction, it leads to a high I(zp:.,) In contrast, IB-based fusion explicitly compresses X, while preserving task-relevant information, even without Xa. ZiB encodes minimal yet informative patterns: I[218; X) < 12p;:))
As the result, in both cases, (T(B)) S (T,,)) will hold. It proves that the generalization upper bound for the sequential IB-based fusion model remains strictly tighter than those with parallel fusion architectures. In the following, we will discuss how IB-based fusion demonstrates tighter Lipschitz bound that promotes robustness across different missing modality scenarios.
Assumption 2 (I-Lipschitz Continuity of Modular Components), Fusion-bused missing modality learning framework consists of following modules: (i) an encoder fü X; - Zi for each modality, (ii) Let Ø : 21 ..... ZM - Ziueed be the multimodal fusion function that aggregates all encoded modality features { into a joint representation Ziused and (íii) a decoder g : Zfused Y for prediction. We assume all such components: encoder (Lx), fusion (Li, for parallel fusion and Lo. for sequential fusion)), and decoder (Lg) are 1-Lipschitz continuous and all larger than zero.
While achieving strict 1 1-Lipschitz continuity can be challenging for softmax-based self- attention, all baselines in our study apply LayerNorm directly after the fusion module. This stabilizes gradients and prevents their uncontrolled growth. Since such normalization can be easily incorpo- rated into similar architectures, the required theoretical conditions remain practically attainable.
Remark 2.
A formal justification of this assumption is provided in Appendix Sec. D Based on Assumption 2
we provide the Lipschitz bound of parallel and sequential fusions in Appendix Sec. E In the follow- ing Proposition, we would like to compare bounds of different fusions.
Proposition 3 (Bound of Different Fusion Methods). Based Assumption
2 the Lipschitz constant
M of the parallel and sequential fusion model satisfies: Ippraated < Lg LL V EM L. L S
sequeeniill
Lg I1 Lo: Li. If each encoder and fusion module are normalized such that Li S and Lo. 1, IIM, Ls. L, S min; L, S EM L2, which implies that, under these conditions, the Lipschitz bound for the sequential fusion model is tighter than that of the parallel fusion model.
L3,
Proposition 3 is proved in the Appendix Sec. F It establishes that the sequential IB-based fusion model satishes tighter Lipschitz continuity constraint, which encourages smoother decision boundary and contributes to greater robustness.
To empirically validate the robustness across fusion strategies, visualize and compare the loss landscapes across various missing modality scenarios of: parallel fusion (including concatenation- based fusion and attention-based fusion), and the proposed sequential bB-based fusion. As illustrated
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NM
NM
(a) Concatenation- Fusion (Parallel)
(b) Attention-based Fusion (Parallel)
(c) IB-based Fusion (Sequential)
Figure 2: Visualization of the loss landscapes across different missing modality scenarios (NM denotes the number of missing modalities) for Concatenation-base Fusion, Attention-basee fusion, and IB-based fusion. Warm colors represent smooth plains, while cold colors depict sharp terrain in the landscape. The bar range for cancatenation-basee Fusion is [0, 0.4], while those for Attention- based and IB-based ones are [0, 0.05).
in Figure 2 the sequential IB-based fusion model consistently produces smoother and more stable loss surfaces compared to the baselines. Notably, as the NM increases, the loss landscapes of parallel fusion models become increasingly irregular and exhibit sharper curvature. In contrast, the sequen- tial IB-based fusion model maintains a flatter and more structured loss geometry, even with high NM values. These observations match theoretical findings in Proposition 3] demonstrating that the sequential bBsed fusion model achieves tighter Lipschitz bound and thus improved smoothness.
4 METHODOLOOGY
In multi-mode mootii learning, information encoded in each modality can be decomposed into two irrel- evant components that would be orthogonal between one and the other in high-dimensional fea- ture space: modelity-specific component and modality-common one (Zhao et al.. 2023). The modality-specific component one captures uniqueness in each modality. In contrast, the modality- common factor encapsulates information that is consistent and shared across multiple modalities. They are afterwards aggregated together to reduce possible information redundancy that might exist in the original modality feature representation (Tsai et 2018).
The proposed Sequential Multi-modal Segmentation Network (SMSN) consists of two-stage in- formation bottleneck fusion module, a specific feature extraction module, and loss of orthogonal- ity, to achieve the objective that separating modality-specific and modality-common representations of each modality. In partieular, based on our discussions in Sec. 3. such sequential information bottleneck fusion strategy processes appealing robustness and generalization properties. They are afterwards aggregated and sent to the decoder, to perform segmentation.
Modality Reordering Strategy. We adopt N dedicated modality encoders extract modality fea- tures, corresponding to modalities. Following the Information Bottleneck objective as Eq. I these features sequentially fused into shared representation (see Two-Stage Information Bot-
Please note that the architectures of both the encoder and the decoder follow configurations of the mm- Former (Zhang al. 2022) and the M2FTrans (Shi et al. 2023)

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tleneck Fusion), starting from an initial reference modality. However, placing missing modality (represented as a zero tensor) at the beginning of the sequence may degrade the IB objective. To ad- dress it, we propose modality reordering strategy: available modality is randomly selected as the initial reference, while the remaining N modalities, regardless of availability, are randomly re-ordered and fused sequentially.
Two-Stage Information Bottleneck Fusion. Inspired by the ITHP (Xiao et al. 2024), we de- sign a two-stage Information Botteneck Fusion Module extract coddalttycoommat represen- tations. Specifically, given four input modal- ities, denoted as fusion process into two stages: the first stage fuses modalities 21 and z2. and the second stage fuses 23 and 244 based on the output of the first stage. Specifically, as illustrated Fig. 3 obtain two bottleneck representations, 21 and 22, with each of them containing com- pressed latent representations from both stages. The resulted fusion objective F is formulated with the Information Bottleneck (IB) objective as:
D2
(xi Y P we plan the
Presest
Mistrg Kodidiy
X
Fraell
Figure 3: x = {m,)i= are the input modality rep- resentations. They are re-ordered and fused by us- ing a two-stage information bottleneck.
F [(
x2) m2); 21) [(115 vo) (I(z), [rr,, sta;: =2) - 7 (22;
(4)
stage 1
stage 11
where yo and y1 are the task-related targets for each stage. 3,7 are hyperparameters control- ling the trade-off between compression and relevance, refer Eq. [ Inspired by the variational approximation of the Information Bottleneck objective (Alemi et al. 2017), the mutual informa- divergences (DKL) (Kullback & Leibler 1951) with respect to tractable prior. The loss Le is formulated as:
tion terms / [[[x), x2 [2]:21] 21) and [ (21 [23, 22) are approximated by KullbcckLeiibe
Le E ((()) [Dxr. (p(2)
r(=1))] (<),,)))))))))))))
(p(es) [PKL( (x,, m44) |I r r==)))
where r(.) is typically a standard normal prior.
Additionally, two individual decoders will be employed by collecting 21 and respectively to reconstruct input modalities from the compressed latent representations to preserve task-relevant information. To adapt to the missing modality task, we introduce modality- reconstruction loss by multiplying the decoder output with a binary availability mask M, E {0, 1}, where M, = indicates that modality 2, is present. Thus, the reconstruction is:
C, = BIEEO
Σ Mj log Ivw (x: 20) + Es,
Σ M, log qoh (æy 21) 3
(6)
where (x; z) denotes the decoder that reconstructs modality x; from the latent representation z. This reconstruction strategy ensures that the network focuses only reconstructing the modalities that are available, improving robustness under missing modality conditions.
Specific Feature Extraction. We employ transformer blocks disentangle modality-specifie in- formation by collecting the concatenation of modality features extracted from N modality encoders {r,)]- and the fused representation 22- After this, the output will be split to retrieve the updated modality features corresponding to each of the four input modalities as N podalltt-sppecfii components x, Here, we expect X,, will contain information that is not properly included in B
To achieve it, we introduce the orthogonality loss: Lo = EM (22 x²)²² Then, we can obtain
features of each involved modality by x; = Ns. + 22-
Final Loss. Following (Zhang et al. 2022 Shi et al. 2023). we encapsulate all the segmentation losses into L,, in which Le, Lo, and E, are also jointly optimized.
2 As discussed in Sec. and Flair.
5 in datasets that we used in this paper, four modalities are involved: T1, Tlee, T2,

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Table 2: Missing modality segmentation results of different fusion-based models on BRATSI8 and BRATS20. For each scenario, from left to right, the four circles represent T2, Tlee, T1, and Flair, respectively. represents a modality is present while represents a modality is missing. The best results are highlighted in bold.
Modaliny
BRATSI8
manFoemer
$4.66
73.05
73.40
86.61
K5.24
76.85 84
HH.54
54.93
89: 18
35.58
58.54
89.46
89.70
85.31
89.20
84.88
FFTTnns
$4.11
73.86
76.88
88.16
85.52
79.04
88.34
63.63
89.22
85.88
$5.41
89.20
88.74
85.95
88.87
$5.39
MMMVIT
77.92
70.38
70.70
79.23
78.77
73.67
80.57
79.29
81.5 51
80:46
80.83
82.00
81.66
79.0 19.19
81 11.56
78.54
Trans
67.12
05
84.74
Ours
85,49
76.33
76.36
84.38
86.45
79.62
87.82
$6.61
58.5 51
88.7 71
89.09
89.98
86.93
89.39
88.71
85.62
Fomiermmer
64.11
75.04
62:50
60.95
79.42
79.50
68.76
69.17
65.67
79.34
50.82
70.08
79.57
79.95
80.33
73.25
MMMVVT
75.62
63.48
60.49
65.11
64.51
67.56
78:95
TC
IMS Trans
58.23
72.48
49.00
18
75.06
73.83
64.89
62.96
66. 16
76.70
76.70
66.27
77.
75.02
76.60
68.76
FFaan
78.03
65.91
62.02
67.85
78.13
79.
79.28
72.78
Ours
79.72
62.
61
83.57
N0.75
67.70
68.55
70.78
W2.35
83.17
70.77
82.81
82.96
82.35
75.20
mim Vermer
36.93
70.93
30.72
30.70
70.76
69.51
35,20
37.31
38.30
71.13
72:49
35,70
70.91
69.92
70.54
$4.34
MFFaaass
39:51
32.40
34,03
71.24
39,41
39.07
41:15
70:03
69.44
54.95
ET
MMMVIT
37.25
65.46
35.00
41.82
67.57
66.38
13.94
39.19
42.68
70.97
68.85
41.59
69.93
67.87
70.08
55.21
IMS Trans
67.28
24.75
31.48
70.75
42.22
70.82
41.09
71.02
54.56
Ours
78.87
36.55
39.31
79.70
46.25
46.09
75.38
50.30
78.91
78.70
78.58
DRA
5220
muniormme
83.88
75:30
75.11
86.84
N6.57
79.71
86,10
89:22
39.40
89.70
86.40
89.85
MMMVIT
80.67
72.10
72.10
82,60
81.82
75.16
94.08
83.25
84.30 89
83.06
53.92
85.16
84.88
82.09
84.87
81.31
IMS Trans
$4.35
72.91
70.83
86.30
86.51
75.58
88.94
86.64
89.43
98.16
58.96
89.99
89.91
87.27
90.27
85.08
FTFaas
76.07
75:21
87.12
79.46
87,90
85.55
55. 44
17
58.22
85.49
$8.99
87.28
88-97
85,43
Ous
$7.03
78.12
77.44
87.11
88.17
82.40
89.59
58.14
90.20
89.66
59.86
90.07
90163
88.45
90.50
$7.14
69:30
K2.83
03.54
08.02
54.27
64.21
72.35
72.11
72.37
63.32
$4.50
74:11
B5.44
84.91
64.83
77.79
MMMVIT
98
60.19
68.18
81.93
68.11
71.39
62.45
$2.03
82.95
81.89
62.75
75.45
IMS Trans
66.39
90.14
56.09
62.15
$4.94
81.06
67.90
67.20
09.58
83.09
$3.30
69.88
84.57
84.67
84.25
75.05
FTann
62:77
68.94
$4.55
72,40
71.30
73.24
$4.50
07
85.19
85.19
85.39
77.27
Ours
70.65
K3.46
65.15
68.17
85.20
84.45
73.75
71.49
73.84
85.96
$5.67
75.44
86.27
85.62
$6.90
75.80
mamFormer
42.56
76.95
31.80
39.61
76.09
76.50
11,38
43.91
44.98
76.27
76.72
66.81
75.21
76.62
75.67
60.09
MMMVIT
73.69
50.05
53.27
72.90
74.98
73.57
75.34
73.95
62.15
IMS Trans
44.25
74.90
30.77
31.54
77.50
76.73
41.95
44.12
50.50
78.85
79.46
49.99
79.50
78.40
79.85
61.62
M FTTans
38.
76.06
45.96
46.15 15
79.00
80.63
79.09
Ours
45.88
78.98
38.67
40.45
79.50
76.86
43.07
46.32
49:21
80.54
$0.09
47.63
79.88
79.75
79.74
63.06
EXPERIMENTS
5.1 ROBUSTNESS ON BRATS MRI
Experimental Settings. To validate the robustness of the proposed SMSN, we perform comparisons on gliomas segmentation tasks on the BRATS18 and BRAT$20 Menze et al. 2014) for the Multi- modal Brain Tumor Segmentation Challenge without any pre-training performed. Specifically, four modalities (TI, Tlce, T2, and Flair) are involved in both datasets. We employ the Dice similarity coefficient the evaluation metric. For fair comparison, we follow data splits of both sets from F2FTrans (Shi et al. 2023). We also reproduced the results of each basidn-based baseline with the respective released codes.
We present the comparison results, including the proposed SMSN and other fusion-based baselines in Table demonstrating robustness brought by the SMSN in handling missing modality scenarios. Specifically, SMSN consistently outperforms other baselines in both datasets by evaluating the averaged segmentation performance. Mcanwhile, in each missing modal- ity scenario, the proposed SMSN still demonstrates superiority. Importantly, it particularly excels worth mentioning
Segmentation Results.
in more challenging scenarios when two or three modalities are not present. that although MMVIT predicts better ET than SMSN in certain cases on the BRATS20 dataset, the average performance does not demonstrate consistency. We think it a dataset-sensitive approach, as in the BRATS18 18 dataset, we can only observe suboptimal performance with the MMViT model.
Except for fusion-based approaches, the proposed SMSN has been proven to outperform non-fusion methods such as M AE (Liu et al.
2023 and ShaSpec (Wang et al. 2023). Relevant results are
presented in the Appendix Table 6
Grad-Cam Visualization. Figure 4 presents Grad-CAM visualizations the fused feature to il- lustrate attention focus to predict tuomors on parts of the source image. Specifically, we present results of the proposed SMSN and F2Fara that performs relatively better than other baselines in Table 2 From these heatmaps, we can observe that the proposed SMSN achieves a more focused activation pattern, which also well aligns with the ground truth depicted by orange and red contours.
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This finding supports our discussion in Remark I that with the proposed SMSN, even though some certain modality is missing, the fusion still able to focus on the task-relevant representation and the prediction task.
5.2 GENERALIZATION FROM GLIOMAS METASTASES
Experiment Settings. Except for gliomas, metastases are another kind of malignant brain tumor. As seen in Sec. G.6 they differ greatly in morphology. Gliomas appear as infiltrative lesions with indis- tinct margins and heterogeneous enhancement, whereas metastases are typically well-cireumseribed, round or ovoid with sharp borders and marked surrounding edema. It is challenging to generalize a prediction model trained only with gliomas to metastases predictions. Here, we employ trained SMSN and other relevant baselines only with BRATS20 to the Brain Metastases (BM) dataset (Ra- makrishnan et al. 2024) with identical modalities: TI, Tlce, T2, and Flair.
Segmentation Results As presented in Table the proposed SMSN consistently outperforms other fusion-based methods, which proved appealing generalization performance. Furthermore, compared to the second-best F2rara model, SMSN exhibits lower standard deviations, indicating enhanced robustness in varying imput conditions. The detailed results Table 3 with each individual scenario is presented in the Appendix Table
5.3 ABLATION STUDIES
Table presents ablation studies of the proposed SMSN by evaluating prediction performance upon removing each constructing individual module/loss discussed in Sec. 4 Notably, the orthogonality loss will is in line with the specific feature extraction module, it will also be removed when that module is absent. These obtained results demonstrate that each constructing module/loss is essential the final prediction result.
is important to be noticed that IB theoretically can decompose common information from a mixed feature. However, real practice, some modality-speciffe information will still be preserved in the IB module. To promote modality decomposition, the specific feature extraction module and the orthogonal loss is additionally applied. Based on acquired results from the ablation study, canceling orthogonal loss degrades segmentation performance, which confirms our aforementioned analysis.
Table 3: Segmentation results under missing- modality conditions on the meta dataset, with models trained BRATS. NM denotes the number missing modalities, and FM indi- cates all modalities values correspond to the mean and standard deviation of Dice scores for each missing- modality scenario.
Table 4: Ablation results of models trained un- der different combinations of modules/losses on BRATS20. From left to right, the four circles repre- sent modality reordering strategy, C,, specific fea- ture extraction module, and Lo, respectively. rep- resents a modality is module/loss while represents module/loss missing.
available. Reported
C#9*
6800
WT
85.75
$3.05
83.57
$5.09
S7.14
Madalit
Meon
NME3
Sid
Mean
NME2
Std
Moan
NME1
Std.
Moan
Moom
AVE
76.38
76.82
76.19
76.61
78.30
32.53
28.43
MFFTraus
49.99
5.75
55:40
3.94
58.87
3.43
59.58
55.16
MMMVIT
46.82
3.76
90.31
2.23
51.90
0.65
52.72
49.96
IMS
48.95
Ours
51.69
4.93
57.64
4.25
60.33
2.36
61.55
$7.01
10.34
5.59
3.18
3.50
13.30
8.59
M MPParass
28.83
9.67
38.48
10.01
45.44
3.88
51.36
38.62
MMMMVT
27.52
10.96
36.04
11.42
43.13
9.88
48.64
36.50
28.04
Ours
35.50
12.95
45:37
1321
53.03
10.36
59.17
45.70
mun
6.85
5.55
5.63
4.00
4.63
4.07
6.73
3.78
GindeCan (Oun)
Pirans
21.34
11.31
31.24
12.92
39.16
11.83
46.67
31.74
TC
MMMMVT
21.90
12.89
29.54
14.00
37.23
12:48
43.86
30.54
Figure 4: This figure presents comparative visual-
21.90
Ours
25.07
14.12
36.43
14,65
$4.69
13.69
51.72
36.89)
ization of Grad-CAM heatmaps.

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Published as a conference paper at ICLR 2026
5.4 SENSITIVE ANALYSIS
Referring to Eq. 5 7,7 are hyper-parameters controlling the trade-off between compression and relevance. As shown in Table our experiments indicate that the performance of the information bottleneck compression is indeed sensitive to the choice of the hyper-parameters 7 and B. This sensitivity expected because these parameters directly control the trade-off between compression and task-relevant information preservation: larger / enforces stronger compression, potentially discarding useful features, while smaller / retains more information but may reduce the regu- larization effect. Similarly, " adjusts the relative weighting of different components in the loss, affecting how strictly the model satisfies the information constraints.
Despite this sensitivity, we observe that across wide range of y and 3 values, the proposed method consistently outperforms involved baselines, indicating that the information bottleneck framework provides robust gains when the
are not finely tuned.
Table 5: Sensitive Analysis of hyper-parameter trained BRATS18 and BRATS20. The two numbers in the first line of each scenario are the values of 3 and 7, respectively.
BRATS18
[0.1.1]
00.3.
10.7.0.3
0.5)
[1.0.1
BRATS30
[0.1.
[0.3,0.7]
[0 0.33
00.5. 0.5]
0.1
74.19
72.72
75.20
74.14
73.55
IC
78.00
79.22
78.80
79.34
79.72
ET
36.71
61.69
62.39
57.34
57.56
ET
62.29
63.59
63.00
61.89
60.34
6 CONCLUSION
We presented the Sequential Multi-modal Segmentation Network (SMSN) to address missing modalities in multi-modal MRI brain tumor segmentation. By leveraging an Information-Botttleekk Fusion Module (IBFM), SMSN sequentially disentangles information. IBFM provides Lipschitz-continuous lower bound and tighter generalization upper bound, improving robustness and cross-domain adaptability. Experi- ments on BRATS18 and BRATS20 show that SMSN outperforms the fusion-based haselines under various missing-modaliy settings. Result on transferring the model to brain metastasis dataset without further fine-tuning confirms its strong generalization capability.
common features while recon-
structing modality
ACKNOWLEDGE
The work was partially supported by the following: National Natural Science Foundation China under No. 92370119, and 62376113; Xi'an Jiaotong- Livernn-Liverpool University Postgraduate Research Scholarship PGRS2206013. Special thanks to Dr. Fan Zhang, from Xi' an Jiaotong- Uni- versity, for the constructive advice on the writing of this paper.
ETHICS STATEMENT
Our study does involve human subjects, sensitive data, or personally identifiable information. The datasets we use are publicly available and commonly adopted in the community. We are not aware of potential ethical risks related privacy, fairness, or misuse.
REPRODUCIBILITY STATEMENT
We are committed to ensuring the reproducibility of our results. Implementation details, including model architecture and training setup, are provided in Sec the main paper. We also include the source code and scripts the supplementary materials to facilitate replication of our results.
REFERENCES
Alexander A Alemi, Ian Fischer, Joshua Dillon, and Kevin Murphy. Deep variational information bottleneck. In ICLR, 2017.
10

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Published as a conference paper at ICLR 2026
Spyridon Bakas, Hamed Akbari, Aristeidis Sotiras, Michel Bilello, Martin Rozycki, Justin S Kirby, John Freymann, Keyvan Farahani, and Christos Davatzikos. Advancing the cancer genome atlas glioma mri collections with expert segmentation labels and radiomic features. Scientific data, (1):1-13, 2017.
Yuhang Ding, Xin Yu, and Yi Yang. Rfnet: Region-aware fusion network for incomplete multi- modal brain tumor segmentation. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 3975-3984, 2021.
Chengyu Fang, Chunming He, Longxiang Tang, Yuelin Zhang, Chenyang Zhu, Yuqi Shen, Chubin Chen, Guoxia Xu, and Xiu Li. Integrating extra modality helps segmentor find camouflaged objects well. arXiv preprint arXiv:2502. 14471, 2025.
Chengyu Fang, Heng Guo, Zheng Jiang, Chunming He, Xiu Li, and Minfeng Xu. Photon: Speedup volume understanding with efficient multimodal large language models. The Fourteenth Inter- national Conference on Learning Representations, 2026.
Solomon Kullback and Richard A. Leibler. On information and sufficiency. The Annals of Mathe- matical Statistics, 22(1):79-86, 1951. doi: 10.121 12t.11//oo///1777299999
Hong Liu, Dong Wei, Donghuan Lu, Jinghan Sun, Liansheng Wang, and Yefeng Zheng. M3ae: multimodal representation learning for brain tumor segmentation with missing modalities. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 1657-1665, 2023.
Tianyi Liu, Haochuan Jiang, and Kaizhu Huang. Kmd: Koopman multi-modality decomposition for generalized brain tumor segmentation under incomplete modalities. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp.
2025a.
Tianyi Liu, Zhaorui Tan, Muyin Chen, Xi Yang, Haochuan Jiang, and Kaizhu Huang. Medmap: Promoting incomplete multi-modal brain tumor segmentation with alignment. IEEE Journal of Biomedical and Health Informatics, 2025b.
Bjoern H Menze, Andras Jakab, Stefan Bauer, Jayashree Sallpath-Cramme Keyvan Farahani, Justin Kirby, Yuliya Burren, Nicole Porz, Johannes Slotboom, Roland Wiest, et al. The multimodal brain tumor image segmentation benchmark (brats). IEEE transactions on medical imaging, 34 (10):1993-2024 2024,, 2014.
Chengjian Qiu, Yuqing Song, Yi Liu, Yan Zhu, Kai Han, Victor S Sheng, and Zhe Liu. Mmmvit: Multiscale multimodal vision transformer for brain tumor segmentation with missing modalities. Biomedical Signal Processing and Control, 90: 105827, 2024.
Divya Ramakrishnan, Leon Jekel, Saahil Chadha, Anastasia Janas, Harrison Moy, Nazanin Maleki, Matthew Sala, Manpreet Kaur, Gabriel Cassinelli Petersen, Sara Merkaj. et al. A large open access dataset of brain metastasis 3d segmentations mri with clinical and imaging information.
Scientific Data, 11(1):254, 2024.
Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedi- cal image segmentation. In Medical Image Computing and Computer-Assisted Intervention (MIC- CAI), pp. 234-241. Springer, 2015.
Abdelrahman Shaker, Muhammad Maaz, Hanoona Rasheed, Salman Khan, Ming-Hsuan Yang, and Fahad Shahbaz Khan. Unetr++: delving into efficient and accurate 3d medical image segmenta- tion. JEEE Transactions on Medical Imaging, (3(9)33377-3390 2024.
Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, 2014.
Junjie Shi, Li Yu, Qimin Cheng, Xin Yang. Kwang- Kwang-Ting Cheng, and Zengqiang Yan. ftranns: Modality-masker fusion transformer for incomplete multi-modality brain tumor segmentation. IEEE Journal of Biomedical and Health Informatics, 2023.
Noam Slonim and Naftali Tishby. Document clustering using word clusters via the information bottleneck method. Proceedings of the 23rd annual international ACM SIGIR conference on Research and development in information retrieval, pp. 208-215, 2000.

---

Published as a conference paper at ICLR 2026
Naftali Tishby and Noga Zaslavsky. Deep learning and the information bottleneck principle. In 2015 ieee information theory workshop (itw), pp. 1-5. leee, 2015.
Naftali Tishby, Fernando C Pereira, and William Bialek. The information bottleneck method. In Proceedings of the Annual Allerton Conference on Communication, Control and Computing, pp- 368-377, 1999.
Luan Tran, Xiaoming Liu, Jiayu Zhou, and Rong Jin. Missing modalities imputation via cascaded residual autoencoder. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 1405-1414, 2017.
Yao-Hung Hubert Tsai, Paul Pu Liang, Amir Zadeh, Louis-Philippe Morency, and Ruslan Salakhut- dinov. Learning factorized multimodal representations. arXiv preprint arXiv:/806.06/ 76, 2018.
Hongqiu Wang, Wu Chen, Xiangde Luo, Zhaohu Xing, Lihao Liu, Jing Qin, Shaozhi Wu, and Lei Zhu. Toward fair and accurate cross-domain medical image segmentation: A vlm-driven active domain adaptation paradigm. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 24102-24111 2025.
Hu Wang, Yuanhong Chen, Congbo Ma, Jodie Avery, Louise Hull, and Gustavo Carneiro. Multi- modal learning with missing modality via shared-specifie feature modelling. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 15878-15887, 2023.
Mike Wu and Noah Goodman. Multimodal generative models for scalable weakly-supervised learn- ing. Advances in neural information processing systems, 31, 2018
Xiongye Xiao, Gengshuo Liu, Gaurav Gupta, Defu Cao, Shixuan Li, Yaxing Li, Tianqing Fang, Mingxi Cheng, and Paul Bogdan. Neuro-inspire information- -hheoretcccc hierarchical perception for multimodal learning. arXiv preprint urXiv:2404.0940 09403, 2024.
Aolin Xu and Maxim Raginsky. Information-theorett analysis of generalization capability of learn- ing algorithms. Advances in neural information processing systems, 30, 2017.
Jiangpeng Yan, Shou Chen, Yongbing Zhang, and Xiu Li. Neural architecture search for compressed sensing magnetic resonance image reconstruction. Computerized Medical Imaging and Graphics, 85:101784, 2020.
Dongsong Zhang, Changjian Wang, Tianhua Chen, Weidao Chen, and Yiqing Shen. Scalable swin transformer network for brain tumor segmentation from incomplete mri modalities. Artificial Intelligence in Medicine, 149: 102788, 2024.
Yao Zhang, Nanjun Hc, Jiawei Yang. Yuexiang Li, Dong Wei, Yawen Huang, Yang Zhang, Zhiqiang He, and Yefeng Zheng. mmformer: Multimodal medical transformer for incomplete multimodal learning of brain tumor segmentation. In International Conference on Medical Image Computing and Computer-Assiste Intervention, pp. 107-117. Springer, 2022.
Zixiang Zhao, Haowen Bai, Jiangshe Zhang, Yulun Zhang, Shuang Xu. Zudi Lin, Radu Timofte, and Luc Van Gool. Cddfuse: Corvelation-driven dual-branch feature decomposition for multi- modality image fusion. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 5906-5916, 2023.
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A PROOF OF PROPOSITION 1
Proof. From Theorem
2 the MI-based generalization bounds for hIB and hp are
T(ZIB:
(r(h) S es cs ov T(Zp; X)
er (h(1B) S cs(hIB) + ev
n
n
Subtracting the second inequality from the first gives an upper bound on their difference:
eT(hIB) - ( S A + (V ([ZiBis)
X)
A= e Es(hp)
n
71
The second term c(.) in the aforementioned inequality will be negative because the IB objective explicitly penalizes redundant information from the input:
(h)(h) = + (((:)))))()))-----))))))))))>))) (I),, B> 0.
Thus, ZiB compresses X to preserve only task-relevant subset, often with even smaller [(ZIB: B: X) than [(X; Y). In contrast, the parallel fusion representation Zp does not restrict I(Z; XX) and typ- ically retains more task-irrelevant noise, given (Zin; X) < (Zp; X). Denote g = I(Zp: X) T( X) >> 0, then we will obtain
(V [(ZIBiX)
I(Zp:
cg
<0.
Vnl//((Zp:X) + VI(ZIB:X))
The threshold condition
((Zxi
I(ZiB:X)
A <c
typically easy to satisfy: remains small because the IB-based fusion model primarily discards lusk-irrelevant information. Empirical risk will not be increased significantly, while g is positive as the parallel fusion model retains additional redundant information. Therefore, the right-hand side of the inequality for (T(hBB) (h,,) is strictly negative, leading to er(hIB) eT(p)) Therefore, the IB model achieves a strictly tighter generalization bound.
B JUSTIFICATION OF ASSUMPTION 1
We now explain that this assumption reasonable in the case of medical multi-modal fusion tasks.
The term I(Zp: Xes X;) represents the conditional mutual information between the fusion latent variable Zp and all other modalities X given modality X,, This term measures the amount of information retained by Z, about the other modalities once X; is known. The term T(Zi X; X41) represents the conditional mutual information in the IB model, capturing the dependence of each modality the rest of the modalities. We have 1 [(Zp: Xzi (x,) > X4) Xzt).
In practice, the modalities in data are strongly correlated. This means that the parallel fusion model Zp can preserve more information about the inter-modal relationships compared to the IB fusion model, which is designed to compress information to retain only the most relevant aspects for prediction. As result, 7 T(Zp: Xx; X,) tends to be larger than the corresponding terms in the IB model. We may relax the bound to T(Zp: Xxi X.) > 27(ZIB; X²s) T(ZIn; X; Xx1)-
To empirically validate this assumption, we compute the mutual information for both the parallel fusion and IB fusion models on our dataset. The computed values show that: Σ I(Z,; Xei X,) 0.2817 and E (-I(ZIB:X) X+4) I [Z ((1)::++;))
0.0709. These results support the validity of the relaxed bound, demonstrating that the information preserved by the parallel fusion model is indeed larger than equal to the relaxed bound defined by the IB fusion model.
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C PROOF OF PROPOSITION 2
Proof. We start by expanding the mutual information for both the parallel fusion model Zp and the information bottleneck (IB) fusion model ZıB. For the parallel fusion model, we have the following expansion for the total mutual information:
I(Zp: X1 x Σ
X.,) -
X2) - Xei))
i=1
For the information bottleneck model, we expand the total mutual information as:
[ XI........... X,,) Σ (I(ZIB:X)) - | Xxs) + [( Xx:)) 2=1
We have more Inequalities: Information of single modality preserved by parallel fusion larger than that preserved by IB fusion: Σx=1 / (Zp;X,) 2 1 ((11;;
Negative value of the information of the preceding modal set in parallel fusion smaller than that in IB fusion: -im1 (Zpi X<i) I - - I(Zr;; Xzi).
Therefore, rewrite the total mutual information for the parallel fusion model Zp follows:
T(Zp; X,, , x,) = Σ x Xea X2) X(x)
I(Zini X:)
(x: |
[(2;:x))(((11:88)
+
(-I(Znn:
Σ + - I(Zrn;Xe Xys) I(Znn;
-
Σ (T(Z)B; X,) I(ZIB; X, Xx4) + I(ZIB: X+1))
X,,
D JUSTIFICATION OF ASSUMPTION
We decompose the fusion-based missing-modalii model into three components: encoders, fusion function, and a decoder, and show that each satisfies Lipschitz continuity.
For the i-th modality, let the input space be X; and the encoder Si X, Z. Assume that for any Iz x E Xr the encoder is Lipschitz continuous, i.e.,
[[f((x;) f(x))) L,1x; x/ح1,
where || denotes the norm in the respective space. The fusion function at each step, denoted by Φ, Zi-1 Z: Ziiued also Lipschitz continuous, i.e.
[1 2:) dx(2)_ 2/)l < Lop (1l=-1 2 ll + ||2, =;ll),
and the final decoder g : ZM + y is Lipschitz continuous with constant Lg.
Since the composition of Lipschitz functions is Lipschitz continuous with constant given by the product the individual constants, the full function
G(x) g ΦM
á1 (f1....,
Lipschitz continuous, where o represents the function composition. In practice, spectral normal- ization ensures that each module can be implemented as 1-Lipschitz. Therefore, without loss of generality, the entire missing- model can be regarded as 1-Lipschitz, which justifies As- sumption 2
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E LIPSCHITZ BOUND OF FUSION MODELS
Proposition 4 (Lipschitz constants of IB fusion). Suppose that there are M modalities to be fused.
Let F(115...,2A, FM) := 00.00o---0000 (fi(=))...., (Zx)) denote the multi-modal prediction function based on step-wise IB fusion. o represents the function composition. Under Assumptions the function F Lipschitz continuous with Lipschitz constant bounded above by induction on the number of fusion steps: LF 2 bg II Lø. -i.
Proof. Let 8 = (21 the output of the first encoder, which is -Liischittz by Assumption 2
For the first fusion step, define スσ Φ1 (²1, f2(12)) By Assumption 2 is L Lipschhiz in each argument. Since f2 is Lz-Lipschitz, the composition satisfies 22 is Lø, L1 Lz-Lipschitz.
Suppose after fusion steps, the representation 2,41 is Lipschitz with constant
L4+1
II Lo, Lg
Lit1-
Then for the 1)-th step,
E ox+1 (žt41, (2+2(2242))
Applying the Lipschitz property of Φs+1 in each argument and the inductive hypothesis, we obtain
Li+2 S Lous L Li+2-
By induction, after all the M modalities are step-wisely fused, the obtain representation MM+ sat- isfies the Lipschitz constant
II Lo: Li.
Finally, applying the decoder with Lipschitz constant Lg. we can obtain:
Fl xM) = (EM++1)
Thus, the upper bound of Lipschitz continuous function Ly with constant will be greater than Lg II Lo: L,, which is represented by:
M
LF < Lg
II Lo. Li.
This completes the proof.
Proposition 5 (Lipschitz constant of concatenation- fusion). Let Fronens (I1..., Tar) g heoncar (f1 (x1), f2(2)),... (xM) denote the overall multi-modal prediction function based on concatenation fussion, where heoneat Zi X
ZM + Ziused performs concatenation followed by mapping (e.g., fully connected layer), and g Ziased + y is the final decoder. Assume each encoder fa X, Z, Lipschitz continuous with constant Li, and heoneat- 9 are Lipschitz continuous with constants Lroneat and Lg. respectively. Then F Fooncat is Lipschitz continuous with constant bounded by
M Σ
LFanna S Lbg Leoneat
1
Proof. Let & =
E B1 x..... .... x Zas. Then, by engaging the Euclidean norm,
|| 2/11
Σ [1(().) {(()))1
Σ I 22 2r!1?
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By the Lipschitz continuity of heoncat and 9, have
|| concaat (x) Feoncat (2 llg (Aconcat (2)) g g (cconcat (z'))l
Lg heoncat (z) hooncar (2')l
Lg Lconcct ||
2'1l
M
S Lig Leoneat
Σ
1 a| - a/11?.
This proves the stated bound.
Proposition (Lipschitz constant attention-based fusion). Let Fatta (atta(a1,... ".11....,11 hauta (fi (x1)........ (xsss) denote the multi-moda prediction function with aitention-based fu-
sion, where each encoder fo Xg + Z, is Li-iipshitzz continuous, hava is the attention based fusion, and is the decoder. Assume hattn and g are Lipschitz continuous with constants Taatn and Tyg, respectively. Then Pattn is Lipschitz continuous with constant bounded by
M Σ
LFasu S Lg Lastn
D
Proof. Let = (Ji(z1),... (M(())))...,M((M))))) E, x.... ...x EM. Then
M || - 2'11 [1(((z)) -(
M
Σ
17 - x!11?.
By the Lipschitz continuity of hattn and g.
|Faut (xx Fattn (x')ll (1g(heeen (z)) @/harea (=)))1
< Lg llaeenn (2)
-atnn (z'))l
< Lg Lattn
|| z'1l
M 11| - =2,112
Σ Lg Luttn
This proves the stated bound.
Remark 3. Both concatenation- fusion and attention- based fusion are examples of parallel fusion. They share the same Lipschitz constant upper bound:
M
L T. Lp .
Σ
L
T=1
where Ly is replaced by Leoncet or Lattn depending on respective fusion method.
F PROOF OF PROPOSITION
Proof. Since all L, < 1, their product satisfies: I L, S min, L, By definition of la norm M
and lo norm, we have: min; L; < max; L; S / E LJ. Similarly, since Lo, have: M
I Le, Combining them together, we will obtain:
Lo.
L
II ==1
L < min I
Σ
17. 1=1
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Multiplying both sides by Lg. and noting LA 2 typically for concatenation mappings, gives
M
M
II
Lo.
S Lg
Σ
1 S Lg
Ln
Σ L
Therefore,
I.paratlel 1.
I.equential L.
It theoretically evidences that the fusion is potentially
smoother.
G ADDITIONAL EXPERIMENT RESULTS
G.1 SEGMENTATION RESULTS ON NO-FUSION SOTAS
Table presents the comparisons of segmentation with the proposed SMSN and non-fusion ap- proaches, including Shaspec and m3ae on the BRATSI8 18 and the BRATS20 datasets. SMSN demon- strates consistent improvements across most missing-modality scenarios. particular, we observe average improvements of about 1 DICE for the WT and TC classes, and more than 5 DICE for the ET class.
Table Missing modality segmentation results of MRI on BRATS18 and BRATS20: Num denotes the number of missing modalities for different settings. NM is the missing number. Each column shows the average dice of different NM. The results of each setting are presented accordingly. The best results highlighted in red while the second best highlighted in blue.
Class
Method
NME3
NSE2
BRATSIS
NMEI
Full
AVG.
NYES
NMF3
BRAIS20
NMET
Full
AVG
85.65
88.34
85.25
77,60
89.19
Shaspes
78.12
78.77
59.91
ours
8006
86.29
88.85
88.71
85.02
82:43
33.97
89775
50.00
87.34
68.60
75.01
79.42
74.87
70.32
77.64
51.76
77.21
shaspec
ours
08.05
75.02
29.93
82:35
75.20
71.86
79.12
83.25
50.90
78.30
minlommer
42.32
53.81
63.01
70.94
54.34
47.54
56.82
64.43
71.
$7.34
shaspee
71.43
OUTT
70.91
51.00
G.2 DETAILED GENERALIZATION RESULTS
Missing modality segmentation results of different dusion-basedd models pretrained on BRATS20 and predicted without any finetuning the Brain Metastases (BM) dataset is illustrated in Table 7 Our proposed approach consistently outperforms other fusion-based methods across all missing modality configurations, demonstrating its superior generalization performance.
Table 7: Missing modality segmentation results different fusion-based models pretrained on BRATS20 and predicted without any finetuning Brain Metastases (BM) dataset. The best sults are highlighted red while the second best is highlighted in blue. ~ means without, From top bottom, illustrates the results of WT, TC, and ET respectively.
TIC
<TT2
</T1
o.F
AVG.
mmForrer
32.17
36.20
18.12
43.61
27.38
15.29
32,00
44.36
34,87
30.47
24.03
4.70
33.43
12.04
57.15
25.43
58.04
62.
55.16
51.91
51.34
51.95
49.96
IMSTrans
50.71
46.02
40.97
57.51
53.91
47.62
59.04
54.33
39.05
59.3
60.11
39. 86
59.59
54.93
60.14
54.98
OZES
54.22
08.87
55.42
57.23
56.23
50.65
60.35
56.25
39.25
62.89
02.36
00.72
60.50
57.35
61.35
57.03
mmFurmer
M2FT
21.81
41.09
23.73
46.52
45.60
31.5
26 17
49.9
52.
47.13
38.62
MMVIT
22.78
43.75
20.80
22.77 75
46.18
43.63
27.07
23,80
26.40
49.09
40.74
78
47.51
47.04
36.90
IMSTrans
23.90
47.77
16.71
23. 76
50.36
47.10
24.44
27.34
29.75
52.63
53, 28
31.21
52.33
51.57
53.51
39.01
mimi GEHNCE
8.07
14.33
3.10
1.50
6.01
2.87
3.10
10.2
1.1b
10.12
5.08
0.38
8.15
1,92
5.73
5.78
MIFTmas
15.25
38.25
15:34
16:49
41.34
40.76
20.95
17.52
20.000
46.29
47.38
21. 21.82
45.95
41.50
46.67
31.74
MMVII
42.14
30.64
10.86
13.17
43.56
19.27
43.02
43.62
20:78
44.01
3062
20.36
47.37
19:30
17.53
49007
47.05
22.84
24.13
22.55
52.92
53.23
24.25
51.27
50001
51.72
36.0
17

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Published as a conference paper at ICLR 2026
G.3 SENSITIVE ANALYSIS OF DIFFERENT ORDER
As shown in Table 8 both a fixed ordering and a purely random ordering without ensuring that the first modality corresponds to present modality lead to degraded segmentation performance. These findings underscore the importance of the proposed reordering strategy, which ensures that the sequential fusion process begins with a valid and informative modality, thereby enabling more stable and effective feature integration.
G.4 SESSITIVE ANALYSIS OF DIFFERENT BOTTLENECK SIZE
To evaluate the sensitivity of SMSN to the bottleneck dimensionality and the sequential fusion order, we conducted additional experiments using various combinations of bottleneck sizes (see Table 9 Since the channel dimension of each modality is 128, we tested range of bottleneck sizes around this value. The results indicate that SMSN achieves the best performance when the two bottle- neck dimensions are 128 and 256. This observation suggests that the chosen bottleneck sizes are appropriate, as excessively deviating from the original modality channel dimension may hinder effective feature transformation and cross- modall interaction.
G.5 SEGMENTATION RESULTS ON BRATS24
Missing modality segmentation results different fusion-based models on the BRATS24 dataset (200 samples) is illustrated in Table 10 Our proposed approach consistently outperforms other fusion-based methods across all missing modality configurations, demonstrating its superior gener- alization performance.
G.6 MORPHOLOGICAL DIFFERENCE BETWEEN GLIOMAS AND METASTASES
As illustrated in Figure gliomas typically originate within the brain parenchyma and present as infiltrative lesions with indistinct margins, often demonstrating heterogeneous signal intensities and irregular, infiltrative enhancement patterns. In contrast, metastases usually appear as well- circumscribed, round or ovoid lesions with sharp boundaries, often accompanied by pronounced peritumoral edema that exceeds the size of the enhancing lesion itself. These differences in margin definition, enhancement pattern, and surrounding edema provide important radiological clues for differential diagnosis.
Table 8: Missing modality segmentation results of SMSN on BRATSI8 with fixed and random fusion order. Fixed means fixed order and started from a modality contains less information (TI). The order is T1, T2, Flair and Tlc. Fixed means fixed order and started from modality with more information (Tlc). The order is Tlc, T2, Flair and TL. means without. From top to bottom, illustrates the results of WT, TC, and ET respectively.
11
FT1
<112
Fised
83.49
71.72
73.72
86.21
85.11
77.12
86.94
84.88
87 70
53.01
87.52
87.58
53.24
85.44
88.
84.16
Fixed
53.00
71.79
72.93
87.44
85.18
77.32
89.04
85.37
89
89.56
89.14
89.10
90.09
85.60
89.95
$4.99
only
Random and present first
76.35
76.26
87.82
$3.71
89.00
$6.93
88.71
Fixed
58.51
36.79
62,39
60.20
79.64
79.45
68.44
68.75
65
79.31
30.80
69.38
79.27
81.33
81.46
72.70
80.54
Random only
76.30
63.09
78.73
78.70
78.99
Random and present first
08.27
79.72
62.34
61.35
83.57
30.25
67.70
68.55
70.78
82.35
85.17
70.77
$2.81
82.96
81.35
75.20
Fixed
41.56
67.62
33.80
33.53
73.79
72.06
39.26
45.16
41 44
73.27
73.85
44.66
72.88
74.22
73.71
$7.30
Random only
31.29
63.77
33.55
33.36
65.00
64.68
39.02
39.87
40.52
66.80
65.80
42.53
69.51
66. 34
67.40
52.58
Random and present first
44.51
78,87
36.55
39.31
79.70
79.37
44.42
46.25
46.09
78.38
80.30
45.71
78.91
78.70
78.58
62.39
G.7 COMPARISON OF COMPUTATIONAL COSTS
Compared with pure parallel fusion frameworks such mmFormer, SMSN does not require sub- stantial increase in the number of learnable parameters, as shown Table II Despite a relatively longer training time. SMSN achieves superior segmentation accuracy while maintaining compara- ble inference time. This demonstrates that sequential fusion can provide performance gains without incurring significant parameter overhead.
18

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Published as a conference paper at ICLR 2026
Table 9: Missing modality segmentation results of SMSN on BRATSI8 with (two) different bot- tleneck size. means without. From top to bottom, it illustrates the results of WT, TC, and ET respectively.
Size
T2
TTC
T1
T3TIC
TITIC
FTI
T1T2
FT2
FTTC
mxT2
<.
-
A-F
AVG
51,
50,49
69.39
27
65.77
K2.23
71.95
84.82
81.90
56.02
84.86
61.92
56.63
56.64
82.20
86
61
178
88.62
43
83.01
128. 256
85,49
76.33
76.26
81.38
96.45
79.62
87.82
85.61
38.51
98.71
89.09
89.98
86.93
89.39
88.71
85
256. 512
82.38
71.40
73:46
86.91
$4.70
77.03
88.67
84.94
55.
87.89
68.30
88.91
89.05
85.28
89.40
64.46
82.40
72,42
70.22
83.91
$4,29
76.34
85.98
83.98
96.51
96.25
87.17
84.46
87.08
K3.79
64,
59.64
76.34
58.58
59.63
77:12
67.74
65.07
78.69
80002
69.74
79.28
79.77
M0.36
64, 128
55.55
74.59
57.80
56.18
78.
77.54
65.07
62.95
00:43
78.59
78.64
64.46
77.69
78.64
78,80
69
128. 256
68.27
79.72
62:34
61.85
83.57
60.75
67.70
68.55
70.78
82.35
83.17
70.77
82.81
82.96
82.35
75.30
65.30
78.92
71.33
512, 512
57.87
74.77
54,90
58.13
76.57
75.10
66.05
63.87
75.99
77.53
67.92
76,81
77.51
78.12
69.33
61.61
34,55
65.87
29.14
29.10
70.85
68.59
35.11
36.01
35.48
71,95
72.11
40.73
7185
71.36
71.00
$2.93
64, 128
35.97
63.77
29.56
27.60
69
65.90
32.53
39.40
37.03
68.82
69.
38.47
71.52
69.68
73.31
53.61
44.51
78.87
79.37
46.09
78.58
80
45.71
78.91
78.70
78.58
62.39
256, 312
39,67
71.99
35.51
34,90
72.85
72.08
40.57
44.47
43.62
73.89
73.94
46.15
73.81
73.83
73.50
$8.04
512, 512
36,82
68.58
26.09
25.11
72.35
71.82
34,03
41.37
38.58
70.20
73.65
42.62
72.41
73.26
73.70
55.89
Table 10: Missing modality segmentation results of different fusion-based models trained on BRATS24, means without. From top to bottom, it illustrates the results of WT, TC, and ET respectively.
Method
T2
TIC
T2 TIC
TI TIC
FTI
TI
FT2
FTIC
<012
~T
AVG.
mmFoonter
71.42
66.39
78.31
74:55
69.75
81.43
74.90
82.35
50.49
82.01
82.07
83.31
75.90
83.25
76.67
M-PTrans
72.77
63.49
66.95
75.13
76.45
66
81.48
74.31
$1.93
83.97
82.76
83.05
83.00
77.62
83.63
76.76
MMMVIT
27.41
26.41
23.66
28.12
29.5
78.
IMS Trans
63.81
53.80
57.04
69.49
69.51
59.56
76.10
70.24
76.56
74.74
75.70
77 40
78.35
71.54
78.47
70.15
SMSN (ouns)
71.67
63.55
69.47
82.67
76.77
66.93
82.76
72.38
26
50
84.07
84.88
84.85
74.91
84,70
77.76
cenner
35.27
12.59
11.45
41.74
41.67
13.49
19:07
13:45
41.33
41.54
17.05
23.87
21.75
M PPrras
6.27
21.31
10.22
8.95
22.63
23.08
11.45
7.06
9.07
24.18
25.05
10.32
24.19
23.66
24.59
16,80
MMMVIT
1.73
4.27
2.39
2.82
2.25
2.14
4.39
4.23
4,51
3.33
Iransrans Trans
5.08
28.67
10.50
7.90
32:13
36.90
11.95
9,46
7.91
33.13
36.65
13:65
33.97
38.96
38.46
23.02
SMSN (ouns)
9.14
35.44
17.43
17.43
39.09
45.61
27.37
9.80
21.32
44.57
47.21
22.55
43.97
45.36
42.60
31,25
Conner
20.59
31.50
59.30
25.31
27.85
20.51
55.62
60.05
26.51
35.21
37.25
11.43
PTrans
22.38
49.21
28.72
17.46
52.74
57.10
25.05
26.10
25.14
49.97
57.97
27.61
55.30
58.45
57.89
40.94
MMMVIT
28.95
55.58
27.38
30.91
58.14
58.39
29.97
33.83
31.50
58.27
62.91
33.57
55.71
60.50
45.45
Irans
Trans
20.13
28.41
9.87
9.22
57.16
38.94
14.08
17.26
24.92
35.56
43.92
22.02
42.64
44.17
49.98
29.22
SMSNN (ouns)
22.07
51.00
32.77
25.54
53.82
00.84
28.28
27.00
27.55
55.13
59.88
28:15
54.54
00.53
58.27
43.01
In addition, SMSN delivers strong performance under incomplete-modality scenarios without in- troducing notable computational overhead relative to attention-based fusion methods. In particular, compared with the second-best approach, F2Farans, the Two-Stage Information Bottleneck Fu- sion Module in SMSN adds only a marginal number of trainable parameters and results in nearly identical training time. These observations indicate that SMSN attains its improvements without imposing a substantial trade-off in computational efficiency when compared with attention-based fusion strategies.
Table 11: Comparison of the number of model parameters, Gilops, training time, inference time, throughput, complexity, and average segmentation performance of different models on different classes (WT/TC/ET). Assume there are n modalities and the feature dimension of each modality is d.
Pummeters
Giflops
Training Time//poch Inference: Timo/Epach Thrughput
Camplesity BRATSIR DSC Generalization
mmFaaneer
36.65
125.83
53.89
34,50
2.66
O(ndF)
8438873.2555444
28.4378 69/5.995.. 78
M-PTrass
113.36
1.27
O(n2d)
55.16/38. 02338.662/1..74
MMMVIT
16.98
107.51
48,80
12.26
237
O(n
78.5471.9955.21
49.90236.3033.644
IMS-Tram
101.18
43.27
44.53
331
O(n
83.3768 76054.66
54.98/39.044 094729044/3.64
SMSN (ours)
111.33
109.22
33,09
1.28
O(nda)
5362775.2006239
77,0644577036..8
H LLM USAGE STATEMENT
We employed ChatGPT 5 to help polish the language and improve the readability. No LLMs were involved in designing experiments, analyzing data, or contributing to the scientific findings of this work.
19

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Published as a conference paper at ICLR 2026
(a) Gliomas
(b) Metastases
Figure 5: Comparison between gliomas and metastases. Gliomas are typically infiltrative with ill-defined margins and heterogeneous enhancement, whereas metastases usually appear as well- circumscribed lesions with sharp boundaries and prominent peritumoral edema.
20


Reviews:
[{"review_id": "YNwPdPHcVE", "reviewer": "Reviewer_KjqD", "summary": "This paper proposes a Sequential Multi-modal Segmentation Network (SMSN), a novel method for brain tumor segmentation in the context of missing-modality MRI settings. The key idea is to perform sequential fusion using an Information Bottleneck Fusion Module (IBFM), instead of standard parallel fusion. The authors provide theoretical justification (generalization bound, Lipschitz robustness), and empirically validate SMSN on BRATS18/20 and a metastasis dataset. Results show improved robustness and cross-domain generalization.", "questions": "1. How sensitive is performance to the chosen bottleneck size and sequential order?\n2. Is there a trade-off compared to pure parallel fusion?\n3. Can the proposed method scale to more than 4 modalities or other domains, such as CT + MRI?\n4. What is the computational overhead of sequential IB vs. attention-based fusion?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper proposed a novel sequential IB-based fusion with two-stage IB and modality reordering, which is a meaningful contribution.\n2. The paper provides generalization and Lipschitz analysis and connects it to empirical behavior.\n3. Evaluation on multiple MRI datasets, missing-modality scenarios, and cross-dataset generalization demonstrated the improved performance.", "weaknesses": "See the questions part.", "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": "NjteLW7Bxt", "reviewer": "Reviewer_u9EX", "summary": "This paper proposes the Sequential Multi-modal Segmentation Network (SMSN). The shared information across modalities is gradually extracted via a two-stage Sequential Information Bottleneck Fusion approach, while modality-specific information is separated using a Transformer-based module and orthogonal loss. This design enhances the robustness and cross-domain generalization of segmentation in modality-deficient scenarios. The paper provides theoretical derivations to demonstrate the proposed method’s advantages, and these derivations include a tighter generalization upper bound and Lipschitz boundary comparison. It also conducts extensive modality-deficient experiments on the BRATS18 and BRATS20 datasets. Furthermore, to verify cross-domain generalization, the model trained on BRATS20 is directly transferred to a brain metastasis dataset. Experimental results show that SMSN outperforms multiple parallel fusion baselines in terms of average Dice score and performance under modality absence.", "questions": "1. In Proposition 2, the authors prove that the sequential information bottleneck model can ensure a tighter upper bound on generalization errors under the condition that the encoder, fusion module, and decoder are all 1-Lipschitz continuous. However, this condition faces challenges in the actual implementation of deep networks. Specifically, when using Transformers, self-attention with softmax often results in a Lipschitz constant greater than 1 during gradient propagation, and other modules also tend to amplify gradients. As a result, the network does not naturally satisfy Lipschitz continuity. How should this issue be addressed?\n2. The derivation of sequential information bottleneck relies on the assumption of conditional independence between modalities. Have the authors theoretically proven or empirically verified the approximate validity of this assumption? If there is strong correlation between modalities, are there corresponding mitigation strategies?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The advantages of sequential information bottleneck fusion in terms of the Lipschitz upper bound and the mutual information-based generalization bound are proposed and proven, forming a complete theory-proposition-proof chain that is rigorous and reliable.\n* Comparisons with multiple parallel fusion and non-fusion baselines were conducted on BRATS18 and BRATS20 datasets, encompassing scenarios with different modal absences, cross-domain tests transferred to brain metastasis datasets, as well as ablation and hyperparameter sensitivity analyses. These experiments are comprehensive and thorough.\n* The paper is accompanied by source code and supplementary materials. The method section provides detailed modular implementation details, including two-stage information bottleneck fusion, modal reordering, reconstruction loss and orthogonal loss, to facilitate reproducibility.", "weaknesses": "* While the paper's primary motivation is to address the issue of missing modalities and claims that the sequential information bottleneck framework exhibits greater stability under such conditions, it lacks direct theoretical validation or quantitative analysis to demonstrate that the information bottleneck objective remains valid under the distribution of missing modality scenarios.\n* The paper fails to discuss the computational overhead of SMSN, such as the number of model parameters, training or inference time, and complexity in comparison to baseline methods. Sequential fusion, additional reconstruction processes and orthogonality losses may introduce substantial computational costs, which is an important practical consideration for resource-constrained real-world environments.\n* In Section 4, this paper introduces a modal reordering strategy, motivated by the need to avoid initiating sequential fusion with a missing modality represented by a zero tensor, thereby preventing degradation of the information bottleneck objective function. While this design is logically sound, the paper lacks sufficient empirical support and provides no comparative experiments like fixed-order fusion versus random reordering.", "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": "NDCQhRorH0", "reviewer": "Reviewer_yaho", "summary": "This paper addresses the challenge of brain tumor segmentation in multi-modal MRI when some imaging modalities are missing. Unlike traditional parallel fusion methods that risk losing shared inter-modal information, the authors propose a Sequential Multi-modal Segmentation Network (SMSN) based on an Information-Bottleneck Fusion Module (IBFM). By sequentially fusing modalities, the approach preserves shared information and reconstructs modality-specific features, leading to more robust and generalizable representations. Experiments on the BRATS18 and BRATS20 glioma datasets show that SMSN outperforms parallel fusion baselines, maintaining strong performance even with missing modalities and transferring effectively to a brain metastasis dataset without fine-tuning.", "questions": "N/A", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The sequential fusion design preserves shared information, maintaining high segmentation accuracy even when some MRI modalities are absent.\nIt achieves improved cross-domain performance, successfully transferring to new datasets without fine-tuning.\nThe method is supported by information-theoretic analysis, ensuring more efficient and reliable feature fusion than parallel approaches.", "weaknesses": "It is confusing for this missing-modality task, as the authors use the BraTS series datasets, which already contain complete modalities. However, in real scenarios, if some modalities are missing, it becomes difficult to obtain accurate segmentation labels. How do the authors explain this situation?\n\nMoreover, the datasets used in this paper are somewhat outdated, which may affect the evaluation of the proposed method.\n\nBesides segmentation, I think other related tasks should also be tested, for example the classification task.", "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": "pfNgrSImzg", "reviewer": "Reviewer_2A7s", "summary": "To address the problem of missing modality segmentation in multimodal brain tumor MRI, this paper proposes the Sequential Multi-modal Segmentation Network (SMSN). Its core is information bottleneck-based sequential fusion (IBFM), which gradually aggregates modalities to extract modality commonalities while preserving modality specificity. The authors theoretically demonstrate that this sequential fusion approach has a tighter generalization upper bound and is more robust to missing modalities than parallel fusion. The paper also implements SOTA on BRATS18/20.", "questions": "1. Is the modal fusion order designed in the article fixed or random? Figure 3 shows a sequential fusion method for all modalities, but there are no examples of cases where one, two, or three modalities are missing.\n2. Does a different modal order significantly affect model performance? Most existing unified/parallel fusion methods are not affected by modal order and appear more stable.\n3. Do the parameter settings for β and γ change depending on the missing modalities, or are they fixed?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Compared to most existing unified/parallel fusion methods (such as mmFormer, M2FTrans, MMMViT, and IMS2Trans), this paper's approach is highly innovative.\n2. The paper's theoretical proofs are rigorous and contribute significantly to the field of modal fusion.\n3. The paper's experimental design is comprehensive, with detailed reporting of various scenarios.\n4. The paper's visualizations compare existing methods and strongly demonstrate the model's effectiveness.", "weaknesses": "1. The article provides very little explanation of the specific implementation method. Is the modal fusion order designed in the article fixed or random? Figure 3 demonstrates a sequential fusion method for all modalities, but does not include examples of cases where one, two, or three modalities are missing.\n2. The article's core innovation builds on the previous work on ITHP, which proposed the core concept of sequential fusion. This paper implements SOTA on a medical dataset and further provides theoretical proof.\n3. Compared to most existing unified/parallel fusion methods, does this method consume more computational resources? This article suggests addressing model overhead (number of parameters, FLOPs, throughput, video memory, and training time) to facilitate a fair comparison of lightweight solutions.", "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)