Permutation-Consistent Variational Encoding for Incomplete Multi-View Multi-Label Classification
Authors: Chengliang Liu
Bo Li
Bob Zhang
Xiaoling Luo
Yabo Liu
Jie Wen
Venue: ICLR 2026 Poster (2026)
Keywords: Multi-Label Classification
Multi-View Learning
Information bottleneck
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: We propose a Permutation-consistent variational coding framework that permutes and aligns multi-view latent encodings to robustly classify incomplete multi-view data with multiple labels.

Abstract: Incomplete multi-view multi-label learning is fundamentally an information integration problem under simultaneous view and label incompleteness. We introduce Permutation-Consistent Variational Encoding framework (PCVE) with an information bottleneck strategy, which learns variational representations capable of aggregating shared semantics across views while remaining robust to incompleteness. PCVE formulates a principled objective that maximizes a variational evidence lower bound to retain task-relevant information, and introduces a permutation-consistent regularization to encourage distributional consistency among representations that encode the same target semantics from different views. This regularization acts as an information alignment mechanism that suppresses view-private redundancy and mitigates over-alignment, thereby improving both sufficiency and consistency of the learned representations. To address missing labels, PCVE further incorporates a masked multi-label learning objective that leverages available supervision while modeling label dependencies. Extensive experiments across diverse benchmarks and missing ratios demonstrate consistent gains over state-of-the-art methods in multi-label classification, while enabling reliable inference of missing views without explicit imputation. Analyses corroborate that the proposed information-theoretic formulation improves cross-view semantic cohesion and preserves discriminative capacity, underscoring the effectiveness and generality of PCVE for incomplete multi-view multi-label learning.

Published as a conference paper at ICLR 2026
PERMUTATION-CONSIITEENT VARIATIONAL ENCOD- ING FOR INCOMPLETE BULTI-VIEWS MULTI-LABEL CLASSIFICATION
Chengliang Liu!
Bo Li!
Bob Zhang
Xiaoling Luo²
Yabo Liu
Jie Wen
University of Macau
Shenzhen University
Ocean University of China
Harbin Institute of Technology, Shenzhen
1iucl19968 63 com
bo_li 1ilill1666 (3.16..o com bobzhang@um, edu mo
xioliingluooeettoooo com
yaboliu. ama.aa....mmmmmm.mmmmmmmm....... com. jiewen.pr@12 p22 com
ABSTRACT
Incomplete multi-view multi-label learning is fundamentally an information in- tegration problem under simultaneous view and label incompleteness. We in- troduce Cermutation-Consisse information bottleneck strategy, which learns variational representations ca- pable of aggregating shared semantics across views while remaining robust to incompleteness. PCVE formulates principled objective that maximizes varia- tional evidence lower bound to retain task-relevant information, and introduces permutation-consister regularization to encourage distributional consistency among representations that encode the same target semantics from different views. This regularization acts as an information alignment mechanism that suppresses view-private redundancy and mitigates over over-alignment, thereby improving both sufficiency and consistency of the learned representations. To address incom- pleteness, PCVE further incorporates masked multi-label learning objective that leverages available supervision. Extensive experiments across diverse benchmarks and missing ratios demonstrate consistent gains over state-of-the-art methods in multi-label classification, while enabling reliable inference of missing views with- out explicit imputation. Analyses corroborate that the proposed information- theoretic formulation improves crews-view semantic cohesion and preserves dis- criminative capacity, underscoring the effectiveness and generality of PCVE for incomplete multi-view multi-label learning.
Variational Encoding framework (PCVE) with
INTRODUCTION
Multi-view multi-label learning has become central paradigm for modeling complex entities that are naturally described by heterogeneous sources (e.g., image-text pairs, multi-sensor signals, or multimodal clinical records) and annotated with multiple, potentially correlated labels. By jointly exploiting complementary and redundant information across views, multi-view learning methods can efficiently enhance semantic coverage, reduce ambiguity, and capture high-level discriminative feature for downstream tasks Fang et al. (2022); Qin et al. (2025a); Fang et al.) (2025). However, real-world deployments rarely enjoy complete data: views and labels are frequently missing due to acquisition failures, privacy constraints, cost. Under such inevitable view and label incomplete- ness, extracting and aggregating shared information across views becomes markedly challenging due to unreliable cross-vies view alignment, dominated view-private noise, and sparsely informative pervision, degrading representation sufficiency and predictive performance Qin et al. (2025b); Li al. (2025a). In this paper, define this multi-view learning task with double missing issue incomplete multi-view missing multi-label classification (iM3C).
"Corresponding authors

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Despite recent advances, multi-view learning still struggles with the core goal of representation suf- ficiency, i.c, joint embeddings should retain as much task-relevant information as is shared across views while discarding view-private nuisance Qin & Qian (2024). von-probabiilistic deep methods, typically based on contrastive learning or InfoMax objectives, often depend on model architecture and the chosen estimators for good results; they help in practice but do not provide clear guarantees about sufficiency. Probabilistic and information- key goals, i.e., retaining shared information and removing nuisance information [i et al. (2025b), However, many existing information theory-based approaches implement only single-varialle con- sistency in the shared latent space, i.e., maximizing pairwise dependence or aligning multi-view data and cross-view representation. Such scalar constraints are coarse, providing neither sufficiency guarantees nor protection against contamination from not fully trained or low-quality views. That may lead to the information aggregation process in joint representation learning being affected by insufficiently learned views (i.c., information redundancy or learning collapse).
methods are able to explicit model two
In this work, we enforce cross-view alignment early in the encoding stage within information bottleneck (IB) formulation, encouraging compact yet sufficient shared representations. Concretely, employ cross-view encoders where each view's observations condition shared latent distribu- tion cluster, enabling decoupled per-view inference while supporting distribution alignment across views. To strengthen semantic consistency, we introduce permutation-consiitenny objective that exchanges distributions of latent variables corresponding to different views, to regularize cross-view matching with scalable complexity. In parallel, we incorporate view-specific reconstruction terms that preserve view-valid information and prevent over-compressio of task-relevant content. These components are unified under a principled IB-style objective with a variational derivation, for which we provide complete variational derivation.
Our contributions are summarized follows:
We propose a universal variational encoding framework for incomplete multi-view multi- label classification that accommodates arbitrary patterns of view and label incompleteness, while learning deep semantic consistency from constrained observations.
We develop a sermutation-consistene empowered IB model that exploits permutation in- variance of cross-view representations to impose view-wise consistency constraints, which maximizes task-relevant information extraction while retaining view-specific content as much as possible.
We present extensive empirical evidence demonstrating that the proposed framework con- sistently outperforms strong basclines and achieves statc-of-the- results both missing and fully observed regimes.
2 PRELIMINARY
2.1 INCOMPLETE MULTI-VIEW MISSING MUL.TI-LABEL CLASSIFICATION
Multi-view learning leverages both redundancy and complementarity across views to improve bustmess and downstream performance. Early approaches emphasize consistency and complemen- tarity regularization (e.g., co-training and kernel alignment), and later evolved toward deep represen- tation learning and semi-supervised regimes to cope with missing observations and noise in practice Andrew et 2013 Liu et al., 2022 2020). For incomplete multi-view settings (missing views), dominant strategies include: matrix/tensor completion with low-rank priors to recover cross-view structure (Wen et 2019 ; cross-view alignment and shared-private factorization
disentangle common semantics from view-specific factors (Liu et al.) 2023a, Lin et al.) 2024); and deep con- trastive or consistency-bant based methods that maintain discriminative representations despite missing views (Luo et 2024 Bian et al. (2024). Under missing multi-label supervision (partially observed labels), existing methods typically combine label-dependency modeling with self-training, extrap- olating unobserved labels via graph regularization, conditional dependencies, or deep pseudo-label estimation (Xie et al. 2024 Chen et al. 2019 Li al. 2024). Overall, strategies for handling either incomplete multi-view view learning missing maulti-labe classification are diverse, however, research that simultancously addresses both forms of incompleteness has only recently emerged. Represen- tative work includes: DICNet, which first introduces multi-view contrastive learning into the iM3C
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task and achieves significant performance gains (Liu et al. puted views via graph-based based neighbor retrieval (Liu et al.
2023b); AIMNet, which generates im-
2024a). and NAIM3L, which cleverly
employs dual-index information mitigate the adverse effects of missing views and labels (Li & Chen 2023).
2.2 INFORMATION THEORY- BASED MULTI-VIEW LEARNING
Variational autoencoder (VAE) (Pu et al. 2016) provides probabilistic framework for information theory-based multi-view representation learning. which is commonly used to unify cross-modal gen- eration, missing-data completion, and uncertainty quantification under shared latent variables (Wan cct al. 2021). Early multi-view VAEs posit a joint latent space to explain multiple sources, thereby
enabling coherent generation and inference across views (Vedantam et al. 2018 Wu & Goodman 2018). Representative lines of work include jointly inference-basee multimodal VAEs that fuse multiple sources with shared latent space Vedantam al. (2018); Wu & Goodman 2018); Khattar eet al. (2019), posterior aggregation via product of experts (PoE) or mixture of experts (MoE), en- abling robust inference when arbitrary modality subsets are observed (Qiu et al. 2025 Chakrabarty & Pal. 2024 Tan et al. (202)), and alignment or mutual-information regularization to strengthen semantic sharing and identifiability (Liu et al. 2024b). For incomplete inputs, key focus con- ditional posteriors and marginal generation to support inference and reconstruction from any subset
of views (Liao et 2022 Chen al. 2025).
2.3 PROBLEM FORMULATION
Consider an incomplete multi- view multi-label dataset = {(xx y)} with samples. Each instance described by m views, denoted x = (xx(*) |== with (*)) E Rd Due to view incompleteness, set V with [V] < to denote the set of observed views for any instance. The label assignment is given by y E {0, 1] where C is the number of categories and y = 1 indicates the membership in class Similarly, we define G with [ < C. the available label set for any instance. Our goal is to encoding the joint multi-view representation z given the incomplete data D with prior missing information V and G, and classify the instance into corresponding categories. Note that in the context of information theory, we use random variables to describe data and problem definitions.
2.4 SUFFICIENCY OF MULTI VIEW REPRESENTATIONS
When is multi-view representation "good enough" for multi-labe prediction? Our answer builds on a simple intuition and turns it into a practical, trainable target. Different views of the same sample describe the same subject: they may look different in low-level details, but the task-relevant meaning should be consistent. With this in mind, we adopt a semantic consistency assumption:
Assumption 2.1 For the prediction of y, there exists semantic information that is shared among multiple views x(1) x(2) ,...,, x(m). Then, for mutual information between views and target, have:
1(x()) = =..
=.. =xxx (x)))))))
This assumption intuitively demonstrates that each available view x(() carries essentially the same information about the target y. Unlike single-view setting, the multi-view setting provides more chances to filter out content irrelevant to the task. Therefore, following previous work (Liu et al.) 2024b), we introduce joint multi-view representation associate multiple views in the embedding space and state a direct proposition:
Proposition 2.2 multi-view joint representation z contains all the information shared by all views, is sufficient for predicting y.
An appropriately constructed cross-view representation can, in principle, contain the information required for downstream prediction. However, raw multi-view observations usually contain substan- tial view-specific variability that is not aligned with the target. Thus naive fusion often carries these irrelevant factors into z, introducing redundancy that obscures the shared task-relevant signal and weakens the predictive efficacy of for y (Federici et al. 2020 Liu et al. 2024b). These consid-
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3
2
3
3
3
3
2
3
2
3
3
Permutation-consist information bottleneck framework
2
2
classifier
2
2
2
2
PoE
2
Z
Objective: max
1(x(0),
1(x 2(10)((00000)))
[V]
[
Raw/reconstructed view x(1)
2 Latent variable 211-2)
Cross-view joint representation
Our main framework of PCVE. The multi-view view shared information learning and recon- struction is shown at the top; the cross-view fusion and multi-label classification process is in the bottom.
Figure I:
erations motivate learning strategies that emphasize shared semantics while suppressing non-shared information, thereby maintaining the sufficiency of under realistic conditions.
METHODOLOGY
In this section, we detail the proposed permutation-consisste variational encoding (PCVE) frame- work. The overall pipeline is illustrated Fig. [ the top panel depicts multi-view shared informa- tion learning and reconstruction, while the bottom panel shows cross-view fusion and multi-label classification.
3.1 CONSISTENCY INFORMATION BOTTLENECK FRAMEWORK
Building on Proposition semantically sufficient for prediction. Further constraining the model to remove all non-shared redundancy, ensuring that z retains only shared information, will be more beneficial for downstream tasks. Concretely, for given views (x) and ("), consider the mutual information between (a) and joint variables and ("),, we have:
shared representation that captures cross-view commonality
[(x("); x z) = [(x(")) : x())) + I(x(()) =I(x(") z x))) I(z:x(") I(x (x)")) + xxx x((") z))
x(()) 2) + x(2)
Minimum sufficiency
Sufficiency
This decomposition subject two assumptions. First, contains the shared information across views, then the mutual information between any views is equal O, i.e., [(x(=); x(w) 2) 0. Second, if contains only the shared information, then the mutual information between and any view is equivalent to the shared part between views, i.e., T(2; x(")) - ; = 0. Under these two conditions, we can get I(x(")); z x())) = 0. which formalizes the notion of minimal sufficiency with respect to the cross-view common semantics.
Corollary 3.1 For any pair of views v, let be joint multi-view representation that contains and only contains the shared information across views, then the conditional mutual information T(x("); x(())= 0.

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To attain minimal sufficiency of z while maximizing shared information, it suffices to minimize the conditional dependence between views given 2, i.e., to drive [(x("); x(() z.) toward zero. Previous work typically represents the multi-view joint coding with a single variable z and models distribu- tion from multi-view data using PoE or MoE, while imposing posterior-consistency constraint during fusion. This strategy implicitly assumes one-to-one mapping between each view and its view-specific latent component, e.g., the component of attributed view solely originates from x(*), Although intuitive, such fusion can suffer from view imbalance and training insufficiency: some dominant views may steer the PoE/MoE aggregation and overshadow weaker views. We therefore propose to impose the cross-view consistency constraint carlier, specifically at the stage of view-specific distribution modeling, to suppress non-shared information. Concretely, we introduce explicit view-specific components {z(e) Joev as a decomposition of the joint representation z, and replace the learning objective with sum of conditional terms JVT / [(x(1);xxx/) (()) (x()). Intu-
itively, minimizing ((x())z(?) xx())) helps to compress z(") to remove redundant view-specific information. However, minimizing this term alone risks information collapse in (z("),, yield- ing degenerate non-informative representations. Therefore, we complement that objective with an informativeness regularizer that preserves the valid information within raw data, by maximizing (2)1)) x(")) while simultaneously minimizing the conditional mutual information:
max
(z (0)
S.L.
Σ
( 20)) = O.
(2)
V
IV
BEV
KRPEV
Introducing a Lagrange multiplier 3 2 0 yields the unconstrained objective:
1 V
Σ (z(2) B
(3)
VEV
U
3.1.1 VIEW-SPECIFIC INFORMATION EXTRACTION AND CROSS- VIEW CONSISTENCY MODELING
In Eq. the first term maximizes T(z(x); x x()) preserve the view-specific information, and the second term minimizes E, T(x(")); (())) to enforce cross-view consistency. We adopt the trade-off coefficient 3 to balance information compactness and effectiveness.
= / p(x(
(('))log [ ((x) log p(x(r))
(xx())2(()) dz())
((x());((0))
(z(")
(4)
2 p(x(oo) / p( log p( (((1) )x))))x(())))))))))))))))))))))) (xx(")
For the lower bound of Eq. (4. direct solution is intractable due to the unknown conditional dis- tribution. Therefore we introduce a variational coding network (z((x) x(v) to approximate
((z(") (v)).. Then Eq. (4 can be rewritten as follows:
1(x(0) ((()) 2 ((x f 1)2 (x() log p(x!(()))) (dx)) (z)
>BxMM)~(X)))) 1( (x(x)) log g" (x (z [)
(z))
(5)
(x)() log q" (x( (o))
Obviously, we can maximize the lower bound in Eq. (5) to achieve our optimal goal of max (xx())=(()) (o)). For the second term in Eq. we have the following formulation:
T(x("), ((1))
= =/ p(x(") x(() 2(0) log p(x(()) x((), 2 (p(x(0))
p(x(1), ( (z( x(1)) dx dx(()) dx(")) (z())
(6)
/ Mxle x(()) (()) log p(z(") (1) x((), x(1))
dx (1) dx dz(
(x)
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Existing approaches typically employ simple Multilayer Perceptron (MLP) to model the dis- tribution of p(z(=))(()), However, under our cross-view consistency encoding framework, where m views are expected to be encoded with shared semantic features, we decouple the process of approximating distribution ((z(")/x(")) Specifically, we model distributions (x(())))((())) "...., r (z(() )x(")) separately, which fre means the stochastic encoders from source view target view n, and then employ PoE fusion to obtain distribution r" ("(2(") x(()) to approximate (x(o))
" (x()) = x (z = r((z"))
II n=1
r (x)
where we set r((()) standard Gaussian distribution r(2(")) N I) for vanilla implemen- tation. Then we can get the following variational upper bound:
1(x M); (1) (x))))
= -/ p(x(()) x(()) (0)) log
((x(o)) Dr" dxl")
p(z(v)/x(0) "r" (z(()) x(())
(8)
/ p(x(l), xx ,(z( log p(z p((m, x(()
dx dx dz(e)
r(z(0) x(())
-xxls) (pt) x DKL (p(z
where DKL is the Kullback- divergence. Aggregating over Eqs. and (8 and introducing the penalty coefficient B3 we obtain the training objective for Eq. i.e. minimizing the loss function Lib:
Ls Cre + PCpe
1
Σ
Eg xp(p())(())))))))))))))))))))) (()) log (x
1V
VEV
(9)
+ 8 V
Σ
DRIlt "=
n=
3.2 PRIOR ALIGNMENT VIA RANDOM PERMUTATION
To regularize view-specific posteriors in Lye while avoiding cubic complexity, we introduce permutation-consiset alignment principle that serves a role analogous to cross-view prior sharing. From loss function Lpe, encourages the latent posterior of view to be close to that constructed from another view u. A naive implementation evaluates all ordered pairs (u, v) with u * v, incur- ring (()))) complexity per batch. Instead, we attempt randomize the association between views so that each view is matched with a single view u & per iteration, reducing the cost to ((2)22 while preserving the intended regularization.
Definition 3.2 For given view v, the latent distribution cluster drawn on it is defined as:
C { (m-m) (z(z())
x(")) }
where z (-))) denotes the latent sub-variable from source view to target view
Proposition 3.3 (Permutation consistency) By randomly swapping the corresponding elements of
the latent distribution clusters C" and other available views, the distributions of the corresponding latent sub-variables within each cluster remain consistent before and after the swap, i.e., let
TT ym Ty V be random view index sequence of length and C {z (5 1 (z) (a.)) n=l
m be the cluster after random permutation, then we have:
D DxI(Z(0
(n)) 0, Vn (1,..,,m,
The permutation consistency defined in the proposition is based on the assumption of semantic en- coding consistency in the latent space, i.e., the ideal cross-view representations should contain only

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shared semantic information. This design enforces the network to encode semantic information from all available views, ensuring cross-view semantic alignment while effectively improving com- putational parallelism. Note that, given the diversity of source views within each cluster, we further constrain the selection of т such that [m; } = [V]; that is, we randomly select view indices from the available view set V without replacement. For example, if V {1,2, 6), possible permutation of the indices π could be {4, 1,6, 6, 2}.
3.3 INTRA- AND INTER-VIER VIEW ALIGNMENT
To further enhance cross-view semantic coherence and robustness within the PCVE framework, we introduce two complementary alignment objectives: intra-view alignment term that encourages each view-specific latent posterior to match its corresponding PoE-fused counterpart, and an inter- view alignment term that aggregates per-view means across views in multi-view fashion.
Intra-view alignment. Let (z(")) x(*)) denote the stochastic encoder that maps source view to the target latent variable of view n, and let r (2(2(*) x(*)) be the view-u posterior obtained by PoE fusion over the set of available views V. For each sample, we define an intra-view KL divergence that encourages the per-source encoders to align with the fused posterior on the same latent component:
m
Lintra
Σ
Σ VEV
DRL (r (r [x()))).
(10)
[V
Intuitively, this term drives the latent distribution cluster C' induced by view v align with its PoB-fused posterior, preventing view-specific drift and reinforcing distributional consistency at the component level.
Inter-view alignment. Besides the intra-view alignment, we also encourage cross-view consensus by directly regularizing the per-view posteriors toward shared latent mean. Specifically, we adopt a softmax-weighter similarity matching across views of the same instance. Let 24"") E Rd be the embedding of sample under view v, and let z((") = 14; and V; denote the available view set of sample i. Define the temperature-scaled cosine similarity
(w) /llu{"/22 denote its fg-normalized form
(v.a) (a("),a(()) where r a temperature. The inter-view alignment loss is the negative i.j log-likelihood of assigning the anchor to its within-instance views:
Σ exp (s (n.a) NEV.
Linter
Σ log VE
(11)
Σ Σ exp (8,u) 88
3 NEV;
This objective increases the probability mass same-instance cross-view pairs and reduces it on different-instanee pairs, which naturally accommodates missing views by restricting sums to the available view sets.
3.4 MULTI-LARBE, CLASSIFICATION AND OVERALL ORJECTIVE
After obtaining the components of latent shared representation on each view, we fuse available views via a PoE to form the joint posterior: q(z (x(*) brev) x [usy r" x())). To enable differentiable prediction path, we sample latent variable from q(z (x(")) using the reparameterization trick. Let q(z (x("))eew)
[N Epoc) with mean /'poc and covariance Epee. times sample is: == - Ed Mque + =po @ e(d) e(d) ~ (), Then is mapped to multi-label prediction probabilities E [0, 1] via a small MLP followed by Sigmoid layer: p (f)( In the missing-late label setting, supervision is accumulated only over the available label set g C "il.....), The multi-label cross-entropy loss is:
1
Vi log P: + ye) log(1 pi)
Lee
(12)
g
1E0
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where y4 E {0, 1 is the observed label for class i and p; is the predicted probability and unknown labels (i $ () are excluded. Aggregating the regularization and task terms, our overall objective comprises permutation consistency loss Lpc, reconstruction loss, missing multi-label classification loss Lee, and intra/inter-view alignment loss Limer + Limtra
L Loe + a Lis + Linter + + Lintra
(13)
where 2 0 balance the proportion of IB strategy. Note that the Lib composed of L and fre with coefficient 3 to balance the information compression and retention across views. Penalty parameters 7 and are set to 0.1 for convenience.
EXPERIMENTS
We introduce the experimental setup, main experimental results and analysis in this section. For other experimental results and ablation study, please refer to the appendix.
4.1 EXPERIMENTAL SETTINGS
Datasets. Following common practice (Liu et al. 2023a Li & Chen, 2023). we evaluate on five standard multi-view multi-label benchmarks: Corel5k Duygulu et al. (2002), Pasca107 Everingham er al. (2009), ESPGame Von Ahn & Dabbish (2004), IAPRTCI2 Henning et al. (2006). and MIR- FLICKR Huiskes Lew (2008). Each sample provides six views (GIST, HSV, DenseHue, Dens- eSift, RGB, LAB). We adopt the same data statistics and feature settings as prior work to ensure fair comparison.
Incomplete data construction and splits. To simulate the domly mask views and labels: for each sample, we drop the view with fixed probability while ensuring least one view remains; for labels, we randomly mask both positive and negative entries with the same probability. Unless otherwise specified, the missing-view rate and missing-label rate are both set to 50%. Then, we split all data into [70%//5%%/15% for training, validation, and test.
setting, we ran-
Baselines. We compare our PCVE against nine strong methods: complete multi-view multi-label learning method like CDMM (Zhao et al. 2021) and LVSL. (Zhao et al. (022);; single-view missing
multi-label methods DM2L (Ma & Chen 202 and methods tailored for iM3C. like iMVWL (Tan
et al. 2018), NAIM3L (Li & Chen 2023). DICNet (Liu et al. (2023)), DIMC (Wen et al.) 2023). MSLPP (Long al, 2024) and SIP (Liu et al., 2024b). For methods not natively supporting iM3C task, we follow standard adaptations in previous work (Zhao et al. (022): mean imputation over available views for methods unsuitable for missing views, and reporting the best single-view for single-view method; for methods not supporting missing labels, unknown entries are excluded from supervision term. We use authors' code and recommended hyperparameters when available.
Metrics. We report six widely-used metrics: Ranking Loss (RL), Average Precision (AP), Ham- ming Loss (HL), Area Under ROC Curve (AUC), One-Error (OE), and Coverage (Cov). To unify the direction, we present I-RL, HL. OE, 1-Cov along with AP and AUC. so higher is better for all. Each experiment is repeated multiple times with reported mean and standard deviation.
Implementation details. For our method PCVE, the latent dimension is 512, batch size 128, opti- mizer SGD with initial learning rate 0.001. Per mini-batch we draw 10 samples for latent variables and use their average as a robust estimate. Training is conducted on Ubuntu with a single NVIDIA RTX 5090 GPU under PyTorch 2.x. The key hyperparameters selected via grid search on the validation set and fixed for test reporting.
4.2 EXPERIMENTAL RESULTS AND ANALYSIS
We compare PCVE with the nine baselines on all five datasets under 50% missing views and 50% missing labels. From Table I baseline across all six metrics on all datasets. Compared with the best prior baselines, PCVE exhibits statistically consistent improvements. For example: On the Corel5k and Pasca107, PCVE improves
observe that PCVE matches outperforms the top
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Table 1: Results under 50% missing views and 50% missing labels. The decimal in the lower right corner is the standard deviation. The best result is marked in bold.
Data
Metric
CDMM
DM2L
LVSL.
SMVWL
NAIM3L
DICNet
DIMC
MSLPP
SIP
PCVE
AP
0.354exe
0.262
0,342axe
0.2833am
0.30% om
1.38
0.353
0.4133cos
0.418
0.423acc
1-HL
0,987oues
0.987am
0.987um
0.978xa0
0:987cam
0,988
0,987uxe
0,988s22
0,988uxe
0,988
Corel5k
1-RL
0.884coe
0.843aa
0.88
0.865
0.878
0. 0.882scs
0.867
0.901ams
0.91 Inoro
0.914..o0
AUC1 f
0.888ues
0.845uac
0.884uxs
0.881 0.86819e
0. 0.8844004
0.870umm
0.903
0,913uue
6.916
1-OE
0.400uer
0.295sm14
0,39
0.31 loms
0.350s way
0 0:408am
0 0.422mm
0.485azoo
0.489umme
0.494
1-Cov
0.723wx
0.647ame
0.7
0.702
0.725
0.727ecu1
0 0,684um
0.766scm
0.787uxe
0.792
AP1
0.508soes
0.47
0,504etss
0.437
0.488 oos
0. 0.505acca
0.532
0.544acio
0.562.com 0.555
co
1-HL
1o93
0.928
0.930ue
0.928: 0.882aa
0.929ec01
0.93Imm
0.932ac01
0,93 Ioans
0.934.c01
Pasca00
I-RI.
0.8 2ooes
0.761
0.806osea
0.736va15
0.783 on
0.783
0.81 Joxe
0.819
0.8300o
a.835
AUC1
0.838use
0.779ka
0.832xxs
0.767aau
0:811smm
0. 8080
0.833vxa
0.841ac54
0.850ure
0.857
1-OE
9.419
0.420va1
0.419kxa
0.362
0.42 ow
0.427ars
0.456xmn
0.4666s
0.46440ss
l.471
1-Cuv
0.759kss
0.692zaw
0.751
0.677aaus
0.727
0.731
0.769kum
0.771scos
0.7833ure
0.790
AP1
0.289
0.212
0,285
0.244
0.246 oet
0.297
0.287ooe
0.3 1.310n cos
0.31 Inoes
0.314.
ESPCome
1-HL
0,983uxe
0.982
0,983um
0,983s 0.972
0.983
0.983uuee
0.983xza
0,983uuee
0.983..0
I-RI.
0.832
0.78
0.829
0.808
0.818e
0. 0.832
loxe
0.843so0
0.8499uxe
0.852.
AUC
0.836ue
0.785
0.833
0.813:ac
0.824:
0. 0.836.m
0.826uue
0.847aozz
0.853uue
0.856
1-OE
0.396see
0.294:
0.389
0.343
0. 0.
0 0.439
0.435uxe
0.457axe
0.455unn
0.460h ox
1.Cov
0.574mme1
0.488
0.567oxss
0.548
0.57
0. 0.593s.00
0.5622me1
0.622sco5
0.6288ore
0.634
APT
0.305
0.234
0.304
0.237
0.261s oot
0.323
0. 0,3088001
0.340s.as
0,33
0.336..os
MIRFLICKR IAPKIC12
1.981
0.980s.0
0,981cu
0,9694..0
0,980s
0.980uuxe 0,981a200
0,981aza0
0,980uxee
0,981
I-RL
0.802ume
0.823
0.86
0.833
0.848
0.873
0 0.864uxe
0.882
0.885uuee
0.888
1
0.864o
0.825
0 0.863uu
0.835
0.850s
0. 0.874s.00
0.86oo
0.883
0.886ure
0.889
1-0E
0.432uxe
0.340
0.429kue
0.352xsx
0.390s
0.408
0.43 luxe
0.474ezx
0.463uue
0.477
1-Cov
0.597oxe
0.529kaw
0.564aae
0.5977ue4
0.672ac06
0.675ume
0.680..oM
AP1
0.570kme
0.5l
0.55
0.490
0.55 1551emm onn
0.889a
0.602awe
0.6
0.61 4ores
0.618
0.8866e
0.878
0.885oo
0.882: 0.839
0. 0.888ac02
0.888uue
0.892sc01
0.89 Ioaes
0.895x00
I-RI.
0.85
0.831a
0.856ore
0.803
0.844: on
0. 0.86
0.865
0.879pmm
0.877
0.880 con
AUC1
0.846oue
0.828
0.844oxm
0.787sa12
0.837a
0.849
0.8522o0
0.865a.02
0.860urr
0.868.c02
I-FE
1o63
0.510
0.607ose
0.51 Iaam
0.585
0.637am7
0.647
0.667am07
0.6622mc
0.670 no
0.640uee
0.604
0.636
0.572aar3
0.631s
0.652ae07
0.679
0.678uor
0.682.c0
(1
17 (198)
00L
AIC
1:WW
1-08 (b) TAPRTC12
1,6W
1-08
(a) Corel5k
(c) MIRFLICKR
Figure 2: Experimental results of ten methods on the three full databases without any missing views or labels. The center of the radar map shows the worst results and the vertexes mean the best results on the six metrics.
AP and AUC by about 0.3-3.5 points over the second best method SIP: On the larger-scale datasets with around 20k samples like ESPGame, IAPRTCI2, and MIRFLICKR, the improvement trends are modest yet steady across all six metries, indicating improved robustness under severe double- incompleteness. In addition, a holistic view of Table I shows that methods explicitly designed for the iM3C setting (e.g.. DICNet, SIP, and our PCVE) systematically outperform those not natively addressing dual incompleteness (e.g., CDMM and LVSL). For example, on Pasca107, iM3C-oriented methods (SIP with AP 0.555; PCVE with AP 0.562) surpass non-iM3C counterparts (e.g., CDMM with AP 0.508 and LVSL with AP 0.504). Similar trends recur on other datasets, which underscores the necessity of introducing prior missing information, rather than relying on coarse imputations.
We further evaluate all methods under the complete data setting by setting both the view-missing and label-missing rates to O. The radar plots in Fig. 2 visualize results on three representative datasets, where curves closer to the center indicate worse performance. Two observations stand out: Incompleteness imposes a substantial negative impact on all methods; Even with full views and labels, PCVE maintains consistent edge over strong baselines, confirming its compatibility
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0.7
25
0.6
0.4
633
10
0.2
10gua
1og
log
(a) Loss curve on the CorelSk
(b) Loss curve on the MIRFLICKR (c) AP values on the two datasets
Figure 3: Impact of different information--allacee parameter B on loss Lres L.
(3a 3b), and AP
3ch. The blue area shows the standard deviation.
beyond the doubly-incomples regime. In particular, on the Corel5k dateset, PCVE achieves notable advantages on 1-HL and 1-Cov compared to the second-best approach.
4.3 ANALYSIS OF THE BALANCE IN THE IB.
We further examine how PCVE balances representation sufficiency and compactness through its IB loss by tuning the trade-off between the reconstruction term fre and the cross-view permutation consistency term Cye in Eq. (9.. where C aims to preserve view-specific information necessary for reconstruction, while Lpe for enforcing semantic invariance across views by aligning their posteriors toward a compact task-relevant shared space. To be specific, we sweep 3 on Corel5k and Pasca107 under the doubly-incomplete setting and track the dynamies of Lre, Lpe, and AP values across training (see Fig. 3}. Three consistent phenomena emerge: (i) When 3 is too small, Lre dominates and the model over-retains view-specific information, leading to weaker cross-view generalization and degraded performance despite low reconstruction error. (ii) When 3 is too large. excessive compression harms sufficiency well: Epe remains low but Lre rises rapidly, accompanied by noticeable declines in AP, indicating information underflow. (iii) A moderate balance yields the best outcomes: performance peaks when the pull between Lye and Lpe reaches balance (typically / in the mid-range), suggesting that PCVE benefits from jointly promoting semantic alignment and preserving reconstructive fidelity.
CONCLUSION
In this paper, we present PCVE, a permutation-consisett variational encoding framework for in- complete multi-view multi-label classification. We adopt an information bottleneck framework that couples view-specific information preservation with a permutation-baat jective to achieve efficient semantic alignment across views. Our key contribution is early-stage consistency regularization based on distribution-cluster swapping, which effectively suppresses view redundancy and promotes the learning of sufficient shared representations. Extensive experiments on five benchmarks under both doubly-incomplete and fully observed settings show consistent gains across all metrics. Analyses further verify that balanced trade-off between information preser- vation and compression is critical to avoid information collapse and redundancy. PCVE offers general and effective solution for iM3C task, with potential to extend broader multi-view learning scenarios.
cross-view consistency ob-
ACKNOWLEDGMENT
This work was supported by the Science and Technology Development Fund (FDCT), Macao S.A.R under Grant 0028/2023RRAA1, and the National Natural Science Foundation of China under Grant 62372136.
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A APPENDIX
A. USE OF LARGE LANGUAGE MODELS (LLMS)
We used large language model solely as writing assistant to improve the clarity, grammar, and style of the manuscript. The model was involved research ideation, experimental design, im- plementation, analysis, or result interpretation. We sincerely appreciate the contribution of the large language model in enhancing the readability and linguistic quality of this work. Its assistance was instrumental in refining the presentation of our research. All technical content, including methods, experiments, and conclusions, was fully developed and verified by the authors. The authors take full responsibility for the content of this paper.
A.2 COMPLETE DERIVATION OF SHARED INFORMATION LEARNING MODEL
In this section, we give detailed derivation of model
1 V
Σ ((2("):x(())
B V
Σ T(x(1), (z))))
(14)
WeeV
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For the first term in Eq. (14 we have:
(xx())=(1))
=/ p(x((0) ((1)) log p(x((1) 2(11)
p(x((s) dx (x dz
-t/ /ooloo (0o) logp(x (0)) d2)
(15)
/ placoopetoo) / p(x((1) log p(x(o)) d22
= =t/ p(xlo), logg(x 10 (v) (0) + H(x((1))
Due to the information entropy H(x(1)) 2 0. we have:
1 ((x())=((0)
/ p(x(1), ((11) (0gp((("//()))) dz
= / / ((21)) log 1x (0)) dz)) (0)
I mide / (()(1)221)) log ((((00))(() dx dz (0)
(16)
/ S plat))x(")) logo" (x d (w) (0)
/
(x 1z (0) ))dx(() (0)
Since (10"" 2 O, we can get: (((
2 / p(x(li) f (x(1))))()) logg" (2( )dx( (z)
= / f pixem).2l log (x ( (3) dz(")
(17)
f / f (x log (x (2 d2())
-pte (x(() 2(0))]]
For the latter term in Model [14 we have:
T(x(")) ((1))((11)
= =/ʃ p(x(m) x(() (00) log p(x(1)) x(()) 2(11 (px(()))
p(x((1), x(1) )p(((0), x(1)) dx(()) dx dz(1)
(18)
= = [/mbd Mele x(0) (00) log p(z(") x((), x(())) dx (1) dx dz()
(
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By introducing approximate distribution r" r"(z(") (x( we have:
I(x! 20 (1)))
=/ Mx((1) x(1), (0)) log p(z(v) (x(a), x(0)) (2)))r"(((0)) (x(0)
p(z ()"((()))))))) x(11) dx(( dx (d(())))))
= / p(x( x()) log
plal") ((
dx dz
/ p(x(1)
(z
log
p(z(0) x(0))
/ p(x(0), x(1) (oo) Bog p(z(1)
("(2(")
(19)
/ p(x(1) ((oo
log
dx (x())
/ / Mix()), (( (lan F
/ Mxx()) ((o) (ooo Bol p(
dx (0)_
(pl (x dx())
p(x()) x( p(z)))) log (x(
(1)
Exxin (Dxz
((])
A.3 POE FUSION
Given the distribution Nuv: Me), v V of each sub-expert for PoE fusion, the formulation of PoE fusion is as follows:
EvEV Mu Must. so Evev E, +1²
Upoc
(20)
Epee
Ever +1'
where ppoe and Epoe are the fused mean and variance of multiple views, respectively. te and E,, mean the w-th view's mean and variance, respectively. Then, we have (x(xx)))c M[upoe Expe)..
A.4 STATISTICS FOR FIVE DATASETS
In this section, we present details of the five databases used in our experiment in Table 2 The introductions of five widely used datasets are follows:
Corel5k Duygulu et al. (2002): The Corel5k dataset contains 4,999 images and 260 anno- tations, with each image labeled by 1 to 5 tags.
2. (aocal07/eeringhaaia et al. (2009): PASCAL VOC 2007 is a widely used image dataset for visual object detection and recognition. In our experiments, we use 9,963 images spanning 20 object categories.
3. ESPGame Von Ahn & Dabbish (2004): The ESPGame dataset comprises 20,770 images collected from online interactive games, with to 15 labels extracted per image. On aver- age, it has 4.69 semantic labels per image and includes 268 unique labels in total.
4. IAPRTC12 Henning et al. (2006): IAPRTC12 is large-scale dataset with 19,627 im- ages across 291 categories. Each image has up to 23 labels, extracted from the slogans or subtitles appearing in the image.
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5. Mirflickr Huiskes & Lew (2008): The Mirflick--25k open evaluation project consists of 25,000 images downloaded from Flickr, with 38 labels used in our experiments.
Table 2: Detailed information about five multi-view multi-label datasets in our experiments.
Dataset
# Sample
Label
# View
# Label/#Sample
Corel5k
4999
260
6
3.40
IAPRTCI2
19627
291
6
5.72
ESPGame
20770
268
6
4.69
Pascal07
9963
20
6
1.47
MIRFLICKR
25000
38
6
4.72
A.5 STATISTIC' FOR EIGHT COMPETITORS
In this section, we give details of the eight comparison methods in Table
Table 3: Simple information of nine comparison methods. 'Multi-view' denotes the method is designed for multi-view data; 'Missing-view" and 'Missing-label" represent their compatibility with missing views and missing labels.
Method
Sources
Multi-view
Missing-vier view
Missing-label
CDMM
KBS '20
DM2L
PR '21
LVSL
TMM '22
iMVWL
UCAI '18
NAIM3L
TPAMI '22
DICNet
AAAI '23
DIMC
TNNLS '23
MSLPP
Neur Netw '24
ICML '24
A.6 EXTRA EXPERIMENTAL RESULTS FULL DATASETS.
In this section, we show the results of nine methods two datasets without any missing views and labels in Fig.
A.7 VISUALIZE THE CONSISTENCY OF EMBEDDING FEATURES
To demonstrate the constraints of our permutation strategy on multi-view consistency, caleu- late the KL. divergence between the private embeddings corresponding to any six views and draw heat maps in Fig. 5 We calculate the KI. divergence among six views (r"(2(") (x)))) of two samples at three training epochs. It can be seen from the figure that the training progresses tinuously, the distribution consistency among views gradually increases reaches a balance. With the improvement of the prediction performance of the model, the encoding of each view in the latent space is evolving towards semantic consistency. However, due to the existence of the reconstruction regularization, the KL divergence does not decrease indefinitely.
A.8 ABLATION STUDY
To assess the contribution of each component in PCVE, conduct ablation experiments focusing on the two terms in our information- informaation-bottleeeckk objective: the view-specific reconstruction loss Ere and the permutation consistency loss Lpe- We report results two representative datasets (Corel5k and Pascal07) under the -ibblli setting (50% missing views and 50% missing labels), and use the same training protocol and evaluation metrics in the main experiments. Specifically,
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CDMM DME2L LS34
3-H1L
D.C DMCC
CCVN
1-HL
DiClnn
DNDL
BMC
055
[0 (0.82,0.89)
10.25,0.40
[0.84,0.91
0.25.0.421
1:0E
1-Cay [0.57.0.70]
1-0E
1-Cov
[0.38,0.88]
(a) ESPGame
(b) IAPRTCI2
Figure 4: Experimental results of nine methods on the two full datasets without any missing views or labels. The worst results are indicated at the center of radar chart, while the best results represented by the vertexes, considering six evaluation metrics.
(a) epoch
(b) epoch = 25
(c) epoch 50
(d) epoch
204
83
201
213
80
100
324
21
332
25
X1
61
(e) epoch =
(1) epoch 25
(g) epoch = 50
(h) epoch 75
Figure 5: Visualization of KI. divergence among views for samples in three training epochs. (a)-(d) are for sample and (e)-(h) are for another sample. "v1" denotes the view I.
Table Ablation results on Corel5k and Pascal07 datasets with 50% missing views and 50% miss- ing labels. "w/o" means 'without'. Loss Fre and Lpe denote the reconstruction term and permutation consistency constraint term, respectively.
CorelSk
Pascal07
Method
1-HL.
AUC
1-Cov
1-HL
AUC
1-Cov
PCVE w/o Leee & Epc
0.350
0.987
0.870
0.876
0.424
0.727
0.537
0.930
0.811
0.826
0.456
0.760
PCVE w/o Eyc
0.389
0.987
0.898
0.901
0.454
0.761
0.547
0.929
0.825
0.847
0.464
0.777
PCVE w/o C...
0.261
0.987
0.853
0.858
0.289
0.677
0.511
0.931
0.788
0.815
0.441
0.740
PCVE
0.423
0.988
0.914
0.916
0.494
0.792
0.562
0.934
0.835
0.857
0.471
0.790
remove Lp and Cre, respectively, and name them "PCVE Lpc" and Table 4
and "PCVE Lre" in
From Table 4 it can be observed that removing Epc consistently degrades the performance all metrics. Without permutation consistent alignment, the model retains more view- new-prrvvate informa- tion and exhibits weaker cross-view generalization. Besides, dropping Lre leads to unstable training
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Published as a conference paper at ICLR 2026
and notable declines in AP and AUC. Over-aggressive compression causes information underflow: while cross-view posteriors appear compact (lower Lpe), the shared representation becomes umin- formative for accurate prediction. The full model yields the best overall performance, indicating that free supplies view-valid content to prevent collapse, while Lpe suppresses redundancy and enforces cross-view semantic invariance. The two terms complementary in maintaining compact yet sufficient representation.
A.9 TIME COST STUDY
To assess the training and inference efficiency of PCVE, we report the training and testing time of ten methods on the Corel5k dataset (70% training split) in Table 5 Because model training time highly sensitive to convergence criteria, we measure all methods under their default convergence settings. For single-view methods, record the total training time summed over all views, and the inference time for single view. For DICNet, SIP, and PCVE, we conduct 100 epochs for the training phase.
Phase
CDMM
DM2L
LVSL
IMVWL
NAIML
DICNet
DIMC
MSLPP
SIP
PCVE
Training Inference
16.02
713.37
63.73
313,89 0.05
141.85 0.04
4889 0.05
336.11
1.73
0.04
0.64
0.02
0.01
0.01
0.03
Table Time cost of training and inference phases on the Corel5k dataset with 70% training sam- ples. (Unit: s)
A.10 LIMITATIONS
Although PCVE shows strong effectiveness for iM3C and sheds light on aligning cross-view se- mantics via early permutation-coniisten regularization, several limitations remain. First, our ap- proach assumes that shared information suffices for prediction. This assumption may be strained under highly heterogeneous modalities (e.g.. vision-language laggaaan-audiiinn where view-private cues can be indispensable. Second, while permutation- baasattto--bbadd alignment reduces complexity, its stochastic matching scheme may introduce variance and could underperform with severely imbalanced or low- quality views. Third, information bottleneck relies variational bounds and KL-bbaed rogates; more accurate or adaptive mutual-information estimators might further improve stability and fidelity. Finally, we evaluate established benchmarks with controlled missingness. Broader validation on real-world large-scale deployments with structured missing patterns and distribution shifts is needed fully assess robustness and generality.
18


Reviews:
[{"review_id": "oxxoXWs8oo", "reviewer": "Reviewer_RiXu", "summary": "This paper explores the challenging problem of multi-view and multi-label classification with both view and label incompleteness. The authors propose a framework named Permutation-Consistent Variational Encoding (PCVE), which incorporates an information bottleneck strategy to learn variational representations that can aggregate shared semantics across views. PCVE maximizes a variational evidence lower bound (ELBO) to preserve task-relevant information and introduces a permutation-consistency regularization to encourage distributional alignment between encoded representations of the same semantic content across different views.", "questions": "1 Regarding Assumptions and Information Loss: Assumption 2.1 posits that all views havethe same mutual information with the target, When this assumption doesn't hold in practice(e.g. one view is significantly more discriminative), how does PCVE prevent valuable, unique semantic information from this \"strong view\" from being prematurely suppressed ordiscarded during the permutation-consistency process?\n2 Comparison of Alignment Mechanisms: Compared to traditional alignment methods thatdirectly minimize distribution distance (e.g., KL divergence) in the latent space, could youprovide more direct experimental evidence (e.g., visualizations or quantitative metrics) todemonstrate the specific advantages of permutation consistency in avoiding \"over-alignment\" and preserving necessary diversity?\n3 Real-World Missing Patterns: The current experiments use random missingness. Howwould PCVE's performance be affected if the missing pattern were non-random (e.g. theabsence of a certain view is strongly correlated with samples of specific categories)? What isyour view on the robustness of your method to such bias?\n4 Applicability beyond image features: Has the approach been validated on truly multimodaldata (e.g., image-text or audio-visual tasks)? lf not, what challenges would arise whenextending PCVE to such heterogeneous domains?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The work defines an interesting and meaningful learning setting, incomplete multi-view missing multi-label classification (iM3C).\n- The proposed universal variational encoding framework is flexible and theoretically capable of handling arbitrary missing-view and missing-label patterns.\n- The idea of permutation consistency provides a potentially simple yet effective strategy for encouraging cross-view semantic consistency.", "weaknesses": "1. The experimental results are not convincing and the novelty of this paper is not supported by the experiments. In Table 1, PCVE achieve trivial gains against other methods. \n2. The paper is difficult to follow. For example, Fig. 1 is neither properly referenced nor introduced in the main text, which harms overall readability.\n3. The derivations are extensive and dense; many could be moved to supplementary materials. Some portions appear overly “formulaic,” potentially obscuring the main conceptual contributions.\n4 Though the paper emphasizes learning shared semantic information, there is no intuitive or visual analysis of the latent variable z(v).\n5. Stochasticity Risk in Permutation Strategy. While random permutation reduces computational complexity, it may introduce training instability. This could be particularly problematic with severely imbalanced view quality (e.g., pairing a high-quality view with a low-quality/noisy one, potentially hindering convergence or leading to sub-optimal performance.\n6 Limitations in Experimental Setup.  The missing data pattern is randomly generated, failing to simulate the more common real-world scenario of non-random missingness (e.g., where the absence of a view correlates with sample characteristics), which limits the demonstration of robustness in practical applications.", "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": "lfQZLJAW6b", "reviewer": "Reviewer_gaes", "summary": "This paper tackles the double-missing problem in incomplete multi-view and multi-label (iM3C) learning by proposing a Permutation-Consistent Variational Encoding (PCVE) framework based on the Information Bottleneck principle. To suppress view-private redundancy and prevent over-alignment, the framework introduces a scalable permutation consistency regularization mechanism via \"distributed cluster swapping\" with random permutations. Additionally, reconstruction terms are incorporated to preserve essential information and avoid representation collapse. Extensive experiments under various benchmarks and missing ratios verify that the proposed approach achieves consistent improvements over existing state-of-the-art techniques.\n.", "questions": "1. In PoE fusion and consistency regularization, are unequal weights of views considered? For example, the weight of low-quality views with large variance is reduced.\n2. How does the PCVE handle missing labels? It seems that this part (handle missing labels) should be clarified. \n3. There is a typo in line 59, \"IIn\".", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This work innovatively advances cross-view consistency to the encoding stage and introduces a \"permutation consistency\" regularization strategy, which effectively achieves efficient alignment while balancing sufficiency and compactness of representations. The proposed method is intuitive with a unified framework.\n2. The objective decomposition and variational lower/upper bounds are derived from the Information Bottleneck perspective, which is clearly motivated and well defined. (e.g., the motivation for the minimum sufficiency of conditional mutual information).\n3. The authors conduct extensive evaluations across five standard datasets and six metrics, considering both complete and double-missing scenarios. Comparison against nine strong baselines demonstrates stable and leading performance.\n4. The readability of this paper is good, with clear motivations and strong experimental results supporting.", "weaknesses": "1. Suppose the mutual information of each view about y is equal, and \"the shared information is sufficient for prediction\". It may not be suitable in strong heterogeneous modes or tasks (such as visual-language-audio).\n2. In this paper, each view needs to construct the encoder sub-distribution $r_v^n$ to each target view, but there is a lack of analysis regarding the number of model parameters, training time, etc. I suggest the authors supplement the relevant experiments.\n3. The explanation of some symbols needs to be strengthened, such as what is the relationship between $p$ and $p_i$. The lack of a clear explanation will lead to confusion among readers.", "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": "MaOk0RFfhy", "reviewer": "Reviewer_wLuJ", "summary": "The paper proposes a PCVE framework to address the dual incompleteness problem in multi-view multi-label learning. The idea is to use the permutation consistency regularization to constrain the distribution of latent variables of different views in the encoding stage, so that the shared semantics across views are aligned. At the same time, the reconstruction term is used to retain effective information, and PoE is used to fuse to form a shared representation for multi-label prediction. The authors give the target decomposition from the IB perspective and the corresponding variational upper and lower bounds, claiming that it can outperform a variety of strong baselines at different missing rates. The highlight of the work is to pre-place the consistency constraint in the encoding stage and introduce the distribution cluster exchange of random permutation to reduce complexity.", "questions": "Please refer to the weaknesses for my considerations and concerns.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The problem is highly motivated for the practically important dual incomplete scenario. The complexity of this problem has not been considered in existing research, and this paper grasps this difficulty and helps real-world applications.\n \n2. The methods proposed in this paper have a unified form, such as encoding consistency, view-private information reconstruction, PoE fusion and masked multi-label learning, and the overall design is self-consistent.\n\n3. This article systematically derives the objectives from IB and provides the variational bounds and training objectives that can be implemented for optimization.", "weaknesses": "1. Will the random permutation proposed by the authors introduce additional noise? Also, will swapping them at each training epoch affect the stability of the training?\n\n2. The $z^1$ in Figure 1 does not match the description in the text, which may cause ambiguity. I suggest that the authors revise Figure 1 to keep the symbols consistent.\n\n3. There is a lack of sufficient explanation on how missing views are handled. How did the authors handle missing views during the encoding stage? I believe that the way to handle missing view is an important step in the method of this paper.\n\n4. What is the scope of application of PCVE proposed in this paper? In real applications, can it handle heterogeneous multimodal data?\n\n5. Although the computational complexity has been greatly reduced thanks to the proposed random permutation strategy, I am still interested in the overall parameter count and computational efficiency because it is different from the conventional VAE framework based on single modality encoding.", "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": "NDqCiBRgcG", "reviewer": "Reviewer_jgRE", "summary": "This paper introduces Permutation-Consistent Variational Encoding (PCVE), a novel framework for addressing the challenges of incomplete multi-view multi-label classification (iM3C). By leveraging information bottleneck (IB) principles with a permutation-consistency regularization, the framework promotes semantic alignment across views while mitigating redundancy and over-alignment. The framework is extensively evaluated on five multi-label benchmarks under both incomplete and complete settings, achieving SOTA performance.", "questions": "See the Weaknesses.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1.\tThe paper introduces a novel permutation-consistency objective that aligns cross-view latent representations while reducing computational complexity, offering a scalable and effective solution for semantic alignment.\n2.\tThe proposed framework balances view-specific information preservation and cross-view semantic consistency well, avoiding over-compression and ensuring task-relevant representation adequacy.\n3.\tPCVE achieves SOTA results across multiple metrics in both doubly incomplete and fully observed settings, demonstrating its robustness and generality.", "weaknesses": "1.    The permutation-consistency mechanism and information bottleneck formulation are innovative, but the novelty over existing methods (e.g., DICNet, NAIM3L) is not sufficiently clarified. Additionally, the framework’s reliance on PoE-based fusion and variational inference may be similar to prior multi-view learning approaches, like SIP.\n2.\tSome statements are unclear, such as \"we randomly select view indices from the available view set V without replacement.\" What does this mean?\n3.\tParameter sensitivity experiments on alpha seem to be missing, do the authors have any reason to clarify it further?\n4.\tThe dataset descriptions lack sufficient detail, making it difficult to assess their relevance to iM3C tasks. Authors are advised to provide more details about the datasets.", "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)