Improving Evolutionary Multi-View Classification via Eliminating Individual Fitness Bias
Authors: Xinyan Liang
ShuaiLi
Qian Guo
Yuhua Qian
Bingbing Jiang
Tingjin Luo
Liang Du
Venue: NeurIPS 2025 spotlight ()
Keywords: Multi-View Classification; Evolutionary Multi-View Classification;  Individual Fitness Bias
Primary area: general_machine_learning

Abstract: Evolutionary multi-view classification (EMVC) methods have gained wide recognition due to their adaptive mechanisms. Fitness evaluation (FE), which aims to calculate the classification performance of each individual in the population and provide reliable performance ranking for subsequent operations, is a core step in such methods. Its accuracy directly determines the correctness of the evolutionary direction. That is, when FE fails to correctly reflect the superiority-inferiority relationship among individuals, it will lead to confusion in individual performance ranking, which in turn misleads the evolutionary direction and results in trapping into local optima. This paper is the first to identify the aforementioned issue in the field of EMVC and call it as fitness evaluation bias (FEB). FEB may be caused by a variety of factors, and this paper approaches the issue from the perspective of view information content: existing methods generally adopt joint training strategies, which restrict the exploration of key information in views with low information content. This makes it difficult for multi-view model (MVM) to achieve optimal performance during convergence, which in turn leads to FE failing to accurately reflect individual performance rankings and ultimately triggering FEB. To address this issue, we propose an evolutionary multi-view classification via eliminating individual fitness bias (EFB-EMVC) method, which alleviates the FEB issue by introducing evolutionary navigators for each MVM, thereby providing more accurate individual ranking. Experimental results fully verify the effectiveness of the proposed method in alleviating the FEB problem, and the EMVC method equipped with this strategy exhibits more superior performance compared with the original EMVC method. (The code is available at https://github.com/LiShuailzn/Neurips-2025-EFB-EMVC)

Improving Evolutionary Multi-View Classification via Eliminating Individual Fitness Bias
Xinyan Liang" 12, Shuai Li', Qian Guo Yuhua Qian'; Bingbing Jiang',
Tingjin Luo Liang Du
Institute of Big Data Science and Industry, Shanxi University
State Key Laboratory of Al Safety, Beijing, 100086
3 School of Computer Science and Technology. Taiyuan University of Science and Technology
4 School of Information Science and Technology. Hangzhou Normal University
College of Science, National University of Defense Technology (1iangxinyan48, Luzhaaa, czgu com, jinchenggyh@126 com j jiangbbühzmu.c edu. en, singjinluu@hoomail com, duliang@sxu. edu. cn
Abstract
Evolutionary multi-view classification (EMVC) methods have gained wide recog- nition due to their adaptive mechanisms. Fitness evaluation (FE), which aims to calculate the classification performance of each individual in the population and provide reliable performance ranking for subsequent operations, is a core step in such methods. Its accuracy directly determines the correctness of the evolutionary direction. That is, when FE fails to correctly reflect the apperiorityiiffeioortty relationship among individuals, it will lead confusion in individual performance ranking. which in turn misleads the evolutionary direction and results in trapping into local optima. This paper is the first to identify the aforementioned issue in the field of EMVC and call it as fitness evaluation bias (FEB), FEB may be caused by variety of factors, and this paper approaches the issue from the perspective of view information content: existing methods generally adopt joint training strategies, which restrict the exploration of key information in views with low information content. This makes it difficult for multi-vies model (MVM) to achieve optimal performance during convergence, which in turn leads to FE failing to accurately reflect individual performance rankings and ultimately triggering FEB. To address this issue, we propose an evolutionary multi-view classification via eliminating individual fitness bias (EFB-EMVCC method, which alleviates the FEB issue by introducing evolutionary navigators for each MVM, thereby providing more accu- rate individual ranking. Experimental results fully verify the effectiveness of the proposed method in alleviating the FEB problem, and the EMVC method equipped with this strategy exhibits more superior performance compared with the original EMVC method. (The code is available at https://github..om httpggghwww.ooooiSaaaaaaaa/ee/ee LiShuailzn/Neurips
1 Introduction
Multi-view classification (MVC) aims to integrate data from multiple views to improve classification accuracy. A large number of methods have been proposed in this field [+-] Among them, evo- lutionary multi-view classification (EMVC) methods differs from traditional approaches where dynamically fuses different views through the adaptive mechanism of evolutionary algorithms (EA) 77. rather than relying on static modeling. They have obtained important applications like protein
"Corresponding Author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Existing methods
Ours
donuinnto souaad
Eacodo
Decord
Tour
Rxabutionary
Explorer
Iadisidual
Malti-iew medel
guide
anvigador set
Indisidual
Muld- model
Jnrufficionn optinization of wook modallites
Sufficient sprinizattio of weak modalles
V4 only
only V4 WWM
2
V4 only
Vi only
Vn WVW
V4 with EN
with EN
ovaluation
ovalution
evalustion
evolution
TAST
KL.55
Search space
spuce
Figure 1: The issues of existing evolutionary multi-view classification and our solutions
secondary structure prediction [8] Notably, fitness evaluation (FE). as a core step of such methods, runs through the entire process of individual selection, crossover, and mutation. It provides reliable basis for performance ranking for subsequent operations, and thus its evaluation accuracy directly determines the correctness of the evolutionary direction.
However, when FE fails to correctly reflect the superiority-nffeiorityy relationship among individ- uals, it will cause confusion in the ranking of individual performance, which in turn misleads the evolutionary direction and traps the process in local optima. This paper is the first to identify the above-mentioned issue in the field of EMVC and formally define it as fitness evaluation bias (FEB). FEB does not generally refer to any еπоо in FE: instead, it specifically refers to the kind of bias that is sufficient to disrupt the true performance ranking of individuals. Given the core role of FE in the entire EMVC method, the occurrence of the FEB issue will in turn lead to systematic distortion in the whole evolutionary process. Specifically, in the selection phase, such biases will interfere with the screening of high-quality individuals, resulting in the abnormal loss of superior genes; in the crossover operation, due to the lack of accurate individual ranking relationships as guidance, is difficult to form efficient gene combinations; mutation strategies, for lack of reliable guidance, degenerate into random perturbations. More seriously, the iterative optimization characteristic of EA will lead to the continuous accumulation of this bias, which in turn misleads the evolutionary direction and eventually causes the algorithm to fall into local optima (as shown Fig. D.
FEB may be caused by variety of factors, and this paper approaches the issue from the perspective of view information content: in the multi-view model (MVM) decoded from individuals, there are sigmificant differences in the information content among different views. Although the joint training strategy commonly adopted in existing methods can make full use of key information in views with high information content, it fails to fully explore key information in views with low information content. This leads to suboptimal utilization of multi-view data, which in turn causes MVM to fail to achieve optimal performance during the convergence process 9 10] Consequently, FE cannot accurately reflect the performance ranking individuals, thereby triggering FEB. This phenomenon can be analogous to mountaineer misjudging the highest point due to cognitive bias toward the terrain: the mountaincer chooses a path based only on a local perspective (partial view information), they may stop prematurely
suboptimal mountain top, thus missing the main peak that represents the global optimum. To our knowledge, none of the existing EMVC methods have considered this issue, which limits their performance.
To address the issue, we propose an evolutionary multi multi-view view classification via eliminating individual method, which alleviates the FEB problem by equipping each MVM with
fitness bias evolutionary navigators (ENs). EN realizes the directional optimization of view branches based on the knowledge distillation mechanism. Meanwhile, recent studies [1] have pointed out that cross-category information also plays a key role the distillation process. Inspired by this, we further design EN to distill both corresponding category and cross-category information simultancously.

---

so as to better guide the optimization of view branches. Specifically, we propose wasserstein Distance-orientedd loss function (WDOLF) and construct a dual-path optimization mechanism to alleviate FEB: (1) MVM optimization ensures the consistency of the overall training objective; (2) the view distillation process fully explores the rich corresponding category and cross-category information in EN, thereby utilizing multi-view data more comprehensively. This mechanism can provide more accurate individual performance ranking, and based on this, calibrate the evolutionary direction in real time to guide the EA to iterate along a more correct path. This process is similar to an explorer moving forward under the guidance of a guide who is familiar with the terrain: with each step taken, the explorer can promptly obtain the correct route leading the highest peak, thus avoiding falling into local optima (as shown in Fig. for details). By virtue of the concise and efficient strategy of "global control + local in-depth exploration", the potential of EMVC methods is fully unleashed. Notably, EN can be seamlessly integrated with other EMVC methods, demonstrating strong generality. The core contributions of this paper summarized as follows:
1. In the field of evolutionary multi-view classification (EMVC), are the first to identify and formally define the problem of fitness evaluation bias (FEB), and systematically analyze its impact on the entire evolutionary process.
2. To alleviate FEB, we equip multi-view model with evolutionary navigators (ENs) to fully explore the rich corresponding category and cross-category information therein, thereby achieving efficient utilization of multi-view data.
3. Experimental results fully verify the effectiveness of the proposed method in alleviating FEB. Moreover, EN can be seamlessly integrated into other EMVC methods, demonstrating strong compatibility.
2 Related Work
Evolutionary Multi- View Classification (EMVC): The EMVC method utilizes the adaptive mechanism of evolutionary algorithms (EA), enables continuous iterative optimization, and ultimately screens out satisfactory multi-view model (MVM) from the population. EDF 7 initializes the population in the search space composed of views and basic fusion operators, and gradually searches for satisfactory MVM through operations including fitness evaluation, selection, crossover, and mutation, pioneering research in this field. However, due to its inherent drawbacks such as long computation time, series of improvement works have been initiated. For example, DC-NAS [12 accelerates the search process by adopting a divide-and-conquee strategy for data; CSG-NAS and CoMO-NAS [4] further reduce complexity through the core structure search space, significantly improving algorithm efficiency; KS-NAS (15) reduces computational costs via introducing a dynamic knowledge base. As research advances, the credibility issue of MVM has gradually attracted attention. For instance, TEF [66 uses EA as a generator for high-quality pseudo-views, thereby further enhancing the credibility of MVM. Despite the fruitful achievements, the existing EMVC methods have not taken the problem of fitness evaluation bias (FEB) into account, which limits their performance. In contrast, the EFB- EFB- method proposed in this paper effectively alleviates the FEB problem by evolutionary navigators (ENs) into each MVM.
13
Knowledge Distillation (KD): The core idea of KD is to alleviate the challenges of complex models in deployment by transferring knowledge from the teacher model to the lightweight student model [17]. In this study, we draw on the basic idea of KD and introduce it into the EMVC framework, but its implementation relies on the EN. Through the EN, we can transfer knowledge in a targeted manner to the corresponding view branches of the MVM assist in its training. Unlike traditional KD, the focus of this study is not on proposing new distillation paradigm, but on using EN to alleviate the inherent FEB in the EMVC framework. Recent work [II] found that the cross-category information contained in the teacher model plays key role in knowledge transfer. Inspired by this, the EN designed this study not only provides corresponding category information, but also transmits cross-category information to better guide the optimization of each view branch. It is noted that the EN plays a core role in the process of alleviating FEB, while KD only serves as the implementation mechanism for knowledge transfer.
3

---

whok of evelutionary classifiation
Offipeing pencration
pegahilion
cralention
Iachiiual
Yicett
Eoors
Figure 2: The overview of EFB-EMVC
3 Proposed Method
The proposed EFB-EMVC follows the process the existing evolutionary multi-view classification (EMVC) method. The only difference is that EFB-EMVC alleviates fitness evaluation bias (FEB) by introducing evolutionary navigators (ENs) for each multi-view model (MVM) while cxisting methods do not. Our EFB-EMVC overview is illustrated in Fig.
3.1 The Alleviation of Fitness Evaluation Bias
the first to identify and formally define the FEB issue, which exerts systematic impact the entire evolutionary process. To alleviate FEB, we equip each view branch in MVM with an EN and guide by drawing on the knowledge distillation (KD) mechanism. However, traditional KD can only model corresponding category, while recent studies [IT] have shown that rich cross-category information crucial for the distillation process. Inspired by this, we design EN to distill both corresponding category and cross-category information simultaneously. thereby guiding the optimization of view branches more effectively.
In the field of EMVC,
Specifically, the EN is defined as a pre-trained teacher model. Taking the v-th view as an example: First, the EN corresponding network (DNN), where the dimension of the first layer is the fused view dimension, the dimension of the second layer is the number of categories C, and softmax layer is attached the end of the network. Subsequently, the training data and test data are input into the DNN to complete the training and testing processes. After training, the optimal DNN parameters are frozen. For given dataset, we pre-train ENs for all views and store the results in an EN set for subsequent retrieval. During the individual training process, according to the views corresponding to leaf nodes, the ENs required by the individual are retrieved from the EN set to serve as the knowledge source for that individual. The above process shown Fig. 2 (b) and is achieved via three steps.
this view is decoded into two-layer fully connected deep neural
Step aims to extract the category interrelations from the EN. Taking the v-th view as an example: Obtain the predicted probability distribution outputs of all the training data by passing them into the corresponding EN; Divide the training data into C category groups according to the resulting predicted probability distribution outputs; For the e-th category divided by the EN, assuming it contains be training samples, we collect their logits, and then concatenate them into feature Construct the kernel matrix Kς -x((X)T CxC Notably, in some datasets, the EN corresponding to certain views may end up classifying fewer than C' categories this indicates that the EN judges there be no samples belonging some categories. For the sake of convenient description, we uniformly consider the number of its classified categories as still C. For aforementioned categories with no corresponding samples, the elements in their kernel matrices are replaced with extremely small positive numbers: After obtaining the kernel matrices {K ) for all categories, we measure the category interrelations using the HSIC score, and then construct the mutual information matrix M, for the v-th view as follows: for any two elements K and
matrix X5 E Cxb.

---

KV from {K one computes H KT) = o
K k
where K
H H.
K = H H, and N = 1 I11,, with 1 as the identity matrix and 1 a column vector of ones. The resulting mutual information matrix quantifies the statistical correlations between categories in the e-th view, where larger values indicate stronger associations between their feature distributions.
Step 2 aims to effectively guide the training of each view branch by leveraging EN, thereby alleviating FEB. To this end, we have designed an optimization objective referred to as EN guidance loss (ENL). The core idea of ENL is follows: during the training process, each view branch not only needs to learn information of their corresponding category from EN, but also should capture knowledge of cross-category relationships provided by EN-this enables the achievement of better optimization effects. The ENL loss function consists of two components: The first component is the cross-entropy loss between view branch and EN with respect to the target category; The second component is the wasserstein distance (WD) between the output distributions of the two (i.c., a view branch and EN) with respect to non-target categories.
The loss function for the first part is L, = -p=); log(p")). ). where denotes the target category, p" softmax(=") and ' softmaax represent the output probability distributions of the EN and the view branch. 27 and 8 denote the logits outputs of the EN and the view branch, respectively,
The second part is to calculate the WD between EN and view branches with respect to the probability distributions of non-target categories. For two discrete distributions and Q, WD is defined as:
W(P, Q) = min yET'
ΣΣ
7as Cijs
Ei Pip = qj. and 7i 2 0. Here, "ry denotes the transport plan from p; to Oj. Gij the transportation cost, and I is the set of feasible couplings that satisfy the marginal constraints. = 7ky where Ej Pty
Since both the EN and the view branch output discrete probability distributions over non-tat non-target categories, adopt the discrete WD formulation. Specifically, first mask the target category in the logits of both models to obtain the non-target feature vectors 2 and ك and apply the same masking to the mutual information matrix to derive the masked mutual information matrix M.. Then, we apply temperature-scales softmax to 2 and & yielding the non-target categories probability distributions p² and es.
To efficiently approximate WD, we employ the rntrooy-reeullriized Sinkhorn algorithm [8]. The kernel matrix is defined as K = exp( MM,/)M. where 0.05 is the regularization parameter. The iteration matrix U is initialized as: U C-1 1. Then, the updates are performed iteratively as:
1
V
KTU
KV
and after 10 iterations, the optimal transport plan is obtained as:
7" diag(U) K diag(V).
The WD is then computed as:
Lond ΣΣ Ro (Mn)iy.
(4)
Finally, the ENL loss is defined as:
LENL aL, + BL
(5)
where a and 8 are hyperparameters used to balance the contributions of the target-category cross- entropy loss and the non- con-target categories WD.
Step 3 aims to combine the proposed ENL loss function with the traditional cross-entropy loss to jointly optimize the MVM and its individual view branches. This combined loss not only ensures the consisteney of the overall training objective but also makes full use of the critical information from each view, thereby effectively alleviating the FEB problem.
When considering V views, the whole loss function WDOLF is formulated as follows:
v
V
LWDOLF= = 21 LoE + 72
Σ
L ENT. = YI + 720
Σ
+ 72
(0)
(6)
wd?
1=1
v=1
5

---

where LCE represents the cross-entropy loss between the output of the MVM and the ground-truth labels, and L L represents the ENL loss between the v-th view branch of the MVM and the corresponding EN.
3.2 The EMVC Method Driven by Unbiased Fitness Evaluation
The core steps of the EFB-EMVC method include population initialization, unbiased fitness evalua- tion, offspring generation, and selection.
Population initialization: First, in the search space composed of views and basic fusion operators, randomly initialize population P consisting of l: individuals encoded in the form of binary trees, where the leaf nodes consist of views and the branch nodes consist of basic fusion operators, In this paper, the basic fusion operators consists of concatenation, addition, multiplication, maximize and average 77. For each individual, if the binary tree contains V views, then it must contain V - basic fusion operators. Each individual corresponds MVM.
Unbiased fitness evaluation: First, according to the views corresponding to the leaf nodes of an binary tree, the ENs required by the individual are retrieved from the EN set of the current dataset. Next, the individual is decoded into an MVM. In this MVM, each view first passes through a fully connected layer (whose dimension is set to the dimension of the fused view). Subsequently, the data is processed through two streams: 1) one stream enters a fully connected layer (with the dimension equal to the number of categories) to generate a logits vector, and then the LENE distillation loss between this vector and the logits output by the EN corresponding to the view is calculated; 2) the other stream is fused with other views via fusion operator, then passes through fully connected layer (with the dimension equal to the number of categories) to generate the logits vector of the MVM, and finally enters the softmax layer obtain a probability distribution, with which the cross-entropy loss is calculated against the true labels. Finally, all losses are combined into the Iw DOLF loss function, which is used to optimize the entire MVM and each view branch. Finally, the test accuracy at the optimal state during training is taken as the unbiased fitness value of the individual. The above process is detailed in Fig. (b).
The crossover rate is r = r1, and the mutation rate is - r2. At this stage, following the principles of traditional evolutionary algorithms, the probability of the crossover operation is significantly higher than that of the mutation operation. For the crossover operation, a non-root node is first randomly selected from each of two randomly chosen binary trees to serve as the crossover point. The selected node along with its subtree is then pruned from the original tree and exchanged with the counterpart from the other tree. These subtrees are subsequently grafted onto the parent node of the original crossover point in the opposite tree, thereby generating two new individual structures. For the mutation operation, node is randomly selected from the individual's tree structure. If the selected node is a fusion operation node, new fusion operation is randomly sampled from predefined list to replace the original operation. If the selected node is a view node, new view is randomly chosen from a set of views to replace the original one.
Crossover and mutation:
Algorithm EFB-EMEE Framework
1: Input: D (X,Y): training dataset; ò (X, y): test dataset; F: a set of basic fusion
operators; T: iteration number; evolutionary navigator set;
2: Output: The satisfactory MVM and its corresponding accuracy;
3: Population initialization: Generate an initial population Po;
4: Fitness evaluation: Obtain the unbiased fitness values of all individuals in Pa;
5: for = 1 to T do
6: Generate offspring Q: using the crossover operator;
7: Conduct mutation on each individuals in Q::
8: Obtain the unbiased fitness values of all individuals in Qc:
9: Select next generation population P++1 from Q₂ U P, using a selection operator;
end for
11: return The satisfactory MVM and its corresponding accuracy.
Selection: Adopt the binary tournament selection method. Specifically, the selection operation has three application scenarios: (1) Crossover phase: Randomly select two individuals, compare their

---

fitness values, and retain the better one as Parent 1. Repeat this operation to select Parent 2. Then, perform the crossover operation on the two parent individuals: (2) Mutation phase: Randomly select two individuals and directly choose the one with the better fitness value for mutation; (3) Generating the next generation population: Merge the current population with the offspring population, randomly select two individuals, and retain the better one to be added to the next generation. Repeat this operation K times.
The algorithm framework of the EFB-EMVC method is shown in Algorithm
4 Experiments
In this section, we aim to verify the effectiveness of EFB-EM method from four aspects: (1) Comparison with SOTA methods; (2) Impact analysis of the evolutionary navigator (EN) EFB- EMVC; (3) Impact analysis of the distillation loss function ENL on EFB-EMVC; (4) Generality of
evolutionary navigator. In addition, we conducted an in-depth analysis of the hyperparameters of EFB-EMVC and the experimental results are presented in Appendix A.4
4.1 Experimental Setup
Datasets. In the experiments, nine multi-view datasets are used and they MVoXCeleb [16]. YoutubeFace 19], NUS-WIDE-128 (NUS) [20], Reuters [21]. CB [7]. MM-IMDB [22]. NTU RGB- D 23 and EgoGesture 224. For the Reuters dataset, two variants named Reuters5 and Reuters3 are generated by adding Gaussian noise [66] Their detailed descriptions can be found in Appendix A.3
Evaluation metrics. In the experimental process, to effectively avoid the randomness interference caused by data partitioning and network initialization operations, 5-fold cross- cross-valideen validation strategy was adopted for the MVoxCeleb [6].. YoutubeFace [19]. NUS-WIDE-128 (NUS) [20], Reuters5 16 and Reuters3 [16] datasets, dividing each dataset into a training set and a test set. The specific partitioning ratio is as follows: 80% of the samples are used for model training, and 20% used for model testing. For the remaining datasets, since their original authors have already completed the partitioning of the training and test sets, the experiments were independently repeated five times. The final experimental results are presented in the form of average performance metrics and standard deviations to intuitively reflect the statistical stability of the model performance. For the MM-IMDB dataset, considering the existence of class imbalance, the weighted F1 F1-score is selected as the evaluation metrie; a higher value of this metric indicates better model performance. For the remaining datasets, accuracy is used as the evaluation metric.
4.2 Experimental Results
Comparisons with SOTA methods. In this section, we aim to validate the EFB-EMVC's effective-
ness by comparing with four kinds of SOTA methods. They are (1) fixed fusion operators- sperators-based
methods including addition, average, max, multiplication, concatenation, MLB (25 MFB (26]. TFN
(27]. LMF (28). and PTP [29]: (2) trustworthy multi-view classification methods including TMC B0),
TMOA BI. ETMC
332
RCML 33 (3) traditional adaptive multi- mult classification methods
including BV 77 SSV 7
MR 77, EmbraceNet [34], AWDR [35], RMAR (36]; (4) EMVC methods
including EDF 77. DC-NAS
12
CoMO-NAS 14, CSG-NAS 1 and TEF [6].
The results are shown in Table Based on these results, one can observe that: (1) Compared with the fixed fusion strategy, the EMVC methods demonstrate significant performance advantages on all datasets. This is attributed to its acquisition of high-performance multi-view model (MVM) through adaptive selection. However, traditional multi-view classification methods, due to being restricted by manually designed features, sometimes have lower performance than that of the fixed fusion strategy. At the same time, the trusted multi-view classification method, because it adopts the way of late-stage desision fusion, results in insufficient feature interaction, and its performance sometimes cannot surpass that of the fixed fusion strategy. (2) Compared with existing EMVC methods, it can be observed that: although these methods outperform other types of methods in terms of performance metries, the existence of fitness evaluation bias (FEB) causes such methods to fall into local optima, thereby preventing their performance potential from being fully unleashed. In contrast, EFB-EMVC effectively alleviates the FEB issue by introducing ENs into MVM, ensuring that the evolutionary algorithm (EA) can iterate and optimize along relatively more correct direction to find a more
7

---

Table 1: Accuracy comparison results with SOTA methods (mean standard deviation), where the best performance is highlighted in bold.
Methods
MVoxCeleb YoutubeFace
NUS
Reuters5
Reuters3
CB
Add
87.33#0.41
82.40=0.233
79.70= 72.81=0.70
83,46=0.28
87.16+0.117
Mul
83.18+0.14 72.9
64.58=0.63
77.02=0.38
81.89=0.70
10.87#1.16
Cat
0..9
03.05
72.32:+0.50
79.91
83.66:1..17
86.58:10.11
Max
01.57:0.41
01.49:0.29
71.36=#0477
80.02+0.20
84.01+0.288
84.21--0.11
Avg
87.27+0.33
82.23++.117
73.00=0055
79.69=0.30
83,58++0.88
87.05++0.20
MLB (ICLRI7)
07.11
85,2010.28
70.60=0.29
80.1610.155
83.8010.28 82.38:1.322
MFB (TNNLS18)
85.23
82.85
71.34=0.40 79.28-0.21
83.25:0.18 87.94:1.32
TEN (EMNLP17)
5..53.0.92
81
63.66:11.22
79.95 83.73:10.11 73.45:10.30
LMF (ACL18)
09.92+0.25
8..58+0.22
71.74+0.70
80.03+0.15 83.75+0.28 82.81+0.18
PTP (NcurIPS 19)
08.61+0.36
85. 0.30
71.83+0.50
80.10+0.10 84.06+00200 85.08+00111
TMC (ICLR22)
73.1310.15
71.1812.27
72.73.0.30
79.60.10.56
84.23.1.335 77.8710.22
TMOA (AAA122)
84.72+0.21
0..35+0.25
72.60=0.48
79.11=0.43 84.19=0.22 86.80+0.10
ETMC (TPAMI23)
88,70+0.15
79.63+1.89
73.05=0.67
79.80=0.41
84,25=0.42
RCML (AAA124)
80,51+0.41
01.95+0.20
72.53=0.55
81.39=0.118
85.88=0.29
BV (TEVC2021)
63.25.10.14
82.0111.118
68.6910.59
80.6110.25
83.98.10.14
17.08.10.15
SSV (TEYC2021)
85.10=0.23
0.343+0.31
63.70=0.64
79.51=0.41
84.71=0.22
07.02
MR (TEVC2021)
79.92+0.29
84.78=0.21
64.39=0.85
78.24=0.45
84.17=0.19
03.3
EmbraceNet (IF19)
81.74=0.334
10,90=1.04
72.43=0.38
80.07=0.21
83.58=0.25
85,09
AWDR(PR 19)
91.08
85.11=0.15
7..44-0.66
79.69++0277
83.32-+0.22
06.66
RMAR(INS22)
91.54+0.11
05.21
72.51
79.84+-.225
83.48-+0.25
06.36
EDF (TEVC2021)
93.0910.20
85.83
74.73=:0.45
81,12:0.25
85.49:0.21
08.55
CoMO-NAS (ACMMM24)
7..24+0.29
88.69+00.38
CSG-NAS (UCAI24)
74.52+0.40
89.20+-0.06
DC-NAS (AAAT24)
92.19+0.077
0..2
0.53
01.25 0..8
88.52+00.13
TEF (ICLR25)
92.4110.12
86.0211041
75.12:0.57
82.26110.23
86.4911.110
EFB-EMVC (ours)
94.82+0.12 87.67+0.17
75.79=0.76 8.266 0..51 89.67
satisfactory solution. For instance, on the MVoxCeleb, YouTubeFace, and NUS datasets, the accuracy of EFB-EMVC is improved by approximately 1.73%, 1.65%, and 0.67% respectively compared with the suboptimal model. These results fully verify the effectiveness of this mechanism.
To further explore its performance, we carried out additional experiments on other datasets that are often used to validate the effectiveness of the EMVC methods. In this experiment, the SOTA methods compared with EFB-EMVC are roughly divided into two categories: (1) Single-view classification methods, such as Maxout MLP (37), VGG Transfer (38), Inflated ResNet-50 [3). Co-occurrence 40 ResNext- 101
41: (2) Multi-view classification methods, such as Two-stream, GMU [22] CentralNet
441. MFAS 43 VGG-16 LSTM (4)), C3D LSTM + RSTTM (45. I3D 44). MMTM (47).
MTUT 48). 3D-CDC-NAS2 [49). BM-NAS [50]. DC-NAS (2), CoMO-NAS [4), CSG-NAS
13. and MCTS-CSG (5I) and HF-MNAS 12 According to the results in Table 2 compared
with single-view classification methods, multi- classification methods generally achieve better performance. This is mainly due to their ability to fully utilize the rich information across different views, thereby achieving performance breakthroughs. Compared with SOTA methods, EFB-EMVC achieves the best performance methods on the EgoGesture dataset. This advantage stems from the EN mechanism of EFB-EMVC this mechanism corrects the evolutionary direction in real time by alleviating the FEB issue.
most datasets and also reaches performance comparable to SOTA
Impact analysis of the evolutionary navigator (EN) on EFB-EMVC. In this experiment, we aim to analyze the impact of EN on EFB-EMVC (i.c., whether EN alleviates the problem of FEB?) by an ablation analysis on Tubeaaeacee dataset. To ensure the generality of this method, we took a population consisting of 15 randomly initialized individuals the research object.
As shown in the left side of Fig. 3] the accuracy of all individuals after applying the EN exhibits a consistent improvement. It is noticed that its core value lies in the reconstruction of the performance order relationship on which the EMVC method relies. The selection mechanism of the EMVC method essentially depends on the performance order relationship to identify high-quality solutions. If this order relationship remains unchanged, means that the EN only plays a role in enhancing performance and does not address the core defect of the EMVC method, that is, the FEB problem.
8

---

Table Accuracy comparison results with SOTA methods (mean standard deviation), where the best performance is highlighted in bold.
MM-IMDB
NTU RGB-D
EgoGesture
Method
Modality
FI-W (%)
Modality
Acc (5)
Modality
Acc (%)
Vniw methods
Modality
Text (1)
57.54
Video (V)
83,91
RGB (R) Depth (D)
93.75
Modality
Image (1)
49.21
Pose (P)
85.24
94.03
Multi-view methods
Two-stream (NeurIPS14)
I+T
60.81
V+P
88.60
GMU (ICLR17)
I+T
61.70
V+P
85,80
CentralNet (ECCV18)
I+T
62.23
V+P
89.36
MFAS (CVPR 19)
1+T
62.50
V+P
89.50==0.60
MMTM (ICCV20)
V+P
88.92
R+D
93.51
MTUT (3DV19)
R+D
93.87
3D-CDC-NAS2 (TIP21)
R+D
94.38
BM-NAS (AAA122)
I+T
62.92+0.03
V+P
90.48+0.24
R+D
94.96+00.0
DC-NAS (AAA124)
I+T
63.70=0.11
V+P
90.85=00055
R+D
95.22++:.05
CoMO-NAS (ACMMM24)
I+
63.84
V+P
90.94+0.02
R+D
95.25++0.03
CSG-NAS (IICA124)
IT
64.12.10.12
V+P
91.12.10.03
R+D
95.25
MCTS-CSG (UMLC25)
V+P
91.21110.10
R+D
95.27-10.01
HF-MNAS (TIP25)
I+T
64.17
V+P
91.15
R+D
95.31
EFB-EMVC (ours)
I+T
64.53:10.05
V+P
91.30=0003
R+D
95.30::0.03
0.90
EN(/)
ENL
0.85
0..00
Accura
0.75
0.70
0.65
0.60
0.70
1.0
12
34
10 12
14
Individual Index
Individual Index
Figure 3: Impact of the EN and the ENL on EFB-EMVC EN (X) represents that the final loss function only includes cross-entropy loss LeE and there no single-view distillation loss LENL.
Experimental results in T that EN significantly changes the performance ranking rela- tionships of 15 individuals. By calculating three correlation coefficients of the performance ranking relationships before and after applying EN, results indicate extremely low correlation between the two. Meanwhile. Table T ssysteaaiiaally presents the distribution individual pairs with changed performance ranking relationships before and after applying EN among the 15 individuals in the EN ablation experiment. Result shows that within the sample space consisting of 15 individuals, there are 11 pairs of individuals with significantly restructured performance ranking relationships.
The above experimental results fully demonstrate that the distortion effect of FEB individual performance ranking relationships extremely prominent, confirming that FEB is a key issue urgently needing be addressed in the EMVC method. Meanwhile, the role of EN is not limited to performance improvement; instead, fundamentally corrects the distorted individual performance ranking relationships, enabling EMVC methods to conduct effective optimization based on more accurate performance rankings. This reconstruction of ranking relationships breaks through the constraint bottleneck faced by traditional EMVC methods due FEB, providing a new solution for algorithm design and theoretical development in this field.
Table 3: Rankings and Correlation Coefficients (PC: Pearson Correlation; SRC: Spearman's 's Rank Correlation; KT: Kendall's Tau)
EN
Sort the fitness values of 15 individuals
PC
SRC
KT
x
14, 15, 5, 7, 1, 13, 10, 1I, 14, 6, 12,
0.2143
0.2143
0. 0419
14, 15, 7,8. 13,
10, 12, 14,

---

Table 4: Pairs of individuals with changed fitness value relationships between EN (X) and EN (V)
Individual Pair
EN (X)
EN (V)
4,0.2.3,-0.I1-00 vs
(0223344-22-3300)
82,00 78.70
83.09 83,92
(4.02233-0,11.-0) 1.0,42,4422.222
82.00 vs 81.81
83.09 vs 84.12
[4.0,2.3,-0-11, vs [3,2,4,33,44]
82.00 vs 79.09
83.09 vs 83.11
[4.0,2.3,40,11, 00] vs 41,2
82.00 81.71
83.09 84.02
[0,2,3,4,2,-33-0] vs [0,4,3,44-00]
78.70 vs 79.75
83.92 vs 82.93
(0,2.3,4,2.33,00) 33,44,33,44
78.70 vs 79.09
83.92 vs 83.11
[2,4.-4] vs [0.3.-4]
70.17 58,39
72.33 vs 79.11
[3,4,-3] vs [3,4.022-00-22-33
77.73 vs 76.69
82.41 vs 82.66
[3,4,-3] vs [3,2.1]
77.73 vs 78.45
82.41 vs 79.12
[0,4,3,-4.-0] vs [3,2,4,33-4]
79.75 vs 79.09
82.93 vs 83.11
[3,4,0,2--0,22-33] vs [3,2-1]
76.69 vs 78.45
82.66 vs 79.12
Table 5: Classification accuracy comparison of EDF and DC-NAS before and after applying EN
Methods EDF
MVoxCeleb
YoutubeFace
NUS
Reuters5
Reuters3
93.0911.200
85.83100.08
74.73.10.45
81.12:1.225
85,4910.221
EDF+EN
94.70-10.23
87.29.10.43
75.81-10.71
82.72.10.16
86.48
DC-NAS
92.19:10.07
85.28
74.35:1:0.58
81.35
85.86:10.14
DC-NAS+EN
9.122
0..67
75.79:10..7
82.66:10.24
86.51-10.12
Impact analysis of ENL on EFB-EMVC. In this part, we will conduct an in-depth analysis of the impacts of the KL divergence and the custom loss function ENL EFB-EMVC to demonstrate that rich cross-category information is an important component of the KD process. To this end, we have selected the YouTubeFaace dataset for the experiment. We first randomly initialize 15 individuals. Subsequently, we perform knowledge KD by applying the KL. divergence and the ENL loss function respectively. Conclusions can be drawn from the results the right side of Fig. After applying the ENL loss function, the accuracy of individuals in the population has been improved to varying degrees. This also fully demonstrates the importance of the ENL loss function in leveraging rich cross-category information.
Generality of the proposed evolutionary navigator. In this experiment, we aim to verify whether EN can achieve a high degree of compatibility with other EMVC methods. To this end, we have selected two methods, EDF (7) and DC-NAS [12]. In EDF, individuals are encoded in the form of sequences, while in DC-NAS, individuals are encoded in the form of trees. As shown in Table 5 after integrating EN into these improvements across all datasets. Taking the M VoxCeleb and YoutubeFace datasets as examples, the performance of EDF has been improved by 1.61% and 1.46%, and the performance of DC-NAS has been improved by 2.63% and 2.39%. This experimental result indicates that EN is capable of achieving high degree of compatibility with various EMVC methods.
methods, both methods have achieved significant performance
5 Conclusion
In the field of evolutionary multi-view classification (EMVC), this paper is the first to identify and formally define the fitness evaluation bias (FEB) issue, and systematically analyze its impact on the entire evolutionary process. On this basis, we propose an effective method to alleviate FEB from the perspective of view information content, namely EFB-EMVC. Specifically, EVC introduces evolutionary navigators (ENs) into each multi-view model (MVM), and leverages the rich corresponding category and cross-category information contained in ENs guide the optimization of each view, thereby effectively alleviating the FEB that is prevalent in existing EMVC methods. It is worth emphasizing that ENs can be seamlessly integrated into various multi-view learning methods, demonstrating strong compatibility and extensibility. In future work, there are still several important issues regarding FEB that require in-depth research. For instance: Beyond differences information content, what other potential factors can cause FEB and what are the corresponding countermeasures? How to integrate efficient optimization techniques to reduce the training cost of EFB-EMVC? These issues will all be key directions for advancing the further development of EMVC.
10

---

Acknowledgements
This work was supported by National Natural Science Foundation of China (Nos. 62306171, T2495251, 62406218, 62506219). the Science and Technology Major Project of Shanxi (No. 202201020101066, and Open Funding Programs of State Key Laboratory of Al Safety (No. 2025- 12).
References
[1] Xinyan Liang, Yuhua Qian, Qian Guo, Honghong Cheng, and Jiye Liang. AF: An association- based fusion method for multi-modal classification. IEEE Transactions on Puttern Analysis and Machine Intelligence, (M(12):9336-9255 2022.
[2] Jueqing Lu, Wray Buntine, Yuanyuan Qi, Joanna Dipnall, Belinda Gabbe, and Lan Du. Nav- igating conflicting views: Harnessing trust for learning. In Proceedings of the 42nd Interna- lional Conference on Machine Learning, 2025. URL id=uJ3JqtBYWk
wwt.:/iwwwweeeeftteee net/forum?
[3] Xinyan Liang, Shijie Wang, Yuhua Qian, Qian Guo, Liang Du, Bingbing Jiang, Tingjin Luo, and Feijiang Li. Trusted multi-view classification with expert knowledge constraints, In Proceedings of the 42nd International Conference on Machine Learning, 2025. URL https //openreview
[4] Yake Wei, Di Hu, Henghui Du, and Ji-Rong Wen, On-the-fly modulation for balanced mul- timodal learning. IEEE Transactions Pattern Analysis and Machine Intelligence, 47(1): 469-485, 2025.
[5] Yang Yang, Hongpeng Pan, Yuan Jiang, Yi Xu, and Jinhui Tang. Learning to rebalance multi-modal optimization by adaptively masking subnetworks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(6):4553-4566 2025,
[6] Gengyu Lyu, Zhen Yang, Xiang Deng, and Songhe Feng. L-VSM: Label-driven view-specific fusion for multiview multilabel classification. IEEE Transactions on Neural Networks and Learning Systems, 36(4):6569-6588, 2025.
[7] Xinyan Liang. Qian Guo, Yuhua Qian, Weiping Ding, and Qingfu Zhang. Evolutionary deep fusion method and its application in chemical structure recognition. IEEE Transactions Evolutionary Computation, 25(5):883-893, 2021.
[8] Yining Qian, Lijie Su, Meiling Xu, and Lixin Tang. Enhanced protein secondary structure pre- diction through multi-view multi-feature evolutionary deep fusion method. IEEE Transactions on Emerging Topics in Computational Intelligence, (5):3322-3363, 2025.
[9] Yang Yang, Hongpeng Pan, Qing- Yuan Jiang, Yi Xu, and Jinhui Tang. Learning to rebalance multi-modal optimization by adaptively masking subnetworks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 47(6):45534456 2025.
[10] Xiaokang Peng, Yake Wei, Andong Deng, Dong Wang, and Di Hu. Balanced multimodal learning via on-the-fly gradient modulation. In Proceedings of the IÉEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8238-8247, 2022.
[11] Jiaming Lv, Haoyuan Yang, and Peihua Li. Wasserstein distance rivals kullback-leibler diver- gence for knowledge distillation. Proceedings of the Advances in Neural Information Processing Systems, 37:65445-65475, 2024.
[12] Xinyan Liang, Pinhan Fu, Qian Guo, Keyin Zheng, and Yuhua Qian. DC-NAS: Divide-and- conquer neural architecture search for multi-modal classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 13754-13762. 2024.
[13] Pinhan Fu, Xinyan Liang, Tingjin Luo, Qian Guo, Yayu Zhang, and Yuhua Qian. Core- structures-guided multi-modal classification neural architecture search. In Proceedings of the 33rd International Joint Conference on Artificial Intelligence, pages 3980-3988, 2024.

---

[14] Pinhan Fu, Xinyan Liang, Yuhua Qian. Qian Guo, Zhifang Wei, and Wen Li. CoMO-NAS: Core-structures strructurrs-guudee guided multi-objectivv neural architecture search for multi-modal classification. In Proceedings of the 32nd ACM International Conference on Multimedia, page 9126 9135, 2024.
[15] Zhihua Cui, Shiwu Sun, Qian Guo, Xinyan Liang, Yuhua Qian, and Zhixia Zhang. A fast neural architecture search method for multi-modal classification via knowledge sharing. In Proceedings of the 34th International Joint Conference on Artificial Intelligence, pages 5003-5011 1, 2025.
[16) Xinyan Liang, Pinhan Fu, Yuhua Qian, Qian Guo, and Guoqing Liu. Trusted multi-view classification via evolutionary multi-view fusion. In Proceedings of the 13th International Conference Learning Representations, page 1-14, 2025.
[17] Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv preprini arXiv: /503,0253,,
[18] Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems, volume 26, 2013.
[19] Siwei Wang, Xinwang Liu, Li Liu, Wenxuan Tu, Xinzhong Zhu, Jiyuan Liu, Sihang Zhou, and En Zhu. Highly-efficient incomplete largescale multiview clustering with consensus bipartite graph. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9766-9775, 2022.
[20] Jinhui Tang, Xiangbo Shu, Guojun Qi, Zechao Li, Meng Wang, Shuicheng Yan, and Ramesh Jain. Tri-clustered tensor completion for social-aware image tag refinement. IEEE Transactions on Puttern Analysis and Machine Intelligence, 1666)166, 2017.
[21] MassihReza Amini, Nicolas Usunier, and Cyril Goutte. Learning from multiple partially observed views an application to multilingual text categorization. In Advances in Neural Information Processing Systems, page 28-36, Vancouver, Canada, 2009.
[22] John Arevalo, Thamar Solorio, Manuel Montes-y Gómez, and Fabio A González. Gated multimodal units for information fusion. arXiv preprint 1702:077000099. 2017.
[23] Amir Shahroudy, Jun Liu, Tian-Tsong Ng. and Gang Wang. Ntu rgb+ d: A large scale dataset for 3d human activity analysis. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1010-1019, 2016.
[24] Yifan Zhang, Congqi Cao, Jian Cheng, and Hanqing Lu. EgoGesture: A new dataset and benchmark for egocentric hand gesture recognition. IEEE Transactions on Multimedia, 20(5): 1038-1050, 2018.
[25] Jin-Hwa Kim, Kyoung Woon On, Woosang Lim, Jeonghee Kim, Jung- Ha, and Byoung- -Tak Zhang. Hadamard product for low-rank bilincar pooling. In Proceedings of the 5th International Conference on Learning Representations, pages 1-10, 2017.
[26] Zhou Yu. Jun Yu, Chenchao Xiang, Jianping Fan, and Dacheng Tao. Beyond bilinear: General- ized multimodal factorized high-order pooling for visual question answering. IEEE Transactions on Neural Networks and Learning Systems, 29(12):5947-595 2018
[27] Amir Zadeh, Minghai Chen, Soujanya Poria, Erik Cambria, and Louis- Philippe Morency. Tensor fusion network for multimodal sentiment analysis. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 1103-1114 1114, 2017.
[28] Zhum Liu, Ying Shen, Varun Bharadhwaj Lakshminarasimhan, Paul Pu Liang, AmirAli Bagher 7adeh, and Louis-Philippe Morency. Efficient low-rank multimodal fusion with modality-specifie factors In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pupers), pages 2247-2256, 2018
[29] Ming Hou, Jiajia Tang, Jianhai Zhang, Wanzeng Kong, and Qibin Zhao. Deep multimodal multilinear fusion with high-order polynomial pooling. Proceedings of the 33rd Conference on Neural Information Processing Systems, 32, 2019.
12

---

[30] Zongbo Han, Changqing Zhang, Huazhu Fu, and Joey Tianyi Zhou. Trusted multi-view classification. In Proceedings of the International Conference on Learning Representations. pages 1-11, 2021.
[3]] Wei Liu, Xiaodong Yue, Yufei Chen, and Thierry Denoeux. Trusted multi-view deep learning with opinion aggregation. Proceedings of the Proceedings of the AAAI Conference on Artificial Intelligence,3666 36(7):7585-759. Jun. 2022.
[32] Zongho Han, Changqing Zhang, Huazhu Fu, and Joey Tianyi Zhou. Trusted multi-view classification with dynamic evidential fusion. IEEE Transactions Pattern Analysis and Machine Intelligence, 45(2):2551-22 2266,, 2023.
[33] Cai Xu, Jiajun Si, Ziyu Guan, Wei Zhao, Yue Wu, and Xiyue Gao. Reliable conflictive multi-view learning. Proceedings of the AAAI Conference on Artificial Intelligence, 38(14): 16129-16137, 2024.
[34] JunHo Choi and JongSeok Lee. EmbraceNet: A robust deep learning architecture for multimodal classification. Information Fusion, 51:259-270, 2019.
[35] Muli Yang, Cheng Deng, and Feiping Nie. adaptive-weighting discriminative regression for multi-view classification. Pattern Recognition, 88:236-245, 2019.
[36] Bingbing Jiang. Junhao Xiang, Xingyu Wu, Yadi Wang, Huanhuan Chen, Weiwei Cao, and Weiguo Sheng. Robust multi-view learning via adaptive regression. Information Sciences, 610: 916-937, 2022.
[37] Ian Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio. Maxout networks. In Pruceedings of the International Conference on Machine Learning, pages 1329-1327. PMLR, 2013.
[38] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:14099 /556, 2014.
[39] Fabien Baradel, Christian Wolf, Julien Mille, and Graham W Taylor. Glimpse clouds: Human activity recognition from unstructured feature points. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 469-478, 2018.
[40] Chao Li, Qiaoyong Zhong, Di Xie, and Shiliang Pu. Co-occurrence feature learning from skeleton data for action recognition and detection with hierarchical aggregation. arXiv preprint 1rXiv:1804000055, 2018.
[41] Okan Köpüklü, Ahmet Gunduz, Neslihan Kose, and Gerhard Rigoll. Real-time hand gesture de- tection and classification using convolutional neural networks. 2019 14th IEEE International Conference automatic Face & Gesture Recognition, pages 1-8. IEEE, 2019.
[42] Valentin Vielzeuf, Alexis Lechervy, Stéphane Pateux, and Frédéric Jurie. Centralnet: multi- layer approach for multimodal fusion. Proceedings of the European Conference on Computer Vision Workshops, pages 0-0, 2018.
[43] Juan-Manuel Pérez-Rúa, Valentin Vielzeuf, Stéphane Pateux, Moez Baccouche, and Frédéric Ju- rie. MFAS: Multimodal fusion architecture search. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6966-6975 2019.
[44] Xiaodong Yang and YingLi Tian. Super normal vector for activity recognition using depth sequences. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, pages 804-811, 2014.
[45] Pavlo Molchanov, Xiaodong Yang, Shalini Gupta, Kihwan Kim, Stephen Tyree, and Jan Kautz. Online detection and classification of dynamic hand gestures with recurrent 3d convolutional neural network. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4207 4215, 2016.
[46] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? new model and the kinetics dataset. In Proceedings of the IEFE Conference on Computer Vision and Pattern Recognition, pages 2899, 2017.
13

---

[47] Hamid Reza Vaezi Joze, Amirreza Shaban, Michael L Iuzzolino, and Kazuhito Koishida. MMTM: Multimodal transfer module for enn fusion. Proceedings of the IEEE/CVF Confer- ence on Computer Vision and Pattern Recognition, pages 35289-13299 2020.
[48] Vikram Gupta, Sai Kumar Dwivedi, Rishabh Dabral, and Arjun Jain. Progression modelling for online and early gesture detection. In 2019 International Conference on 3D Vision, pages 289 297. IEEE, 2019.
[49] Zitong Yu, Benjia Zhou, Jun Wan, Pichao Wang, Haoyu Chen, Xin Liu, Stan Z Li, and Guoying Zhao. Searching multi-rate and multi-modal temporal enhanced networks for gesture recognition. IEEE Transactions on Image Processing, 30:5626-5640, 2021.
[50] Yihang Yin, Siyu Huang, and Xiang Zhang. BM-NAS: Bilevel multimodal neural architecture search. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 3901-8909, 2022.
[51] Guoqing Liu, Yuhua Qian, Xinyan Liang, and Pinhan Fu. Core structure- multi-modal classification via monte carlo tree search. International Journal of Machine Learning and Cybernetics, pages 1-11, 2025.
[52] Kaifang Long, Guoyang Xie, Lianbo Ma, Qing Li, Min Huang, Jianhui Lv, and Zhichao Lu. Enhancing multimodal learning via hierarchical fusion architecture search with inconsistency mitigation. IEEE Transactions on Image Processing, 34:5458- -5452, 2025. doi: 10.1109/TIP. 2025.3599673.
[53] Arsha Nagrani, Joon Son Chung, Weidi Xie, and Andrew Zisserman. Large-scale speaker verification in the wild. Computer Speech & Language, 60:101027, 2020.
[54] Tat-Seng Chua, Jinhui Tang, Richang Hong, Haojie Li, Zhiping Luo, and Yantao Zheng. Nus- wide: a real-world web image database from national university of singapore. Proceedings of the A CC International Conference Image and Video Retrieval, 2009.
14

---

A
Appendix
In the supplemental material:
A.1. Variables and Corresponding Meanings
A.2. Experimental Settings
A.3. Datasets
A.4. Hyperparameter Analysis of EFB-EMVC
A.5. Individuals Used in Ablation Experiment
A.1 Variables and Corresponding Meanings
To help readers understand the content of this paper more clearly, this section provides a detailed orga- nization and explanation of the variable symbols involved in the paper, with the specific corresponding relationships shown in Table
Table 6: Variable names and their corresponding meanings
Variables
Meaning
The number of categories
The e-th category
The w-th view
t
The target category
bc
The number of samples assigned to the e-th category by the teacher model
The number views contained the MVM
X
The feature matrix of the e-th category in the v-th view
K
The kernel matrix of the e-th category in the w-th view
M.
The mutual information matrix of the w-th view
M.
The mutual information matrix the v-th view after masking the target category
K
The kernel matrix in the Sinkhorn algorithm
HSIC(KS, K3)
The HSIC score between the 4--th and cy-th category in the u-th view
2T
The logits output of the evolutionary navigator
The logits output of the view branch
27
The logits of the evolutionary navigator after masking the target category
The logits of the view branch after masking the target category
pd
The probability distribution of the evolutionary navigator
The probability distribution the view branch
The probability distribution of the evolutionary navigator after masking the target category
ps
The probability distribution of the view branch after masking the target category
The regularization parameter
U.
The iteration matrix
y²
The optimal transport plan
A.2 Experimental Settings
In our experiments, all methods are implemented using TensorFlow 2..0... The computing environ- ment includes Ubuntu 24.04.2 LTS the operating system, equipped with an AMD EPYC processor with 160 physical cores (320 logical threads), 566 GB of DDR4 memory, and 8 NVIDIA GeForce RTX 5090 GPUs, each with 32 GB of VRAM. The experimental setup based on Python 3.9.23 and CUDA 11.2.
Parameter settings:
a) Training multi-view model (MVM): All MVM are trained using the Adam algorithm. The learning rate is set to 0.001, with first-moment exponential decay rate of 0.9 and second-moment moment
15

---

exponential decay rate of 0.999. Each network undergoes training for 200 epochs. To prevent overfitting, if the performance of MVM does not improve after 10 epochs, the training process will be halted.
b) EFB-EMVC Algorithm: Inspired by the work of EDF(7), we set the population size to 28, the number of iteration rounds to 20, the crossover rate to 0.9, and the mutation rate to 0.2. For the MVoxCeleb [16] and CB 77 datasets, especially the CB dataset with up to 10,000 categories, directly applying our proposed LENT, loss function will lead to an excessively large dimension of the mutual information matrix, resulting in the program being unable to run. In the ablation study section, we have fully verified the key role of cross category information in the distillation process. To facilitate code reproduction. we use the traditional KL divergence loss instead of ENNL L on these two datasets to ensure the executability of the method and the stability of the experiment. In addition, for the MM-IMDB 22 dataset- -a a multi-label and multi-category dataset- - the application of the LENZ loss function may cause numerical instability during the optimization process due to potential dimension mismatch issues of the mutual information matrix. To address this issue, we still use the traditional KL divergence to replace the ENNE loss function. To facilitate the experiment, only the following simplified settings are made for the weights of the loss function: The weight of the fusion output, 71, is set to 1.0xV, where V represents the number of views of the current individual. For datasets using the ÉENL L loss function, the output weight of each view, Y2. is set to 1.0. For the cross- cross-entropy loss between EN and the view branch the target category, the parameter is set to 1.0; for the Wasserstein distance between their output distributions on non- target categories, the parameter f is set to 0.3. In addition, for datasets using KL divergence, the weight of each view is directly set to 1.0. The temperature coefficient is uniformly set to 1=2..
A.3 Datasets
All used datasets in our paper can be downloaded from the Neurips- 2025-EFB-EMVC
MVoxCeleb 16 is a multi-view audio classification dataset that is constructed with Vox-
Celeb dataset [53] Each audio are extracted five view features and they are two deep feature including ecapa and resnet, and three traditional features including fbank, mfce and spec. To study aim, Gaussian noise is added on ecapa and resnet mfcc. On this dataset, the specific parameter configuration of our EFB- method is as follows: the fusion view dimension to 128 and the reuse of view features is not allowed.
The dataset includes 3,425 videos of 1,595 different people downloded from YouTube. Similar to, the same five features are extracted. The parameter configuration of the dataset is as follows: the fusion view dimension to 1 128, and the reuse of view features is not allowed.
YouTube-Facees 19.
subset consists of 101,499 frames of 31 subjects and
NUS-WIDE-128 (NUS) [20]. NUS dataset contains 43,800 single label images from 128 categories. For each image, six types of image features including color histogram (CH), color correlogram (CORR), edge direction histogram (EDH), wavelet texture (WT), block- wise color moments (CM) and bag of words based on SIFT descriptions (BoW), and one text feature are extracted. The dataset extended from the NUS- WUDE dataset [54]. In our experiments, we use its a subset consisting of 23,438 images from 10 category, including animal, architecture, art, flowers, food, man, person, sky, toy, and water. In this subset, each image is related to one label and each category includes at least 1,500 images. For the EFB-EMVC evolutionary algorithm parameters, the fusion view dimension to 128, and the reuse of view features is not allowed.
Reuters 21 Reuters is multilingual multi-view dataset, each document is described
by five different languages including English, French, German, Spanish and Italian. To make used model can work on this data, the dimensions of all views are reduced to 1,000 using PCA. Then, following, Gaussian noise is added to all views or 3 views for obtaining its two versions, named Reuters5 [T6] and Reuters3 [6). respectively. The parameter configuration of the dataset is as follows: the fusion view dimensions are set to 128, and the reuse of view features is not allowed.
CB 77. CB dataset designed for chemical structure image recognition in patent retrieval studies, which contains 100,000 chemical structure images distributed into 10,000 categories.
16

---

Among them, the specific experimental parameter settings are as follows: the fusion view dimension 256, and the reuse of view features is not allowed.
MM-IMDB 22
MM-IMDB dataset for the multi-label film genre classification task, which contains a total of 23 categories. The dataset is divided into a training set of 13,552 films, validation set of 2,608 films, and test of 7,799 films. To ensure fair comparison with other explicitly multi-view fusion approaches, we adopted the same neural network backbone models as BM-NAS and DC-NAS to extract various view features, using weighted FI score as the evaluation metric. The specific parameter settings are as follows: fusion vector dimension FD is 128, and the reuse of view features not allowed.
NTU 23 NTU dataset for multi-view action recognition task containing 60 categories. The training, validation and test sets include 23,766 23,760, 2,519 and 16,558 samples, respectively. To ensure the fairness of the experimental results, followed the data preprocessing pipelines of BM-NAS and DC-NAS. Specifically, we used Inflated ResNet-50 and Co-occurrence feature extractors for the skeleton and video views. For the EFB-EMVC evolutionary algorithm parameters, the fusion view dimension to 1024, and the reuse of view features is allowed.
Ego [24] Ego dataset for multi- view gesture recognition task containing 83 categories. The training set of this dataset includes 14,416 samples, the validation set includes 4,768 samples, and the test includes 4,977 samples. We followed the methods of BM-NAS and DC-NAS, using ResNext- as the backbone network for RGB and depth video views. For the EFB-EMVC evolutionary algorithm parameters, the fusion view dimension 512, and the reuse of view features is not allowed.
A.4 Hyperparameter Analysis of EFB-EMVC
Impact Analysis of the fusion dimension on EFB-EMVC. In this experiment, selected the YoutubeFace and NUS datasets to investigate the impact of fusion view dimension on the performance of the EFB-EMVC method. Specifically, we first randomly selected 15 individuals population. Subsequently, within the framework of this fixed initial population, we independently validated the performance of the model when the fusion view dimension was set to 32, 64, 128, 256, and 512 respectively. Experimental results were quantitatively presented using the average performance and maximum performance of the fixed initial population, as shown in Figure It can be observed that on the YoutubeFace dataset, as the fusion dimension increases, the performance of the model shows a trend of continuous improvement and tends to stabilize at high dimensions; whereas on the NUS dataset, increasing the dimension does not bring significant benefits. The above results indicate that the impact of fusion dimension on the performance of the model exhibits dataset dependence: for datasets with higher representation complexity, higher dimensions can effectively enhance feature representation capability, while on datasets with more information redundancy, the benefits of blindly increasing dimensions are limited.
fixed initial
A.5 Individuals Used in Ablation Experiment
In this section, we will list in detail the individuals used the ablation experiment part. Specifically, in Table 7 the left side shows the sample set of the EN ablation experiment, and the right side shows the sample set of the ENL ablation experiment.
17

---

(a) YoutubaFace Nean
(b) YoutubaFace Maximum
Hian
Marmun
60
22
338
226
312
32
128
256
(c) NUS Mean
(4) NUS Maximum
15.5
7..
40.4
752
Figure 4: Mean and maximum value variations with integrate the view dimension (FD) on Youtube- Face and NUS datasets
Table 7: The set of individuals used in the ablation experiment
EN
ENL
[4.0.2.3,-0-11--00
[4,0,4]
(0,2.3.4.-2,-3--0
[1,0,-2]
[2,4,-4]
[4,1,1,-0,-2]
14.3,0,1,,,-1,11,222,
10,0,-3,2,1,,33-31
10.2.443311,1122-33-)2
[4.4.1,11-0,-1.-1]]
[3,4,-3]
2.4.2,1.-1,-33001
[1..33.0,2.1,,4222223
(3,44444112224433.000
(1,0,4,2,4,,2.-22
2.2.44.0.3.0.....0..333
[0,3,44
0.1111.22-11.22-11..2
[0,4,3,-4--0]
220-0.2.333300000-----2
[3,2,4,-3-41
0.444.4-142-000--
(3,4,0,2,-0,2,-33
4.4.2,2,11,003333
[1,4.2,-4-22]
[14.2,1100,22.-31
[3,2,-1]
[4,1,-3]
[1,4,11
[2.4.0,-0.-]]
18

---

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
Justification:
The abstract and introduction have clearly identified the contribution of this paper as introducing evolutionary navigators for each multi-view model to address the fitness evaluation bias problem. Experimental results fully demonstrate the effectiveness of our proposed method, and evolutionary navigators can be seamlessly integrated into other evolutionary multi-view classification methods, demonstrating their strong compatibility. See section 4.2 for details.
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 other settings.
is fine include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: Yes
Justification: This paper elaborates on the limitation of high training costs in the section 5
and mentions that optimization techniques will be considered in future work to reduce training costs.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors encouraged to create separate "I "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results 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 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 of 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 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 to not penalize honesty concerning limitations.
19

---

3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: Yes
Justification: This paper provides detailed explanations for all the formulas involved.
Guidelines:
The answer NA means that the paper does 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 the statement of any theorems.
The proof' can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proof's provided in appendix 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 ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: Yes
Justification: In Appendix A.2 and Appendix A.3 this paper elaborates on details such as the datasets used, the acquisition method for each dataset, the preprocessing workflow for each dataset, the specific values of all hyperparameters applied to each dataset, the network training approach, and the selection of optimizers. Additionally, section [4.] provides detailed description of the five-fold cross-validation method employed in the experiments, while section 4.2 thoroughly outlines the comparative methods involved. Through the above descriptions, the experimental results can be fully reproduced. 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 to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, descríbing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided instructions for how to replicate the results, access to a hosted model (e.g.. in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
detailed
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 nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.
(b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution a new model (e.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-source dataset instructions for how to construct the dataset).
20

---

(d)
We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to 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 to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: Yes
Justification:
We will release the code and data with sufffcient instructions.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (nttps://nips.co cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is 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 exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
/ //nips.co... ctailss.c/pubbbicguuu..u httpa///guiideee/eeeubbbbiiiii
wwt.subbiissooooooooooooooo for more details.
The authors should provide instructions on data access and preparation, including how 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 are reproducible, they 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 as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is 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: All implementation details were provided in Appendix A.2 Appendix A.3 and
section 4.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented the core the paper to 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: this paper, to avoid the randomness caused by data partitioning and network initialization, we adopt five-fold cross-validation strategy across all datasets. The experi- mental results are presented in the form of mean values and standard deviations, Details can be found in section 4.1
21

---

Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by enror bars, confi-
dence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
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 or the standard error of the mean.
is OK to report I-sigma error bars, but one should state it. The authors should preferably report a 2 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 range (e.g. negative етгог rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables 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 reproduce the experiments?
Question:
Answer: No
This paper provides detailed explanations of the types of computing devices, memory, and storage information used in the experiments, include relevant computation time. This is because the focus of this paper is on addressing the fitness evaluation bias problem rather than accelerating the process.
Justification:
Appendix [A.2] but does not
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, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported the paper (e.g., preliminary or failed experiments that didn't 't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics https: htttlosssttttt://// httpp//pp......pp.p...ecccccaaad
Answer:
Yes
Justification:
We have checked the NeurlPS code ethics for our paper.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require a deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
22

---

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: Yes
Justification: The work in this paper enhances the accuracy and generalization of evolution- ary multi-view classification methods in specific societal applications, including chemical structure recognition and medical image classification.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact why the paper does address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.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 a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an 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 to 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.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: NA
Justification: Our paper poses such risks.
Guidelines:
The answer NA means that the paper poses no 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 a 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: Yes
Justification: The assets (datasets, code, models) used the paper are open source, and our use follows the relevant protocols.
23

---

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 or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g.. CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if 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: Yes
Justification:
Documentation will be provided alongside the released code.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create 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 applicablle as well as details about compensation (if any)?
Answer: NA
Justification: Our paper doesn't involve the crowdsoureing experiments and research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing 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 the NeurIPS Code of Bthies, 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:
Our paper does not involve crowdsourcing nor research with human subjectss.
Guidelines:
The answer NA means that the paper does involve crowdsourcing nor research with
human subjects.
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 NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it 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.
Answer: NA
Justification: The core method development in this research does not involve LLMs as any important, original, or non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not non non- stanstandard components.
involve LLMs as any important, original,
Please refer to our LLM policy for what should or should not be described.
25


Reviews:
[{"review_id": "xzgTHlUlzB", "reviewer": "Reviewer_MP9p", "summary": "This paper innovatively identifies a key limitation in evolutionary multi-view classification (EMVC): due to significant differences in information content across views, multi-view models (MVMs) using uniform training objectives fail to achieve optimal convergence performance, termed the \"fitness evaluation bias (FEB) problem\". It systematically expounds the impact of this problem on the entire evolutionary process. To address this, the authors propose an evolutionary multi-view classification via eliminating individual fitness bias approach (EFB-EMVC), which uses an evolutionary navigators mechanism to partition knowledge distillation (KD) into intra-class and inter-class distillation for full utilization of information from each view. Experiments on numerous benchmark datasets validate the effectiveness of EFB-EMVC. Meanwhile, evolutionary navigators serve as a flexible plug-and-play module, enabling seamless integration into various methods.", "questions": "In Section A.2 of the supplementary materials, I noticed that the proposed method was applied with only 5 iterations of population evolution on the MVoxCeleb dataset, whereas the baseline method TEF was trained with 20 iterations. According to the experimental results in Table 1 of the main paper, the proposed method achieves a 1.94% performance improvement while using only about one-fifth of the iteration budget compared to TEF. This raises an interesting question: if the proposed method were also trained for 20 iterations, would its performance continue to improve significantly, or has it already converged and stabilized around 94.35% after 5 iterations? I suggest the authors further analyze or provide additional evidence to clarify this point, which would help strengthen the validation of their method’s effectiveness.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1）\tThe paper is rich in content and solid in argumentation, with smooth and accessible writing, comprehensive experiments, and in-depth analysis. In particular, Table 3 in the paper shows the performance rankings of 15 individuals before and after applying evolutionary navigators, along with extremely low correlation coefficients. These experimental results fully validate the existence of the FEB problem in the field of EMVC and the effectiveness of the proposed method.\n2）\tThe paper's diagrams are clearly structured. The EMVC process and method framework in Figure 2 accurately convey the authors' intentions, making it easy to understand how each module interacts.\n3）\tI have reviewed the supplementary materials. The paper provides very sufficient details for the experimental part, including the experimental environment, training methods, hyperparameter selection, selected datasets, etc.\n\nWeaknesses:\n1）\tIn Section A.2 of the supplementary materials, I noticed that the proposed method was applied with only 5 iterations of population evolution on the MVoxCeleb dataset, whereas the baseline method TEF was trained with 20 iterations. According to the experimental results in Table 1 of the main paper, the proposed method achieves a 1.94% performance improvement while using only about one-fifth of the iteration budget compared to TEF. This raises an interesting question: if the proposed method were also trained for 20 iterations, would its performance continue to improve significantly, or has it already converged and stabilized around 94.35% after 5 iterations? I suggest the authors further analyze or provide additional evidence to clarify this point, which would help strengthen the validation of their method’s effectiveness.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate your positive recognition and constructive feedback on our work. We are truly pleased to see that you acknowledge the fitness evaluation bias (FEB) problem we proposed and our solution strategy, as well as your high appreciation for our experimental design and analysis.\n\n**Q1: If the proposed method were also trained for 20 iterations, would its performance continue to improve significantly, or has it already converged and stabilized around 94.35% after 5 iterations?**\n\nA1: To more comprehensively verify the convergence behavior of our method on the MVoxCeleb dataset, we take the first fold of data as an example. We set the maximum number of iterations to $T$ = 20 and record the model's best performance at $T$ = 5, 10, 15, and 20, to illustrate the trend of performance improvement as the number of iterations increases.\n\nAs mentioned in our supplementary material, we also adopted a smaller number of iterations on the YouTubeFace and Reuters5 datasets. To further demonstrate the convergence trend of our method across different datasets, we additionally conducted experiments on these two datasets, again setting the maximum number of iterations to $T$ = 20 and recording the best performance at $T$ = 5, 10, 15, and 20. The corresponding experimental results are shown in Table (1).\n\nThe results indicate that our proposed EFB-EMVC method demonstrates a steady performance improvement on the MVoxCeleb dataset from $T$=5 to $T$=15, reaching its peak at $T$=15 and stabilizing thereafter. **This suggests that the model has essentially converged by the 15th iteration on this dataset**.\nIn contrast, on the YouTubeFace and Reuters5 datasets, the model's performance continues to improve throughout the entire iteration process, showing no clear signs of convergence.\n\nThis phenomenon indicates that the EFB-EMVC method exhibits varying sensitivity to the number of iterations across different datasets. Nevertheless, the overall trend suggests that appropriately increasing the number of iterations allows the algorithm to more thoroughly explore the solution space, thereby improving the likelihood of obtaining a global or near-optimal solution and ultimately enhancing model performance.\n\n**Table(1) : Classification accuracy (%) of EFB-EMVC under different iteration rounds $T$.**\n| Dataset      | $T$=5 | $T$=10 | $T$=15 | $T$=20 |\n|--------------|-------|--------|--------|--------|\n| MVoxCeleb    | 94.30 | 94.40     | 94.78     | 94.78     |\n| YouTubeFace  | 87.51    | 87.98     | 88.19     | 88.51     |\n| Reuters5     | 83.59 | 84.02  | 84.36  | 85.05  |\n\nWe once again sincerely thank you for your professional review and insightful comments. Regarding the performance trend of EFB-EMVC under different numbers of iterations, we will include the relevant experiments in the revised version to further strengthen the validation of our method's effectiveness and provide a clearer direction for future research."}, {"review_id": "MV24Uah5cy", "reviewer": "Reviewer_gxm7", "summary": "This paper first discovers the \"fitness evaluation bias (FEB) problem\" in the current evolutionary multi-view classification (EMVC). The problem is manifested in that existing EMVC methods all adopt a joint training strategy, leading to insufficient utilization of low-information content view information in the multi-view model (MVM). As a result, the MVM fails to reach its performance limit when converging. Subsequently, the authors propose an evolutionary navigators mechanism based on intra-class and inter-class distillation. This mechanism can fully utilize the information of each view while ensuring the overall training direction of the model. Experimental results show that this method outperforms various state-of-the-art (SOTA) methods on all datasets, and the proposed evolutionary navigators mechanism can be well integrated into various methods to achieve significant performance improvements.", "questions": "Please see Weaknesses.", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1）\tThe method proposed in the paper effectively reveals and solves the FEB problem in current EMVC (as shown in Figure 1 and Table 3), which will become an important approach to promote the development of this field.\n2）\tThe experiments are very comprehensive, covering various SOTA methods, including but not limited to trustworthy multi-view classification methods, traditional adaptive multi-view classification methods, and EMVC methods, etc. The authors also elaborate in detail the reasons for selecting each category of comparative methods and the suboptimal performance of the corresponding methods. Meanwhile, the authors provide evidence support for the strong adaptability of evolutionary navigators through detailed experimental results (as shown in Table 4).\n3）\tReading this paper has provided me with very valuable insights into the limitations of the EMVC field and the corresponding solutions.\nWeaknesses：\n1）As mentioned in the paper, evolutionary navigators are introduced into the MVM to fully utilize the information of each view and solve the FEB problem. I have reviewed the experimental section and supplementary materials of the paper. Although the authors have conducted relatively comprehensive experiments with broad coverage, they have not reported the accuracy of the pretrained teacher models for each view on the respective datasets. I suggest the authors include this information in the revision to enhance the interpretability and credibility of the experimental results.\n2） Moreover, the paper uses well known public datasets such as MVoxCeleb, YoutubeFace, NUS-WIDE-128, Reuters, CB, MM-IMDB, NTU RGBD, and EgoGesture. These datasets are suitable for the multi-view classification task, but it should be mentioned if any preprocessing was performed, as it may affect the results.\nOverall, although there are some weaknesses in the paper, I am still happy to see that this paper proposes a new task in EMVC, called eliminating individual fitness bias, which might lead to some future works. Besides this, I also think that the proposed individual fitness bias elimination strategy would have a positive impact on the existing EMVCs. Thus, I tend to accept it.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for your careful review and high praise of our paper. We are glad to see that you recognize our work’s positive contribution in identifying and addressing key issues in the evolutionary multi-view classification (EMVC) field, and we also appreciate your acknowledgment of the comprehensiveness of our experimental design.\n\n**Q1: As mentioned in the paper, evolutionary navigators are introduced into the multi-view model (MVM) to fully utilize the information of each view and solve the fitness evaluation bias (FEB) problem. I have reviewed the experimental section and supplementary materials of the paper. Although the authors have conducted relatively comprehensive experiments with broad coverage, they have not reported the accuracy of the pretrained teacher models for each view on the respective datasets. I suggest the authors include this information in the revision to enhance the interpretability and credibility of the experimental results.**\n\nA1: For each of the nine multi-view datasets, we pretrained a separate teacher model for each individual view to ensure reliable knowledge transfer. The architecture of the teacher model is consistent with the single-view encoder used in the multi-view model, specifically consisting of two fully connected layers. The output layer employs a softmax function to produce a predicted probability distribution, and the model is trained using the cross-entropy loss function.\nFor the MVoxCeleb, YouTubeFace, Reuters5, Reuters3, and NUS datasets, we adopted a five-fold cross-validation strategy and reported the final accuracy of the pretrained teacher models in the format of “mean ± standard deviation.”\nFor the MM-IMDB, NTU RGB-D, EgoGesture, and CB datasets, we followed the experimental setup of DC-NAS, conducting five independent runs using predefined train-test splits for each view. The results are likewise reported in the format of “mean ± standard deviation.”\nThe corresponding experimental results are summarized in Table 1. In the revised version of the paper, we will additionally include the accuracy of the pretrained teacher models for each dataset to enhance the transparency and interpretability of our results.\n\n**Table(1) : Accuracy of the pretrained teacher models for each view on the nine multi-view datasets.**\n\n| Dataset    | $V_0$ Acc           | $V_1$ Acc           | $V_2$ Acc           | $V_3$ Acc           | $V_4$ Acc           | $V_5$ Acc           | $V_6$ Acc           | $V_7$ Acc           | $V_8$ Acc           | $V_9$ Acc           |\n|-------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|\n| MVoxCeleb  | 71.54 ± 0.26     | 75.56 ± 0.57     | 26.71 ± 0.44     | 53.39 ± 0.64     | 28.33 ± 0.77     |                 |                 |                |                 |                 |\n| YoutubeFace| 27.03 ± 0.06     | 78.48 ± 0.29     | 32.49 ± 0.41     | 79.81 ± 0.41     | 70.45 ± 0.36     |                 |                 |                 |                 |                 |\n| Reuters5    | 39.63 ± 0.12     | 37.51 ± 0.33     | 57.55 ± 0.27     | 66.95 ± 0.21     | 82.31± 0.25     |                 |                 |                |                 |                 |\n| Reuters3   | 39.70 ± 0.21     | 37.78 ± 0.14    | 57.55 ± 0.19     | 85.01 ± 0.11    | 84.40 ± 0.06    |                 |                 |                 |                 |                 |\n| MM-IMDB    | 44.63 ± 0.14     | 45.14 ± 0.27     | 44.54 ± 0.12     | 44.43 ± 0.31     | 61.25 ± 0.11     | 61.12 ± 0.18     |                 |                 |                 |                 |\n| NUS         | 36.59 ± 0.47     | 37.21 ± 0.35     | 38.95 ± 0.54     | 29.74 ± 0.59    | 33.67 ± 0.79     | 37.49 ± 0.38     | 69.15 ± 0.45     |                 |                |                 |\n| NTU RGB-D    | 71.11 ± 0.22     | 81.94 ± 0.17     | 83.90 ± 0.13     | 84.29 ± 0.17     | 34.98 ± 0.52     | 70.50 ± 0.25     | 80.69 ± 0.28     | 83.20 ± 0.11     |                 |                 |\n| EgoGesture   | 72.46 ± 0.28     | 92.38 ± 0.27     | 93.25 ± 0.09     | 93.07 ± 0.13     | 69.55 ± 0.31     | 92.69 ± 0.14     | 93.66 ± 0.12     | 93.58 ± 0.08     |                 |                 |\n| CB           | 65.59 ± 0.28     | 74.63 ± 0.31     | 70.61 ± 0.27     | 72.48 ± 0.30     | 76.57 ± 0.20     | 67.57 ± 0.29     | 67.32 ± 0.14     | 77.28 ± 0.13     | 75.80 ± 0.10     | 71.68 ± 0.32     |\n\n\n\n\n\n\n**Q2: The paper uses well known public datasets such as MVoxCeleb, YoutubeFace, NUS-WIDE-128, Reuters, CB, MM-IMDB, NTU RGBD, and EgoGesture. These datasets are suitable for the multi-view classification task, but it should be mentioned if any preprocessing was performed, as it may affect the results.**\n\nA2: **None** of the nine multi-view datasets used in our experiments underwent any additional preprocessing. All data were loaded strictly according to the original dataset formats used by the corresponding baseline methods, ensuring fairness and reproducibility of the experimental comparisons.\n\nThank you once again for your valuable suggestions regarding critical details such as the accuracy of the teacher models and dataset preprocessing. We will carefully consider and address these points in the manuscript revision to further enhance the credibility and persuasiveness of our experimental results. We sincerely appreciate your recognition and support of our research."}, {"review_id": "guMly1qESa", "reviewer": "Reviewer_9NF9", "summary": "This paper proposes a novel knowledge distillation (KD) mechanism called evolutionary navigators (ENs), aiming to address the fitness evaluation bias (FEB) problem in evolutionary multi-view classification (EMVC). The method demonstrates outstanding performance on various datasets. Notably, ENs serve as a flexible plug-in that can be integrated into different approaches to achieve significant performance improvements.", "questions": "See weaknesses.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The claims proposed in the paper are supported by clear and persuasive evidence.\n2. The method proposed in the paper and its evaluation criteria are highly compatible with the research questions and application scenarios.\n3. The experimental design and analysis in the paper are highly reasonable and effective. In the ablation experiments, the authors systematically removed or modified different components of EFC-EMVC (such as ENs, KL divergence, and WDK loss function). This design effectively evaluates the impact of each module on overall performance, clearly addressing the question of their individual contributions. \n4. This paper first identifies the FEB problem in EMVC and proposes a highly effective solution from this perspective. The method is expected to promote the development of the EMVC field.\n\nWeaknesses:\n1. In the hyperparameter analysis section of the supplementary materials, the paper analyzes the impact of different view fusion dimensions on performance. However, hyperparameters such as batch size also affect model performance, and I hope to see detailed information on how such hyperparameters influence performance.\n2. There are some missing details. For example, in line 133, the novel distillation loss function proposed by the author is named \"WDK\", and the ablation experiment on the right side of Figure 3 also ablates \"WDK\". However, in Table 5 of the appendix, the distillation loss function is \"WDT\". If this is a typo, it is recommended to rewrite it. If they are two different loss functions, it is suggested to provide more explanations.\n3. Some sentences in the paper have incomplete semantics or unclear expressions. For example, the part about feature matrix construction in lines 117-120. The term \"feature vector\" is somewhat ambiguous. In this context, it is unclear which part of the output result the \"feature vector\" specifically refers to.", "was_revised": true, "final_justification": "My initial review was generally correct, and the authors addressed my concerns well, so I am leaving my original score unchanged.", "rebuttal": "We sincerely appreciate your positive evaluation of our work. We are delighted that you recognize our introduction of the “fitness evaluation bias (FEB)” problem for the first time in the context of evolutionary multi-view classification (EMVC), and that you acknowledge the effectiveness of the proposed evolutionary navigators (ENs) in enhancing multi-view classification performance. We are also deeply grateful for your recognition of the soundness of our experimental design and the depth of our analysis, particularly the dissection of each module’s individual contribution through the ablation studies.\n\n**Q1: In the hyperparameter analysis section of the supplementary materials, the paper analyzes the impact of different view fusion dimensions on performance. However, hyperparameters such as batch size also affect model performance, and I hope to see detailed information on how such hyperparameters influence performance.**\n\nA1: To more comprehensively analyze the impact of hyperparameters (such as batch size) on the performance of EFB-EMVC, we conducted additional experiments using the NUS dataset as an example. We first randomly initialized a fixed population consisting of 15 individuals and examined the influence of hyperparameters on model performance within this fixed population. The experimental results are quantitatively presented using the population’s average performance (Avg) and the best individual performance (Max) as metrics. Besides batch size, we further analyzed the effects of epoch and patience on model performance to gain deeper insights into the model behavior.\n\n**① Batch Size:**\n\nThe related results are summarized in Table (1). The results show that both Avg and Max performance exhibit a rising-then-falling trend, with both reaching their peak at a batch size of 256. Our analysis is as follows:\n1) A small batch size (e.g., 32) allows MVM to see only very few samples at a time, resulting in unstable training and difficulty fitting the true distribution;\n\n2) A moderate batch size (e.g., 256) provides enough samples to represent the overall distribution while avoiding local optima, leading to more stable training;\n\n3) An excessively large batch size (e.g., 1024), although representative of the true distribution, tends to fall into sharp minima, which harms generalization ability.\n\nIn our main experiments, a unified batch size of 512 was used across all datasets.\n\n**Table(1) : Batch Size Impact on EFB-EMVC Performance (Avg and Max Accuracy)**\n| Batch Size| 32  | 64  | 128 | 256 | 512 | 1024 |\n|--------|-----|-----|-----|-----|-----|------|\n| Avg    | 65.03  | 65.62  | 66.27  | 66.65  | 66.59  | 66.23   |\n| Max    | 73.18  | 73.95  | 74.53  |74.89  | 74.85  | 74.85   |\n\n\n**② Epoch:**\n\nThe relevant results are shown in Table (2). We observe that the Avg performance remains relatively stable, while the Max performance shows slight fluctuations, which can be attributed to the randomness in network initialization. Given the limited potential for further performance improvement, we hypothesize that most individuals have already converged before epoch 50. To verify this assumption, we further examined the convergence behavior of 15 individuals at epoch=50. The results, presented in Table (3), indicate that all individuals indeed completed convergence before 50 epochs, thereby confirming our hypothesis. \nIn the main experiments, we uniformly set the number of training epochs to 200. Thanks to the adoption of an early stopping strategy with a patience of 10, this setting not only prevents excessive resource consumption but also effectively mitigates overfitting.\n\n**Table(2) : Epoch Impact on EFB-EMVC Performance (Avg and Max Accuracy)**\n| Epoch | 50  | 100  | 150 | 200 |\n|--------|-----|-----|-----|-----|\n| Avg    | 66.57  | 66.66  | 66.66  | 66.59  |\n| Max    | 75.53  | 75.36  | 75.34  |74.85  |\n\n**Table(3) : Distribution of Convergence Epochs for 15 Individuals**\n| Individual | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10 | 11 | 12 | 13 | 14 | 15 |\n|------------|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|\n| Epoch      | 25 | 27 | 25 | 30 | 35 | 45 | 22 | 23 | 24 | 27 | 29 | 23 | 29 | 23 | 39 |\n\n\n**③ Patience:**\n\nThe related results are summarized in Table (4). Both Avg and Max improved as patience increased, with more noticeable gains when increasing patience from 10 to 20, but limited improvement from 40 to 50. We believe that moderately increasing patience helps the model achieve better solutions, but excessive training may lead to overfitting in MVM. Balancing efficiency and performance, we adopted a uniform patience of 10 across all datasets.\n\n**Table(4) : Patience Impact on EFB-EMVC Performance (Avg and Max Accuracy)**\n| Patience | 10  | 20  | 30 |40 |50 |\n|--------|-----|-----|-----|-----|-----|\n| Avg    | 66.59  | 66.68  | 66.74  | 66.77  |66.78  |\n| Max    | 74.85  | 75.25  | 75.51  |77.53  |75.56  |\n\n\n**Q2:There are some missing details. For example, in line 133, the novel distillation loss function proposed by the author is named \"WDK\", and the ablation experiment on the right side of Figure 3 also ablates \"WDK\". However, in Table 5 of the appendix, the distillation loss function is \"WDT\". If this is a typo, it is recommended to rewrite it. If they are two different loss functions, it is suggested to provide more explanations.**\n\nA2: Thank you for pointing out the inconsistency in naming. We confirm that this was a typographical error: it should be “WDK,” but it was mistakenly written as “WDT” in Appendix Table 5. We will correct and unify the term to “WDK” in the revised version to eliminate any ambiguity.\n\n**Q3: Some sentences in the paper have incomplete semantics or unclear expressions. For example, the part about feature matrix construction in lines 117-120. The term \"feature vector\" is somewhat ambiguous. In this context, it is unclear which part of the output result the \"feature vector\" specifically refers to.**\n\nA3: In lines 117–120, our approach is to input the data of the $i$-th view into the pretrained teacher model for that view and extract the logits before the softmax layer as the feature vector. Therefore, **the term “feature vector” here specifically refers to the logits output by the teacher model**.\n\nWe sincerely appreciate your valuable comments regarding hyperparameter settings, consistency in terminology, and clarity of expression. In the revised manuscript, we will include additional experiments to analyze the impact of such hyperparameters on model performance, standardize relevant terminology, and refine the corresponding descriptions to enhance accuracy and clarity. Once again, thank you for your thorough review and constructive suggestions, which are of great significance in improving the quality of our paper."}, {"review_id": "UQv2zgHX0I", "reviewer": "Reviewer_zTdX", "summary": "This paper proposes an evolutionary multi-view classification via eliminating individual fitness bias approach (EFB-EMVC). By introducing the evolutionary navigators mechanism, it realizes the migration of rich intra-class and cross-class information from the pre-trained teacher model to the view branches of the multi-view model (MVM), addressing the fitness evaluation bias (FEB) problem that has not been previously concerned in the evolutionary multi-view classification (EMVC) task. Experimental results show that the method proposed in this paper achieves optimal experimental results compared with various state-of-the-art (SOTA) methods. In the ablation experiment section, detailed and reasonable experimental settings and data verification demonstrate that this method effectively solves the FEB problem.", "questions": "1. In Figure 1 of the paper, the performance curves of View 4 under three different scenarios are presented. Among them, \"V4 only\" refers to the pre-trained teacher model of View 4, and its pre-training method can be clarified according to the content shown in Figure 2 (b). However, there are still questions regarding the determination methods of the performance curves of View 4 in \"V4 in MVM\" and \"V4 with EN\". It is recommended to supplement the relevant details.\n2. Compared to Table 1, Table 2 show that the proposed method has the limited improvement, it is necessary to provide more deep discussion. \n3. Table 3 shows the rank relationship between with-En and without-EN, it is very key for showing the necessary of the individual fitness bias elimination. So, it is suggested to add the detailed formulations of PC, SPC and KT, and give the association criterion.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "My comments on the strengths are:\n1. I verified the relevant steps of extracting rich cross-class information from the pre-trained teacher model by constructing a progressive matrix, and implementing knowledge transfer of cross-class information through a Wasserstein distance (WD)-guided loss function. Overall, the logic is reliable.\n2. I reviewed the experimental design and performance report. The overall setup is reasonable.\n3. This study first bridges EMVC and knowledge distillation (KD), overcoming the FEB problem that has not been addressed in the EMVC field before. The novel \"evolutionary navigators\" mechanism achieves effective improvement in KD performance, realizing cutting-edge accuracy in complex and unknown multi-view scenarios.\n4. In numerous complex multi-view datasets, this method achieves performance improvements compared to cutting-edge technologies, demonstrating practical application value.\n\nMy comments on the weaknesses by seeing the questiongs.", "was_revised": true, "final_justification": "My concerns have been addressed in the author response, and I am going to raise my score, reaching the final score to 5.", "rebuttal": "We sincerely appreciate your thorough review and positive evaluation of our work. We are glad that you recognize our novel introduction of the knowledge distillation (KD) mechanism into the evolutionary multi-view classification (EMVC) task, as well as the effectiveness and practical value of our proposed evolutionary navigators (EN) mechanism in complex multi-view scenarios. At the same time, we thank you for acknowledging the soundness of our methodology, the rigor of our experimental design, and the thoroughness of our performance evaluation.\n\n**Q1: In Figure 1 of the paper, the performance curves of View 4 under three different scenarios are presented. Among them, \"V4 only\" refers to the pre-trained teacher model of View 4, and its pre-training method can be clarified according to the content shown in Figure 2 (b). However, there are still questions regarding the determination methods of the performance curves of View 4 in \"V4 in MVM\" and \"V4 with EN\". It is recommended to supplement the relevant details.**\n\nA1: In Figure 1, we present the performance curves of $V_4$ under three different scenarios: “$V_4$ only”, “$V_4$ in MVM”, and “$V_4$ with EN”. Their specific meanings and determination process are as follows:\n\n① “$V_4$ only” refers to the performance of the teacher model corresponding to this view during the pretraining stage;\n\n② “$V_4$ in MVM” represents the performance of this view when used as a branch in a conventional EMVC framework;\n\n③ “$V_4$ with EN” indicates the performance of this view as a branch in our proposed EFB-EMVC framework.\n\nThe performance curves were obtained through the following process:\n\n① Model Transfer: We extract the trained parameters of the $V_4$ branch from the final multi-view model and transfer them into a single-view neural network with an identical encoder structure;\n② Feature Extraction: We input the training and testing data of $V_4$ into this single-view network to obtain intermediate representations;\n③ Construction of the classification head network: This network consists of a fully connected layer (with output dimension equal to the number of classes) followed by a softmax layer. It takes the intermediate feature representations extracted by the single-view network as input and is trained using the standard cross-entropy loss; \n④ Performance Plotting: Classification accuracy is recorded at each training epoch to plot the performance curves of $V_4$.\n\n**Q2: Compared to Table 1, Table 2 show that the proposed method has the limited improvement, it is necessary to provide more deep discussion.**\n\nA2: The core of the EFB-EMVC method lies in addressing the issue of fitness evaluation bias (FEB), which arises from the unbalanced utilization of views in traditional MVM frameworks. The degree of variation in information content between views across different datasets directly affects the severity of the FEB problem, which in turn influences the performance gains achieved by our method.\n\nTaking the MVoxCeleb dataset from Table 1 and the NTU RGB-D dataset from Table 2 as examples, we present the classification accuracy of the pretrained teacher models corresponding to each view. The experimental results are summarized in Table(1) below. Based on these results, we draw the following conclusions:\n\n① In the MVoxCeleb dataset, the number of strong and weak views is relatively balanced. Specifically, $V_0$, $V_1$, and $V_3$ are classified as strong views, while $V_2$ and $V_4$ are weak views. During the construction of the MVM, weak views have a higher probability of being selected. However, the joint training strategy employed by MVM tends to cause the model to overly rely on strong views, neglecting the weak ones. Our proposed EN mechanism effectively alleviates this bias, leading to a significant improvement in performance; \n\n② In the NTU RGB-D dataset, strong views dominate, with only one weak view ($V_4$). Due to the large number of strong views, the probability of selecting the weak view is relatively low. Even when the weak view is selected during MVM construction, the abundant information from the strong views largely compensates for the weak view's shortcomings. Therefore, the performance improvement brought by the EN mechanism on this dataset is comparatively smaller.\n\n**Table(1) : Performance of Pre-trained Teacher Models for Each View on the MVoxCeleb and NTU RGB-D Datasets**\n| Dataset     | $V_0$ Acc           | $V_1$ Acc           | $V_2$ Acc           | $V_3$ Acc           | $V_4$ Acc           | $V_5$ Acc           | $V_6$ Acc           | $V_7$ Acc           |\n|------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|------------------|\n| MVoxCeleb  | 71.54 ± 0.26     | 75.56 ± 0.57     | 26.71 ± 0.44     | 53.39 ± 0.64     | 28.33 ± 0.77     |                |                 |                | \n| NTU RGB-D    | 71.11 ± 0.22     | 81.94 ± 0.17     | 83.90 ± 0.13     | 84.29 ± 0.17     | 34.98 ± 0.52     | 70.50 ± 0.25     | 80.69 ± 0.28     | 83.20 ± 0.11     |\n\n\nNonetheless, across all datasets, our method consistently achieves the best performance, which further demonstrates its broad applicability and effectiveness.\n\n**Q3: Table 3 shows the rank relationship between with-En and without-EN, it is very key for showing the necessary of the individual fitness bias elimination. So, it is suggested to add the detailed formulations of PC, SPC and KT, and give the association criterion.**\n\nA3: Thank you for your valuable suggestions concerning the statistical metrics used in Table 3. We fully agree that PC (Pearson Correlation Coefficient), SPC (Spearman’s Rank Correlation Coefficient), and KT (Kendall’s Tau Coefficient) play a crucial role in demonstrating the existence of the Fitness Evaluation Bias (FEB) problem and the necessity of its mitigation. To enhance the clarity and reproducibility of our paper, we will include formal definitions of these metrics in the revised manuscript.\n\n**① PC (Pearson Correlation Coefficient)**: PC measures the linear correlation between two variables. Its formula is:\n$$\\text{PC} = \\frac{\\sum_{i=1}^{n} (x_i - \\bar{x})(y_i - \\bar{y})}{\\sqrt{\\sum_{i=1}^{n} (x_i - \\bar{x})^2} \\cdot \\sqrt{\\sum_{i=1}^{n} (y_i - \\bar{y})^2}}$$\nwhere $x_i$: the value of the $i$-th observation of variable $X$; $y_i$: the value of the $i$-th observation of variable $Y$. Similarly, $\\bar{x}$ and $\\bar{y}$ denote the sample means of variables $X$ and $Y$, respectively.\n\n**② SPC (Spearman's Rank Correlation Coefficient)**: SPC measures the monotonic relationship between two ranked variables. Its formula is:\n$$\\text{SPC} = 1 - \\frac{6 \\sum_{i=1}^n d_i^2}{n(n^2 - 1)}$$ where $d_i$ is the difference in ranks of the $i$-th sample between the two rankings.\n\n**③ KT (Kendall's Tau Rank Correlation Coefficient)**: KT is based on the number of concordant and discordant pairs among all sample pairs, calculated as:\n$$\\text{KT} = \\frac{C - D}{\\sqrt{(C + D + T_x)(C + D + T_y)}}$$\nwhere:\n\n- $C$ is the number of concordant pairs;\n- $D$ is the number of discordant pairs;\n- $T_x$, $T_y$ are the numbers of ties (equal ranks) in $x$ and $y$, respectively.\n\nRegarding the “correlation discrimination criterion,” within the context of this paper, we consider that a low correlation (correlation coefficient close to 0) between the rankings with and without EN indicates a significant change in ranking caused by the introduction of EN. This suggests that the fitness evaluation is strongly influenced by EN, thereby validating the existence of FEB and its interference with the final results. Conversely, a high correlation (close to 1) would imply minimal impact of EN on fitness ranking, which contradicts our observations.\n\nIn the revised version, we will explicitly add the mathematical definitions and corresponding decision criteria for PC, SPC, and KT, provide a more detailed description of the process for plotting the performance curve of \\$V\\_4\\$, and further analyze the reasons behind the limited performance improvement observed in Table 2.\nWe sincerely thank you once again for your thorough and insightful review comments, which are invaluable for the further refinement of our paper."}, {"review_id": "92JBy66szz", "reviewer": "Reviewer_iYFx", "summary": "The paper proposes a novel approach for evolutionary multi-view classification (EMVC). It highlights that existing EMVC methods suffer from fitness evaluation bias, primarily due to significant differences in the information content among views, resulting in the model not to achieve optimal performance when converging. To address this issue, the authors introduce evolutionary navigators for each multi-view for calibrating the evolutionary direction in real time. This approach demonstrates superior performance across nine multi-view datasets.", "questions": "(1) How do the crossover and mutation operators work? More details are necessary to the readers that do not very familiar with this topic.\n\n(2) How are the hyper-parameters of compared baselines set?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "***Strengths***\n\n(1) The paper presents an important and novel problem—fitness evaluation bias (FEB)—which has not been previously explored in the community of the EMVCs.\n(2) The paper is well-structured with logic flow and nice graph illustrations. For instance, Figure 1 clearly differentiates the existing EMVC methods and the proposed EFB-EMVC.\n(3) The experiments are well-designed and comprehensive, comparing the EFB-EMVC with four kinds of strong SOTA baselines on popular benchmark datasets. Analysis and experiment results also provide inspiring viewpoint.\n\n***Weaknesses***\n\nI find this work well-organized and convincing, with no apparent shortcomings. One thing I can suggest is to provide more descriptions for crossover and mutation (Line 202), and the compared baselines (Line 233). Int this version, they are too simple, which brings difficulty to the readers that do not very familiar with this topic.", "was_revised": true, "final_justification": "All my questions have been addressed. I keep the rating for acceptance.", "rebuttal": "We sincerely thank you for your thorough reading and positive evaluation of our work. We are grateful for your recognition of our contribution in identifying and addressing the novel issue of fitness evaluation bias (FEB) in evolutionary multi-view classification (EMVC). We also appreciate your affirmation of the clear structure, well-designed illustrations, and comprehensive experimental setup of our paper. Your encouragement and suggestions are of great significance for the improvement of our future work.\n\n**Q1: How do the crossover and mutation operators work? More details are necessary to the readers that do not very familiar with this topic.**\n\nA1: **For the crossover operation**, a non-root node is first randomly selected from each of two randomly chosen binary trees to serve as the crossover point. The selected node along with its subtree is then pruned from the original tree and exchanged with the counterpart from the other tree. These subtrees are subsequently grafted onto the parent node of the original crossover point in the opposite tree, thereby generating two new individual structures.\n**For the mutation operation**, a node is randomly selected from the individual's tree structure. If the selected node is a fusion operation node, a new fusion operation is randomly sampled from a predefined list to replace the original operation. If the selected node is a view node, a new view is randomly chosen from a set of views to replace the original one.\n\n**Q2: How are the hyper-parameters of compared baselines set?**\n\nA2: Given that our proposed EFB-EMVC method essentially falls under the category of EMVC approaches, we have only listed the hyperparameter settings of representative methods within this category in the table. Considering the wide variety of EMVC methods, we selected two of the most representative works—namely, the pioneering method EDF and the latest state-of-the-art method TEF. Their detailed hyperparameter configurations are provided below.\n\nIn both EDF and TEF, all deep neural network models are trained using the Adam optimization algorithm. The learning rate is set to 0.001, with exponential decay rates of 0.9 and 0.999 for the first and second moment estimates, respectively. Each network is trained for 100 epochs. To prevent overfitting, early stopping is applied if the model performance does not improve for 10 consecutive epochs.\nTo efficiently utilize GPU resources, the population size is set as a multiple of the number of GPUs, and is configured as 28. The number of generations is set to 20, with crossover and mutation probabilities of 0.9 and 0.2, respectively.\nIt is worth noting that the primary goal of TEF in the first stage is to obtain a fusion architecture capable of generating high-quality pseudo views. The detailed hyperparameter configurations for the second stage of TEF are presented in Table (1).\n\n**Table(1): The detailed hyperparameter configurations for the second stage of TEF**\n\n| Dataset       | NUS   | Reuters5 | Reuters3 | MVoxCeleb | YoutubeFace |\n|--------------|-------|----------|----------|----------|-------------|\n| Learning rate | 1e-3  | 1e-4     | 1e-4     | 1e-4     | 1e-4        |\n| Weight decay  | 1e-5  | 1e-5     | 1e-3     | 1e-4     | 1e-5        |\n| Batch size    | 64    | 128      | 64       | 256      | 256         |\n| Optimizer     | Adam  | Adam     | Adam     | Adam     | Adam        |\n| Maximum Epoch     | 500   | 500      | 500      | 500      | 500         |\n| Fusion dimension    | 128   | 128      | 128      | 128      | 128         |\n| Lr-patience   | 20    | 10       | 10       | 50       | 10          |\n| Lr-factor     | 0.3   | 0.3      | 0.3      | 0.3      | 0.3         |\n| Seed          | 1     | 1        | 1        | 1        | 1           |\n\n\nIn response to your comments, we will include detailed explanations of the \"crossover mutation operation\" (line 202) and the \"baseline method settings for comparison\" (line 233) in future revisions, in order to enhance readability and understanding for non-expert readers. Thank you once again for your valuable feedback and suggestions. We will carefully consider them and make corresponding improvements to the paper."}]

Author rebuttal:

Meta-review: **Summarization**

This paper identifies the Fitness Evaluation Bias (FEB) problem in evolutionary multi-view classification (EMVC), a systematic issue arising from joint training across heterogeneous views. The authors propose EFB-EMVC, introducing evolutionary navigators with a novel Wasserstein-based distillation loss (WDOLF) to provide unbiased fitness evaluation and correct the evolutionary trajectory. Extensive experiments on nine datasets show consistent improvements over state-of-the-art methods.

**Strengths**

1. Novel and important problem formulation (FEB), with clear motivation and theoretical significance.

2. Elegant and generalizable solution, compatible with existing EMVC frameworks.

3. Strong empirical validation across diverse datasets with detailed ablations and convergence analysis.

4. Clear presentation and well-structured figures/tables that aid understanding.

**Weaknesses**

1. Initial iteration settings raised fairness concerns (5 vs. 20 iterations), but additional convergence experiments provided in rebuttal resolved this.

2. Missing teacher model accuracies and hyperparameter details were clarified in the rebuttal.

3. Minor clarity/typo issues in the methodology section.

**Rebuttal & Discussion**

Reviewers appreciated the novelty and thorough experiments. Concerns about iteration fairness, teacher model transparency, and hyperparameter sensitivity were satisfactorily addressed. Additional experiments on convergence behavior and hyperparameter effects strengthened the empirical case. Minor issues (naming inconsistencies, clarity of descriptions) will be addressed in revision.

**Decision**
The paper makes a clear advance by exposing FEB, provides a simple yet powerful solution, and demonstrates consistent improvements across benchmarks. Given the novelty, broad applicability, and potential to shape future EMVC research, I recommend Accept, with Spotlight consideration for its conceptual contribution beyond raw performance improvements.
Decision: Accept (spotlight)