Theory-Driven Label-Specific Representation for Incomplete Multi-View Multi-Label Learning
Authors: Quanjiang Li
Tianxiang Xu
Tingjin Luo
Yan Zhong
Yang Li
Yiyun Zhou
Chenping Hou
Venue: NeurIPS 2025 spotlight ()
Keywords: Multi-View Multi-Label Learning
Primary area: deep_learning
TL;DR: To tackle the complex yet highly practical challenges,  we propose a Theory-Driven Label-Specific Representation (TDLSR) framework.

Abstract: Multi-view multi-label learning typically suffers from dual data incompleteness
 due to limitations in feature storage and annotation costs. The interplay of hetero
geneous features, numerous labels, and missing information significantly degrades
 model performance. To tackle the complex yet highly practical challenges, we
 propose a Theory-Driven Label-Specific Representation (TDLSR) framework.
 Through constructing the view-specific sample topology and prototype association
 graph, we develop the proximity-aware imputation mechanism, while deriving class
 representatives that capture the label correlation semantics. To obtain semantically
 distinct view representations, we introduce principles of information shift, inter
action and orthogonality, which promotes the disentanglement of representation
 information, and mitigates message distortion and redundancy. Besides, label
semantic-guided feature learning is employed to identify the discriminative shared
 and specific representations and refine the label preference across views. Moreover,
 we theoretically investigate the characteristics of representation learning and the
 generalization performance. Finally, extensive experiments on public datasets and
 real-world applications validate the effectiveness of TDLSR.

Theory-Driven Label-Specific Representation for Incomplete Multi-Vier Multi-Label Learning
Quanjiang Lift 1 Aiquanjiang@nunn .du.
Tianxiang Xu²t
Tingjin Luo!" tingj inluohhotmail.commmmmmmmmmmmmmmm com
xtx09@hotmail.cm com
Yan Zhong
Yang Li Liyang_albert@feeee wwwerttffomaaaaiil...a com
Yiyun Zhou'
zhongyan@stu, pku, edu on
yiyunzhouêzju edu. cn
Chenping Hou'
hepnudt@hotmaill. com
National University of Defense Technology, "Peking University, 'Zhejiang University
Abstract
Multi-view multi-label learning typically suffers from dual data incompleteness due limitations in feature storage and annotation costs. The interplay of hetero- geneous features, numerous labels, and missing information significantly degrades model performance. To tackle the complex yet highly practical challenges, we propose Theory-Drived Label-Speciff Representation (TDLSR) framework. Through constructing the view-specific sample topology and prototype association graph, we develop the proximity-aware imputation mechanism, while deriving class representatives that capture the label correlation semantics. To obtain semantically distinct view representations, we introduce principles of information shift, inter- action and orthogonality, which promotes the disentanglement of representation information, and mitigates message distortion and redundancy. Besides, label- semantic-guided feature learning is employed to identify the discriminative shared and specific representations and refine the label preference across views. Moreover, we theoretically investigate the characteristics of representation learning and the generalization performance. Finally, extensive experiments on public datasets and real-world applications validate the effectiveness of TDLSR.
Introduction
The popularity of multi-view learning stems from its ability to provide comprehensive representations
of samples (29 99. Integrating multi-source information effectively reveals latent semantic associ- ations in multimodal data, thereby enriching the feature space and improving model accuracy and generalization [10]. With the advancement of information technology, single-label proves inadequate in meeting the object labeling and recognition demands 33. In practice, objects frequently fall under multiple categories simultaneously. with a document in text classification [40] being assigned labels like topic, intended audience, sentiment and so on. Benefiting from the holistic characterization offered by multi-view approaches [1 and the capacity multi-label methods [31 capture all sample attributes, diverse views and labels are emerging as the dominant form of training data. Con- sequently, multi-view multi-label classification (MvMLC) has attracted significant research attention, as it delivers refined understanding of the complexity and diversity inherent in real-world situations.
1 Equal contribution
* Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Existing MvMLC methods are capable of implementing both multivariate feature fusion and multi- objective joint discrimination. For example, LVSL [3] performed view-specific label learning and leveraged low-rank label structures to enhance performance. EF [12] proposed an embedded feature selection model that integrated feature aggregation and enhancement. However, these ideal methods assume the presence of both features and labels, whereas limitations in feature collection techniques and annotation complexity result in the unavailability of partial views and tags [37), motivating researchers to explore the incomplete multi-view multi-label classification (iMvMLC) approach. Early efforts like iMVWL [33 employed a joint learning strategy to refine the shared subspace and enhance the robustness of the weak label classifier. NAIM3L 21 combined matrix factorization with global high-rank and local low-rank constraints to obtain a shared label space. Given the ability to capture complex semantic information, deep learning based methods have demonstrated promising performance. The pioneering work DICNet [25) introduced an incomplete instance-level contrastive learning method for improved consensus representation, while LMVCAT (6) designed two wransfomme-bbaee modules for cross-view feature aggregation and category awareness.
Despite the emergence of various effective iMvMLC methods, they remain deficient in feature information reconstruction, semantic distinctness of extracted representations and the coupling between label correlation semantics with feature connotation. (i) The absence of views severely undermines both the capture of cross-view dependencies and the stability of downstream modules. Approaches [4] that only mask missing samples tend to circumvent the challenge, rather than engaging in robust information recovery. AIMNet [23] attempted to perform missing imputation via cross-view global attention computation. However, the integration of global weighting scheme may further exacerbate reconstruction noise since not all samples are strongly correlated. (ii) The essence of multi-view learning lies in extracting the complementarity and consistency across diverse views (36
Additionally, increased attention should be devoted to feature separation in multi-label scenarios 42 as distinct labels exhibit varying sensitivities towards particular features. DIMC (38), TSIEN
34
and SIP 27 primarily focused on shared subspaces while overlooking the unique characteristics of individual views. MTD 24] attempted to obtain shared and specific representations through geometric distance constraints. However, this linear interaction pattern struggled to reflect the intricate inter- view relationships. (iii) Label relevance is fundamental
multi-label learning and distinguishes from multi-class problem [44] which makes multiple independent binary classifications insufficient as done in some methods 24 Besides, instead of being considered in isolation, mutually dependent label semantics should interact seamlessly with feature information to facilitate both the perception of label-specific features and the selection of the preferred labels corresponding to those features.
To tackle these issues, we propose a Theory-Driver Label-Specific Representation framework named TDLSR. The motivation behind TDLSR minimize view reconstruction errors, improve the seman- tic discriminability of extracted representations and strengthen the interaction between label-relevant semantics and feature information. We first construct view-specific instance relation graphs using the attention mechanism integrated with neighborhood-aweer -warre selection. Without any discrepancy arising from network parameter updates, the reconstruction risk minimized by propagating highly relevant sample information across views. By introducing the principles of information shift, interaction and orthogonality, we develop a mutual information optimization model that aligns the core constituents of representations with their respective views, facilitates interaction among shared representations, suppresses cross-talk between private components and enforces orthogonality of shared and specific information from the same view. Label correlation information is transmitted via graph-induced rela- tional network modeling, which results the emergence of interdependent category representatives. Through discrete engagements between each class prototype and semantically distinct features, the most sensitive feature ensemble for each label across both shared and specific feature pools can be identified. We further establish the generalization error bound via error decomposition. showing that feature disentanglement maximizes the mutual information between representations and objects and reduces generalization error. The main contributions of our work are summarized follows:
We propose a general multi-view representation extraction model inspired by information theory. This model guarantees unbiased representations through the constraint of information shift, sep- arates shared and specific semantic via the regulation of information interaction, and eliminates representation redundancy by strengthening information orthogonality.
TDLSR enhances the propagation of feature dependencies and label correlation semantics by constructing relational graphs. Besides, it introduces label-specific shared and private feature
2

---

learning for the first time. Theoretically, we prove the discriminability and effectiveness of feature extraction and derive the generalization enror bound.
Extensive experimental results across diverse public available datasets, along with applications on real-world NBA data, validate the effectiveness and robustness of our method.
2
Method
In this section, we present the following critical components of our TDLSR as shown in Fig. | proximity-aware graph attention recovery mechanism, universal view extraction framework under mutual information constraints and multi-label semantic and label-specific representation learning.
2.1 Problem definition
We define (X(=)) Ju=ı as original multi-view setting, where X = (n(("))) E R represents d, dimensional feature matrix of the u-th view. The label matrix Y E [0,1] corresponds to C' categories, with Y,, = if sample is tagged as class j. Besides, we let W E 1 and G E {0. NxC denote the missing indicator for views and labels, respectively. Specifically, i.j 1 if the j-th view of the i-th sample is available, otherwise Wij O. Similarly, G. 1 or 0 reflects the certainty of the corresponding label. Our goal is to train an end-to-ens to-end neural network capable of performing classification inference on incomplete multi-view weak multi- label data.
(a) Proximity-sware Graph Atlention Recovery
(b) Universal View Extraction Fammoockk
(c) Mulii Mulii-Labe Semantic and Label Specific Representation Learning
Doosder
Stook
Erodkyy
Specife
Photety::
Shared
Saveé
Mesegg: Pripaptionn
Kay
Sumplin
GNN
Spezifee
Munul Information
Lahel Cammdation
X
Sharal
Skandla
Massagg Propagtion
Anmin
Dennder
Enookle
Spetie
Speci
X
Stael
Weak Inseritioon
Completion
Shift
Orthogonaity
Interaction
Chositeer
Figure 1: The main framework of proposed TDLSR. Different shapes signify different samples.
2.2 Proximity-aware Graph Attention Recovery Mechanism
The lack of diverse views limits the capacity of deep neural models extract high-level represen- lations (20). Consequently, data augmentation through reconstruction techniques is essential for improving model accuracy and stability. To mitigate information deficiency arising from incomplete- ness, we propose an attention-
relational graph construction strategy to propagate similarity signals across samples for missing imputation. For any view v, the attention score for an instance pair
computed by ( c MM //T where is the temperature parameter and h(-) denotes the
normalization function. Each row of the matrix (()) quantifies the degree of similarity between the corresponding sample with all other samples 23 which facilitates the identification of the k-nearest
neighbors for each instance. Therefore, construct the view-specific graph (v)) R through
iutentiioninducad proximity awareness, where 5(0) = means Wi, W = and B is one of
the top-k largest elements the i-th row, ie., z; is the neighbor of x Considering similarity relations between instances in existing views are applicable the missing views, the transferred graph for finding the available instances related to the missing ones can be obtained:
V
K
S (k) diag (W..),
(I)
1=
1=1
3

---

Raw Information
(b) Information Theory
runs flying a lite, two delighted daughters chise after him.
Shift
Interaction
Orthogonality
kite sours high above, as family haughter Gila the air mear
green under clear slay
sky
wooden fence with distant bare trees.
Fience
Shared
Specific
Fother
Specific
Sky
Shared
Red
Daughter
Pince
Kice
Father
Specific
Chase
Field
Fly
Text
Red jate
Chese
Figure 2: Depiction of information shift, interaction, and orthogonality.
where diag(-) creates a diagonal matrix and W is the v-th column. Besides, the contribution of available samples reconstruct missing ones is governed by the maximal computable correlation from alternative views:
B max BB..
B B
where B. encapsulates the influence of the j-th sample in the recovery process of the i-th sample. By treating K as the adjacency matrix and B as the edge weight, we can get the reconstructed data after message propagation:
Σx!221
(v) B B
a (0)
Ex(O B
Since (v) serves as an approximate proxy of missing instances, we combine it with the original view to generate the final recovery matrix for downstream tasks:
(1 W.,)) + W...-
2.3 Universal View Extraction Framework under Mutual Information Constraints
Previous studies 27 have primarily concentrated enabling networks to extract shared information, while overlooking the contributions of each unique view. Moreover, the reliance on linear geometric constraints in early view-specific representation learning [24] falls short of capturing complex feature interactions. To effectively assess both the consistency and the complementarity distinct features, we propose general model that directly constrains the mutual information between representations for precisely measuring their interaction degree. Two groups of multi-layer perceptrons {M, Jy=1 and (MO)V= Jv=ı are employed as shared and view-private channel extract the corresponding representa- tions, i.e., {M5 (()) + 5( J==1 and {MO (()) O J Taking the image-text retrieval task (32 for explanation, as illustrated in the Fig. 2 an image is typically paired with multiple textual descriptions that emphasize on individual relationships and environmental context, respectively. requires the model to simultaneously extract the consistent shared representations (central actions) and unique modality-specifff elements (e-g., distinct individual identities and background details) for holistic multimodal perception. To achieve this, maximizing [(s!*); (()) is critical for guaranteeing that the representations stay consistent with the core semantics of raw modalities, such as people, kit, background, etc. Besides, comprehensive feature disentanglement is facilitated by maximizing
the mutual information T(s("") |[((") ((("), (()) [z())) and minimizing I (v( (2(")) (=()) between representations from any pair of views v and v" (1 S S v" VV). which focuses on capturing the
central characteristics of the actions and preserving unique information embedded in each modality, respectively. Furthermore, establishing complete representation orthogonality from the same modality,
as indicated by [(s (=)()))2(() " (2())) = 0. effectively minimizes semantic redundancy, such as the identification of the individual and their actions.
As mentioned above, feature separation is driven by the following three criteria: (i) prevent informa- tion shift, (ii) optimize information interaction and (iii promote information orthogonality. Under

---

the condition of mutual information constraints, the universal model can be expressed as
V Σ
((( 1=1
(1 (1 (2 -1000))))) -1
max
information
information interaction
(5)
information orthogonality
By employing the Lagrange multiplier method, the equality constraint can be appropriately scaled. Direct computation of mutual information is impractical due to the challenges distribution inference and the complexity of figh-dimensional integrals. Thus, stability and feasibility are typically ensured by refining estimable mutual information bounds [35]. Regarding the information shift term, its lower bound commonly represented through reconstruction loss 15]. where the representation s(") decoded via ((=(1) (")[s(() faithfully preserve the original view:
((s("); (0)) E (p ,a()) [log (z()))s(1))
(6)
For the second term, based on the definition expansion and the non-negativity of entropy, we can derive the following lower bound by introducing another variational distribution q(s(()
([s(0)) 12((0) ) = / p()(0)/2(0) /s(")//(())))) (12(0)))((( |2((1)) log (()(1) s "ds("" ds!
dsl())
log p(s(n)|((0) (20) /g("') (((")) do(") do(o')
p( p(sl0) p(s)))))))(()))))))))))))))))))) 12(0)//)000/00000 /1(00)
((s(0)|8")
Kullback I Leibler divergence
where p( (2()) /s("")) (x))) refers to the conditional distribution between the shared representa- tions from 2 (z) and 20)) Leveraging the non-negativity of Kullback-Leibler divergence between the
distributions p(s(t)(2(v) //(v"))(v)))))))))) (z(")))())) and (({(())(((")) the tighter lower bound further obtained. Similarly, upper bounds for the remaining two negative terms can be derived following the same rationale. Therefore, the problem (I6) is transformed into optimizing the following objective:
LIB = -- (p(t [log [2)
/ p(s(0) s("' (('')) (2(")) log q(s (*) |s" )ds(")) ds(()
lower hound information shift
lower bound for shard information interaction
+ DKi(p(o (o') (r(), o (2 lp((o (v') 112(0) (0)) ("
upper bound for specific information interaction + 33 DKI(p(s(") (0)) (()
((()) (") (o()))
upper bound information orthogonality
where 3 is the Lagrange multiplier. Minimizing LıB promotes effective distinction between shared and specific feature semantic, with implementation details provided the Appendix.
2.4 Multi-Label Semantic and Label-Specifie Representation Learning
In multi-labed classification tasks, binary encoding struggles to capture the underlying label semantics 19.. To overcome this limitation, we employ a data-driven approach learn label prototypes (27), which provides clear insight into label structures and enhances effective semantic associations with features. After initializing the one-hot vector b; E RC for each category, we utilize two stochastic encoders to model the prototype distribution i.e., h; ~ N (ui, of I). where the mean μi, and variance o; are determined by the encoders 9p (b.) and (b:). Then, we sample from the distribution with the reparameterization trick to obtain the prototype representation hς Ed= (14 + o, C 84) [ where 8d means the d-th individual sampling and + denotes the element- deie product.
5

---

The prototype representations are independently learned for each label, yet investigating intrinsic label correlation remains a core challenge in multi-label learning []. For bridging this gap. graph neural networks are leveraged to propagate prior correlation information and refine the label representations to encapsulate the inherent relationships of label semantics. Prototypes are regraded as a set of nodes positioned on the label relation graph, with edge weights reflecting the correlation between corresponding label pairs. Besides, the label correlation matrix A quantitatively characterized on the training data serves the appropriate substitute for the adjacency matrix. Rather than utilizing co-occurrence frequency to evaluate correlation degree, we use the Jaccard distance [30] calculated over positive labels, computing the intersection and union of two classes regarding positive values, we can obtain
only concerned with the categories assigned to each instance. By
Y Y..a)
Arj Ex_ Ya,) (Y. Y.))
(9)
where Aa is set to 0 to eliminate self-dependen seff-dependency. Given an aggregated matrix H E RCxdd the label embeddings corresponding to each row can be updated by passing through the GIN layer with propagated correlation information M. i.e., E = f [[1 + H + AH), where f() denotes a fully-connected layer followed by Batch Normalization and Leaky ReLU activation, and e is a learnable scalar that controls the influence of node's 's own features. To reinforce cohesion between relevant prototype representations and distinguish unrelated ones, we employ the following objective that aligns representation similarity with label correlation:
-
C
Lie -ie C DE
Ais log (cos E,) + (1 - A.z) log (1 cos (E,, E2)).
(10)
where cos EE, Eÿ) is the cosine similarity and Å = A + with denoting an identity matrix. Multi- label classification tasks often involve labels with varying sensitivities to different feature subsets (14] Consequently, label-specific feature learning has become a widely adopted technique to select the most relevant features tailored to classifying each label. However, label-specific disentangled feature learning remains underexplored, despite its potential to boost model performance. For instance, in image recognition, shared information capture general visual cues, while private features highlight other distinctive traits tied to each label, such as breed for "dog" and texture for "cat". Thus, we treat activated label prototypes as feature importance scores and engage them with both shared and private representations to discern the label-specific view embeddings:
P.(") os (E1) @ x ( as (E2) 3 ;...".....s (Ec) G x,
(11)
(II. can obtain the label-specific shared where dg is the Sigmoid function. According to the Eq.
and private features, i.e., (S(v) iT()) E NxCx
and (O(.) ( NR-xx V-1
The interaction between label semantics and view representations supports a bidirectional selection mechanism, in which discriminative views are assigned to specific labels, while information-related label subsets are uncovered associated with distinct views. Processing through the linear classifiers, view-specific predictions U+)) E NCC and V(r) E R NCC are generated. Given the variability in reconstruction quality, views with higher recovery accuracy should be emphasized in the fusion process. For this aspect, certain reconstructed views characterized by low attention scores in relation to their associated samples naturally exhibit reduced confidence (23) Thus, we calculate the maximum original attention for each instance with respect to other instances as its confidence score:
Qie max (fr log Br, W
(12)
where B is computed by Eq. and Q E NNV stores the confidence score for individual instances. Since Q is mailor-made for the missing samples, the confidence matrix is updated as Q' (1- W) o Q + W. During the late fusion, we combine the feature reconstruction efficiency
to obtain the final prediction:
VV Qh
EV
Que
P Og
(13)
L
Then, we employ the weighted cross-entropy loss to mitigate the impact of missing labels:
C
1
Live - Eis G
(Yi log (Ps.) + (1 Yis) log (1 -PPa)) Guj.
(14)
=1

---

By incorporating \ and X to balance the loss effects, our total training loss can be expressed as Lbce + A1L + X2hie.
(15)
2.5 Theoretical Results
In this subsection, we aim to theoretically explore the fundamental mechanisms that contribute to the model performance and the generalization capability of TDLSR. Through rigorous derivations (proofs in the Appendix), we obtain the following theorems:
Theorem 1. (Discriminability of Label-specific Representation.) For label prototypes E, and Eg such that lo + for all k, and view representations X(") and X x(")) such that v * u for all v², the discriminability of p(o) for class j necessitates that either of the following conditions be satisfied:
N
E
X
0s
EE)
1
3 as
(Es)E))
1 (s(
(Ex) [x)
z
(v)
(as(E))
ass
Ex))
N
N
E
Ej} os
0s (E)) Σ
E
x
os OOs( (E)
2 Σ as
0 (E(
N
Theorem 2. (Effectiveness of Disentangled Representation. Let the disentangled representation
be denoted as R (S O0) ,O.,...... OVV), where the information entropy of each repre- sentation is assumed to be fixed, ie., H(S())) = H(O())= H (1 S V). Then, in the case where each shared and specific representation is indispensable for prediction, I(R; Y) will attain its maximum when R = R., with R. being the optimal solution of the problem (T6).
Theorem (Generalization Error Bound.) Our model is designed to learn a vector-valued
function (f1....,fc) X RCC The expected risk and empirical risk w.r.t. the training dataset D) are denoted as R(f) = xxxxy)x.x
Q), Y)) and RD(s) NC Eee Ee E(En= QQiu )))),, Yi,),, where (av(.) refers the late fusion of multiple views. With probability at least 1 ò, we have the following generalization error bound:
K1
K
R(f) (DD()
gen ( QQ,,YY)
VNV
N3/4V1/4
Ee
EV I(X() StD, O , + K.s)
+ Ks
NC
where K, = k2 = O(VO), KA constant of order Õ(1) as N, N.V - 0o, and
gell QQXXY)) is the generalization error related to the view reconstruction quality. Moreover the generalization error bound becomes increasingly lighter during the optimization of the problem (66.
Experiments
3.1 Datasets and metrics
our experiments, we utilize six popular multi-view multi-label datasets to validate the performance of our TDLSR, i.e., Corel 5k [5, ESPGame M1. IAPRTC12 (8). Mirflickr [16], Pasca107 (6), OBJECT
[3. accordance with 25 38 we select six metrics to construct comprehensive evaluation system, i.c., Hamming Loss (HL), Ranking Loss (RL), OncError (OE), Coverage (Cov), Average Precision (AP), and Area Under Curve (AUC). To facilitate comparison, we present 1-HL, 1-OE, 1-Cov, and 1-RL values in the report, where higher values correspond to better performance.
3.2 Comparison methods
To measure advancement our TDLSR, nine state-of-the-art methods are selected for comparison experiments, i.e., AIMNet 23 DICNet (25], DIMC (38), iMVWL 33 LMVCAT (66), MTD 24,
SIP (7), LVSL DM2I. (8 Specifically, the first seven methods can simultaneously address the issues of missing views and labels. LVSL is MyMLC method unable to handle missing data.

---

Thus, we use the mean of available instances to complete the missing views and fill the unknown labels with "0". DM2L a kernel-based nonlinear method for incomplete multi-label learning. Then, we concatenate all views into a single-view representation for the execution of DM2L.. All parameters of compared methods are configured as the recommended values in their original codes.
3.3 Implementation details
Each dataset is divided into training, validation and test sets in the ratio of 7:1:2. To simulate the partial view setting, a specified proportion of instances based on the Partial Example Ratio (PER), are randomly marked unavailable in each view. Additionally, least one complete view to avoid invalid cases. For weak supervision, we introduce label omissions for both positive and negative tags in each category applying the same proportion determined by the Label Missing Ratio (LMR). The process of constructing incomplete data is repeated multiple times to mitigate the impact of experimental randomness. Our model is implemented by PyTorch on one NVIDIA GeForce RTX 4090 GPU of 24GB memory.
ensure that each sample contains
3.4
Experimental results and analysis
COR, PER-90%
ESP, PER-90S
PER-900%
PAS, PIR-S0%
0.30
DIUNN:
0.30
0.40
DINC
0.20
DMIL
0.20
IMVWL.
0.10
0.50
0.50
0.70
0.90
0.50
0.50
0.50
0.90
0.10
0.30
0.50
0,70
0,90
0,50
0.50
0.70
0.90
LYSL
CDR, 100-
ESR, 1.MR-9055
TAR. LMM--90
PAS, LMR-90%
MID
0.40
0.30
0.30
0.60
SIP
0.20
0.20
0.10
0.10
0.30
0.50
0.50
0.90
Figure 3: Experimental results on four datasets with PER and LMR changing from 30% to 90%.
To evaluate the effectiveness of our TDLSR in handling absent views and labels, we benchmark it against nine closely related algorithms across six datasets with varying levels of data sparsity. The proportion of missing views (PER) and labels (LMR) encompasses values of {30%, 50%, 70%, 90%). The mean and standard deviation of the results with PER and LMR fixed at 50% reported in Table I Besides, the average ranking of each algorithm based on the six metrics is calculated to perform a thorough assessment. Fig. iilustrates the variation in AP as PER and LMR changes from 30% to 90%. The other relevant results will be presented in the Appendix.
Drawing from the comparison results, we have the following observations: (i) Our method exhibits outstanding performance on almost all metrics across all six datasets. As shown in Table despite the fluctuating rankings of other methods, TDLSR consistently holds the top position. Therefore, our method effectively addresses the iMvMLC problem and maintains stable outcomes. (ii) SIP and MTD are top-performing methods that always appear among the top three. The reason our method surpasses these leading approaches lies in the mutual information optimization, which constrains complex interactions between representations that are insufficiently addressed by MTD. It also overcomes the limitations of SIP by accounting for the impact of private features and transmitting label correlation information to refine label prototypes. Compared to AIMNet that similarly engages in view recovery. our method achieves an improvement in AP from 0.40 to 0,45 on Corel 5k, which demonstrates strategy can greatly suppress reconstruction noise. Achieving over a 10% performance gain against traditional multi- methods like DM2L and deep learning frameworks such as DIMC and DICNet that disregard label correlation, our approach highlights its strength in capturing high-level view representations and leveraging label dependencies to enhance overall performance. (iii) As depicted Fig. 3 our method exhibits remarkable performance and strong robustness across a wide range of missing ratios. Moreover, our method is particularly well-suited for highly incomplete settings. For instance, when PER reaches 90% on Corel5k and ESPGame, all baseline methods collapse, while our approach continues to deliver commendable results.
that our proximity-avee
8

---

Table 1: Experimental results of nine methods on the six datasets with 50% PER and 50% LMR. 'AveR' refers to the mean ranking of the corresponding method across all six metrics.
DATA
METRIC
AIMNet
DICNet
DIMC
DM21,
IMVWL
LMVCAT
LNSL.
ATD
SIP
TDLSK
I-IIL
0.988a.c00
0.987g.00
0.987a.00
0.987
0.978p.00
0.986
0.9876.co
0.988g.000
0.985au000
0.9888.000
1-OE.
0.478a611
0.660..012
0.146
0,378,.014
0.308
0.448au11
0.353
0.492a.011
0.192am14
0.5414.014
1-Cov
0.766u.co
0.726p..77
0.709
0.600..00
0,70
0.720uocc
0.720..
0.75
0,780u.04
1.800
COR
1-R1.
0.000.002
0.881 c.04
B874u
0 0.55.00
0.86
0876
0.893
0.9085usss
0.917a.000 70.00
AP
0.58 go0s
D. 0.370
0 0.318
0.281 ooo
0.37%
0 0.1o.o
0.410
4.41-4
AUC
0
0.883
0.846 0.877gg04
0.867
0.879uss
0 ..8
0.898
0.910
0.919
AVR
3.5
3.167
2.333
1-HL
c.083..coo
0.9833.00 00
0.98%%.coo co.
0.9
0.983.ccoo
0.983..00
0,M833
0.9833.co
1-OF:
0,440g.00
0 0.3022.200
0.34
0.45
0 3665.com
01452
0.450uuzze
0.477
I-Cov
0.621gx0
0.601amm
0.586
0.5322.00s
0.548,00
0.58700ss
0 0,578
0.617
0.6222.024
0.6466.000
ESP
L-RL.
0.545
0.836
0.830
0 0.8046.00
0.825 008
0 0.829..com
000
0.85% 0.847
AP
0.305
0.300
0.294
0.229.000
0.293 0.24
2.26..co
0.309
0.30%
0.328s.00
AUC
0.850 cot
0.841am2
0 0.808 0.835uase
0.81
0.832 oc1
0 0.8344.c0 con
0.847a.002
0.85 In.02
0.8663.000
AVE
3,833
4.5
5,833
9,667
9.167
7,333
7,167
3,833
2,667
I-IIL
0.98lo.co
0.98
0.98 000
0,980,
0.969
0. 0,980,oco
0.981a.co cco
0.981
0.98
0.98
I-OE
0.457..co
0.464l.m
0,378
0.4
0.377m.cor
0.479%.077
0.45% osc
1.491a.
IAP
1-Cov
1-RL.
0.673.coo
0.6
0.8744..02
D. n28
0.630
0.555
0.837g.002
0.833
0.565
0.6166.004
0.8660..02
0 0.8576.002
0
0.00..co
0.670
0.8822.002
o9t
0.678a.n23
0.8866.003
0.7066,000 200
0.899
AP
0.3298,c0s
0.326uuuu
0.318
0 0.25k.002
0.236uu01
0.3 0.313
2626.00
0.340p..02
0.33
0.358,,004
AUC
0.88S
0.876a o0z
0.870
0.838
0.835
0.870u
0.859
0.883
0,887ax93
0.89
AVE
4.333
8883
9.833
6,833
2,833
2,833
1-HL
0.89t
0.890
0.876
0.8-40)
0.8800
0.877
g.893
0.8900.03
0.8966
14FE
0,66,.000
0.647a.012
B.645u02s
0.5335.20s
0.51
0.63
0 0..0oo
0.6677.00
8.6544.227
1-Cov
0.673
0.661
8.687
0.615,
0.588
0.665uu2
0264
0.6688
0,6944,000
MIR
I-RI.
0.869
8.867
0.355.co co
0.80%
0.862.00
0 8476.co
0.878.00
0.8736
0.888.000
AP
0.595
D. D,592a o36
0.519%.00 mo
014 7
0. 0.58%% oc4
O 54%
0.6144.00
0.603 otc.
1..31a.00
AUC
0,855 c00
0.828..0 0.85
g.901
0.852
0.839
0.864
0.859u
0.875p.00
AVE
38833
4.667
6.167
6.667
3.667
0.948
0.948 mo
0.947
0.935,.co c00
0.899
0:940,
0.935).co
0.949
0,948 031
0.953
1-OE
0.601am1 0.619
0.59
0.537 011
0.465,
01604
0,450 ccs
0.627
0.626 ose
0.685
I-Coy
0.794..m: 0.806
D. 0.793
0.7688.202
0,7446
0. 0.79%).0s
0. 0.759%.com
0.8122.00
0.80%
018345,007
OBJ
L-RL.
0.888
0.876a.004
0.875
0.860.00
0.833
0.878a
0 0.850..om
0.890s.om
0,889u.024
0.9,00.004
AP
0.627amm 0.639
0.623p.00
0.577a.cm
0.630,.rs
0.537
0.649..om
0.692 0.649,.00
AUC
0.897o.co 0.886 mi
0.885
0.872 2od
0.816 oos
0.888, occ
0.8611.co.
0.900 ous
0.898
0.918
AVE
4
5.835
6,833
8. 8.167
9,833
5,333
3
I-HL
0.931a.co
0.931
0.931au0
0.927
0.882
0.915a..cs
0.928o.co
0.9333..0t
0.932a.023
0.933p.001
1-OE
0.462
0,443g,077
0.435uu010
0.419
0,366
0.433
0.415o.cos
0.4733.005
0.495 0.468..22
I-Cov
0.78lacur
0.749gum
0.738u
0.720
0.759
0.738
0.790u.0s
0.778
0.81 7o.0
PAS
1-RL
O 0.830
0.8033..02
0. n,792a.ns
0.778p.00
0.736p.01
0.80%
0.7976.0r2
d.836
0.8280.094
0.8622,004
AP
548
0.517a.0
0.510uu0s
014826.000
0.438
0.524
0 0.466..co
0.362a.00
0.557au02e
0.590l..00
AUC
0.851q.co
0.827
0.806
0.767
0.830
0.823
0.85%..m
0.848,
0.8881,.00s
AVE
3.5
5.667
7.167
3.5
3.5
Ablation Study
The ablation experiments are conducted to deeply investigate the effect of the three crucial modules of TDLSR, i.e., proximity-aware graph attention recovery mechanism (S1), information theory- representation extraction framework (S2), multi-label semantic and label-specific representation learning (8x). After individually removing S1, S₂ and Ss, we use mean imputation for missing samples, rely solely on single multilayer perceptron (MLP) for feature extraction while discarding LIB, and directly employ classifier based on fully connected layers without exploring label semantics, respectively. Based on the ablation results provided in Table we have the following observations: (i) When either module is removed, the performance declines, which indicates the effectiveness and thoughtful design of our TDLSR. (ii The recovery mechanism is crucial for enhancing performance, as it provides downstream modules with rich feature information. Moreover, feature separation outperforms the single-channel representations and incorporating category semantic learning enhances performance beyond that of classifier-only approaches. It demonstrates our thorough consideration of feature extraction and label associations.
4 Application to Comprehensive Potential Prediction of Players
To validate the practical applicability of our TDLSR, we evaluate its ability to predict multiple attributes of NBA players under partial data missingness. The NBA dataset was collected from 22. which contains 16,992 player-season records from the 2002-2022 seasons. Each sample is structured across six principal statistical views including scoring efficiency, rebounding and physical metrics, technical statistics, advanced efficiency metrics, player background, and season context. The prediction tasks comprise career stage classification, positional identification and awards prediction. Career stages are partitioned into early (first 25%), peak (middle 50%), and late (final
Basketball-Referemn
9

---

Table 2: Ablation study Pascal07, OBJECT and Mirflickr with PER=50% and LMR=50%.
and
X
represent the used and not used corresponding item, respectively.
Pascal07
ORJECT
Mirflickr
S
S2
S
AP
AUC
1-RL
1-0B
AP
AUC
I-RL
1-OE
AP
AUC
1-RL
1-OE
X
V
0.546
0.852
0.830
0.455
0.650
0.903
0 0.894
0.633
0.594
0.859
0.872
0.649
V
X
V
0.576
0.874
0.853
0.478
0.687
0,914
0.906
0.678
0.614
0.872
0.881
0.652
V
V
x
0.582
0.874
0.857
0.486
0.690
0.912
0.904
0.680
0.616
0.870
0.882
0.659
/
0.599
0.882
0.864
0.519
0.702
0.924
0.916
0.688
0,631
0.875
0.889
0.687
25%) phases according to each player's professional timeline. Player positions (PG, SG, SF, PF, C) represented using one-hot encoding, and multiple binary indicators corresponding to honors such as MVP awards and Defensive Player of the Year, are included to provide multi-task objectives and comprchensive modeling of player achievements.
Across varying levels of data incompleteness, with PER and LMR ranging from 50% to 90%, our method consistently surpasses baseline approaches, demonstrating superior robustness and reliability in attribute prediction. Moreover, all comparison methods fail to surpass an AP of 0.6 at 90% missing ratio, whereas our TDLSR achieves 0.668. Despite incomplete technical statistics and constrained annotation resources, our method remains effective in predicting player potential, including career development and honor attainment, which offers considerable promise for real-world applications.
(4) NBA Daitect Deseription
(b) Performanee with PER and MLR Changing from 30% to 90%
nice
5
1-LL
1:00
2TFS Appici
Treg
0375 0xm--
up e
HAL SAY IML DCVV BEY
Figure 4: Overview of the NBA dataset and performance with missing views and labels.
5 Conclusion
In this paper, we propose theory-driven label-specific representation (TDLSR) framework for addressing the iMvMLC problem. Specifically, structural dependencies are modeled through graph attention mechanism inside each view for recovery, with the reconstruction fidelity adaptively tailored to enhance classification efficacy. Meanwhile, we construct a universal feature extraction model, where mutual information optimization serves to regulate information shift, interaction and orthogonality between representations. On the basis of complete feature semantic separation, we independently interact each representation with label prototypes that encode correlation semantic, aiming to extract label-specific discriminative features and uncover cennssentttioossnsstte label subsets. Moreover, we theoretically validate the effectiveness of representation learning and its influence on the generalization performance. Finally, the superiority of TDLSR are validated through extensive experiments and application to the NBA dataset. In the future, we will explore leveraging the prior knowledge embedded in LLM to facilitate label semantic learning.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 62376281, the NSF for Distinguished Young Scholars under Grant No. 62425607, and the Key NSF of China under Grant No. 62136005.
10

---

References
[1] Ahm, L. V:; and Dabbish, L. 2004. Labeling images with computer game. In SIGCHI Conference on Human Factors in Computing Systems, 319-326.
[2] Basketball Reference. 2025. NBA Player Totals Statistics, https://www.basketbaal/// Accessed: 0025-03-03.
[3] Chen, T.; Wang. W.; Pu. T.: Qin, J.; Yang. Z.; Liu, J.; and Lin, L. 2024. Dynamic correlation learning and regularization for multi-label confidence calibration. IEEE Transactions on Image Processing, 33: 4811 1-4823.
[4] Duan, K.; Cui, S.; Shinnou, H.; and Bao, S. 2025. View-Channel Mixer Network for Double Incomplete Multi-View Multi-Labes learning, Neurocomputing, 617: 129013.
[5] Duygulu, P.; Barnard, K.; de Freitas, J. E.; and Forsyth, D. A. 2002. Object recognition as machine translation: Learning lexicon for fixed image vocabulary. In Proceedings of European Conference on Computer Vision, 97-112.
[6] Everingham, M.; Van Gool, L.;; Williams, C. K.; Winn, J.; and Zisserman, 2010. The pascal visual object classes (voc) challenge. International Journal of Computer Vision, 88: 303-338.
[7] Federici, M.; Dutta, A.; Foréé P.; Kushman, N.; and Akata, Z. 2020. Learning Robust Representations via Multi-View Information Bottleneck. In International Conference on Learning Representations.
[8] Grubinger, M.; Clough, P.; Müller, H.; and Deselaers, T. 2006. The iapr 12 benchmark: A new evaluation resource for visual information systems. In International Workshop onto Image, volume 2, 1-11.
[9] Guan, R.; Liu, T.: Tu, W.; Tang, C.: Luo, W.; and Liu, X. 2025. Sampling Enhanced Contrastive Multi- Remote Sensing Data Clustering with Long-Shor Range Information Mining, IEEE Transactions on Knowledge and Data Engineering, 1-15.
[10] Guan, R.; Tu, W.; Wang. S.; Liu, J.; Hu, D.; Tang, C.; Feng, Y.; Li, J.; Xiao, B.; and Liu, X. 2025. Structure- Adaptive Multi- View Graph Clustering for Remote Sensing Data. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, 16933-16941.
[11] Hang, J.;Y.; and Zhang, M.-L. 2021. Collaborative learning of label semantics and deep label-specific features for multi-label classification. IEEE Transactions on Patlern Analysis and Machine Intelligence, 44(12); 9860-9871.
[12] Hao, P.; Gao, W.; and Hu, I.. 2025. Embedded feature fusion for multi-view multi-label feature selection. Pattern Recognition, 157: 110888.
[13] Hao, P.; Liu, K.; and Gao, W. 2024. Anchor-guided global view reconstruction for multi-view multi-label feature selection. Information Sciencey, 679: 121124.
[14] Huang, J.; Li, G.; Huang, Q.: and Wu, X. 2016. Learning label-specific features and class depended labels for multi-label label classification. IEEE Transactions on Knowledge and Data Engineering, 28(12):
[15] Huang. W.: Yang. S.; and Cai, H. 2023. Generalized information-thhoreet multi-view clustering. Advances Neural Information Processing Systems, 36: 58752-58764.
[16] Huiskes. M. J.; and Lew, International Conference on Multimedia Information Retrieval, 39-43.
2008. The mir flickr retrieval evaluation. In Proceedings of ACM
[17] Jia, X.; Jing, X.-Y.; Zhu, X.; Chen, S.; Du, B.; Cai, Z.; Hc, Z.; and Yue, D. 2020. Semi-supervised multi-view deep discriminant representation learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7): 2496-2509.
[18] Kawaguchi, K.; Deng, Z.; Luh, K.; and Huang, J. 2022. Robustness implies generalization via data- dependent generalization bounds. In International conference on machine learning, 10866-10894. PMLR.
[19] Li. Q.: Luo, T.: Jiang. M.; Jiang, Z.; Hou, C.: and Li. F. 2025. Semi-SSpperiseed Multi- View Multi-Label Learning with View-Specific Transformer and Enhanced Pseudo-Label. Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, 84430-18438.
[20] Li, Q:: Luo, T.: Jiang, M.; Liao, J.; and Jiang, Z. 2024, Deep Incomplete Multi- Multi-View Network Semi- Supervised Multi-Label Learning with Unbiased Loss. In Proceedings of ACM International Conference on Multimedia, 9956.
11

---

[21] Li, X.: and Chen, S. 2021. concise yet effective model for non-aligned incomplete multi-view and missing multi-label learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(10); 5918-5932.
[22] Lin, Y.; Gou, Y:; Liu, X.; Bai, J.; Lv, J.; and Peng, X. 2022. Dual contrastive prediction for incomplete multi-view representation learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45():: 4447-4461.
[23] Liu, C.; Jia, J.; Wen, J.; Liu, Y.; Luo, X.; Huang, C.; and Xu, Y. 2024. Attention-induced embedding imputation for incomplete multi-view partial multi-label classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, 13864-13872.
[24] Liu, C.: Wen, J.; Liu, Y.; Huang, C.; Wu, Z.; Luo, X.; and Xu, Y. 2023. Masked two-channel decoupling framework for incomplete multi-view weak multi-label learning. Advances in Neural Information Processing Systems, 36: 32387-32400.
[25] Liu, C.; Wen, J.; Luo, X.; Huang, C.; Wu, Z-; and Xu, Y. 2023. Dicnet: Deep instance- contrastive network for double incomplete multi-view multi-label classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, 8807-8815.
[26] Liu, C.; Wen, J.: Luo, X.; Xu, 2023. Incomplete multi multi-labed learning via label-guided masked view-and category- aware transformers. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, 8816-8824.
[27] Liu, C.: Xu, G.; Wen, J.; Liu, Y.: Huang, C.: and Xu, Y. 2024. Partial multi-view multi-label classification via semantic invariance leamning and prototype modeling. In Forty-first International Conference on Machine Learning.
[28] Ma, Z.; and Chen, S. 2021. Expand globally, shrink locally: Discriminant multi-label learning with missing labels. Pattern Recognition, 111: 107675.
[29] Pan, E.; and Kang, Z. 2021. Multi-view contrastive graph clustering. Advances in Neural Information Processing Systems, 34: 2148-2155
[30] Park, L. A.; and Read, J. 2019. A blended metric for multi-label optimisation and evaluation. In Machine Learning and Knowledge Discovery in Databases: European Conference, 719-734. Springer.
[31] Si, C.; Jia, Y.; Wang, R.; Zhang, M.-I..; Feng. Y.; and Qu, 2023. Multi-lahel classification with high-rank and high-order label correlations. IEFE Transactions on Knowledge and Data Engineering, 36(8): 4076-4088.
[32] Song, Q:: Gong, T.; Gao, S.; Zhou, H.; and Li, J. 2024. QUEST: Quadruple Multimodal Contrastive Learning with Constraints and Seff-Penalization Advances in Neural Information Processing Systems, 37: 28889 28919.
[33] Tan, Q.: Yu, G.: Domeniconi, C.; Wang. J.: and Zhang, Z. 2018. Incomplete multi-view weak-label learning. In International Joint Conference on Artificial Intelligence. 2703-2709.
[34] Tan, X.; Zhao, C.; Liu, C.; Wen, J.; and Tang. Z. 2024. A two-stage information extraction network for incomplete multi-view multi-label classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38,
[35] Tian, X.; Zhang, 7.; Wang, C.; Zhang, W.; Qu, Y., Ma, I., Wu, 7.; Xie, Y.; and Tao, D. 2023. Variational distillation for multi-view learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(7): 4551 45666.
[36] Wang, S.; Liu, X.; Liao, Q.: Wen, Y.: Zhu, E.; and He, K. 2025. Scalable Multi-View Graph Clustering With Cross View Corresponding Anchor Alignment, IEEE Transactions on Knowledge and Data Engineering, 2932-2945.
[37] Wang, I. Q.: Chang, D.; Wen, J.; Xiao, F.; and Zhao, 2025. A Category-Driven Contrastive Recovery Network for Double Incomplete Multi-view Multi-lahel Classification. IEFF Transactions on Multimedia, 1-10.
[38] Wen, J.: Liu, C.; Deng, S.; Liu, Y.; Fei, L.; Yan, K.; and Xu, Y. 2023. Deep double incomplete multi-view multi-label learning with incomplete labels and missing views. IEEE Transactions on Neural Networks and Learning Systems, 35(8): 11396-1 1408.
[39] Wen, W.: Gong, T.: Dong. Y.; Yu, S.; and Zhang, W. 2025. Towards the Generalization of Multi-view Learning: An
Analysis, arXiv preprint 16766.2501.1668.
12

---

[40] Ye. H.: Sunderraman, R.; and Ji, S. 2024. MatchXML: an efficient text-label matching framework for extreme multi-label text classification. IEEE Transactions Knowledge and Data Engineering. 36: 4781-4793.
[41] Yuan, H.; Sun, Y:; Zhou, E; Wen, J.; Yuan, S.; You, X.; and Ren, 7. 2025. Prototype Matching Learning for Incomplete View Clustering. IEEE Transactions Image Processing, 34: 828 841.
[42] Zhang, X.; Wang, R.; Chen, S.; Jia, Y;; and Wang. D. D. 2024. AME-LSIFT: Altention-Aware Multi-Label Ensemble With Label Subset-Speclfic FeaTures. IEEE Transactions Knowledge and Data Engineering. 7627 7642.
[43] Zhao, D.; Gao, Q.: Lu, Y:; and Sun, D. 2022. Non-aligned multi-view multi-label classification via learning view-specific labels. IEEE Transactions on Multimedia, 25: 7235-7247.
[44] Zhu, Y:; Kwok, T:; and Zhou, Z.-H. 2017. Multi-lahel learning with global and local label correlation. IEEE Transactions Knowledge and Data Engineering. 30(6): 1081-1094 1094.
13

---

A Derivation and Implementation of the Loss Function for the Universal
View Extraction Model
A.1 Derivation of the Loss Function
The universal view extraction model under mutual information constraints is
(( 1(01)) v=vvia g0
(000)/1)1)))
I1aX
information shift
information interaction
(16)
s.t.
Σ
0.
information orthogomality
By incorporating variational derivations from the information theory, we arrive the following objective function for optimization:
LIB - E p((tt),at)) [log (s (s/m)
/ 1()(")
s((")( s(0)) log q(s ((s(") Is" )ds("")
(os(")) ds(())
lower bound information shill
lower bound for shard information interaction
DKi(p(o (v') 122(1) (z())
Ip(o (v') (((
upper bound for specilic information interaction 3 DRI(p(s(") 12(") (0) p(o ( (1) (o))))
upper hound
orthogonality
(17)
Proof. Due the challenge of distribution inference and the complexity of high-dimensional inte- gration, directly computing mutual information is impractical. Therefore, it is common to ensure stability and feasibility by optimizing estimable bound of mutual information. For the information shift term, we have the following transformation based on the definitions of mutual information and information entropy:
1(8("); 1(8());(())
= =/ʃ p(s(1), (0)) log p(=())10(e)
p(z(0)) ds (2())))(())
// p(s(1), z0)) log (ogp(z(0))) (d)))d dz) + p(=()))(()) / ((=(")))og log p(z())) d2(v)
dz())
= =|/ p(s(t), z(0) logp(z(") (0)) H(z())).
(18)
Since Eq. 18) is intractable, we approximate (((()))((e) using stochastic variational distribution ((2()))(()),, which can reasonably estimated. Combing the fact that entropy ((2())) 2 0, we can further obtain the lower bound:
((s());(())
(19)
2 /ʃ p(z(1), (("))oog(ee log "z) dz()
=f p( / (()()) log (x())((1))) ((()) (ds (2(())
(ool (( log ((2(0))((1)
((z(0)){()) ds (z
14

---

The Kullback-Letie Leibler divergence is denoted as
1o) (ا())
DKL(p(z(0) (s(0) (0)) (0022))))1))
log ((((0) s(w)) dz(w) 2 0
(20)
Thus, we have
;(10)
/ plzlo0) / ((5(1)11 logg(z(")) dz(")
+ / p(s( (
(21)
/ mistoo I 1001
d2(")
/ p(
)dsl
= at))) [108((((0)((0)
For the second term, based on the definition and non-negativity of entropy, a lower bound can be derived by introducing another estimable variational distribution q(s())) mutual information in its integral form, we have
(g(("))) 1). By expanding the
If p(s|"))2 s00)2 log p(s(")220) s(y" s("")) 12(0))
I(s(")) 1 (0)
p(s [2(00))))))))))))(()))))))))[[ (2())))(((())) 20)) ds ds
dss""
(22)
Considering p(s("") "12(0") s/00 12(0)) (((()))2()) /s(0 1()(t)) of (01))
|2("")) can get
(23)
= =/ʃ (( 1
x((00) (p)((t))2)(0)) log p(s(U)12(0)
p(s(o)) (2(1)) )p(()))())))))))))) )p(s) (p(((())10)))
/z(0)) ds(v') ds(()
ds(()))s())
-l (((10))
log (0))))
(1)))/))////)))))//) /s("*) ("" ds(()
+ */ʃ p()(1))
|( ds ( (t)
Since H(s(() 2(11) - pp((( ((01 log (r)
obtain
I(s ( (0))
Iʃ p(s p(
"lgp""''ps''' (1) / /s(0)) 12 ds(
// ((
log (( )ds ds(")
+ *// p( (0)
log p(s(") 12000/////)00///>>>>/)))) dslu") (24)
((s()))((u))
Based on the definition of Kullback -ullback-Leibler divergence, we have Dkl(p(s (M) (2()) (7) ) (1)))))))))))
= =ʃ (()(0))2(0)
log p( (1) 12(")² ds(e)
(25)
((((0))(()))
Since DKL(p(s (2)))) ((()))/(())))
2 O. we have
I(s( 122 ((())) /20)) 2 // p(s 1 (.n 1z )p(s ) log ( (d("") (s(")
= =/1 (( ((()) log ( s (11')) ds(n)
(26)
15

---

For the third term I(o" 12(")) ; (2())))))
we derive the following upper bound:
T(o" 12 10 (010)
= =|ʃ p(o 12(1);
log
p(o (2(0)) (((()))(l()))))))))))))))))))))) do do
plan (z(0), (0)))
// p( /200) 00'0 log
22 /0"" 12(00))
do do
p 2(1))
1ʃ p(o" 12(") 12("" o log
12
/000)
do
((olo) ((olo))(()))
+ 1ʃ 1(0")12(0)) oz00)) 8ol
dol")) do
p(o(")|
// p(o" (000)1((0)))) (2(1)) 0 log 10000110100001000
dolo))
/ 1(000))2100 /0'0 "1000"")) )))o(())
$ // p(0" ,(0)())))))))) log
d do
/ʃ p(00
plo"
(2(0) (x(1)) -1)))))))))))))))))))))))))))))) log
p (((o do
dolo (0) do
=Dki(plo" [ lp(o
(((0))))())))
(27)
Similarly, derive the upper bound for the last term, which exhibit structure analogous that of Eq. (
I(s 1s
s (Kz(p(s(") (2()) (*) (t) (lo( (2()) (s(()))))))))))))))))))))))))( (())).
(28)
Combining Eqs.
21
25
and (88). the objective is naturally transformed into minimizing its
upper bound:
[log (z(*))(())
12) g( 12 1z(1))) log ((s(")) 8" )ds("" (g ds(())
LIB p(2(m) (w)))
lower bound for information shift
lower hound for shard information internction
Dkz(p(o (2((")) (²) (2(0) (I((o'))) 0 12((0 (e)) (000(1100""")
upper bound for specitic information interaction + 3 DKi(p(s ol)) (0) (v)
pp (*) (2())))(()))))))))))))))))))(( (g(((())))))))))))))))))))))(() (0))))))())))) (0(1))
upper bound for information orthogonaiity
(29)
A.2 Implementation of the Loss Function
Data-driven contrastive learning 22 is used to compute various complex distributions. Specifically, representations treated probability vectors over D classes (corresponding to d dimension) via Softmax activation function, and the joint distribution matrix is obtained by
((,.0)
(v,0")
M(*
Σ
(v)
(0)
Due to the strong coupling between s(0) and ((=)) the variational distribution (()(t)|s(0) can be effectively estimated by the obtained conditional distribution. In contrast, owing to the extremely
16

---

weak correlation between (*)) and o("") as well as ol)) and s("), the distributions q(ol")/ /o("")
and ((x(1) /o(")) can be approximated by the corresponding marginal distribution. Since the first information shift term is equivalent to the reconstruction loss, we construct decoder for each view to obtain 2", which is used to approximate the original view. Subsequently, by converting the integral
summation form, each term in Eq. (29) can be expressed as
I p( ((0') (z()) (z("") log q(s (0 (dsss""" dsl (0)
D
D
p(v.')
Σ
Σ pl d,d'
log
plv*)
d=1'=11
(n.e
D """"""""""""""""""""""""""""""""
)9(( )) Σ
Σ
addd
(v.e")
log
d,d'
(Q
d=
D D
M M
(((( )) ( m) o (")) (>
= Σ
M d
log
(M (M (5*)
M (or)
d=1='1
(30)
where the Lagrange multiplie 3 is fixed to I, and the marginal distributions p(") and d' can be obtained by summing over the d-th row and the d'-th column of the joint distribution matrix P(u,v"), with other symbols defined as the same. In this conversion, we let g(s"/ "²"") ) = (vb ( (1))
(((()))) )) and
q(z"/ /s" = (1 (M(*))) where & is a fully connected layer, and a is a balance factor to preserve crucial information and ensure model stability [77. We set the value of a to 10 in our experiments.
B Detailed Proof for the Theoretical Results
In this section, we will provide rigorous proof of the theoretical results mentioned in the main text.
B.1 Proof of the Theorem 1
Theorem 4. (Discriminability of Label-specific Representation.) For label prototypes E, and Eg
such that k + i for all k, and view representations X()) and X (x") such that v² + u for all v², the discriminability of p(o) for class j necessitates that either of the following conditions be satisfied:
N
N
E
x
(v)
(OSEE))
[E)
Dos(E,)
oS
> E
X
(e)
Ex)
Σ
x
(v)
ass
(Ex)
N
N
i=1
N
N
E
X
os (Ej)
0s EB) X 10'
E
os oss(
Ex [E)
(v") as TT
Proof. Since our training data is multi-view and multi-label, the discriminative power of view u with respect to label j involves two key considerations. First, among all labels, view v yields the most accurate prediction for label j: second, across all views, view provides the prediction for label with the highest confidence. Thus, proceed with the proof from the following two aspects:
(i) For Eg and Eg such that & + j for all k, the following inequality regrading view v holds:
N Ex) > E os [
N
E x (v) ( E,)
(sE))
(1) Jg (Ex) (31)
N
N 1=1
The j-th component of (corresponding to label j) is
p(v))
P. ( 3 x()))
where (0(0) i.j is vector where each element is the dot product of the corresponding elements of os(E) and az!") Since a linear classifier (e.g., fully connected layers) is used for classification, the prediction score for sample i is
0. wP. + b,
17

---

where W E RCx((xd) is the weight matrix and b E RC is the bias term. Give that p(()) E Roxa we can flatten it into 'ndiiviuall vectors for each label. Besides, W has block-diagonal structure, i.e, the weights for each label j only act on P.,y Then, the prediction score for label j simplifies to
U = m P
+ +b wo (os(E)) @ a; (0) bj.
where wy E Rd is the classifier weight for label j. To express discriminability. we need to show
E
E
vk + j.
The expectation is obtained by averaging over all empirical samples:
N
w/
ass (ss(E))
o oz!" + bj.
N u0k
E
U
(v) 1
(ns(Ex) 4 m + bk-
N
Assuming classifier weights wy are independent of input data (e.g., optimized during training) and biases by are constants, the core comparison reduces to
N
as cas(E
G (Es(EE)
Σ
m
(as(Es) a m!!"))
(32)
During training, the classifier weights wy tend to align with label prototypes E, since E, captures the semantic meaning label j. Thus, we approximate wi Ey Substittting into Eq. (32). the comparison terms simplify to
N
Σ E = (os(E))
vs. Σ Ex (os(Es) o a
Using properties of dot products:
Ej (E) o x
Eyg as (B(())) +ig
Eg (ss(E)) o xz
Σ Exi1 0s (E(.)))) -I
Then, the comparison is further refined into
(0) ΣΣ Egg- - as (Fx,)) zid
VS.
Ex as (FR,) a.f
Note that (E))) 10, and is monotonically increasing. For positive samples of label i, E, and are better aligned, meaning Ezg- Fi, has a higher expectation. Thus, the condition is
E, E
E
x ( os( (Ex)
Then, the following inequality holds:
N
N
(E.)
2i1
(0)
>
os (Ex1) x
Assuming E, and Eg have similar scales [ =
Eg 12) we conclude
N
Σ E, oss(
EE) (E,))
(1)
Σ
Es (as(En) o xr)"))
(33)
18

---

Furthermore, we have
U
E
E
Vk + j.
Therefore, the prediction score for label j exceeds that of all other labels, demonstrating the discrimi- native capability of view e for class j.
(ii) For view u and v" such that v* * for all v², the following inequality regrading label j holds:
N
1 N
E
X Oss
os (Es
E x os (E,)
as BB)
N
(34)
The prediction score for label j assigned by view and v", respectively, is
U w. T p(yy) by wo (os (B) @ a!!") + bj.
ugy w) pily) + bb = mo (ss(E)) o a ) by:
To express discriminability, need to show
E
E
Ve +
Following the same rationale, we can transform the comparison into
N
N
d
Ega- 0s (E,1)
vs.
E os(E,,) x//
E=
Thus, the condition is
E x 1 Os(E)
E
> x "ss"")s(EE) (E
Then, the following inequality holds:
N
N d
as (s(
os Os(Ez,)) x.11
1=1
1=1
1=1
Similarly, we conclude
N
N
Σ
E
Σ
Ej [as( (Ej
ox! oz)
(35)
Furthermore, we have
[ > E U
E
Vu + v²
Therefore, the prediction score of the e-th view for class j is higher than that of all other views, indicating that view exhibits discriminative power for label j. Combining (i) and (ii), we complete the proof.
B.2 Proof of the Theorem 2
Theorem 5. (Effectiveness of Disentangled Representation.) Let the disentangled representation be denoted as R = (S(1)...., S(V) 000 ("").........)),.).)... where the information entropy of each repre- sentation is assumed to be fixed, i.e.. ((S())) = (OO = H (1 <1 where each shared and specific representation indispensable for prediction, T(R: Y) will attain its
OV)),
<V) V). Then, in the case maximum when R = R., with R, being the optimal solution of the problem
T6
Proof. By integrating core features from the raw data to construct shared representations and lever- aging classification loss to derive view-specific representations aligned with particular labels, our approach enables the shared features to encapsulate primary generalization information across mul- tiple views, while the specific features designed to capture discriminative information that is
19

---

.p
2110
2110
xm
x
, Then, specify (a) optimal situation
(b) lack of information shift (c) lack of shared information
(d) lack of specific informarion
(e) lack of information orthogonality
interaction
interaction
Figure 5: Feature extraction visualization. Fig. (a) illustrates the optimal solution obtained by our model, while the remaining four figures display cases where the constraints of information shift, interaction, and orthogonality are successively removed. The shaded areas represent the shared representations, whereas the other colored regions indicate the view-specific representations.
finely attuned to task-specific characteristics. Thus, the assumption that each shared and specific representation is indispensable for prediction aligns well with model. Besides, all represen- tations are extracted into the same dimensional space, it is reasonable to posit that they encode equivalent quantities of information, i.c., =
11 (1 S V). Let define the optimal solution of the problem (16) R. (S. ................................ S.
that identifying each class Y requires corresponding representation setting R to be mined, i.e. (YY)) H (R""), which indicates that the successful extraction of R is sufficient for predicting Y". Based on this, we establish the following formulation:
((RT)=H(ST)) H )(S = E. H(O)) EV H(O!")
DC E. H(SS EC E S. = H(.)).
=
(36)
where for and 9. are indicator functions representing the shared and specific information components that constitute RY According to Eq. (6).. all information contained the extracted representations essential for predicting the target labels. Next, demonstrate from three perspectives that feature extraction model is capable of maximizing the mutual information between the representations and the labels, i.e., the representations contain insufficient information for prediction, just enough information, or redundant information beyond what is necessary for prediction.
(i) (S (5(,,,..,,S" S (
O()) C RY UR .URRR
In this denote the mutual information between R., and Y as 1 i.c.
IRR; Y)
I((SS) S.s ... X9)
I(R": :Y9+ + Σ T((S ,....,!'
s(\) 0. 0!!): Ya)
EEC
CEu
Σ H(Y - HYY Σ H(((S)) (1)
s. s 0.a
0!!))
EEC
CEL
H((S!!) s(n)) !.!) o
Σ H(Y)) Σ H(!!!) !! o. ........!!'))
CEC
cEN
Σ H 2 (V IS (( ro.
EEC
where C and denote the subsets of labels that are fully predictable and not adequately predictable, respectively, and [C] + [24| = C. When the core shared feature information is essential to all labels, reducing I(S(") : ((V) to enhance label-specific information associated with certain labels will not lead to increase in I(R,; Y). Since Enec H(Y") is fixed, postulating the existence of an alternative representation R satisfying 1(R: Y) I(R.; Y) would inevitably contradict the
20

---

assumption that the information entropy of each representation is fixed at H Thus, we can obtain [R,; Y) 2 [R; Y). Given the insufficiency of prediction information and fixed amount of information encoded in the representations, enhancing performance necessitates incorporating usable content beyond raw information and introducing additional constraints offers no further gain the mutual information between representations and labels.
(ii) (SU), S O,,,....... 0()) R UR UR
In this case, similarly, we have the following equality:
T(R,;)) Σ T(((.)) ()) ..... S. "..,.....,!! ).o Vo)
Σ T(RY; Y9)
Σ H(R H(R
aml
C v
C v
fz H(S!) ΣΣ
+ ΣE Le c=1==1
HO.
c=
If the information shift term is not sufficiently optimized as shown in Fig. (b), there will exist shared representation 5(m) the setting such that
(R: ΣΣ fa H(((
Σ Fc f H((
TE
cET == 1,
Σ Jmh (()))m))))))))))))
ΣE
Le -EE
TETm.
where Tm denotes the set of labels whose prediction processes involve contributions from 5(m), while T is the set unaffected by $(m), Since the change in information entropy occurs exclusively in ((m)) we have
EIETa E fo H((())) = = Ev H(S EoETm E. for H(S( Ecern Ee fr H(S) ECET.. fm H()()) < E f H(!!m))
Furthermore, we have the following comparison:
T(R:Y) S Σ E SH H(S!
Σ
Σ
f H(S
TE v=1
cETm v=1,4m
fth (s!)))
Fe H(O)
TET
= =I(R.YY).
If the shared information interaction term is not sufficiently optimized (Fig. (c)), there will exist a set of shared representations whose task-relevant information is significantly reduced due to ineffective interactions. Under such circumstances, it similarly follows that I(R; Y) < I(R.; Y). Moreover, insufficient suppression of interactions among specific representations causes overlap, thereby reducing the useful information entropy of each representation (Fig (d)). Additionally, inadequate optimization of the orthogonality constraint can introduce redundancy between shared and specific representations, which in turn hinders the extraction of the specific representations (Fig. (e)). For this two aspects, we also have I(R; Y) S I(R.: YY.
(ii) R UR ..URY C (S())
S(V), (
00)).
21

---

In this case, we can obtain
IR+; I((5 ,...., S. ,0 .!......!!
) 8
==1
Σ I(R"; ;Yq)
Σ H(Y HYY
H(Y..
Given that E c= HY) quantifies the total label information, the mutual information I(R; Y) obtained from any alternative representation is inherently constrained by this upper bound. Therefore, we conclude that T [R; Y) I Y).
Combining (i) (ii) and (iii), we deduce that the maximization of T(R; Y) is attained when R serves as the optimal solution R, of the problem (16). Moreover, the principles of information shift, interaction, and orthogonality are all indispensable for achieving this.
B.3 Proof of the Theorem 3
Theorem (Generalization Error Bound.) Our model is designed to learn a vector-valued function f (f1....,fc) X + BCC The expected risk and empirical risk w.r.t the
training dataset D are denoted as R(f) NC Ee' Ee E(EV=1 (Q fo(2) (1)))) Yr,). where f""(-) refers to the late fusion of multiple
xxxxr)xxxyl(((( (X, Q). Y) and RD(f)
views. With probability at least 1 - ò, we have the following generalization error bound:
K1
RS
R()) - (Q)))
+ gen ( (Q
VNV
N3/4V1/4
Ee 1(X(0, St)), 0 + R.))
+ Ks
NC
where K, - - R2 = O(VO), RA constant of order Õ(1) as N,V - oo, and getrree (Q,X,Y) is the generalization error related to the view reconstruction quality. Moreover the generalization error bound becomes increasingly lighter during the optimization of the problem (T).
Proof. The training dataset denoted as D {xx; y:) i E [N]] is drawn from probability distri- bution over X' x y. Each x, = (x= (v( consists V views and y, = (Y......., Y,c)). Our strategy learn vector-valued function f =
fc) X' + RC and determine relevant la- bels by applying thresholding criterion. The goal of learning is to find a hypothesis f F with good generalization performance by minimizing the loss on the dataset D. As missing labels inevitably degrade generalization, we focus on deriving the tightest generalization error bound under complete la- beling. Thus, the expected risk and empirical risk w.r.t. the training dataset D are denoted as R(f)) = (")))))))))))))).
Exx Y) )> (X, Q), Y)] and RD( = No Σ. EC { (o D), Y.c), re- spectively, where fav(-) refers to the result fusion of multiple views, Q is the reconstruction quality score serving as the fusion weights. We define the function class of TDLSR as follows:
F=(x(0) (v) + f(x())) f(x (o)) (X d(u) = (di, o.), whe = (w Cc), w E Rixd].
fo(x("))), fo(x(()) (r) = (1 (x (v)),
(37)
where 8² and d0 denote the view-common and view-specific representation extractors. Çj is nonlinear mapping induced by the label-specific representation construction and the classification head. Besides, the disentangled representation R is expressed by R o(X) (6*(X),"*
22

---

(S(1) S(V) O ..... O Let view data X = (X (X
To=1 be produced with a hidden label-specific function #r by X B (Y V). where Y is the randomly generated single label and V = [V(") (V
Vd ) E Rmxd are nuisance variables. Denote the conditional random variables of X and R given the category Y y as y and Ry.. respectively. For
any y E = = {-1,1} 1,, the sensitivity de of the representation function & = (d(1) jb=I w.r. the
nuisance variable v,(") is defined as
2/" = sup nE[V] oi
log(pr o od.. 00. (v) ,...., 2 2 (
sup (())
(38)
-log(pr (g)
Oue
U1 (0]
..... 06(0) (10) )))
where (g-(v( 0(y". v()) and (r) P R = r). Based on Eq. 38 we set the global
sensitivity of @ as cC sepceic cg Let R (0y (v), do (v) : V, y y* denote the
complete multi-view data and their corresponding representations. For any 7 >> O, we construct
the following typical representation subset for each class (3)]
dlog(vNV//) /7)
R
x, E.R.R. R Prg (r) - H(Yr S co
(39)
2
Define the function kyg((v) = -log Prly (v)), where hy (v) = so (0)= Let po(o) P(V v) and hight (r) (w V Ny (v) = r), we have
Ey MMg (V)] = - Σ (w) log Priy (w))
DEV
Σ
Po Po(w)loggri Pog Priv (M (v))
EE ve (n)
Σ EER
Σ Po(
log log Priw (r)
DE (r)
Σ
Priv (r) log (rly
FER:
H (Ryr).
By applying McDiarmid's inequality on hy (V), we get
26
log Priy ( 2 & exp
c(co))
Taking 8 0= exp (-
=expp
2+ "d(e))
we have
d dlog(118)
c= col
2
After setting 8 8= = "////VVVViii.. i.e., X R R.
55 7
VNV we can obtain
exp(-H (Rr.) -e) Priy (r).
Then, further derive the following transformation:
R exp(p (Ry=)) -
Σ PER
exp( spp--1I H(Rr)) - -) Σ Pr(r) =
PER:
which implies
dlog( NNV/2
R S exp H(Ry.) + coy
2
Therefore, regarding the property of the typical subset, the following lemma can be derived:
23

---

Lemma 1. For any and all v E V we have
dlog( dlog(VNV//
P(X, R R
R Rayl exp H(Ry.) + to/
VNV
2
Besides, we need the following lemma for subsequent proof:
Lemma 188 The vector = (Xi...., XR) is defined to follow the multinomial distribution with
parameters p = (pi...., Pk)). Let āj..... ag 2 0 be fixed such that E a:Pr # O. Then, for any
e 0, the following inequality holds:
X,
mm²
a
P:
>e
S exp
(-8
m
where 3 =
322 -x a'pr.
We further define TV = Ro where the typical subset R. consists of elements R [( (,1,,,,))..... ...,........ ( ((r)) Besides, we introduce the following label-specific sets:
40 i E N a."h
(o) (x) (1)) Rayy Y = =.. 4 = fi E [N], [ af ar s000 (x) = (a e.a ,,),,r.o - vr..
(40)
Then, we conduct an analysis the classification generalization error:
R()) RD( Bx,.,./xxxxx (),
1 NC
[(Qrnddaaf")) Yi,
(41)
Since e is convex function, apply Jensen's inequality to obtain
Qunre(a)")) Y.,) S Qi, Σ (SC((a")), V,c)-
(42)
Thus, we define a instance-level loss difference term (eT(Q.... X Yi,)) such that
AG Qu. ((fo(a)"))) Yo,)) - El Σ Qu.efola! )) Y..). v=1
(43)
Define y suPse[N] SuPee[V] Qi the maximum view reconstruction quality among all views. Regarding the cumulative loss calculation for individual views, we have
Qi,
Σ
NC
n
Qi NC
Σ
Σ
Elibe o (2()) + Σ Σ
Elbbe o (z())) ).
==1 *-
k= ieeeyse
Tv
Q NC
Σ
Σ
Us o o (2) ) +
Σ
Σ3ΣΣ
Σ
E
Σ
Elbbla ; a ).0),
NC
a=l 1 E 1,eElv"
C=
Y+EY k= 1eea
C
Twe
qlue elvela G.
9 Σ
Σ
Σ
El o (2(((((()))) (2)
,00 (..).)))
NC
NC
==1 "y i
c=1 y+yx km
(44)
24

---

Furthermore, we can obtain the upper bound for the empirical risk:
N
Σ (r.od((a
Vio)
2 NC
Σ
Σ
liee o (a) )000
NC
1=1 c=1
c=1 y'Ey' i,eetv"
(45)
T
q 6. o y'y
N
C
Σ ΣE -' k=1
+
(Q.... V.o).
NC
NC c=1
The random variables of the quality score of the v-th view and the e-th category are denoted as Q(1)
and Y Similarly, the population risk can be decomposed as
[ Y) Xxxxx (( ( X))
Σ
Σ
P(Y (1 =
D'Ey"
Σ
Σ
P(Y = vf (x, R) R. Q), Y Y -===== = of (X, $ Ren
=lvey)
Σ Σ P(Y y (x, R) E ) EX (X, Y = = VX R) E R clyey
(46)
Since E(X,Y )=)=>>>> [lf
(Xfe"((,00 (x, (E, = xxxxx ( fo((()) YY),,, we
can further decompose based on the convexity of
Xxx, 1 Q), YJ) = EXx ( Q (0) fo(X(1)), Y
(47)
V Q (ff((((())
= =E(xy9-)XX
Yタ] + EXYY'))xX> A (Q, XYYY))) Y
where (Q, Yo) represents the change in loss é associated with class e induced by view fusion. Then, can obtain the following transformation combing Eqs. (46) and (47)
E B(x (X Q..Y))
Σ P(Y yf (X, R) R. [x
Q (((((())))
89)') , R. & Ron
c'
Σ
p(Y 3², (X. E E(
( Y') =
- (X, R) RE
Elr
v=1
Σ
p(Y = y (
C
< Σ Σ
P(Y = (x 1x6(,,((000 (x())) & / = -f, (x())
c=1 x
T
(x(()) & R + ΣΣ
Σ cly-ry+ km
P x(1x = ax (((0)) (a " [ ag (.))))))))))
+
Σ
P = E
12 = 1
e= yyey
(48)
25

---

Putting Eqs. 58 and 48 back into Eq.
41
we have
c
E -xx.Y))=xxD)(( x. Q). Y)
ΣE
Σ (iooeel }), Yic)
NC
1=1
P(Y = yf (x6) 0 (xl1)) ww xx) y (x(,)
(x(()) & Roo
Σ
Σ
P(Y ,f (x (i & Ro
Σ Lvele
El o (zx!"))
c= V'EY
P(Y = 5f (x R [ ) & Read Ru
Σ
e o 15 (x."))
+
i.eEuve
ΣΣ Σ
llve o (x.").
NC
Ely'Ey" iNENN
T2
Σ Σ
= ,x,(x)= =
ax cat
o (x((i) = (ax",
.0% 6.0 Delscaaa c. ,0x% ) )0))))
c= E'E k=1
T2
Σ Σ
NC
VEEY
Σ y'
Σ
P of) B
ΣΣ
Σ ACT
X v9)
K,c
NC E1 V'E)"
(49)
Let Szy sup x'x(xx E (0) ((f(((( Yo) denote the maximum attainable - {(f((=(")) Y,,)) represent the as four terms, with the upper
losses among all classes and Si.,, = sup,e(c suPiE[n] Qi ΣV maximum instance-level losses. We consider the results of Eq. bound of the first term as follows:
Pi
Σ
P(Y vf, (x(), d ((6)) & 1e =f,
Elyey
(x 0 (x (1)
Reyl
Σ
o o (1)) )
|,0001
V
P(Y = 5f, (X, R)
Re E
Q ()(ff((("))) V. $ R.,.l
c=1 "
Cy Cr
P(Y = v
SIN
Sz.y
V NNV
VNV
c=1 "
(50)
Define pf = P( = yf, x ()) x06
= az ca (x(6) = (a c.s "a"")) for & E [T pfu 1. = P(Y
g. (X0), (X & ) and by llvie(a
(. , aa.0), ) for ls [IVV + 1]. Then, we can
obtain the following term:
T
Ps =
Σ (pf
NCq )b9 - (rf
NCq )8g-
(51)
Applying Lemma
for any and A E [Tt]] we have
NCq-1e2
P (Pi 2 S exp
(52)
Eie Ii (1G)² 1& (1G)2)
Tve
26

---

Similarly, we get the following inequality regarding ls = T + 1:
|
NNO 2 +1
P
+r
26
c S exp
(53)
NCq-1
Let ó be the right-hand side of Eq.
(52) and 53
respectively, we can obtain the following variants:
{
IP
P3,k 2 V Vi
PE (bg)²
Pe (bE)²
2log(1/51
S 8, Vk E [TWZ]
NCg
(54)
1u00
2 +1 log(1/6)
P pi Nog
2
S.
NC
Taking union bounds over all of E (ly* = 2)) and k E [T J. we have
P
Pā 2 v VE pi (b9)² - pf (bE)2
Tw
2log(27 /8] NCO-1
S S. vk E [78')
(55)
le00 NC.-
2p +1
lug(2/6)
P p
2
S 6.
NC
Then, for any 5 >
0, with probability at least 1 - 6, have the following scaling regrading the
second term of Eq. (49) by using Jensen's inequality:
gRv""
P2-
(x(), Σ (P yy yf, (1) , ((((()))))))) & RR.)))
Σ
llva a (a)))( ),2"
Ur
NC
D-EY"
C
Σ
b.juur e(p. 2i (ze (o)( )0)
2 2log(2/8)
v( xx $ RE,,)
1100
NCq-1
c=1 y'E"
Di.jeuv 140c00l1 (zo(")) ),
2log(2/8)
Σ
Σ VP (P(Y== V) (( ((X(), 2 (x(i)) $ R
110001
NCq-1
c=l -"
Enseur ElVio o (a())))))) (1) ).
12 221g(2200)
VT
VIDA
Σ
P(Y P(Y==
(NV)
NCq-1
Y'EY"
2/7 St (NV)
Clog(2/8)
Ng
(56)
Similarly, for Ps with probability at least 1 - 8, we have
Tv
2 logg227 /6)
PS.K <
Σ pt (6)))
P (bg)2
NCq-1
Tv
2 2log(2 /8) NCq-1
< S2.01
Σ pp V 1m1
2 log (2T 15)
= -2.. / IP (y==y² = ye N(x, R) E RE, (X(1),00 (x61)) # az c.s (a
.4
NC
22og(2TT 18)
S SS.vVP(Y' -
NCq-1
(57)
27

---

Next, we can derive the constraint result for the third term:
TW
33 Σ
Σ
Σ
P(Y
of x() = ax (x = =aax ,ax)) (a4))
NC
=1 EY km
7
Σ
T
3,k
k=1
Tv
2 2log(2TW /6) NCQ-
Σ Σ
S V P(Y -
TV
2 2log(2TVV /6) NOq-1
2 Σ
Σ
Su.y
P( PP 1r)
(58)
The property of T is as follows:
dlog(VNNV /7)
T = |R S exp H(y+)) + co/
(59)
Combining Eqs.
(58 and 59 y we can get the following bound by using Jensen's 's inequality:
2 H(Rx=) + cov
d /x)
+ 2 (2g()
Sz.y Σ (P(Y==yAソ) yeey"
P3 S 2
NCQ-1
==1
2 H + ccp
clog(VNV/7)
+ 22log(2/8)
2
< 2 Σ
SN. /
Σ P(Yc= S.
NCq-
V*EV"
C
H(Ry-) + co
dlog(vNV// + (2/6(
Sz
NCq-1
c=1
H(R + c
dlog( /NV/>) log(2/6)
4CSS.y
2
NCq
(60)
By applying the chain rule, we obtain the following conclusion:
([R[Y9) (I) R|Y)) (
= -(( s(n) 00)
( ,
1( (); g()) S(V), (O"IY") + + (0
S + (R
(61)
Since model achieves complete feature separation, with seamlessly integrated shared represen- tations, no overlap among special representations, and no redundancy between shared and special features, we have the following equality:
((x (1) (v) DY, s()) , s s.).....".... -(x())
= O.
(62)
Thus, we can further obtain
HRRY)) < ((x(); ((1) s(V) 0000) H(RYS x())
(63)
(v); (S 3 / (RRYS ('))
28

---

Putting the above back into Eq. 60 we have
C Σ
HR ( + Go NCq-
doog(vNV /7) 1og(2/6)
P3 S 4CS
(64)
Regarding the fourth term, as the accuracy of the view reconstruction increases, indicated by larger value of Q, the loss discrepancy (Qi, X.., Y.,)) becomes more significant, while the corresponding generalization error bound becomes tighter. Therefore, we interpret the fourth term as the generalization error induced by the quality of view reconstruction, i.c.,
P4 = gell rec (Q, = Σ Σ
F(Y DA
= y"}
clyy
N C
ΣE AG X Y, = yy)
NC Fay
(65)
Therefore, with probability least the generalization bound of our model is
ΣΣ ((Qinfela()), Nie
V
Xxx,))xxxx! (X
(X, Q).
NC
C7 STN. S (NV)
2/7g
Clog(2/0))
gen ge, (Q,X,Y)
VNV
N
EE ((x()) S(o), 1 HR|YS x +
Alog( NNV/V///
-log(2/6)
+ 4CS.avVV
2
NC
D
EV ((X());S Yo) + +Ri)
K1
K2
Es
gen rea (Q, Q,X,X Y),
VNV
N3/4V1/4
NC
(66)
where
E1 CyS2.N
E2 = 25' Cyq
Kg 4CS
(67)
K. H(RYY, x()) + c dlog( NONV(VVV///
+ 1og(2/6).
Since (() and O (n) generated by X ("), we have the following transformation:
[(x (v), S(0) (0))
yc)) Y
Σ (() S(V) (VV)
o
(((((1) ((V) ( (
((((()) (
I(((()) ...., s "V,...,,, Y).
00
can be inferred that during the model optimization process. S(V). O O(V)); Y) continuously approaches its maximum value, leading to I((((1) ...... S(V)
Based on Theorem
decrease Ee, DV (( S(v), (l)) YY), which indicates improvement generalization performance.
29

---

C Experiment
C.I Experiment Setup
Table Detailed information of datasets.
View
Objoct
VOC 2007
Corel 3k
Esp Game
TAPR TC-12
MIR FLICKR
CH(64)
DenseHue( (100)
DenseHue (100)
DenseHuee(10) (100)
DenseHue(1000
DenseHue((00) (100)
2
CM(225)
DenseSift(1000
DenseSift( (1000)
DenseSift( 1000)
DenseSift(10000
DenseSift
CORR(144)
GIST(512)
GIST(512)
GIST(512)
GIST(512)
GIST(512)
4
EDH(73)
HSV(4096)
HSV(4096)
HSV(4096)
HSV(4096)
HSV(4096)
5
WT(128)
RGB(4096)
RGB(4096)
RGB(4096)
RGB(4096)
RGB(4496)
6
LAB(4096)
LAB(4096)
LAB(4096)
LAB(4096)
LAB(4096)
#Label #instance
20
260
268
291
6047
9963
4999
20770
19627
25000
Datasets and Comparison Methods. In our experiments, six public multi-view multi-label datasets are selected as shown in Table Their specific descriptions are as follows. Corel 5k is composed of 4999 image samples and 260 words, where each word can be regarded as an annotation or label. IAPRTC12 comprises 19627 high-quality natural images and each image contains 261 labels, including sports, actions, animals, cities, and so on. ESPGame is a multi-view multi-label dataset containing 20770 images with 268 corresponding tags. Pascal07 is a widely utilized dataset for visual object detection and recognition, which contains 9963 images and 20 kinds of objects. Mirfickr consists of 25,000 images from the Flickr platform, annotated with total of 38 tags. OBJECT has 6047 instances requiring recognition, which are characterized by five distinct perspectives and annotated with 31 attributes. To validate the effectiveness of TDLSR,
compare it with nine
Mate-of-the--add approaches, i.e., AIMNet (23), DICNet (25), DIMC 388, iMVWL [33], LMVCAT (26). MTD (24). SIP (27), LVSL (43). DM2L
28
We also provide a comprehensive overview of
their sources and functions in T
Construction of the Application NBA Dataset. The NBA dataset crawled from Basketball- Reference (2) includes 16,992 player samples from the regular and playoff seasons spanning 2002 to 2022. Each sample comprises six views capturing different aspects of player performance and background information: 1) Scoring Statistics, 20 features including shooting attempts, shooting percentages (scaled by 1000), points, and per-minute scoring efficiency, representing scoring ability and shooting efficiency. 2) Rebounding and Physical Artribttes, 14 features such as games played, rebounds, fouls, and playing time averages, highlighting physical competitiveness and playing consistency. 3) Technical Statistics, 15 features including assists, steals, blocks, turnovers, and triple- doubles, reflecting player's playmaking and defensive contributions. Advanced Efficiency Metricx, 10 features measuring comprehensive performance like true shooting percentage, usage rate, player efficiency rating, and per-minute rates. 5) Player Background, 41 features encoding age and team membership via one-hot encoding. 6) Seasonal Context, 22 features encompassing season indicators, playoff status, also one-hot encoded. Player attributes are structured as an 18-dimensional multi-label vector per sample, which includes 10 award-related labels (c.g., All-Star selection, All-NBA teams, MVP nomination), 5 positional one-hot labels (PG, SG, SF. PF, C) and career stage one-hot labels categorizing each player-season into Early Career (first 25%), Prime Career (middle 50%), and Late Career (last 25%) according to the player's 's elapsed and remaining career years.
Implementation Details. We employ Hamming Loss (HL), Ranking Loss (RL), OneError (OE), Coverage (Cov), Average Precision (AP), and Area Under Curve (AUC) six metrics unify the experimental standards. Higher AP and AUC values indicate better performance, while lower HI., RI, OE, and Cov values are preferred. Their evaluation contents are described below: 1) ACC measures the proportion of correctly predicted labels across all samples. 2) RL evaluates the accuracy of the model's ranking of predicted labels compared true labels. 3) AP computes the area under the precision- reealll curve, indicating the average precision achieved across all recall levels. 4) AUC quantifies the probability that randomly selected positive instance ranked higher by the model than a randomly selected negative instance across all possible threshold values. 5) OE evaluates whether the top-ranked label predicted by the model is incorrect. 6) Cov computes the number of labels the model needs to traverse to cover all true labels, reflecting the efficiency of the model's predicted label range. The neighbor number & is fixed to 10 for all datasets. Adam optimizer with the initial learning rate of 0.0001 is used for optimization of all datascts. All methods use the same
30

---

dataset partition when conducting experiments, while the locations of view missing and label absence are recorded and kept consistent.
Table 4: Detailed information of comparison methods. v represent the method is able to handle the corresponding problem.
Method
Source
Year
Mubti-Label
Multi-view
Missing-view
Missing-labe
iMVWL
UCAI
2018
DM2L
PR
2021
LVLS
TMM
2022
X
DICNet
AAAI
2023
DIMC
TNNLS
2023
LMVCAT
AAAI
2023
AIMNet
AAAI
2024
MTD
NeurIPS
2024
SIP
ICML
2024
C.2 Experiment Result
Table 5: Experimental results of nine methods the six datasets with 90% PER and 90% LMR. Rvv.R' refers to the mean ranking of the corresponding method across all six metrics.
DATA
METRIC
NeM
DICNet
DIMC
DM21.
IMVWL.
LMVCAT
LVSL.
MTD
SIP
TDLSR
I-HL
0.987
0.987au00
0.987au000
0.987
0.976u.00
0.987aaco
0.987,ccm
0.987a.000
0.986au00
0.987
1-OE
0.277
0.242a.0s
0.239
0.1711.00
0.181a00
0.229
0.2476:000
0.27
0,2899.014
0.374g,000
1-Cm
0.6005.200
0.515a.02
0.518ua2s
0.524p.00
0.600.444
06002.00
0.5736.00
0.601a..2e
0.6926.004
COR
I-RI.
0.823,c01
0.774uu0s
0:772au00
0.756.20
0.762
0.817ams
08230.01
0.809.oo
0.821o021
018666.000
AP
0:340
0.208
0,206
0.18
0.163
0.214
222
0.234.0m
0.242a
0.3233.00
AUC
0.826
0.776
0.774
0.754 c00
0.766
0.820 oes
0.82%
0.81
0.823
0.869
AVI
3.167
6833
7,333
8.333
5.667
4.167
I-HI.
10982.cc0
0.982..00
D.082a
0.933
0.966%.00
0.9830.com
0.9822.00
0.982..00
1-OE
0.310
0.28%
0.283
0.210
0.204..0m
0.266
0.265
0,502
0.327
0.385
I-Cor
0.508
0.464
0.456 034
0.447.000 oo
0.421
0.468, ocs
0.459 con
0.492
0.500 034
0.576y.000
ESP
L-RL
0.7922.co
0.773
0,76%
0.758
0.729
0.771a
0.7833.co
0.786g
0,785p.053
0.825
AP
0.2226.000
0.210b.002
0.207aa00
0.172b.00a
0.1
0. 0.201a006
0 0.20o.com
0.214
0,225
1.27
AUC
0.797a.co
0.777a.m0
0.772a
0.7622.002
0.733
0.775m
0.790p.om 0.7876.com
0.790u.00
0.830s.com
AVE
3,333
5,333
6.5
7.667
10
6.333
5,167
4.167
1,333
I-IIL
0.980%.com
0.980
0.980 azo
0.980p.com
0.966
0,980 oco
0.980s.co
0.9800
0,980g
0.980s.co
1-OE
0.3126.00
0.333
0,318
0 0.247a.004
0.245p
0.290
0 0.294..c
0.3
0.355
0.397a.000
1-Cov
0.521a.c0
0.472a.m1
0.4680.002
0.443
0,438
0.47loxss
0.496.c02
0.510g..os
0.519
0.6166..01
IAP
1-RI.
0.799
8.795
0.781,20
0.761
0.793
807.0.0
0.816
0.81 7a.0ss
0186042.00
AP
0,229
0.222
0.215
0.1 0.1866.
0.1677uus
0.202a
0 2.0
0.232
0.235u.000
0.278
AUC
0.822occo 0.801mm
1.788
0 0.783.00
0.766u
0. 0.797o
0.8 1o.oo.co
0.819
0.8200
0.861a.00
AVR
2.5
3.167
2.333
1-HL.
0.875.c01
a.87%
B877anz2
0.876
0.837
0.865
0.874.c00
0.880
0.875
0188%%.00
1-OF
0.506
0.535
ba
0.43%
0.406
0.4700u
0.535
0.540)
2
I-Coy
0.598
0.594,mm:
0.589
0 0,572,
0.530
0.581oows
0.584).oo
0.60lfi.
0.6044.036
0.6455,000
MIR
1-RI.
0.8276.c06
0.828..0
0.823
0.765
0.819.con
0.834.00
0.8300
11861..00
AP
0.494
0,512amm
0.50
0.467a.00
0.415
0.485
0.422.cce
0.519
0.519%.02
0.5755.000
AUC
0.824, coo
0.823
0.818
0,805,
0.769
0.806, occ
0.816, con
0.827
0.823, o03
0.852,.00 .000
AVE
5,333
5,333
8,333
10
7,333
2.167
3.333
I-IIL
0.9376.co
0.938
0.938,
0.935,
0.927 0.882
0.934.cc
0.938p.00
0.9466 0.92%
1-OE
0.168..o
0.153p.m0
0.13%
0.1155.0mm
0.335
0.105
0.364o.co
0.174r.001
0.185p.013
0.6033.co
1-Cor
0.7277..co
0.720p.os ms
0. 0.709u.o0
0.6822.002
0.657am02
0.705
0.712x.cx
0.740p
0.727o.00
0.7955.000
OBJ
L-RL
0.8233.005 0.829
0.8
0.800p.200
0.7680.012
0.806
0.81
0.835g.003
0.828u.024
0.88 1a,000
AP
0.506
0.502..o0
0.18%
0.170b.000
0.39
fn
0. 0.1766ac0
0.446..0
0.519
0.522a.000
0.624a.011
AUC
0.842a.20
0.836g.mm
0.828u
0.814g,00
0.784f.m:2
0.821
0.7
0.848g
0.840
1a.000
AVK
3667
4.667
58833
8 1667
7.667
3.667
1-HI,
0.927 0.233,000
B.927
0 0.26
0877
0.921oacs
0.926..000
0.926f..o
0.9236,035
0.9277.000
1-OE
0.382
0.402a.022
0. 1.330a3
0 0,380,007
0.306vum
0.376
0.415a.0m
0.395a.01
0,389uu11
0.115
1-Coy
0.65%
0.636
01626
0.636..000
0.58%
0.630
0.654.co
0.674..os
0.6686
0.753
PAS
1-RI.
0.7276..u
0.710k..:
8.7030
0.60%
0.65%
072
d.740la.m
0.80%%.00r 0.72%
AP
0.444,.co
0,440)ams
0.434
0.21p.00
0. 0.368
0.400
444
0.454
0.44%
0.5004
AUC
0.754
0.737am
0.727p019
0.7 0.733
0.690,
0.727
0. 0.754,
0.766
0.761 0.761pms
0.83
AVE
5.333
5.167
7.167
8.5
4.167
3.167
4,167
Comparison Experiment. To validate that our method can adapt to varying degrees of data missing. we conduct comparison experiments with PER and LMR ranging from (30%, 50%, 70%, 90%], Table 5 presents the comparison results and algorithm rankings when PER and LMR are fixed at 90%. Fig- 9 and T0 illustrate the distributional trends of all metrics as PER increases from 30% to 70%, with LER fixed at 30%, 50%, and 70%, respectively. It can be observed that our method
31

---

outperforms the other nine methods in almost all cases, which demonstrates the robustness of our TDLSR handling incomplete multi-view multi-labes problems. Moreover, the effectiveness of our method is especially evident when dealing with high levels of data unavailability. For instance, as shown in Fig. g on Corel 5k, the performance margin of our method over the second-best gradually widens. Additionally, as reported in Table our method achieves more than a 10% improvement in the most representative metric AP on both OBJECT and Pasca107.
Parameter Determination and Convergence. The parameters λ and 22 are used to balance the effects of LıB and Lie. Two parameters are selected from the range of {0.01. 0.1, 1, 10, 100, 1000) and the joint influence are presented in the heatmap shown in Fig. 6 From the result, the performance of TDLSR exhibits variability under different parameter setting. Besides, the optimal results are typically achieved when X falls within the range of (0.01, 1). Overall, the parameter sensitivity relatively low on certain datasets, such as on ESPgame and OBJECT. We also present the simultaneous evolution of training loss and performance metric on the validation set throughout the training process in Fig- 7 The results show that our TDLSR demonstrates great convergence and gradually approaches the optimal network parameters.
0.01
15:44
I1:431
6-4377
0:31
919-
0.514
31
ES5
01 1564
0.954
C.X
635
5.00
0.4444
014427
114413
0.422
9.42
5.455
BL049
IC5487
00000
03000
0.443
0.412
0.4435
014331
6-425
64226
0.254
2:334
8:39
0.4
8:35
0.422
3:45
004429
06412
64234
8.434
8337
0.3177
0J315
00312
0.377
0.337
0.009
0227S
0J243
02255
1000
0.422
084277
014441
0A244
642M
0.541
0U5411
013999
0.322
22391
0.399
0.5097
IL2099
02215
0.440
0011
9.1
106
1830
601
0.1
108
1300
0.1
81
106
1300
(a) Corel 5k
(h) ESPgame
(c) IAPRTC12
0.1
0091
MA01
6251
00
0.766
0.709
8/1072
01/012
06011
66033
8.7
0.760
6.78%
555
0.5004
OLSRET
WA218
6.122
0.302
0/7022
0.705
2914
0.9917
0L3915
8.744
8825
KZ2
IMA256
1833
120
0,000
8:37C
730
93644
0.99K
02834
(d) Mirflickr
(c) OBJECT
(f) Pasca107
Figure 6: Parameter analysis of the trade-off parameters Z and Az-
0.8
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.6
0.6
Training Loss
Trainin
Traiming
20
40
60
80
100
20
40
60
80
100
40
100
Epoch
Epoch
Epach
Corel 5k
(b) OBJECT
(c)
Pasca107
Figure 7: The convergence behavior of our TDLSR during training.
32

---

BALERI
BALE99
(a) Corel 5k, PER=50%
(b) Corel 5k, PER=70%
(c) Corel 5k, PER=90%
PUGLE
LGA
(d) IAPRTCI2, PER=50%
IAPRTC12, PER=70%
IAPRTC12, PER=90%
AFP
ABIO
ATC
HI
POLLE M1
JURLE kg
28 806
(ETX kkg
g ESPGame, 5ER=50%
(h) ESPGame, PER=70%
ESPGame, PER=90%
JUS
BALOO
AEL (k) Pascal07, PER=70%
LOE
13L (I) Pasca107, PER=90%
(i) Pascal07, PER-50%
ENT
I Lig
10
BALL
(m) Mirfickr, PER=50%
Mirfickr, PER=70%
(0) Mirfickr, PER=90%
Figure 8: Experimental results of ten methods on five datasets with PER varying from 50% to 90% while LMR= 50%.
33

---

(ALLES
IUSEADE
(a) Corel 5k, PER=50%
(b) Corel 5k, PER=70%
(c) Corcl 5k, PER=90%
PAGLE
L-s
IAPRTCI2, PER=50%
IAPRTC12, PER=70%
IAPRTC12, PER=90%
AFP
ABI
ATC
HI
W0 ky
2. 844
(8TX kkg
JENCOM
g ESPGame, PER=50%
(h) ESPGame, PER=70%
ESPGame, PER=90%
ESTAR
LO CaL
AEL (k) Pascal07, PER=70%
LO0
(i) Pascal07, PER-50%
(I) Pasca107, PER=90%
ENTLERT
paizon
J Lig
10
Our
(m) Mirfickr, PER=50%
Mirfickr, PER=70%
(0) Mirfickr, PER=90%
Figure 9: Experimental results of ten methods on five datasets with PER varying from 50% to 90% while LMR= 70%.
34

---

228
LOE
100
(a) Corel 5k, PER=50%
(b) Corel 5k, PER=70%
(c) Corcl 5k, PER=90%
PATLE
TE
FR
E-bty
LG
(d) IAPRTCI2, PER=50%
IAPRTC12, PER=70%
IAPRTC12, PER=90%
AFP
ABD
AFC
HI
KOLLO ml
g ESPGame, PER=50%
(h) ESPGame, PER=70%
ESPGame, PER=90%
ESLLT
LOB
LO2
MEL
ii) Pascal07, PER-50%
(k) Pascal07, PER=70%
(I) Pasca107, PER=90%
AAC
JATTORT
Ji Lig
10
(m) Mirfickr, PER=50%
Mirfickr, PER=70%
(0) Mirfickr, PER=90%
Figure 10: Experimental results of ten methods on five datasets with PER varying from 50% to 90% while LMR= 90%.
35

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
The abstract and introduction clearly describe the algorithm implementation. theoretical contributions, and comprehensive experiments presented in this paper, consistent with the subsequent Sections
Justification:
2 and
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer:[Yen
Justification: Sections and mention that the model needs fully separate feature semantics in order to achieve optimal generalization performance, and the prior semantics among multiple labels also need be leveraged, respectively, which are key challenges in model optimization and design.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed not penalize honesty concerning limitations.
3. Theory assumptions and proofs
36

---

Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: The paper provide the full set of assumptions and complete proof needed for each theoretical result Section and Appendix.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proof' can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: The network architecture, datasets, model parameters, and training approaches involved in the experimental implementation are described in detail both the main text and the Appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to model. In general. releasing code and data often one good way to accomplish this, but reproducibilityy can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, other means that are appropriate to the research performed.
specific model and empirical evaluation, may
While NeurlPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily the architecture clearly and fully.
model architecture, the paper should describe
(c) the contribution is a new model (c.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open- open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the partieular way they provide for reproducibiliity In the case of closed-source models, it may be that access to the model is limited in
37

---

reproducible, they some way (e.g., to registered users), but it should be possible for other researchers have some path reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, described in supplemental material?
Answer: [No]
Justification:
We commit sharing our code upon the acceptance of the paper.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips.cm cc/
pwblic/guides/
for more details.
While encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
//nips wtt.cccpppbllccc httpppubbblueessseepppppppppepee guides/ (oweeeumisssiino ssionPolicy for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing much information possible in supplemental material (appended the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Experimental settings, including data splits, hyper parameters, optimizer and learning rate are discussed in both the main text and Appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: Fig 3nd Table I
present the results as the mean and standard deviation over random trials, reflecting the statistical variability.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by emror bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
38

---

The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out range (e.g. negative error rates).
If error bars reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: Section mentiones that our model is implemented by PyTorch on one NVIDIA GeForce RTX 4090 GPU of 24GB memory.
Guidelines:
The answer NA means that the paper does include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental rums as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't itdn't make it into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics httpp:://eurrpppttttee htcp/ppublccEEiccccciieieeeeee
Answer: [Yes]
Justification: The research focuses algorithm design and theoretical analysis. It does not involve human subjects or ethically sensitive applications. We believe it complies with the NeurlPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: There is societal impact of the work performed.
Guidelines:
39

---

The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negatíve societal impacts include potential malicious or unintended uses (e.g.. disinformation, generating fake profiles, surveillance), fairness considerations (c.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of MI.).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
The paper poses no such risks.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [No]
The paper properly cites the sources for existing assets, such as baseline methods and data sources. However, the specific licenses and terms of use for these assets are not explicitly stated in the main text Appendix.
Justification:
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
40

---

For scraped data from a particular source (e.g., website). the copyright and terms of service of that souree should be provided.
assets are released, the license, copyright information, and terms use in the datasets.paperssiii paperswi thcode. www.coo//aaaaa datasets package should be provided. For popular datasets,
has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [No]
Justification:
The paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/mmodel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:
The paper does not involve crowdsoureing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
41

---

Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if' applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Does the paper describe the usage of LLMs if is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, originality of the research, declaration is not required.
Question:
Answer: [NA]
Justification: The core method development in this research does not involve LLMS as any important, original, non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our LLM policy /att::///earrrpsccc/ooooeereeee/ /c/////oeeeeeecc///22////.. for what should or should not be described.
42


Reviews:
[{"review_id": "pH4C4rRHfK", "reviewer": "Reviewer_rTba", "summary": "This work studies incomplete multi-view multi-label classification, simultaneously addressing missing views and missing labels. It first employs available view samples to recover missing views using an attention-based neighborhood imputation approach. Subsequently, it learns view-shared and view-specific representations via mutual information estimation, with learning objectives comprising three terms: information shift, information interaction, and information orthogonality. The authors then introduce label prototype learning. By leveraging a label correlation matrix and a GNN, the semantic representational capacity of these so-called label prototypes is optimized. These prototypes are applied to select label-relevant features from both view-shared and view-specific features. Final predictions are generated via a linear classifier and late fusion: predictions from individual views are first fused, followed by fusion of predictions derived from shared and specific features.", "questions": "What evaluation metric is used for the results in Appendix Figure 2? I cannot find this information in the text or figure.", "limitations": "The paper appears to lack a comprehensive evaluation of the limitations of the proposed method.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n\n1.This paper covers three main research aspects: missing view imputation, extraction of shared and specific features, and the use of label prototypes and label correlations.\n\n2.The writing is clear and easy to follow, and the paper is well organized. The introduction provides sufficient background and related work, and the authors include extensive theoretical analysis.\n\n3.The authors conduct a large number of comparative experiments under different missing rates, both in the main text and the appendix. They compare TDLSR with many existing methods, providing a thorough evaluation of the proposed approach.\n\nWeaknesses：\n\n1. The variable dimensions are not clearly specified. For example, the label correlation matrix $A$ and the label prototype matrix $E$ are not explicitly defined, even though they can be inferred. Clear definitions are necessary.\n\n2. Variable confusion: For example, $S^{(v)}$ refers to the view-specific graph in Section 2.2, but to view-shared features $\\\\{S^{(v)}\\\\}_{v=1}^V$ in Section 2.3. In Section 2.4, $E$ is a matrix, and while readers can infer that $E_i$ is the prototype of the $i$-th label, its form is not clearly defined.\n\n3. Dimension error: In line 178, $H \\in \\mathbb{R}^{q \\times d}$ is incorrect, since the adjacency matrix $A \\in \\mathbb{R}^{C \\times C}$, which makes the operation $E = f[(1+\\epsilon)H + AH]$ in line 180 dimensionally inconsistent. It should be $H \\in \\mathbb{R}^{C \\times d}$.\n\n4. In Section 2.2 of the main text, Eq. (2) uses $B_{i,j}^{(v)}$ in the numerator to compute $\\hat x_i^{(v)}$. However, if $x_i^{(v)}$ is a missing view, it is unclear how $B_{i,j}^{(v)}$ can be computed. It seems that in the case where the $i$-th sample is missing, $B_{i,j}^{(v)}$ is not computable. I cannot understand how Eq. (2) works in the case of missing views.\n\n5. In Section 2.3, regarding the first term (information shift), $s^{(u)}$ in Eq. (5) and Eq. (7) appears to be a typo. Also, line 148 claims that $I(s^{(v)}; z^{(v)})$ is lower-bounded by a reconstruction loss, but Eq. (7) optimizes $-\\mathbb{E}_{p(z^{(v)},s^{(v)})}[\\log q(s^{(v)}|z^{(v)})]$. Since $z^{(v)}$ is the imputed original feature and $s^{(v)}$ is the shared feature, decoding $s^{(v)}$ from $z^{(v)}$ seems conceptually incorrect. Moreover, line 149 refers to $q^v(z^{(v)}|s^{(v)})$ for decoding, which contradicts the optimization objective. This issue also appears in the appendix: in Eq. (3), the final term $\\log p(z^{(v)}|s^{(v)})$ becomes $\\log p(s^{(v)}|z^{(v)})$ in Eq. (5), and in Eq. (6), the second line $\\log q(z^{(v)}|s^{(v)})$ is incorrectly changed to $\\log q(s^{(v)}|z^{(v)})$, which seems to be a derivation error.\n\n6. In Eq. (11), the right-hand side term $\\overline B_{i,j}W_{j,v}$ should be $\\overline B_{i,j}W_{i,v}$. Also, in Figure 1, the imputed feature on the left should be $Z^{(v)}$, not $X^{(v)}$.", "was_revised": true, "final_justification": "I thank the authors for their response. The detailed rebuttal addresses my main concerns regarding Weaknesses 4 and 5, and I will raise my score accordingly. I suggest the authors incorporate the explanation for Weakness 4 from the rebuttal into Section 2.2 of the main text and carefully revise the paper based on my identified weaknesses and the corresponding rebuttal.", "rebuttal": "I sincerely appreciate your thorough reading of my manuscript and your recognition of its strengths, including clear writing, rich theoretical content, and extensive experiments. I am also deeply grateful for your careful identification of the writing flaws, as your feedback is immensely helpful in guiding the refinement and enhancement of the paper.  Please accept my sincere apologies for any inconvenience my oversights may have caused during your review. I will pay closer attention to every detail in subsequent revisions to ensure that all writing errors are addressed and the work attains the highest level of academic rigor.\n\n### **Weaknesses：** ### \n **Clarity for variable dimension.**  $A \\in \\mathbb{R}^{C \\times C}$ is the label correlation matrix, where each element $A_{i,j}$ denotes the degree of correlation between the $i$-th and $j$-th labels, as computed by Eq. (8). $H \\in \\mathbb{R}^{C \\times d}$ denotes the aggregation matrix of all label prototypes, constructed by row-wise concatenation, where each row encapsulates the prototype representation of an individual label.   \n\n **Clarity for variable confusion.**  Following the revision of the symbol $S$, in Section 2.2, $\\hat{S}^{(v)}$ denotes the proximity-aware graph (sample topology graph) for each view, where $\\hat{S}^{(v)}\\_\\{i,j\\}$ indicates that  samples $i$ and $j$ are neighbors and co-exist in the $v$-th view. In Section 2.3, $S^{(v)}$ refers to the view-specific representation matrix extracted from the raw view.  $E \\in \\mathbb{R}^{C \\times d}$ denotes the updated label prototype matrix derived from $H$ via the GIN layer, with each row representing the refined prototype of a label. In Eq. (11), $Q_{i,v}$ represents the maximum confidence with which sample $i$ can be reconstructed using other samples in the $v$-th view.  The term $W_{j,v}$\n  is used here to ensure that only the samples present in the \n$v$-th view are considered for reconstructing sample \n$i$; those that are missing are assigned zero confidence via the missing data mask. In the \"Proximity-aware Graph Attention Recovery\" module of Figure 1, the reconstructed view on the right should be $\\\\{{Z}^{(v)}\\\\}\\_{v=1}^{V}$ rather than $\\\\{{X}^{(v)}\\\\}_{v=1}^{V}$.\n\n **Clarity for the information shift term.** The information shift term $I({s}^{(v)};{z}^{(v)})$ is used to guarantee\nthat the representations stay consistent with the core semantics of raw views. Its lower bound $I({s}^{(v)};{z}^{(v)})) \\geq \\mathbb{E}\\_{p\\left({z}^{(v)}, {s}^{(v)}\\right)} \\left\\[\\log q\\left({z}^{(v)} | {s}^{(v)}\\right)\\right\\]$, derived via variational inference, was mistakenly written as $\\mathbb{E}_{p\\left({s}^{(u)}, {z}^{(v)}\\right)}\\left[\\log q\\left({s}^{(u)} | {z}^{(v)}\\right)\\right] $ in Eq. (5). The term $q^{v}({z}^{(v)} | {s}^{(v)})$ used for decoding in line 149 is the same as $q({z}^{(v)} | {s}^{(v)})$ in the optimization objective. Similarly, in Eq. (4) of the Appendix,  $q({z}^{(v)} | {s}^{(v)})$ is incorrectly written as $q({s}^{(v)} | {z}^{(v)})$, which leads to the subsequent notation errors in Eqs. (5) and (6). However, the overall derivation remains valid, as the mistake lies solely in the reversed notation, not in the underlying logic.\n\n**Explain how Eq. (2) is used for view reconstruction.**  Our reconstruction strategy is designed to exploit the sample correlation structure across the available views to recover the missing ones, without introducing additional network parameters. ${K}^{(v)}$ is a transferred graph that determines the available samples in the $v$-th view to be used for reconstructing the missing ones. In a specific view, the contribution of available samples to the reconstruction of missing samples is determined by the maximum computable sample correlation derived from other views. Specifically,  $\\overline{{B}}\\_{i, j}=\\max \\left({B}\\_{i, j}^{(1)}\\hat{S}\\_{i, j}^{(1)}, {B}\\_{i, j}^{(2)}\\hat{S}\\_{i, j}^{(2)}, \\ldots, {B}\\_{i, j}^{(V)}\\hat{S}\\_{i, j}^{(V)}\\right)$, where $\\overline{{B}}\\_{i, j}$ denotes the contribution of the \n sample $j$ to the reconstruction of the sample $i$.  The term $\\overline{{B}}\\_{i, j}$, which is formally defined in Eq. (11) of Section 2.4, is not explicitly introduced in Section 2.2, and the symbol $\\hat{S}$ is incorrectly denoted as ${K}$ in Section 2.4. We acknowledge this gap and will incorporate the necessary clarifications and revisions to prevent any potential misinterpretation regarding the process of reconstruction.  Consequently, the reconstruction of missing samples is ultimately achieved through a weighted aggregation, i.e., $\\hat{x}\\_{i}^{(v)}=\\frac{\\sum_{{K}\\_{i, j}^{(v)} \\geq 1} {K}\\_{i, j}^{(v)} \\overline{{B}}\\_{i, j}  {x}\\_{j}^{(v)}}{\\sum_{{K}\\_{i, j}^{(v)} \\geq 1} \\overline{{B}}\\_{i, j}}$.  As $\\hat{{X}}$ serves as an approximate substitute for the missing instances,  it is integrated with the original available views to construct the final recovered data ${\\hat{{Z}}}\\_{i,:}^{(v)}=\\hat{{X}}\\_{i,:}^{(v)}\\left(1-{W}_{i, v}\\right)+{X}\\_{i,:}^{(v)} {W}\\_{i, v}$. It is also worth noting that although ${B}\\_{i, j}^{(v)}=e^{h(x\\_{i}^{(v)}) h(x\\_{j}^{(v) T}) / \\tau}$ is computed over all sample pairs,  the value of $\\overline{{B}}\\_{i, j}$ is only retained when both sample $i$ and sample $j$ are available,  as indicated by the sample topology graph   $\\hat{S}^{(v)}$, where $\\hat{S}^{(v)}$ equals 1 only if both corresponding samples exist. Therefore, all valid entries in $\\overline{{B}}$ are computable, and the entire process ensures that no feature information from missing samples is leaked. Moreover, owing to the varying levels of reconstruction fidelity,  the reconstruction quality is closely tied to the weights assigned during the late-stage fusion in our model. The prediction from a reconstructed sample is weighted according to the maximum confidence with which the sample can be reconstructed from other samples, whereas the prediction from an observed sample is assigned a weight of 1. Next, we present a comparative analysis between our proposed reconstruction method and a baseline strategy that utilizes the mean of available views:\n|| Pascal07 | OBJECT | Mirflickr |Corel 5k | ESPGame|IAPRTC12|\n|-|-|-|-|-|-|-|\n| average  | 0.852    | 0.903  | 0.859 | 0.898 | 0.850 |0.871 |\n|ours| 0.882    | 0.924  | 0.875| 0.919 | 0.863 | 0.899 |\n\nIt is evident from the above results that the proposed view reconstruction method is instrumental in achieving superior classification performance. In light of the large number of symbols used in this paper, as well as the presence of certain writing inconsistencies, we provide a summary below listing the key notations along with their corresponding dimensions：\n\n| **Notation** | **Annotation** |\n| - | -|\n| $N$| Number of samples|\n| $V$ | Number of views|\n| $C$ | Number of labels/classes|\n| $d_v$| Feature dimension of view $v$|\n| ${X}^{(v)} \\in \\mathbb{R}^{N \\times d_v}$| Feature matrix of $v$-th view|\n| ${Y}\\in \\\\{0,1\\\\}^{N\\times C}$| Binary multi-label matrix |\n| ${W}\\in\\\\{0,1\\\\}^{N\\times V}$| Missing view indicator matrix|\n| ${G}\\in\\\\{0,1\\\\}^{N\\times C}$| Missing label indicator matrix|\n| ${Z}^{(v)} \\in \\mathbb{R}^{N \\times d_v}$| Reconstructed features for view $v$|\n| ${B}^{(v)} \\in \\mathbb{R}^{N \\times N}$| Attention scores in view $v$|\n| $\\hat{S}^{(v)}\\in\\mathbb{R}^{N\\times N}$| Sample topology graph for view $v$|\n| ${K}^{(v)}\\in\\mathbb{R}^{N\\times N}$| Propagation graph for imputation|\n| $\\hat{{X}}^{(v)}\\in\\mathbb{R}^{N\\times d_v}$| Imputed features for view $v$|\n| $M^S_{v},M^O_{v}$| MLP for shared/private representation|\n| ${S}^{(v)},{O}^{(v)}$| Shared / private representation for view $v$|\n| $I(\\cdot ; \\cdot)$| Mutual information|\n| ${b}_i \\in \\mathbb{R}^C$| One-hot vector of $i$-th category|\n| ${h}_i$| Prototype of label $i$ |\n| ${A}\\in\\mathbb{R}^{C\\times C}$| Label correlation matrix (Jaccard)|\n| ${E} \\in \\mathbb{R}^{C \\times d_v}$| Label embedding matrix|\n| $\\hat{{U}}^{(v)},\\hat{{V}}^{(v)} \\in \\mathbb{R}^{N\\times C\\times d}$ | Label-specific shared/private feature|\n| ${U}^{(v)},{V}^{(v)} \\in \\mathbb{R}^{N\\times C}$| Class predictions from shared/private|\n| ${Q}\\in\\mathbb{R}^{N\\times V}$| Confidence matrix |\n| $\\overline{{P}}\\in\\mathbb{R}^{N\\times C}$| Final fused prediction matrix|\n| $R(f),\\widehat{R}_D(f)$| Expected/empirical risk|\n### **Question 1: Figure 2 in the Appendix lacks evaluation metrics** ### \nFigure 2 in the Appendix illustrates how the balanced parameters $\\lambda_{1}$ and $\\lambda_{2}$ in the training loss jointly affect classification performance.  The values shown in the heatmap represent the AP metric, which evaluates the prediction quality for each class by computing the area under the precision-recall curve and reflects the model’s ranking performance across different labels.\n### **Discussion for the limitations:** ### \nThis study faces two principal limitations. The first concerns the adaptability of the approach to diverse scenarios. Our work primarily addresses situations in multi-view multi-label learning where both views and labels are missing. As the sample size increases, however, additional challenges such as view misalignment and label noise are likely to emerge. These issues warrant further investigation in future research within the multi-view multi-label domain. The second limitation lies in the method design.  We estimate the mutual information between views through a data-driven procedure that approximates their joint distribution as well as the marginal distribution of each view. Although this approach is effective, estimation errors are unavoidable, and future work should aim to develop more precise techniques. Moreover, our method assumes that label prototypes are generated directly from Gaussian distributions. This assumption may be restrictive and inconsistent with the complexity of real-world applications. Subsequent research should pursue more flexible strategies for constructing label prototypes free from conditional constraints."}, {"review_id": "tiC4ffKNSs", "reviewer": "Reviewer_FGNW", "summary": "The paper proposes TDLSR, a theory-driven label-specific representation learning framework tailored for incomplete multi-view multi-label classification (iMvMLC). The model integrates a proximity-aware graph attention mechanism, mutual information-based representation disentanglement, and label prototype modeling to effectively mitigate the challenges posed by data sparsity in both feature and label spaces.  It demonstrates superior robustness and performance across six public datasets and an real-word NBA application.", "questions": "(1)\tA central challenge in multi-view multi-label learning lies in effective feature extraction and label correlation modeling. Please explain how this work addresses these two key difficulties.\n\n(2)\tThe extraction of shared and private representations is no longer considered a novel strategy in the multi-view learning field. Please clarify whether the improvements made in this work on top of that framework are substantial, and whether they lead to significant performance gains in the experiments.\n\n(3)\tHow should the notion of discriminability mentioned in the Theoretical Results section be understood? Could the authors provide a more precise definition? Additionally, why is the theoretical analysis structured from two separate aspects？\n\n(4)\tGiven that many multi-view multi-label classification methods have released their code, would the authors be willing to make their implementation publicly available as well?", "limitations": "Yes, and the relevant comments have already been provided above.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "# Strengths: \n(1)\tSolid theoretical foundation. The mutual information formulation rigorously supports feature disentanglement, with derived theorems explaining generalization ability.\n\n(2)\tInnovative Methodology Design. For the first time, the information shift, interaction and orthogonality principle is applied to feature representation disentanglement, combined with label-specific shared and exclusive representation learning to enhance multi-label classification.\n\n(3)\tComprehensive experiments. The work is evaluated on both public and real-world datasets with extensive metrics, proving its effectiveness and robustness.\n\n# Weaknesses：\n(1)\tThe paper introduces numerous symbols without a centralized notation list, making it difficult to follow the mathematical formulations. The clarity of the writing could be further improved.\n\n(2)\tIn addition to the two hyperparameters in the final loss function, the paper also involves parameters such as top-k and the Lagrange multiplier. How were these parameters selected? Which ones were fixed, and which were tuned during experiments?\n\n(3)\tWhile mutual information is inherently difficult to optimize, the paper offers limited detail on the implementation and underlying rationale, which may leave readers confused.", "was_revised": true, "final_justification": "Thank you for the detailed response from the author, which has answered most of my questions. I have decided to maintain my rating.", "rebuttal": "I sincerely appreciate your professional review of my manuscript and your recognition of its solid theoretical foundation, innovative methodology design, and comprehensive experimental validation. I am also  grateful for your thoughtful identification of the weaknesses and existing issues in my work, which provide essential guidance for its further enhancement. I will undertake a thorough revision in light of your suggestions and endeavor to address each of your concerns with clarity and analytical depth.\n ### **Weakness1: Difficult to understand the numerous symbols** \nThe definitions of the fundamental notations are provided in Section 2.1, and additional symbols are explained as they appear in the paper. Given the extensive use of mathematical symbols, I will conduct a meticulous review to identify and correct any writing issues such as inconsistent notation, redundant symbol usage, or inaccuracies in variable dimensionality. These revisions will ensure that the paper meets a high standard of academic rigor.  Furthermore, a comprehensive notation table will be included in the revised version to facilitate reader comprehension and improve overall clarity. \n ### **Weakness2: A detailed explanation of all parameter configurations**\nIn addition to the balanced coefficients $\\lambda_{1}$ and $\\lambda_{2}$ in the total training loss, the following parameters are also involved, i.e., the temperature parameter $\\tau$, the balanced factor $\\alpha$, the number of nearest neighbors $k$ for each sample,  the Lagrange multiplier \n$\\beta$, the sampling number $s$, and the learning rate. Among these parameters, only the values of $\\lambda_{1}$ and $\\lambda_{2}$ are tuned during the experiments, while the rest are fixed throughout. The detailed configurations are summarized in the table below:\n|Parameter|Annotation|Value|\n|-|-|-|\n| $\\lambda_{1}$  |Balanced coefficient for training loss|$\\\\{0.01,0.1,1,10,100,1000\\\\}$|\n| $\\lambda_{2}$|Balanced coefficient for training loss|$\\\\{0.01,0.1,1,10,100,1000\\\\}$|\n|$\\tau$|Temperature parameter|0.2|\n|$\\alpha$|The balanced factor|10|\n|$k$|Number of nearest neighbors|10|\n|$\\beta$|Lagrange multiplier|1|\n|$s$|The sampling number |5|\n|Learning rate|Network optimization parameter|0.0001|\n ### **Weakness3: Implementation of mutual information optimization**\nBy performing variational derivations for each mutual information term in Eq. (4), we obtain their estimable bounds, which in turn lead to the formulation of Eq. (7) as the optimization objective. In practice, the lower bound for information shift $\\mathbb{E}_{p\\left({z}^{(v)}, {s}^{(v)}\\right)}\\left[\\log q\\left({s}^{(u)} | {z}^{(v)}\\right)\\right] $ in Eq. (7) is implemented as a reconstruction loss between the decoded representation and the original view. The detailed computation of the remaining three terms is provided in Appendix A.2. Specifically, representations are treated as probability vectors over $D$ classes via a Softmax activation function, and the joint distribution matrices (${P}^{(v,v^\\*)}, {Q}^{(v,v^\\*)}, {M}\\^{(s\\^{v},o\\^{v})}$)  between different representations are obtained by cross-view instance-level contrastive learning. By aggregating along different directions of the joint distribution matrices, the corresponding marginal distributions of individual views can be derived. Subsequently,  by converting the integral to a summation form, the remaining three terms can be expressed as\n\n$\\int \\int p({s}\\^{(v)}|{z}\\^{(v)};{s}\\^{(v^{\\*})}|{z}\\^{(v^{\\*})})\\log q({s}\\^{(v)}|{s}\\^{v^{\\*}}) d{s}\\^{(v^{\\*})} d{s}\\^{(v)}=\\sum_{d=1}^D\\sum_{d'=1}^D {P}_{d,d^{\\prime}}^{(v,v^\\*)} \\log \\frac{{P}\\_{d,d\\^{\\prime}}\\^{(v,v^\\*)}}{{P}\\_{d\\^{\\prime}}\\^{(v^\\*)}}$\n\n$D_{KL} (p({o}^{(v^{\\*})}|{z}^{(v^{\\*})};{o}^{(v)}|{z}^{(v)}) \\| p({o}^{(v^{\\*})}|{z}^{(v^{\\*})})q({o}^{(v)}|{o}^{(v^{\\*})}))=\\sum_{d=1}^D\\sum_{d'=1}^D {Q}_{d,d^{\\prime}}^{(v,v^\\*)} \\log \\frac{{Q}\\_{d,d^{\\prime}}^{(v,v^\\*)}} {({Q}\\_{d}^{(v)})^{\\alpha} {Q}\\_{d^{\\prime}}^{(v^\\*)}}$\n\n$D_{KL} (p({s}^{(v)}|{z}^{(v)};{o}^{(v)}|{z}^{(v)}) \\| p({o}^{(v)}|{z}^{(v)})q({s}^{(v)}|{o}^{(v)}))=\\sum_{d=1}^D\\sum_{d'=1}^D  {M}_{d,d^{\\prime}}^{(s^v,o^v)} \\log\\frac{{M}\\_{d,d^{\\prime}}^{(s^v,o^v)}}{({M}\\_{d}^{(s^v)})^{\\alpha} {M}\\_{d^{\\prime}}^{(o^v)}}$\n\nIn this conversion, we let  $q({s}^{v}/{s}^{v^*})= (\\psi({Q}^{(v)}))^{\\alpha}$ and $q({z}^v/{s}^v)=(\\psi({M}^{(s^v)}))^{\\alpha}$, where $\\psi$ is a fully connected layer, and  $\\alpha$ is a balance factor to preserve crucial information and ensure  model stability.\n ### **Question1,2: How this work addresses the feature extraction and label correlation modeling** \n● Previous methods either focus solely on shared representations while overlooking the unique contributions of each individual view, or rely on linear geometric constraints when extracting view-specific features, which are insufficient to capture complex representation interactions. To address this, we adopt a mutual information constrained optimization objective to achieve information disentanglement between shared and specific representations. Given the absence of a unified framework or guiding principles for leveraging mutual information objectives in representation learning, we systematically formulate three information-theoretic principles for multi-view feature extraction: information shift, interaction, and orthogonality. The proposed framework is grounded in three core aspects, i.e., alignment with the original views, cross-view correlations, and intra-view representational interactions. In addition, we provide a theoretical analysis that validates the effectiveness of our feature extraction model and proves its potential to reduce generalization error.\n\n● Label correlation modeling is jointly performed with prototype representation learning in our work. First, we quantitatively estimate label correlations based on the training data. Rather than utilizing co-occurrence frequency to evaluate correlation degree, we use the Jaccard distance calculated  over positive labels, as we are only concerned with the categories assigned to each instance.  By  computing  the intersection and union of  two classes regarding positive values, we can obtain $A_{i,j}=\\frac{\\langle {Y}\\_{:,i} \\cdot {Y}\\_{:,j}\\rangle}{\\sum\\_{k=1}^{N}({Y}\\_{k,i}+{Y}\\_{k,j})-\\langle {Y}\\_{:,i} \\cdot {Y}\\_{:,j}\\rangle}$. Then  we sample the prototype representation for each class, and then update them through a graph network that incorporates $A$ as the adjacency matrix, which yields label prototype matrix $E$ that encodes inter-label dependencies. Besides, to enhance the alignment among semantically related prototype representations while encouraging separation between unrelated ones, we introduce the following objective that aligns representation similarity with label correlation:\n\n$\\mathcal{L}\\_{le}= -\\frac{1}{C^{2}} \\sum\\_{i=1}^{C} \\sum\\_{j=1}^{C}\\hat{{A}}\\_{i j} \\log \\left(\\cos \\left({E}\\_{i}, {E}\\_{j}\\right)\\right)+(1-\\hat{{A}}\\_{i j})\\log \\left(1-\\cos \\left({E}\\_{i}, {E}_{j}\\right)\\right)$\n\nThe ablation experiments demonstrate that the modeling of both challenges offers essential gains.\n### **Question3: Understanding of discriminability** \nIn our work, discriminability refers to the model’s ability to accurately distinguish between different classes by aligning learned prototype representations with view-level features, while also capturing the distinctiveness of each target category across multiple views.  Specifically, discriminability measures whether a given view can provide stronger predictive support for a specific class compared to other classes, and whether it is more competent than other views in predicting that particular class. Therefore, discriminability should be assessed from two complementary perspectives:\n\n● Intra-class discriminability. For a given view $v$, the prediction score for the target class $j$ should be higher than that for any non-target class $k$:\n\n$\\mathbb{E} \\left[ U^{(v)}\\_{:,j} \\right] > \\mathbb{E} \\left[ U^{(v)}\\_{:,k} \\right], \\quad \\forall k \\neq j.$ \n\n● cross-view discriminability. For a given class $j$, the prediction score produced by view $v$ should exceed that of any other view $v^*$:\n\n\n$\\mathbb{E} \\left[ U^{(v)}\\_{:,j} \\right] > \\mathbb{E} \\left[ U^{(v^{\\*})}\\_{:,j} \\right], \\quad \\forall v \\neq v^{\\*}.$ \n\n### **Question4: The issue of code release** \nWe commit to releasing all codes and data on GitHub upon acceptance of the paper."}, {"review_id": "G2Ij0Y5WUh", "reviewer": "Reviewer_NS9F", "summary": "To address the challenges of view and label incompleteness caused by feature storage limitations and annotation costs, this paper proposes the TDLSR framework. It integrates a proximity-aware graph recovery mechanism and mutual information-constrained feature disentanglement to balance cross-view complementarity and consistency. Moreover, label semantics-guided representation is employed to model inter-label correlations.", "questions": "1.In Theorem 2, it is assumed that the information entropy of both shared and private representations is fixed. Does this assumption hold in practice for multimodal or multi-view data? Given the heterogeneous nature of views, large entropy discrepancies might arise and compromise the discriminability of private representations.\n\n2.Constructing and propagating view-specific graphs across all views can be computationally expensive. The paper lacks a discussion or analysis on the training cost or scalability of the proposed method.\n\n3.How is mutual information estimated in Eq. (4)? Additionally, how is the Lagrange multiplier in Eq. (7) set or tuned during training?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.The paper presents extensive experiments demonstrating the superior performance of the TDLSR framework.\n\n2.It is well-motivated by addressing both view and label incompleteness, a limitation shared by many existing approaches.\n\n3.The theoretical derivation, especially on representation disentanglement and generalization bounds, is clear and well-articulated.\n\nWeaknesses:\n\n1.Many technical components (e.g., MI constraints, graph-based imputation, and prototype learning) have been widely adopted in prior work. The novelty of this work lies more in its integration and theoretical refinement rather than introducing fundamentally new paradigms.", "was_revised": true, "final_justification": "The authors’ response addressed all of my questions, and I agree with their explanation. They described the adjustments made to each technical component. They also provided the reason for using fixed entropy, the mutual information estimation process, and the running times. Although TDLSR involves a more complex computation process, this is generally in line with expectations. I will maintain my original score.", "rebuttal": "I am grateful for your careful review of my paper and your valuable comments.  We are deeply motivated by your acknowledgment of the strengths of our work, particularly the breadth of experiments, the methodological advances, and the clarity of the theoretical analysis.  At the same time,  we sincerely appreciate your identification of the weaknesses and issues in our work, which offers significant insights for its further improvement. Next, we will spare no effort to address your concerns and questions,  and carefully revise the manuscript and pursue additional research to resolve its deficiencies.\n ### **Weakness1: Advancing without new paradigms** \nOur approach is grounded in three technically mature components, which are widely adopted in multi-view learning and multi-label classification, i.e., the graph attention recovery mechanism, mutual information constrained feature extraction, and prototype representation learning.  Although these techniques have been previously utilized, our method incorporates distinct adaptations in each technical framework to effectively accommodate the complexities of incomplete multi-view and multi-label learning scenarios.  \n● Firstly, regarding view recovery, previous methods such as AIMNet leverages all available samples to reconstruct the missing ones. However, not all samples exhibit strong relevance. DIMvSML employs graph neural networks to propagate cross-view structural dependencies for recovery, but it introduces a large number of network parameters to model edge weights on the graph, leading to increased computational cost. Besides, these recovery-related parameters, when insufficiently trained in the early stage, can negatively impact the parameter updates of subsequent feature extractors. To address this, we construct instance-level relation graphs by leveraging attention computation to drive neighborhood-aware selection. Without introducing additional network parameters, we perform cross-view propagation of highly correlated sample information on the relation graph to support view recovery.\n\n● Secondly,  for representation extraction, many traditional methods have employed mutual information based technique to capture informative content and characterize view correlations. Currently, existing methods in the multi-view domain lack a unified framework or consensus on how to  employ mutual information constrained loss functions for feature extraction, and they are also unsupported by solid theoretical foundations. Besides, multi-view multi-label learning methods such as SIP focuses solely on extracting shared representations while neglecting the view-specific contributions essential for classification. Accordingly, we systematically formulate three information-theoretic principles for multi-view feature extraction, i.e., information shift, interaction and orthogonality. The information shift term $\\sum_{v=1}^{V} I({s}^{(v)};{z}^{(v)})$ is critical for guaranteeing that the representations stay consistent with the core semantics of raw views. The information interaction term $\\sum_{v=1}^{V}\\sum_{v^*\\neq v}^{V} (I({s}^{(v^{\\*})}|{z}^{(v^{\\*})};{s}^{(v)}|{z}^{(v)})-I({o}^{(v^{\\*})}|{z}^{(v^{\\*})};{o}^{(v)}|{z}^{(v)}))$ can promote information exchange among shared components while mitigating overlap among view-specific components. The information orthogonality term $\\sum_{v=1}^{V} I({s}^{(v)}|{z}^{(v)};{o}^{(v)}|{z}^{(v)})$ is used to ensure that the shared and specific features extracted from each view are mutually independent and completely disentangled.  Therefore, we introduce a comprehensive information-theoretic framework for representation learning grounded in three core aspects, i.e., the alignment with original views, the cross-view correlations, and the interactions between intra-view representations. We theoretically show that all three principles are essential to maximize the mutual information between representations and labels. Besides, we also provide a theoretical guarantee that as representation disentanglement improves, the model's generalization ability is correspondingly enhanced.\n \n● Thirdly,  for label prototype, some methods like SIP fail to account for label correlations during prototype extraction, even though capturing such dependencies is crucial for enhancing performance in multi-label learning. Thus, in our approach, we first sample the prototype representation for each class, and then update them through a graph network that incorporates label correlation information derived from the Jaccard distance. This yields label prototypes that embed inter-label dependencies.\n ### **Question1:  The assumption of Theorem 2 is impractical** \n**Required for the proof:** The fixed entropy assumption in Theorem 2 facilitates a clear analysis of how mutual information objectives influence the association  between learned representations and label semantics, which serves as a necessary simplification for theoretical modeling.\n\n**The Theorem  remains valid under relaxed assumptions:** If the assumption is relaxed such that the information entropy of shared representations differs from that of specific representations  $(H({S}^{(v)})=H^{0}, H({O}^{(v)})=H^{1} (1 \\leq {v} \\leq {V}))$, the validity of Theorem 2 remains unaffected as long as the entropy values are constant.  This is because our proof is based on the relative magnitude between the information  entropy of the representations and that of the labels, rather than relying on the equality between the information entropy of shared and specific components. \n\n**Practical deployment and empirical evidence:** The model does not impose hard constraints on the entropy values.  Instead, by optimizing a variational lower bound of mutual information, the model emphasizes the relative mutual information between representations rather than their absolute entropy magnitudes. As a result, the optimization objective remains valid even when entropy discrepancies exist across different views. Although entropy variation may occur in practice, we mitigate its impact by extracting all representations with the same dimensionality, which effectively regulates the amount of information they can encode. Furthermore, ablation results show that removing the disentanglement module leads to performance degradation, directly validating the theoretical foundation and efficacy of the model.\n ### **Question2: Method complexity** \nThe complexity of our method primarily arises from three components, i.e., the construction of sample topology graph for each view, the dual-channel representation extraction, and the learning of  prototype representation for each label. Next, we present a comparison of the runtime(s) across different algorithms:\n||AIMNet | DICNet | DIMC | LMVCAT|MTD|SIP|iMVWL|Ours|\n|-|-|-|-|-|-|-|-|-|\n| Corel5k  |408.37|765.02 | 559.77 |1198.72|2520.99|1039.93|513.41|2270.64|\n|Espgame| 607.02| 3047.17|995.89|3037.25|4080.72|1605.16|1822.2|3882.59|\n|Mirflickr|159.98|1228.27 |359.66|151.27|562.55|727.26|568.46|520.24|\n\nAs indicated by the comparison, our method incurs higher complexity than most baselines due to its comprehensive treatment of view reconstruction, representation learning, and label correlation. Nevertheless, it achieves faster runtime than MTD, another dual-branch model, suggesting that our loss design contributes to efficient convergence.\n ### **Question3: The estimation method for mutual information**  \n The mutual information terms in Eq. (4) are first reformulated via variational inference to obtain tractable bounds:\n\n $I({s}^{(v)};{z}^{(v)}) \\geq \\mathbb{E}_{p\\left({z}^{(v)}, {s}^{(v)}\\right)}\\left[\\log q\\left({s}^{(u)} | {z}^{(v)}\\right)\\right] $\n\n$I({s}^{(v^{\\*})}|{z}^{(v^{\\*})};{s}^{(v)}|{z}^{(v)}) \\geq \\int \\int p({s}\\^{(v)}|{z}\\^{(v)};{s}\\^{(v^{\\*})}|{z}\\^{(v^{\\*})})\\log q({s}\\^{(v)}|{s}\\^{v^{\\*}}) d{s}\\^{(v^{\\*})} d{s}\\^{(v)}$\n\n$I({o}^{(v^{\\*})}|{z}^{(v^{\\*})};{o}^{(v)}|{z}^{(v)}) \\leq D_{KL} (p({o}^{(v^{\\*})}|{z}^{(v^{\\*})};{o}^{(v)}|{z}^{(v)}) \\| p({o}^{(v^{\\*})}|{z}^{(v^{\\*})})q({o}^{(v)}|{o}^{(v^{\\*})}))$\n\n$I({s}^{(v)}|{z}^{(v)};{o}^{(v)}|{z}^{(v)}) \\leq D_{KL} (p({s}^{(v)}|{z}^{(v)};{o}^{(v)}|{z}^{(v)}) \\| p({o}^{(v)}|{z}^{(v)})q({s}^{(v)}|{o}^{(v)}))$\n\nThe detailed estimation procedures for these bounds are provided in Appendix A.2.  The core idea is to adopt a data-driven approach that leverages cross-view instance-level contrastive learning to approximate the joint distribution between views. By  aggregating along different directions of the joint distribution matrix, the marginal distributions of individual views can be derived, thereby enabling the computation of all distributions involved in the variational bounds. The Lagrange multiplier in Eq. (7) is fixed to 1 in our experiments."}, {"review_id": "ZiZixeu0i5", "reviewer": "Reviewer_P58t", "summary": "This paper presents a theory-driven framework named TDLSR to address the problem of incomplete multi-view multi-label learning. The proposed method introduces a proximity-aware graph attention mechanism for missing view recovery, optimizes mutual information to separate shared and specific features, and models label prototypes to capture label correlation semantics. Theoretical contributions include discriminability analysis and generalization error bounds. Experiments across six public datasets and a real-world NBA scenario demonstrate significant advantages over state-of-the-art methods.", "questions": "(1) Unlike graph neural networks, the proposed view restoration strategy does not involve network parameter fine-tuning. Intuitively, parameter optimization is expected to reduce errors. The authors are requested to explain why the absence of fine-tuning leads to better performance.\n\n(2) Given that mutual information has been employed in prior multi-view feature extraction methods, please clarify the main distinguishing contribution of this work. Furthermore, are all three proposed principles indispensable?\n\n(3) Label-specific representation learning is a common approach in multi-label classification. How is it specifically implemented in this work? Furthermore, how does the proposed method integrate label semantics learning and label-specific representation learning in a unified manner?", "limitations": "Yes, the other aspects have all been mentioned under the weaknesses and questions.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\n(1) The method is forward-looking, with its innovative design built upon the latest SOTA, such as MTD and SIP.\n(2) The paper emphasizes the integration of method and theory, providing theoretical justifications from multiple perspectives, including discriminability, effectiveness, and generalization error.\n(3) This work involves substantial effort and thoroughly validates the effectiveness of the proposed method under a wide range of missing data ratios. Additionally, a real-world NBA dataset is constructed via web crawling to conduct comparative experiments.\n\nWeaknesses：\n\n(1)This paper lacks an algorithmic flowchart. Please provide a detailed explanation of the optimization process, parameter selection, and other relevant implementation details to facilitate reproducibility. \n(2)Figures 1 and 2 lack detailed captions. Please provide comprehensive explanations to help readers understand. In addition, please clarify the intended purpose of these two figures, as they occupy substantial space in the paper.\n(3)As is well known, a general theoretical framework for generalization error in multi-view learning has yet to be well established. Therefore, please elaborate on the technology used to derive the generalization error bound of NAMLL, and explain how the correctness of the proposed theory is validated.", "was_revised": true, "final_justification": "I have read all the reviews and the authors' response. All my questions have been addressed. I keep the ratings unchanged.", "rebuttal": "Thank you for your careful review and insightful comments on my manuscript. Your recognition of the work’s pioneering contributions, its seamless integration of theoretical foundations with practical implementation, and the substantial scope of the experimental efforts is deeply encouraging and serves as a great motivation for our continued research. Meanwhile, we also sincerely accept the shortcomings you have pointed out and will revise the manuscript carefully in accordance with your suggestions. Next, we provide a detailed response to the concerns you have raised regarding our work.\n ### **Weakness1: The detailed algorithmic implementation** \n● Algorithmic procedure. Our method first reconstructs the missing views using Eq. (2) and (3), which results in a new multi-view data denoted as $\\\\{{Z}^{(v)}\\\\}\\_{v=1}^{V}$. This data $\\\\{{Z}^{(v)}\\\\}\\_{v=1}^{V}$ is then fed into dual-channel encoders to obtain the shared representations $\\\\{{S}^{(v)}\\\\}\\_{v=1}^{V}$ and  private representations $\\\\{{O}^{(v)}\\\\}\\_{v=1}^{V}$. Simultaneously, a label prototype matrix H is sampled and processed through a GIN layer to produce the matrix $E$. Subsequently, element-wise interactions are performed between the label prototypes and each representation, followed by a confidence-based fusion process guided by the reconstruction quality, leading to the final prediction matrix $\\overline{{P}}$. Three types of losses are computed, i.e.,  $\\mathcal{L}\\_{IB}$ for feature extraction,  $\\mathcal{L}\\_{le}$ for label prototype learning, and $\\mathcal{L}\\_{bce}$ for classification. These are summed to form the total loss $\\mathcal{L}=\\mathcal{L}\\_{bce}+\\lambda\\_{1} \\mathcal{L}\\_{IB}+\\lambda\\_{2}\\mathcal{L}\\_{le}$. The network parameters are then updated batch-wise using the Adam optimizer with a learning rate of 0.0001. After training for the predefined number of epochs, predictions are performed on the test set, and classification metrics are calculated accordingly.\n\n● Parameter Setting. Except for the balanced coefficients $\\lambda_{1}$ and $\\lambda_{2}$, which are tuned within the range of $\\\\{0.01,0.1,1,10,100,1000\\\\}$, all other parameters are kept fixed. The temperature parameter $\\tau$ is fixed to 0.2, the balanced factor $\\alpha$ is fixed to 10, the number of nearest neighbors $k$ for each sample takes the value of 10,  the Lagrange multiplier \n$\\beta$ is 1, the sampling number $s$ is 5. \n ### **Weakness2: Descriptions of Figures 1 and 2** \n● Figure 1 presents the overall framework of our proposed algorithm, which consists of three components, i.e., \"Proximity-aware Graph Attention Recovery\", \"Universal View Extraction Framework\", and \"Multi-Label Semantic and Label-Specific Representation Learning\". The first component describes the reconstruction of missing views by propagating cross-view neighborhood information, guided by attention-based similarity mechanisms. The second component focuses on extracting both shared and view-specific representations, with core information enhanced and feature disentangled based on three principles, i.e., information shift, interaction, and orthogonality. The third component involves sampling initial prototype representations, followed by refinement through a GIN layer, where label correlations are used as edge weights. Subsequently, the refined label prototypes interact with each representation, and a confidence-aware late fusion is applied to produce the final multi-label classification results. \n\n● Figure 2 provides  a visualization of the proposed information-theoretic modeling based on three guiding principles. The top-left part illustrates the original modalities, where the red region represents shared information, while the blue and green regions denote modality-specific private information. The bottom-left section explicitly shows the disentangled shared and private information. The right side demonstrates the roles of the three principles, i.e., information shift facilitates the extraction of core informative components from the original data, information interaction enhances cross-modal sharing of common representations while promoting separation of private features, information orthogonality encourages the shared and private representations extracted from the same view to be mutually non-redundant.\n\nTherefore, these figures are intended to help readers better understand the overall approach and the key innovations introduced in this work.\n\n ### **Weakness3: How to derive the generalization error bound**\nThe process of deriving the generalization error bound consists of five main stages, as outlined below.\n\n● Definition of risk functions. The expected risk  $R({f})$ and empirical risk $\\widehat{R}_{D}({f})$ are formally defined based on the multi-label classification loss over multi-view inputs, with a late fusion strategy applied using view-specific reconstruction quality scores $Q$ as fusion weights.\n\n● Modeling of function class. The hypothesis space $\\mathcal{F}$ is constructed to represent vector-valued functions mapping multi-view inputs to prediciton scores.  The function includes shared and specific feature extractors $\\left(\\phi\\^{s}, \\phi\\^{o}\\right)$, label-specific mappings $\\zeta$, and classification heads $w$\n\n ● Information-theoretic analysis. By defining ${R}\\_{{Y}^{c}}$ as the informative representations with respect to labels $Y^c$, we introduce the concept of typical subsets $\\mathcal{R}_{c,\\gamma}^{x}$ and derive probabilistic bounds  from information entropy using McDiarmid's inequality.\n\n ● Contrastive sampling and risk decomposition. The risk is decomposed across instance-view-label triplets. By selecting reliable samples as representatives of typical behavior, and the rest as outliers, the bounds for both regions are estimated.\n\n ● Bounding the individual terms. By leveraging the concentration inequality and Jensen’s inequality, we estimate the upper bound on the difference between the expected risk and the empirical risk term by term.\n\nSince the derived generalization error bound becomes increasingly tighter as the representation disentanglement progresses, it indirectly supports the validity of our theoretical conclusions. A better separation between shared and specific representations is particularly beneficial for multi-label classification, as the discriminative features for each label may originate from either the shared information or view-specific components.\n ### **Question1: Explain for non-parametric view reconstruction**\nIf network parameters are introduced into the view reconstruction process, they are likely to be poorly trained in the early stages, resulting in inaccurate or low-quality reconstructed samples. These erroneous reconstructions may mislead the learning of the subsequent feature extractors and lead to a form of negative interplay between the reconstruction module and the representation learning process.  As a consequence, the joint optimization may be steered in an undesirable direction or converge more slowly. Thus, employing a non-parametric view reconstruction mechanism not only reduces computational overhead, but also yields more reliable reconstructed samples in the early stages by leveraging the intrinsic structure of the original views. This approach effectively ensures the stability of subsequent network updates and enhances the robustness of the model.\n ### **Question2: Unique advantage of mutual information-guided representation learning**\nOur unique contribution lies in proposing a general framework for multi-view representation learning under mutual information constraints. This framework is built upon three principles, i.e., information shift, interaction, and orthogonality. Specifically, the proposed information-theoretic framework for is grounded in three core aspects, i.e., the alignment with original views, the cross-view correlations, and the interactions between  intra-view representations. Moreover,  we theoretically establish the effectiveness of our framework for representation extraction, i.e., to maximize the mutual information between the learned representations and the final labels, the representations must correspond to the optimal solution defined within this framework. This highlights the necessity of all three principles, as removing any one leads to reduced mutual information between representations and labels. \n ### **Question3: Design for label semantic learning and label-specific representation learning**\nFor label semantic learning, we first sample the prototype representation for each class. These prototypes are then refined through a GIN layer, where the edge weights are determined by quantitatively measured label correlations. Thus, we can obtain label prototypes that encapsulate inter-label semantic relationships. Next, we perform element-wise interactions between each label prototype and both the shared and specific representations, which results in label-specific shared and specific representations. These label-specific representations are then passed through a fully connected layer, followed by late-stage fusion to produce the final soft labels. This process facilitates the extraction of the most discriminative features for each label prototype from both the shared and specific feature pool, while also refining the label preference across different representations."}]

Author rebuttal:

Meta-review: This paper proposes TDLSR, a theory-driven framework for incomplete multi-view multi-label classification. It addresses missing views via an attention-based imputation method and disentangles shared/specific representations using mutual information constraints. Theoretically, it provides discriminability analysis and generalization bounds. Experiments on six datasets and a real-world NBA application demonstrate superior performance over SOTA methods. After the rebuttal, all reviewers recommended acceptance. Due to its strong theoretical contributions, innovative methodology, and comprehensive empirical validation, the paper is recommended for acceptance.
Decision: Accept (spotlight)