A Dynamic Learning Strategy for Dempster-Shafer Theory with Applications in Classification and Enhancement
Authors: Linlin Fan
Xingyu Liu
Mingliang Zhou
Xuekai Wei
Weizhi Xian
Jielu Yan
Weijia Jia
Venue: NeurIPS 2025 poster ()
Keywords: Dempster–Shafer theory
Dynamic learning strategy
Adaptive diffusion probability transformation
Collaborative decision optimization
Primary area: theory
TL;DR: A nonuniform splitting mechanism and Hilbert space mapping method are proposed to solve the a priori information neglect and data imbalance problems, which show better performance in classification and enhancement tasks.

Abstract: Effective modelling of uncertain information is crucial for quantifying uncertainty. Dempster–Shafer evidence (DSE) theory is a widely recognized approach for handling uncertain information. However, current methods often neglect the inherent a priori information within data during modelling, and imbalanced data lead to insufficient attention to key information in the model. To address these limitations, this paper presents a dynamic learning strategy based on nonuniform splitting mechanism and Hilbert space mapping. First, the framework uses a nonuniform splitting mechanism to dynamically adjust the weights of data subsets and combines the diffusion factor to effectively incorporate the data a priori information, thereby flexibly addressing uncertainty and conflict. Second, the conflict in the information fusion process is reduced by Hilbert space mapping. Experimental results on multiple tasks show that the proposed method significantly outperforms state-of-the-art methods and effectively improves the performance of classification and low-light image enhancement (LLIE) tasks. The code is available at https://anonymous.4open.science/r/Third-ED16.

A Dynamic Learning Strategy for Dempster-Shafer Theory with Applications in Classification and Enhancement
Linlin Fan', Xingyu Liu', Mingliang Zhou'; Xuekai Wei', Weizhi Xian", Jielu Yan', Weijia Jia
Sccoool of Computer Science, Chongqing University,
CChongiing Research Institute of HIT, Harbin Institute of Technology, 'BNU-UIC Institute of Artificial Intelligence and Future Networks, Beijing Normal University 1 sinlinf an@stu. cqu. edu. cn, xingyuliuSstu cqu edu. en, minggliangzhouscqu edu. en, xuekai cityu. edu. hk, wasxxwz8168 com, yanjieluucqu.edu edu. cn, j jiaw abaw. edu. cn
Abstract
Effective modelling uncertain information is erucial for quantifying uncertainty. Dempster-Shafer evidence (DSE) theory is a widely recognized approach for han- dling uncertain information. However, current methods often neglect the inherent priori information within data during modelling, and imbalanced data lead to insufficient attention to key information the model. To address these limitations, this paper presents dynamic learning strategy based nonuniform splitting mechanism and Hilbert space mapping. First, the framework uses a nonuniform splitting mechanism to dynamically adjust the weights of data subsets and com- bines the diffusion factor to effectively incorporate the data a priori information, thereby flexibly addressing uncertainty and conflict. Second, the conflict in the information fusion process reduced by Hilbert space mapping. Experimental results multiple tasks show that the proposed method significantly outperforms state-of-the-as methods and effectively improves the performance of classifica- tion and low-light image enhancement (LLIB) tasks. The code is available https: https:://anonmmuu 4open www.sscceeeeeiciiieee..
Introduction
Uncertain information is inevitably encountered in the process of modelling data-based complex systems via deep learning. Effective modelling and processing of uncertain information is an important technique that plays key role in the decision-making process and improves the ultimate decision-making level. Currently, many methods have been proposed to solve this problem, such as evidence-theoretic methods [57] and fuzzy logic methods [10]. and deep learning-based methods 44] These techniques have been applied several fields, such as graph clustering [49], classification [56), and target detection [32). However, how to effectively handle uncertain information from different sources and combine them effectively while avoiding mutual conflicts is still a challenging problem.
In machine learning, classification is the task of making predictions about new sample categories by learning the features of samples from known categories [26]. In the classification task, the reliability of the classifier plays an important role. However, owing to the uncertainty of the data itself and possible conflict or redundancy of information from different sources, effectively and rationally addressing information from different sources to improve classification accuracy has become an urgent problem. Currently, many classical machine learning methods have been proposed. Denoeux
"Corresponding author: Mingliang Zhou.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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et al. [15] viewed the neighbors of unclassified samples as evidence for the hypothesis, with support as function of distance between the vectors, and used Dempster's combination (DC) rule combine the evidence for the classification task. Freund ef al. [19 proposed the classification method of an alternating decision tree, which solved the problem that the original classifier is complicated and
difficult to understand. Chang et al. [5] proposed a support vector machine (SVM) and an SVM with radial basis functions to implement classification problems. Xu et al. [60] utilized a normality test and normality transformation to address nonnormal data for classification tasks. Hu et al. [23] investigated Bayesian and mutual information classifiers and applied them in a classification task. Xu
et al. [6]] extended the classical probabilistic calibration approach to evidence-theoretic framework when dealing with different sources of information to address the problem that a single probability measure may not adequately express uncertainty when modelling the calibration step. Xiao er al. [58] proposed weighted selief-jensen--sannee of Dempster-Shafe Shafer evidence (DSE) theory. Although the above methods address information from different sources, the importance of the information and the measurement of discrepancies still not comprehensively considered. These shortcomings are reflected mainly in the following aspects:
divergence for decision-making improvement on the basis
In DSE theory, the current method does not consider the a priori information brought by the data itself, nor can it dynamically adjust the tendency of splitting on the basis of the importance between different subsets in the process of splitting, which means that the uncertainty information cannot be well handled.
When fusing multiple basic belief assignments (BBAs), different evidence sources conflict due to uncertainty or data distribution differences. Direct use of DC rules may lead to conflict amplification or even produce unreasonable results. Moreover, traditional methods are usually based on Euclidean space or simple statistical metries to calculate the differences between evidence, which makes it difficult to capture the nonlinear characteristics of complex data distributions.
In practical tasks, data distributions are often unbalanced, which can lead insufficient focus on key information in the model. In addition, current methods are unable to customize the degree of attention according to different data, and traditional training methods treat all features equally, which may lead to insufficient learning of key regions.
To address the above problems, we propose a dynamic learning strategy based on nonuniform splitting mechanism and Hilbert space mapping. First, the framework dynamically adjusts the weights of different subsets through the nonuniform splitting mechanism and uses the a priori information of the data in combination with the diffusion factor to flexibly address uncertainties and conflicts. Second, the data are mapped into the Hilbert space for computation to alleviate the information conflict problem that may occur during the information fusion process. Third, a targeted training strategy is proposed to enhance the model's ability to learn important features and regions, which achieves results in both classification and enhancement tasks. In summary, the main contributions of our work are as follows:
We propose a nonuniform splitting mechanism. This mechanism can be dynamically adjusted according to the importance between different subsets, giving more weight some subsets and less weight to others. The a priori information of the data can be utilized by introducing diffusion factor, and this splitting mechanism, which is based on a priori information, can be more flexible in addressing uncertainty and conflicting information.
We propose a scheme for fusing different BBAs. This scheme maps the data into Hilbert space for computation, which is more responsive to the differences in the true distributions of complex data. A specific way to compute the differences before fusing different BBAs is used to reduce the conflicts between different information.
We propose an effective targeted training strategy (TTS). This strategy enhances the model's ability to learn specific information and regions. Higher weights are assigned to important features to increase attention, thus improving the overall performance of the task. Accuracy is improved in classification tasks, and data imbalance alleviated in low-light image enhancement (LLIE) tasks.

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The rest of the paper is organized as follows. In section 2 related work is briefly introduced, |section 3) describes the proposed method. |section 4 describes the experiments and analysis of the results. Finally.|section
section 5 provides a discussion and conclusion.
2
Related Work
2.1 Modelling of uncertain information
In classification tasks, information uncertainty often leads the classifier to make incorrect decisions. To address this problem effectively, many methods based on statistical and distance metrics have been proposed with the aim of improving classification performance by means of different mathematical models. Cover and Hart [12) proposed a method based on a distance metric function, which is inferred by selecting nearest neighbor samples. Cortes and Vapnik [TT) effectively differentiate between different data distributions by constructing separating hyperplane that can correctly divide the training dataset and has a maximum geometrie interval. Xanthopoulos discriminant analysis on the basis of a statistical approach that uses the grouping information of known samples and their corresponding multivariate variable characteristics to infer the group to which new samples belong. Quinlan el al. [41] designed model that is based on a tree structure, where each internal node represents judgment on a feature and each branch represents a possible output of the judgment. However, the above methods may have difficulty making accurate inferences because of their own limitations when dealing with data with conflicting or redundant information. thus affecting inference efficiency.
al. [55] proposed
2.2 Evidence theory-based modelling of uncertain information
Uncertain information can be classified into either the empty set @ or the whole set Ω the basis of the modelling of the uncertain information, thus addressing the information uncertainty. Zhao et al.
71 obtained the final classification results by evaluating the reliability of single and multiple sources through independent and combined reliability assessments, respectively. Liu et al. (38 combined the inferred results from multiple models and used the average as the final output. Jousselme al. [30 introduced the distance calculation method of the similarity measure to generate more reliable inference results. Zhang el al. [69] proposed multisource information fusion algorithm based on belief x² scatter for inference tasks in complex data scenarios. However, owing to the uncertainty of the data itself and the possible conflicts or redundant information from different sources, effectively combining information from different sources by taking their importance into account remains challenging research problem.
2.3 Deep parning-based modelling of uncertain information
Deep learning models often face the problem of decreased prediction reliability due to uncertain information. Chen et al. X proposed radial basis function network learning algorithm based on orthogonal least squares to solve the underperformance problem caused by randomly selecting the centroid method to improve the performance of the task network. Castro et al. [4] investigated the problem of biased results due to data imbalance based on a multilayer perceptron (MLP) neural network and statistically improved the classification performance of the MLP. Sensoy et al. [45] used the prediction output from the network as subjective information for modelling, which in turn served as data support for the deterministic neural network accomplish the subsequent classification task. Zaidi et al. [67] proposed two methods for automatically building collection of different network architectures that can weigh the advantages of different structures well and use architectural variations as source of diversity. However, these methods rely mostly on specific assumptions, and when there are multiple sources of conflicting contradictions in the input data, these models lack an effective dynamic processing framework, which may lead to bias in the final results.
3

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Method
3.1 Motivation and overview
In DSE theory, when dealing with highly conflicting information, existing methods cannot adequately consider the lack of precision due ambiguity uncertainty in BBAs. First, the existing allocation methods based on the splitting idea assume that the allocation is based on the premise uniform splitting, which assumes that all subsets are equally proportioned distribute the quality and cannot be dynamically adjusted according to the quality among different subsets. Thus, the differences between different subsets cannot be adequately considered. Therefore, nonuniform splitting mechanism introduced to give more weight to some subsets and less weight to others. This splitting mechanism, which is based a priori information, namely the inherent characteristics of the data's 's own structure and the initial evidence distribution, can handle uncertainties and conflicting information more flesxibly. The mechanism is adjustable to assign different split weights different subsets through the diffusion coefficient. Second, conflicts arise from different evidence sources due uncertainty or data distribution differences. To avoid the occurrence of the conflict phenomenon in the process of fusing different BBAs, high-order dynamic maximum mean difference (HODMMD) is proposed, which maps the data into the Hilbert space for computation and more responsive the differences in the real distributions of complex data. A specific way to calculate the difference before fusing different BBAs is used to reduce the conflict between different information. Third, practical applications, the imbalance problem inherent in the data leads to insufficient attention of the model to key information. Therefore, an effective TTS is needed to assign higher weights to important features and increase attention, thus improving the overall performance of the task.
daptive probability transformation
Pallern dataset
Image classification dataset
Low- light dataset
Feature generation
Build BBA
Adaptive transformation
Probabilistic reliability assessment
Collaborative decision optimization
MISH +
McAi
MUN
CC
HDDMMD
MEU
1000: 1000
Mack
MHAA
Reliabilit ssignment
Fusion
Pattern classiication
Image classification
Law- Bihht Image enhancement
Figure I: Overview of our targeted training strategy (TTS).
Given a set of data I, after feature extraction, different BBAs mi, m2,,".. my are obtained via adaptive diffusion probability transformation (ADPT) (Tadpt):
mi, M2, ... my Tadpt(/)
(I)
After that, the reliability of the different BBAs is calculated in the probabilistic reliability assessment (PRA) (Tpra) stage:
à (m.ra(m..))) my (I i,j S n)
(2)
These reliabilities are utilized as discount factors to perform collaborative decision optimization (CDO) (Tedo) operations the BBAs, which are fused to obtain the final decision result:
M = ( 62. ... . 2 ... 6n: my m2.
m.. ". m.))
(3)

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where ø1, 02. bi, ........ on are discount factors. The final decision result is obtained after fusion.
3.2 Adaptive diffusion probability transformation
On the basis the definition of DSE theory, the proposed ADPT model is as follows:
7 11A,1-IA, (T+ |, -IA,, 7-1 (Aj)
ring (A.) = Σ
D(A,, A.CA;
(4)
where A,, Aj (0)) is the number of iterative splits. vig order of mig. and myg is the initial basic belief assignment (BBA). D (5) = ((25)) a diffusion function used to control the quality of the distribution from subset A; to A,, which regulates the process in which the mass function is transferred from a fuzzy hypothesis A; to more specific hypothesis A,, effectively quantifying and integrating prior information. When tends to co, the result of D (A,, AA) tends to 1. and Equation 44) degenerates into a uniform distribution (25], which is no longer affected by the importance of different regions. |- is the number of elements contained, & {01. 02, 0g: ... ON
is the frame of discernment, and 2 = {0, {01}. (82)..... .... {0x). (01 U02). _ 52} is the power set. After normalization processing,
my (A,)
my (A:)
E A:E20
(5)
EA my (A,)
3.3 Probabilistic reliability assessment and properties
When different quality functions are obtained, if they are simply combined according to the DC rule
[8). the integration between different BBAs may be hindered because conflicting information.
For this reason, the idea of discounting techniques [46) is introduced. Defined HODMMD:
HODMMD" (M1, f22)
Σ
m (A.) m. (A.)
(6)
HH
where the regenerated kernel Hilbert space and the kernel function is computed via a Gaussian kernel function. The properties of the HODMMD
follows.
Property 1. When - sc, the HODMMD equivalent to measuring the difference between the pignistic probability transformations BetP with mn and m, of the maximum mean difference.
lim HODMMD (fonM m2) 7-000
Σ
(BetP) Bet22
(7)
7t
Property 2. When mn and fi degenerate into probability distributions, that is, U = (u,, U2....y un)
and V (11, , the proposed HODMMD degenerates into maximum mean difference.
HODMMD" (fn, m2) MMD(M m2)
(8)
Property 3. HODMMD" (m,, m2) and HODMMD" (mzg mi) are equivalent.
HODMMD (ma m2) HODMMD (m2, m.)
(9)
Property 4. When my m2, the value of HODMMD is always equal to 0.
HODMMD (m, m2) 0
(10)
Proofs of these properties can be found in the technical appendix.
3.4 Collaborative decision optimization
When ADPT used to obtain multiple BBAs, the reliability of different BBAs needs to be calculated to measure the impact of different sources of evidence. Let ø (di, Ø2. ..., Φx] be the reliability of
5

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Algorithm 1: A dynamic learning framework based on DSE theory
Input: Training data Xtraniing and testing set X testing.
Output: Category prohabilistic decision results
for 1o K do
Generate values on the basis of the data attribute characteristics of X Xtraining
end
4 Reliability of different classifiers obtained via decision optimization scheme Eq.
5 Calculate the discount factor via Eq. 12 and normalize
for i = to K do
Obtain the results of K classifiers Discounting the different classification results via Eq. 13
Fuse different BBAs via Eq. (14)
10
Test the ktt basic classifiers
11 end
12 Use the decision results for subsequent tasks
different query patterns or BBAs that satisfy di [0, 1] and Σt 0k To measure the reliability of the different BBAs, the HODMMD is used for the calculation:
L
HODMMD (c: Ee Srmi )) s.t.
e = arg min Σ
ΦR =1
(II)
where the index of the different query patterns. G: (i,,), ..., G((K)) is the ground truth. m4 is the possibility of the query pattern belonging to the class 0z. mg (mi((), (1), bility vector that minimizes the BBA error is calculated via sequential least squares programming (SLSQP). Therefore, the discount factor for the kth BBA defined as:
(2)), which also satisfies m'. [0, and - m 1. The relia- ()),),(())) (2), ..), m
a = Φx/ max Φ1, $2...., ......,,k
(12)
According to the idea of discounting techniques 466] the discounted BBA is as follows:
(X) 2. (X), XX 22
(13)
(22 Φ m, ( + 1 Φk
Fusing of different BBAS according to the DC rule:
m 177 + M2 +
+ Mπ
(14)
The probabilities of different patterns obtained after fusion are prepared for subsequent classification and LLIE tasks. In LLIE tasks, the image is divided into different image blocks and then input into the proposed decision framework Trans to obtain the degradation degree representation of different features for each image block. The lower the quality is, the greater the weight assigned the region. Given low-light image How and normal light image Inormais
Apro T Trans (How Inormat)
(15)
where ppro represents the representation of the degree of degradation in different regions of the image. Next, the LLIE task can be formalized as:
arg min Loss(Tnet,) (Jpro (tow); Inormat)
(16)
{
where Loss is the loss function of the original network and where Thetz is the network with parameter
E. represents the dot product. During this process, the network focuses more intensely on regions
of the image that have undergone greater degradation, effectively integrating an understanding of
the image content into the learning process. The above process of our method leads to Algorithm [] which contains three modules: the ADPT, PRA, and CDO of classifiers. These three modules are co-optimized to work together. In this process, initial values are first generated on the basis of the features the training data. Next, adaptive targeted iterations are performed via ADPT to achieve the generation of BBAs under different classifiers. After that, the reliability of each classifier is calculated as discount factor using HODMMD. Finally, fusion performed with the help of a discount factor to obtain the final decision.

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Experimental Results
4.1 Numerical experiment
To better understand the working mechanism of the ADPT, in this section, a discussion of the proposed ADPT is presented. by several concrete examples.
mppe. 9.3)
Figure 2: Diagram of the proportion of the mass function increasing with T in Example 5.1.
Example 5.1 Let a frame of discernment be f = {01. 02). The BBA is as follows:
mi 1 ({01)) 1/6, mi mi((2) 1/3, mi 02)) 1/2.
When split once, when
is substituted into Equation (4). three scenarios exist: my (fa1)) 0.3.
m, (faz)) 0.5, and m. (fa1, a2)) 0.2. When the second, T 2, substituted into Equation (4), there can be three scenarios: m ({a1)) }) = 0.3741, m2 ({a2}) = 0.5839, and m ({a), a2}) = 0.0420. The process was plotted as a radar chart and line graph, and the results are shown in Figure The results show that as T increases, the values the mass function belonging to {01. 02) gradually shift to the mass functions of {01} and {02). The mass function with larger set of initial values still maintains a larger weight.
Example 5.2 Let a frame of discernment be Ω {01, 02]. The BBAs are as follows:
mi mi ((0))) = - (1-2)/3, m1((2) = (1 (1-1=]))))) =3/3, mi ((01, 02}) = (2x + 1)/3,
m2 ((( (1 (1-))) my ((0))) = (1- m 02)) (2y + 1)/3.
The variation of the proposed HODMMD is further explored by changing the values of a and y and plotting Figure 3 As r increases, the difference between mi and m2 gradually decreases, verifying that the uncertainty information of the BBAS gradually decreases with increasing ADPT.
Figure 3: HODMMD between mi and m2 when 7 is 1, 3, in Example 5.2.
4.2 Pattern classification
For each dataset, the same testing method in (58) was adopted to perform fivefold cross-validation according to training set-to-test machine ratio of 4:1. The classification accuracy was evaluated, and then all the results were averaged to arrive at the final result, which ensures a fair comparison between the different methods. The experimental results are shown in Table The proposed method achieves the optimal performance except for the Parkinsons dataset because the features of the different samples in this dataset are too close to each other, resulting in poor differentiation of importance when performing ADPT, On the basis of the evaluation metrie of classification accuracy, improvements of 2.67%, 11.9%, 1.48%, 1.66% and 0.22% are obtained over those of the advanced DMA method on
7

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the Iris, Heart, Hepatitis, Australian and Segment datasets, respectively. This is because our method better handles the contribution of different features the classification and better solves the conflict problem when fusing different BBAs.
Table 1: Comparison of the classification accuracy of different methods. The best, second and third results are the red, green and blue colours.
Dataset
Iris Iris[[8]
Heart 27
Hepatitis [
Parkinsons [36]
Australian 42
Segment 2
CBench [66
NaB 23
94.67%
82.59%
76%
68.75%
79.56%
80.22%
67.68%
KNN
95.33%
57.78%
65.71%
83.02%
67.40%
96.93%
99.02%
REPTree 19
92.00%
70.74%
71.64%
80.94%
80.59%
95.11%
65.45%
SVM(S]
94.67%
83.70%
79.96%
70.13%
80.29%
64.50%
88.48%
SVM-RBF(S
94.67%
82.96%
76.76%
81.03%
79.86%
81.73%
68%18%
MLP[4]
93.33%
75.19%
74.93%
74.39%
82.32%
95.93%
80.40%
RBFN
92.67%
81.85%
81.32%
82.05%
82.61% %
87.58%
83.64%
INN-DSTIFJ
95.33%
76.30%
80.57%
78.01%
78.41%
93.37%
94,42%
NDC
94.00%
82.59%
79.40%
70.26%
80.01%
79.61%
43.13%
E
94.67%
83.70%
79.88%
81.64%
80.60%
95.90%
76.33%
DMA
96.00%
84.07%
83.04%
75.03%
84.14%
99.74%
100.00%
ouTs
98.67%
95.97%
84.52%
82.50%
85.80%
99.96%
100.00%
4.3
Image classification
For the image classification task, we examine the performance on the CIFAR-10 and CIFAR-100 datasets, which contain 10 and 100 categories, respectively. To verify the effectiveness of the proposed fusion framework, which is based on a nonuniform splitting mechanism and Hilbert space mapping
comprehensively, we perform feature extraction via ResNet-18 and the CNN framework proposed in [48] before adopting the proposed method for decision making. In this task, prior information is the initial probability distribution obtained by performing feature extraction the input samples for the CNN and ResNet-16 18, with the last linear layer removed. The comparison Our method achieves better results, which once
results of the different methods are shown Table 2 again validates the effectiveness of the proposed method in addressing uncertain information.
Table 2: Comparison of classification accuracy on the CIFAR-I0 dataset and CIFAR-100
dataset 31
The best, second and third results are in the red, green and blue colours.
Methods
Architecture
Accuracy
Methods
Architecture ResNet-19
Accuracy
DIR-Nei 40 LJCV'2023
ResNet-18
92.80%
Dspike 34
NeurlPS 2021
73.12%
MST [CCV
ResNet-18
93.20 %
GLIF 66
NeurlPS 2022
ResNet-19 19
77.05%
ReSTE
ICCV
ResNet-18
92.63 %
Diet-SNN 43
TNNI.S'200 2021
VGG-16
69.67%
9DMM
TIP3
R8
95.40 %
PASNN KBS' 2023
ResNet-
72.63%
SML
JCML'20033
Re
95.12 %
MPBN 22
1023
ResNet- 19
74.40%
2D
CVPR 2024
ResNet-56
93.78%
MS-ResNet 24
ICCV
MS ResNee8
75.39%
CIFAR-I 10
ResNet-20
93.75%
BiPer [50]
CVPR' 2024
ResNet-18
93.75%
CIFAR-
BKDSNN]63] BCCV'2024
ResNet-19
74.95%
VGG-small
92.11%
TAB 28
2202
VGG-9
93.41%
TAB
ICII'2024
VGG-11
76.31%
APL 2022
ResNet-18
96.00%
APL (70
TPAMI
ResNet-18
78.90%
ESNN 47 BAAI'2025
VGG-16
93.55%
ESNN47
EAAI '025
VGG-16
76.55%
CNN
95.67%
CNN
79.71%
ResNet-18
95.61%
ResNet-18
79.78%
4.4 Low-light image enhancement
In LLIE, dark areas may contain critical information that is often difficult for models to adequately learn and focus on 35 Traditional training strategies, which apply uniform processing across the entire image, are inherently limited in their ability specifically enhance model learning for these critical regions. This often results in suboptimal detail recovery in the target areas during enhancement.

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Therefore, a TTS is proposed in conjunction with the proposed method, which explicitly guides the model increase the level of attention low-quality regions. The method is plug-and-pla module. In this task, prior information refers to the degree of degradation of different regions in the image. We used the LLIE network of the last few years as a baseline network, and the results are shown in Table 3 A consistent improvement in performance can be seen after using the TTS. To obtain a more intuitive sense of the enhancement, we present the results of the baseline method and our method, and the results are shown in Figure Our method effectively improves the quality of images. For the LOL-vI dataset, our method enhances the texture details on the glass; for the LOL-v2-real dataset, dataset, our method recovers the color of the flower petals closer to the ground truth. This finding verifies the validity of the proposed method as well as the idea and further shows that the proposed ADPT can characterize the data well. As seen through the above experiments, applying different learning strategies to different regions can effectively enhance the model's focus on the target region. By adaptively adjusting the learning weights of different regions, the model's ability to focus on low-quality regions is enhanced, the data distribution imbalance problem is alleviated, and the overall performance of the model is improved. To the best of our knowledge, this is the first time that DSE theory has been introduced into LLIE.
method recovers the text the wall more clearly; for the LOL-v2-real
More experiments can be found in the technical appendices.
Table 3: Quantitative comparison of LOL-vI [53
LOL-v2-real
66
and LOL-v2-syn 665
LOL-V
[33
LOL-
-e-rrell
65
LOL
VOL-v2-syp v2-syn
63
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSTM
MIRNet 68
TPAMI 2020
24.14
0.830
20.02
0.820
21.94
0.876
FIDE 59
CVPR 2020
18.27
0.665
16.85
0.678
15.20
0.612
ZeroDCE 21
CVPR'2020
16.76
0.560
18.06
0.577
17.76
0.816
Sparse 53
TIP'2021
17.20
0.640
20.06
0.816
22.05
0.905
DRBN 64]
21P' 2021
20.13
0.830
20.29
0.831
23.22
0.927
RUAS CVPR
18.23
0.720
18.37
0.723
16.55
0.652
ZeroDCE++ 33 TPAMT'2021
16.11
0.530
18.06
0.577
18.03
0.825
SCI[99] CVPR
14.78
0.525
16.19
0.522
16.67
0.811
Restormer 29] (CSVT'2023
22.43
0.823
19.94
0.827
21.41
0.830
SNR|62] CVPR 2022
24.61
0.842
21.48
0.849
24.14
0.928
SNR-TTS
0.846(-0.003)
10.,,,40.18)0..9920-00000
L.FFlow-I [22 2A2
24.99
0.870
25.31
0.805
25.88
0.908
LLFlow-L-TTI
26.70(+1.71)
0.860(-0.01)
26.97(+1.66)
0.865(+0.06)
26.09(+0.21)
0.90(-0.000)
L..Flow-SS5 552
2A2
24.06
0.860
26.80
0.860
25.30
0.877
LLFlow-S S-TTS
26.28(+2.22))
0. 0.848(-0.011)
28.
(51.0000))5533(00000
Retinexlormer B 2023
25.16
0.845
22.80
0.840
25.67
0.930
Retinexformer-TT
26.
5 Conclusion
This paper proposes a dynamic learning strategy based nonuniform splitting mechanism and Hilbert space mapping, which is based on DSE theory, as an efficient method for processing uncertain information. The current method cannot dynamically adjust the tendency of splitting of the importance between different subsets in the process of splitting, and directly using the DC rule fusion will produce unreasonable results owing to the conflict problem. First, the nonuniform splitting mechanism proposed in this paper takes the data's 's inherent a priori information into account and thus can handle uncertainty and conflict information more flexibly while improving the accuracy of the task. Second, mapping the data into the Hilbert space for computation is more responsive to the differences in the true distributions of complex data, thus providing an effective strategy for the subsequent fusion of different BBAs. We conducted experiments on multiple tasks as well as multiple publicly available datasets. The experimental results show that our method significantly outperforms existing machine learning methods and deep learning methods. To the best of our knowledge, we are the first to introduce DSE theory to L.I.E and provide effective performance enhancement for LLIE tasks.
the basis

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100 CTCCUa
10 L.Fowws
2
Figure 4: Quantitative comparison of LOL-vi [33 columns), LOL-v2-real 65 (3rd-4th
columns), and LOL-v2-syn 66 (5th-6th columns). Even columns correspond to the results of adding the TTS module.
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant 62176027, in part by Chongqing Talent under Grant cstc2024ycjh-bgzxm0000 in part by Chongqing in part by the General Pro-
New Yin Cai (YC) Project under Grant SSSB2024YCJH-KXXMUG gram of the Natural Science Foundation of Chongging under Grant ASSB2024NSCQ-MSXXC and in part by Chongqing Postdoctoral Foundation Special Support Program under Grant 2023CQB-
SHTB3119.
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A Appendix/supplemental material
A.1 More Details of Preparatory Knowledge
A.1.1 Dempster-Shafer evidence theory
Dempster-shafer evidence theory is well-established general framework for uncertainty reasoning that was first proposed by Arthur P. Dempster [33 on the basis of statistical inference and later formalized and significantly extended by Glenn Shafer into a framework for simulating epistemic uncertainty [46] Owing to its effectiveness in dealing with uncertain information, DSE theory is widely used in various fields.
Definition 1. Frame of discernment
Define set of classes called discriminant frames:
Ω {01, 0z .......... ...
(17)
where (i 1,2, ..., N) are mutually exclusive. The power is defined as:
2 [00 {01). (O.)...., (ON). {01 U _
(18)
where Q is the whole set, 0 is the empty set and the one containing U is multielement set 13 46
Definition 2. Basic belief assignment
The basic belief assignment (BBA), also known as the mass function, denoted m(-) is defined as mapping of 2 to the interval [0, 1] 13 46).
m m2 - [0
(19)
and is satisfied:
m(A) =
(20)
AE2R (d)
m(0) =
(21)
where A e ((0), 0 the empty set.
Definition 3. Focal set
If m(A) > 0, A is called focal set, and the value of mm-) indicates the level of support of the model 46
Definition 4. Dempster's combination rule
Different fusion algorithms can be used to fuse information from different sources, one of which is Dempster's s combination rule. As can process fusion of different sources of evidence represented by BBA, it is assumed that and m2 are two mutually independent BBAs defined the same recognition frame 20, Dempster's combination rule aims derive a combined BBA, usually denoted mi m2. The combination frame is defined as follows 13
m(As) = (m² ) m2) (Ax) = EAGA,EA mi
(22)
1 1- R
R = Σ mi (A,)ma(A)) <
(23)
where Ai, A,, As Ω and R are the conflict coefficients of my and ma.
A.1.2 Probability transformation methods
Definition 5. Pignistic probability transformation
21

---

Let Ω = {01,02. 02..0.....66 denote the discriminant framework. Given a corresponding BBA defined on 52, denoted m()), the pignistic probabilistic transformation of element 0; Q2 denoted Ppp,, is defined as follows:
m(A)
P ppt (0:)
Σ
(24)
|A]
0:EA|AE2R
where A belongs to 2 A * 9. |A] is the cardinality of A.
Definition 6. Plausibility transformation method
Let Ω = {01, 02, .3......NN denote the discriminant framework, Given a corresponding BBA defined S2, denoted m(-), the plausibility transformation of an element 8, S2 denoted Ppt. is defined as follows:
M (0,)
Ppe (0t)
(25)
Σ iml M (0:)
where M.) is the plausibility function:
((A)
Σ
m(A)).
(26)
A,nA, A..AA C29
A.2 More Proof Details for Properties
When different quality functions are obtained, if they are simply combined according to Dempster's rule 48 the integration between different BBAs may be hindered because of conflicting information.
For this reason, the idea discounting techniques [46] is introduced. The high-order dynamic maximum mean difference (HODMMD) is defined follows:
HODMMD" (m2)
Σ
( (A:) m (Ai))
(27)
where H is the regenerated kernel Hilbert space and the kernel function is computed via Gaussian kernel function, A, E 20) (0). and 7 the number of iterative splits. mi is T order of myg The HODMMD has a variety of properties. The properties of the HODMMD and the corresponding proofs are as follows.
When + the HODMMD is equivalent to measuring the difference between the pignistic probability transformations with my and my of the maximum mean difference.
Property 1.
N
lim HODMMD" (fi, m2) = 7-500
Σ
(BetP) (0.) Bet 22t))(0)))
(28)
Proof. We denote by BetP, the pignistic probability transformations of mn and mzz t = 1, 2. That is,
(A)
BetP.(0.) = Σ
(29)
[A]
0,EA/
If A, 8,, then the cardinality of A, is 1. Thus, when 7 - 0o and |Ail -
(A1) $
-1451-1441
EASA, (1A7))
(r+1) 43 [ me (A₂)
lim my. (At) 700
lim 7-000
(30)
$ -
Ex.oa Exss,
(14))
my (Az)
- 1gg
Let
Σ |A,) 1
1141--A111
m7 (Ax)= A.SA,
m (A₂)
(31)
(14,1)
(T+1) - 1|,
22

---

[Ai1 $ [Ayl)
-lAy--IA.1
lim m (A,)
lim
(T+ 1)1asl - - mh (Az)
7-000
A, A.SA;
-14/1-1
lim 7-000
(T 1)1asl -| Th (A,)
(32)
[A
A,CA,
where A; is a subset of Aj. When |A, 1, there must be |Aj] 2 1: hence, |A,l
Z and
+|451-1 0. The numerator and denominator are equally divisible by ا|
lim my (A:) lim Σ A.CA,
T + m. (Ag)
(33)
[Agl
Let =
1, 7. when J + oa, have 1 + O, which is + 0. A Taylor expansion of (p + 1)1asl has
(o (0+1)1411 = + |4yle + o(p)
(34)
where op) is the infinitesimal of p. have
-lAi1-1
lim m. (A,) = lim 000
(T + 1)1 - -TA mc (Aj)
p00
[A₂]
A:SAs
= lim
Σ
1
[ + 14,1 o(p)) - me (A₁)
p-0
[A,l
A,EA,
my (A,)
Σ
(35)
|A,1
A.C.,
Therefore, when
EASA,
malAy) TAg
lim my (Ai) = EALe29 EACA,
(A,)
1Asl
(p(A
Σ
[Ajl
A,CA,
(A(A)
Σ
|A]
AEEA/AE2A
(At))(A,)
(et).(O.))
(36)
Thus.
N
lim HODMMD' (m, m2) 7-000
=
Σ
(BetP((0)) BetP)
(37)
Property 2. When mi and f' degenerate into probability distributions, that is, U = (u,, u2,..., uN)
and V = (U1,U2,.... U,, UN), the proposed HODMMD degenerates into a maximum mean difference.
HODMMD" (fu, mz) = MMD(M), m2)
(38)
Proof. When my and m² are probability distribution,
VA; E 20 m)(A)) = Ui, (2,A)) vi
(39)
23

---

N
and it satisfies Σ m1 (A.) =, Σ (A2) =
EACA (1411)
اlaاl Lael (1+1)1151-ا11) me (Az)
m (A.) = lim
Ea.529 EA.CA, (145l) (Ide)) ارعاج
(1+1)1481--14) me (A₂)
(mi)Ai)
(40)
therefore,
N
HODMMD" (Mi, =
Σ
mi (Ai) - m/ (Ai))
74
Σ
(m1 (A,)
-m (Ai))
71
Σ (u. vz))
1
MMD (U.
(41)
Property 3. HODMMD" (m,, m2) and HODMMD' (mz m1) are equivalent.
HODMMD' (m,, m2) = HODMMD' " (mz mi)
(42)
Proof.
N
HODMMD" (m., =
Σ
m (Ai) - m (Ai))
14
Σ (mi (A.) ma (Ai))
7L
(43)
HODMMD" (m2, m2)
Σ
m (Ai)
m, (Ai))
92
11
N Σ
(mz (At) m2 (Ai))
1=1
(44)
Thus,
HODMMD (M,, HODMMD (mz, mi)
(45)
L
Property When my m2, the value of HODMMD always equal to
HODMMD" (f,, m2) 0
(46)
24

---

Proof. When m1 = m2
N
HODMMD" (m1, =
Σ
m (Ai) - -m (Ai))
Σ
(m2 (At) mm (Ae))
71
N
Σ (mi (A,) mai (A:))
0
(47)
A.3 Broader Impacts
This paper proposes a dynamic learning strategy based on nonuniform splitting mechanism and Hilbert space mapping promote real-world applications. We apply the proposed method in pattern classification, image classification, and low-light image enhancement encountered in real life, which encourages research their synergistic combination in real life. In addition, we the first to introduce DSE theory to low-light image enhancement and achieve effective performance enhancement for low-light image enhancement tasks. This provides new idea for the low-light image enhancement task. As far as this paper is concerned, we believe that the proposed method does have any significant negative impact.
A.4
Additional details regarding the experiment
A.4.1 Dataset and experimental settings
To rigorously evaluate the performance of the proposed method, we conducted extensive experiments and applied the proposed algorithm in three experiments. For pattern classification, experiments were conducted on the Iris 18], Heart (27), Hepatitis [1]. Parkinsons [36], Australian [42], Segment 21, and Connectionist Bench (CB datasets, and the details of these datasets are shown in Table 4 In this evaluation phase, we compare the proposed method with a class of classical
classifiers; Bayes theorem-basee classifier (NaB) 223 k-nearest neighbor classification method
(KNN) [12]. decision tree algorithm (REPTree) 19 support vector machine classifier (SVM)
5]. SVM method with radial basis function (SVM-RBF) ( a multilayer perceptron method
(MLP) 4 and radial basis function network (RBFN) g Another class is evidence theory-
classifiers: a DS theory- based kNN method (kNN-DST)
15 a data probability distribution- based
method (NDC) [60]. an evidence calibration method (EvC) 61 and generalized divergence-base based
decision-makinn method (DMA) 58
Table 4: Dataset information.
Dataset
Instances Class Features Missing Values
Iris[T8
150
3
4
No
Hcar
270
13
No
Hepatitis 1
155
19
Yes
Parkinsons 36
197
2
22
No
Australian 42
690
2
14
Yes
Segment 2
2310
7
19
No
CBench 16
990
11
10
No
For image classification, experiments were conducted on the publicly available datasets CIFAR- 10[]] and CIFAR-100(II] and the details of these datasets are shown in Table Furthermore, performance comparisons were made with current state-of-the-art methods, including DIR-Net [40).
25

---

MT ReSTE 54 ADMM9) SML[T4, 2DSP[2O, BiPer 500 TAB 28 APL[70] ESNN 47 Dspike 34], GLIF 66
43), P7S. MPBN 222, Als-ResNet (24 and BKDSNN 63
Table 5: Dataset information.
Dataset
Train set
Test
Class
CIFAR-I0 31
50000
10000
10
CIFAR- 100 31
50000
10000
100
Table 6: Dataset information.
Dataset
Train
Test set
1.O.-v (53
485
15
LOL-v2-real 65
689
100
LOL-v2-syn
SID 7
2099
598
SMID 6
20809
5046
In addition, we validated the effectiveness of the proposed method low-light image enhancement task and tested on the publicly available datasets LOL.-v (53, I.LL-V2-real (65) and I.OL.-
v2-syn 165]. The allocation of the datasets and related information is shown in Table 6 In this evaluation phase, our method was compared with several state-of-the-arr lighlight image enhancement methods, including MIRNet(68). [5] ZeroDCE[11] [53), 6RB) RUAS(37), ZeroDCE++(31 SCI and Restormer 29]. In addition, to realistically demonstrate the superiority selected the baseline network, and only targeted
of our method, methods from recent years
training strategies were added to the original methods, including SNR [62], LLFlow-L [52], LLFlow-
S [52] and Retinexformer 3 For fairness, the parameter settings were kept the same those in the original method. All the experiments were run on NVIDIA RTX 3090 GPUs.
A.4.2 Extended ablation studies
To verify the indispensability of the ADPT and HODMMD modules, we perform ablation studies the image classification task of the CIFAR-10 dataset with the architecture of ResNet-18, 18, and the results shown in Table 7
Table 7: Quantitative comparison of ablation study.
Dataset
Methods
Accuracy
w/o ADPT
94.56%
w/o HODMMD
93.55%
Replace HODMMD with Euclidean distance
94.31 %
CIFAR-10
Building BBAs using evidential neural networks
94.57%
Fusion via Dempster's combination rule
93.55%
Replacing HODMMD with Euclidean distance
94.31 %
Ours
95.61 %
The above experiments indicate that the model performance decreases to 94.56% when the ADPT module is removed. This shows that ADPT can use the prior information of the data to better address uncertainty information through nonuniform splitting, thereby significantly improving the classification accuracy. The accuracy of the model decreased by 2.06% after the HODMMD module
26

---

was removed. The accuracy of the model decreased by 1.3% when the Euclidean distance was used replace the HODMMD. This finding indicates that our method can more accurately capture the nonlinear difference between complex data distributions, thereby more effectively assessing the conflict between evidence and more reliable fusion decisions.
A.4.3 Hyperparameter sensitivity experiment
To better compare model performance, we have supplemented the experiments with analyses of key hyperparameter sensitivity and model complexity. The numerical experiments are as follows.
3
1
3
10 mi ((01,0a)) 1
mi :r::mi(10)) ({0:)) mi ((02))
mi ((01, 02]) = 10"
mi ({0a))
20'
4'
5
1
3
m2 m2((()))
m2 (m(2)) = 20
m2 (01, 02)) - mm22 (m20(())) - m2
(000022200 (10,, 0z}) 5
0.5, we tested the variation HODMMD in the range of [1,6], and the variation values of the mass function and HODMMD were plotted as a line graph. As increases, the value of the mass function of the uncertainty information gradually decrease assigned to the mass function represents single category. and the HODMMD value also decreases. In addition, T was fixed, and the variation of HODMMD in the range of [0.05, 10] for was tested. When is between [0.05, 0.1], the HODMMD rapidly decreases, and when is between [0.1, 21. tends to increase and eventually stabilizes.
By fixing the kernel bandwidth
Second, in the classification and LLIE tasks, T controls the degree of nomuniform splitting. We tested the effect on task aceuracy when т was 1,2.3,4.5,6. The results show that when 5, the model performance remains stable and optimal. Similarly, for a, we took the interval as 0.1 to test the effect on task accuracy between [0.1, 2]. The results show that when o 0.5, the model performance remains stable and optimal. In summary, we fix 5 and 0.5.
A.4.4 Analysis of model complexity
We have added parameter (M), FLOPs (G) and FPS comparisons with the baseline method on the low-light image enhancement task. The results are shown in Table g
Table 8: Efficiency Comparison of different methods.
Methods
Param(M)
FLOPs(G)
FPS
SNR
4.01
26.35
1.175
SNR-TTS
5.07
37.56
1.172
LLFlow-L
37.68
287
0.813
LLFlow-L-TTS
38.74
298.21
0.812
LLFlow-S
4.97
37.86
0.943
I.LFlow-S-TTS
6.03
49.07
0.942
Retinexformer
1.61
15.57
1.724
Retinexformer- TTS
2.67
26.78
1.718
The results indicate that the complexity and time of the model both increase after the introduction of the TTS. However, considering the improvement in model performance, this increase is within the acceptable range, which proves the actual application efficiency our method.
A.4.5 Large dataset experiment
The experiments on the SID and SMID datasets to verify the effectiveness of the TTS by using the Retinexformer the baseline networks. The results are shown in Table
A.5 Discussion of Our Method with Machine Learning Methods and Deep Learning Methods
Although different methods are currently available to address decision-making problems, our method has the following advantages over machine learning methods and deep learning methods.
27

---

Table 9: Quantitative comparison of SID and SMID datasets.
SMID 6
SID 7
Methods
PSNR
SSIM
PSNR
SSIM
Retinexformer 2C23
29.15
0.815
24.44
0.680
Retinexformer- TTS
29.23(+0.08) 0.816(+0.001) 24.62(+0.18) 0.682(+0.002)
First, our approach has better ability handle uncertainty. Machine learning and deep learning usually produce only single probability estimate and make predictions under the assumption of mapping relationships. This approach does not model uncertainty well in the face of conflicting or uncertain information. However, our method directly models uncertainty through BBA, which allows assigning confidence to composite propositions. Moreover, it can dynamically adjusted according to the level of importance between different pieces of information, capturing the nonspecificity of the information and quantifying the discrepancies between pieces of evidence more flexible way.
Second, our method can fuse information from multiple sources in more rational way. Machine learning and deep learning approaches tend to use network layers for feature learning and prediction and lack interpretability for information fusion decisions. However, our method can understand the reasons behind the decisions well. For example, the proposed method maps data into Hilbert space for computation, which is more responsive to the differences in the true distributions of complex data, reduces conflicts between different types of information, and highly interpretable.
Third, our approach remains applicable in the presence of limited data. The training process of deep learning suffers from overfitting small unrepresentative data and relies training complex models. However, our method's splitting mechanism, which is based on a priori information, can be more flexible dealing with uncertainty and conflicting information and can work effectively with limited data.
We propose dynamic learning strategy based nonuniform splitting mechanism and Hilbert space mapping enhances the interpretability of the decision. This will promote the application of deep learning technology in wider range of fields. In addition to classification and low-light image enhancement, our ideas can be applied in all uncertainty tasks, for example, image segmentation (uncertainty of the object boundary) and automatic driving (uncertainty in the fusion of multisensor information). Owing to time constraints, this work requires a large amount of computing resources and time. We will continue explore the performance of this method in other fields.
28


Reviews:
[{"review_id": "Em9xqp1iRg", "reviewer": "Reviewer_FkZX", "summary": "This paper is proposed to quantify the uncertainty based on Dampster-Shafer theory. It presents a fusion framework based on a nonuniform splitting mechanism and Hilbert space mapping to incorporate the prior information.", "questions": "See Strengths And Weaknesses", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 2, "strengths_and_weaknesses": "First, this paper is composed with a wrong template. It does not have any line numbers.\n\nOverall, this paper is very hard to follow. The method section includes too many concepts and equations without further discussion (even without meaningful references to the background). The experiments section, especially 4.2 and 4.3, only shows the improvements of performance. It lacks the discussion on why the proposed method is better.", "was_revised": true, "final_justification": "It seems other reviewers give borderline to positive ratings. Given that the authors provide comprehensive experiments and discussion in rebuttal. Hope most of the results can be included in the paper.", "rebuttal": "# FkZX W1\n&emsp;&emsp;Thank you very much for your suggestion. We have used “\\usepackage{neurips_2025}” to correct the template with line numbers.\n# FkZX W2\n&emsp;&emsp;Thank you very much for your suggestion. We have provided more detailed explanations of the concepts and formulas that appeared in the paper. In the experimental section, we have added more detailed experimental analysis and given a systematic and objective evaluation of the advantages and limitations of the proposed method. The specific modifications are as follows:\n\n&emsp;&emsp;**Optimize the explanation and discussion of the concepts and formulas in the paper**\n\n&emsp;&emsp;(1) In the “Appendix/supplemental material” section, the relevant backgrounds of “Frame of discernment”, “Power set”, “Basic belief assignment”, “Focal set” and “Dempster's combination rule” are described in more detail. The classic literature was cited as the theoretical basis.\n> [1] Xiao , F. & Pedrycz , W. (2023) Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 45(2):2054–2070.\n> \n> [2] Sensoy , M., Kaplan , L., & Kandemir , M. (2018. ) Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems 31.\n\n&emsp;&emsp;(2) Definition and quantification of prior information. The prior information in this paper is based on the proposed nonuniform splitting mechanism. The prior information of the data is used by the introduction of the diffusion function. This prior information-based splitting mechanism can address uncertainty more flexibly. In our framework, “prior information” refers to the intrinsic characteristics of the structure of the data itself and the initial evidence distribution. Specifically, a more specific hypothesis will carry more important information than an uncertain hypothesis.\n\n&emsp;&emsp;The “prior information” proposed in this paper was quantified and integrated by the ADPT module, which was introduced through the diffusion function. We used the cardinality of hypothesis set A, that is, $|A|$, to quantify it. The smaller the value is, the more specific the hypothesis, which can be understood as the higher its “prior” importance. The diffusion function $D(A_{i},A_{j})$ regulates the process in which the mass function is transferred from a fuzzy hypothesis $A_j$ to a more specific hypothesis $A_i$. This ensures that the redistribution of uncertainty can be purposefully biased toward more specific and more likely hypotheses, where the hyperparameter $\\tau$ controls the strength of this nonuniform distribution.\n\n&emsp;&emsp;(3) Unified concept. We checked all the concepts and content in the paper and revised some confusing expressions. We changed “a fusion framework based on a nonuniform splitting mechanism and Hilbert space mapping” to “a dynamic learning strategy based on a nonuniform splitting mechanism and Hilbert space mapping (DNHFrame)” (Section 3.1), which is the complete name of the whole theory, including “adaptive diffusion probability transformation” (Section 3.2), “probabilistic reliability assessment” (Section 3.3), and “collaborative decision optimization” (Section 3.4), and the three parts work together.\n\n&emsp;&emsp;LGS is a specific application of DNHFrame in combination with a loss function for LLIE tasks. The idea is to use the proposed DNHFrame to calculate the degree of degradation weight ($I_{pro}$) of different regions in the image to target the training process of an existing LLIE network (Eq. 16). To avoid confusion, we unify LGS as the targeted training strategy (TTS) in the third contribution.\n\n&emsp;&emsp;**Supplementary key implementation details and hyperparameter discussion**\n\n&emsp;&emsp;(1) In the experimental section, the results of sections 4.1--4.4 are more fully discussed. In particular, the slight decrease in individual performance on the LLIE task is explained.\n\n&emsp;&emsp;(2) New numerical experiments are added in Section 4.1 to illustrate the principles of our method.\n$$\n\\\\widehat{m_1}:\\\\widehat{m_1}(\\\\{\\\\theta_1\\\\})=\\\\frac{3}{20},\\\\widehat{m_1}(\\\\{\\\\theta\n  _2\\\\})=\\\\frac{1}{4},\\\\widehat{m_1}(\\\\{\\\\theta_1,\\\\theta_2\\\\})=\\\\frac{3}{10},\\\\widehat{m_1}(\\\\{\\\\theta_3\\\\})=\\\\frac{1}{10},\\\\widehat{m_1}(\\\\{\\\\theta_1,\\\\theta_3\\\\})=\\\\frac{1}{5};\\\\\n  \\\\widehat{m_2}:\\\\widehat{m_2}(\\\\{\\\\theta_1\\\\})=\\\\frac{1}{4},\\\\widehat{m_2}(\\\\{\\\\theta_2\\\\})=\\\\frac{3}{20},\\\\widehat{m_2}(\\\\{\\\\theta_1,\\\\theta_2\\\\})=\\\\frac{1}{5},\\\\widehat{m_2}(\\\\{\\\\theta_3\\\\})=\\\\frac{1}{5},\\\\widehat{m_2}(\\\\{\\\\theta_1,\\\\theta_3\\\\})=\\\\frac{1}{5}.\n$$\n&emsp;&emsp;By fixing the kernel bandwidth $\\sigma=0.5$, we tested the variation in HODMMD in the range of [1,6], and the variation values of the mass function and HODMMD were plotted as a line graph. As $\\tau$ increases, the value of the mass function of the uncertainty information gradually decrease is assigned to the mass function represents a single category, and the HODMMD value also decreases. In addition, $\\tau=1$ was fixed, and the variation of HODMMD in the range of [0.05, 10] for $\\sigma$ was tested. When $\\sigma $ is between [0.05, 0.1], the HODMMD rapidly decreases, and when $\\sigma$ is between [0.1, 2], it tends to increase and eventually stabilizes.\n\n&emsp;&emsp;(3) To verify the indispensability of the ADPT and HODMMD modules, we perform ablation studies on the image classification task of the CIFAR-10 with the architecture of ResNet-18:\n|Dataset|Methods|Accuracy|\n|-|-|-|\n||$w/o$ ADPT|94.56%|\n||$w/o$ HODMMD|93.55%|\n|CIFAR-10|Replacing HODMMD with Euclidean distance|94.31%|\n||Building BBAs via evident neural networks[3]|94.57%|\n||Ours|**95.61%**|\n\n&emsp;&emsp;The above experiments indicate that the model performance decreases to 94.56% when the ADPT module is removed. This shows that ADPT can use the prior information of the data to better address uncertainty information through nonuniform splitting, thereby significantly improving the classification accuracy. The accuracy of the model decreased by 2.06% after the HODMMD module was removed. The accuracy of the model decreased by 1.3% when the Euclidean distance was used to replace the HODMMD. This finding indicates that our method can more accurately capture the nonlinear difference between complex data distributions, thereby more effectively assessing the conflict between evidence and more reliable fusion decisions. Moreover, in the LLIE task, we introduced the TTS to the baseline method, and the effectiveness of our method was verified through the improvement in performance.\n> [3] Tong, Z., Xu, P., & Denoeux, T. (2021) An evidenced classifier based on dempster-shafer theory and deep learning. Neurocomputing 450:275–293.\n\n&emsp;&emsp;(4) Adding hyperparameter sensitivity experiments. For the classification and LLIE tasks, the kernel bandwidth in HODMMD and the iteration settings in ADPT were empirically determined on the basis of experimental observations. $\\tau$ controls the degree of nonuniform splitting. We tested the effect on task accuracy when $\\tau$ was {1,2,3,4,5,6}. The results show that when $\\tau=5$, the model performance remains stable and optimal. Similarly, for $\\sigma$, we took the interval as 0.1 to test the effect on task accuracy between [0.1, 2]. The results show that when $\\sigma=0.5$, the model performance remains stable and optimal. In summary, we fix $\\tau=5$ and $\\sigma=0.5$.\n\n&emsp;&emsp;(5) Comparison experiment with increased model computational complexity. We have added parameter (M), FLOPs (G) and FPS comparisons with the baseline method on the LLIE task. The results are shown in the table below. Notably, LGS is an application of our thoughts in LLIE, which is a specific application to a task. To avoid confusion, we unify LGS as the “targeted training strategy (TTS)” in the third contribution.\n|Methods|Param(M)|FLOPs(G)|FPS|\n|-|-|-|-|\n|SNR|4.01|26.35|1.175|\n|SNR-TTS|5.07|37.56|1.172|\n|LLFlow-L|37.68|287|0.813|\n|LLFlow-L-TTS|38.74|298.21|0.812|\n|LLFlow-S|4.97|37.86|0.943|\n|LLFlow-S-TTS|6.03|49.07|0.942|\n|Retinexformer|1.61|15.57|1.724|\n|Retinexformer-TTS|2.67|26.78|1.718|\n\n&emsp;&emsp;The results indicate that the complexity and time of the model both increase after the introduction of the TTS. However, considering the improvement in model performance, this increase is within the acceptable range, which proves the actual application efficiency of our method.\n\n&emsp;&emsp;(6) In the LLIE task, the experiments on the SID and SMID datasets were added:\n|Dataset|SMID||SID||\n|-|-|-|-|-|\n||PSNR|SSIM|PSNR|SSIM|\n|Retinexformer|29.15|0.815|24.44|0.680|\n|Retinexformer-TTS|29.23|0.816|24.62|0.682|\n\n&emsp;&emsp;In combination with the supplemental experiments, the introduction of TTS consistently improves the performance in all but a few cases (e.g., LLFLow-L and LLFLow-S on the LOL-v1 dataset). The core of this strategy is to guide the model to focus on the most severely degraded areas in the image. This strategy greatly improves the detail recovery and noise suppression in these key areas, thereby significantly reducing the pixel-level error, which directly reflects the increase in the PSNR. However, the TTS may slightly change the local statistical characteristics of the image. For example, to restore textures obscured by noise, some noise patterns may be amplified during the learning process, resulting in a slight loss of structural information. Importantly, from the comparison of the visual effects in Figure 4, the introduction of the TTS in the baseline method, the subjective quality of the image was better, and the overall performance tended to increase, which verified the effectiveness of the proposed method."}, {"review_id": "xM0u7Myhhs", "reviewer": "Reviewer_9jD7", "summary": "This paper introduces a sophisticated information fusion framework based on evidence theory, designed to address the challenges of processing uncertain and conflicting information. The method presents theoretical novelty by incorporating a non-uniform partitioning mechanism (ADPT) for dynamic weight allocation and a Hilbert space metric (HODMMD) to effectively resolve evidence conflicts. The authors successfully apply this framework to tasks such as pattern classification, image classification, and low-light image enhancement, with the latter application demonstrating the potential of using evidence theory as a “learning guidance strategy,” offering a novel perspective on solving practical problems.", "questions": "see weakness", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The framework ingeniously connects abstract evidence theory with concrete application needs. A key example is its use in low-light image enhancement, where the complex theory is transformed into a practical, plug-and-play “learning guidance strategy” (LGS). This cross-domain application highlights the flexibility and practical value of the proposed ideas.\n2. A core innovation lies in the dynamism of the method. Through the adaptive diffusion probability transformation (ADPT) mechanism, the framework moves beyond the static or uniform assumptions of traditional methods regarding information importance. This allows the model to more intelligently handle uncertainty by leveraging the data’s own prior information and the importance of different subsets.\n3. By introducing the kernel-based High-Order Dynamic Maximum Mean Discrepancy (HODMMD), the method surpasses traditional Euclidean-based metrics for handling evidence conflicts. It is better equipped to capture non-linear dissimilarities in complex data distributions, thereby enabling a more accurate assessment and mitigation of conflicts before fusion.\n\nWeakness\n1. The paper frequently mentions leveraging the “prior information” of the data. However, it remains unclear what this “prior information” specifically refers to in the context of different tasks (e.g., image classification vs. LLIE). The authors are requested to provide a clearer, more concrete explanation of how this information is defined, quantified, and integrated into the model for each application.\n2. The proposed framework is composed of several novel components (ADPT, HODMMD, etc.). A significant weakness is the lack of ablation studies. Without them, it is impossible to discern the individual contribution of each component to the overall performance improvement. The authors should conduct thorough ablation experiments to demonstrate the effectiveness of each proposed module.\n3. There is insufficient discussion on the model’s complexity and its sensitivity to key hyperparameters. For instance, the selection criteria and impact of the diffusion coefficient τ and the kernel bandwidth σ (for HODMMD) are not detailed. Additionally, a discussion on computational complexity, including a comparison of training times against baseline methods, should be provided to assess the practical efficiency of the framework.\n4. The results in Table 3 show that applying the LGS module sometimes leads to a decrease in the SSIM metric (e.g., for LLFlow-L and LLFlow-S on the LOL-v1 dataset). These negative results are not addressed in the discussion. The authors should provide an analysis or explanation for these occurrences to offer a more balanced and complete evaluation of their method’s impact.", "was_revised": true, "final_justification": "The authors’ response has satisfactorily addressed the issues I raised during the review process. I therefore maintain my original evaluation score.", "rebuttal": "# 9jD7 S1-3\n&emsp;&emsp;Thank you very much for your opinion. Our method is based on Dempster–Shafer evidence theory, and we effectively address uncertainty information by proposing a dynamic learning strategy based on a nonuniform splitting mechanism and Hilbert space mapping. The validity of the method is also illustrated by numerous experiments.\n# 9jD7 W1\n&emsp;&emsp;Thank you very much for your opinion. We have provided a clearer description of the concept of “prior information” in the paper.\n\n&emsp;&emsp;**(1) Definition of prior information**\n\n&emsp;&emsp;The prior information in this paper is based on the proposed nonuniform splitting mechanism. The prior information of the data is used by the introduction of the diffusion function. This prior information-based splitting mechanism can address uncertainty more flexibly. In our framework, “prior information” refers to the intrinsic characteristics of the structure of the data itself and the initial evidence distribution. Specifically, a more specific hypothesis will carry more important information than an uncertain hypothesis.\n\n&emsp;&emsp;**(2) Quantitative integration mechanism of prior information**\n\n&emsp;&emsp;The “prior information” proposed in this paper was quantified and integrated by the ADPT module, which was introduced through the diffusion function. We used the cardinality of hypothesis set $A$, that is, $|A|$, to quantify it. The smaller the value is, the more specific the hypothesis, which can be understood as the higher its “prior” importance. The diffusion function $D(A_{i},A_{j})$ regulates the process in which the mass function is transferred from a fuzzy hypothesis $A_j$ to a more specific hypothesis $A_i$. This ensures that the redistribution of uncertainty can be purposefully biased toward more specific and more likely hypotheses, where the hyperparameter $\\tau$ controls the strength of this nonuniform distribution.\n\n&emsp;&emsp;**(3) Specific application in different tasks**\n\n&emsp;&emsp;In the image classification task, “prior information” is the initial probability distribution obtained by performing feature extraction on the input samples for the CNN and ResNet-18, with the last linear layer removed. We convert this probability distribution to an initial BBA. This BBA not only assigns belief values to a single class (e.g., cat) but also jointly assigns belief values to multiple classes of uncertainty (e.g., cat, dog, duck). The ADPT module uses a nonuniform splitting mechanism to redistribute the uncertainty beliefs assigned to the joint category. This enables the model to better address situations that are difficult to distinguish and ultimately make more accurate judgments.\n\n&emsp;&emsp;In the LLIE task, “prior information” refers to the degree of degradation of different regions in the image. The proposed targeted training strategy (TTS) first divides the input image into multiple patches. The idea of classification is then used to generate an initial probability distribution for the degree of degradation of each patch. Through the ADPT module, a higher probability value is subsequently assigned to patches with a high degree of degradation, and the representation $I_{pro}$, which represents the degree of degradation of different regions, is finally generated (Eq. 15). $I_{pro}$ quantifies the degradation information of each region and is weighted with the loss function of the original network to guide the training of the enhanced network (Eq. 16). Specifically, the network pays more attention to the image regions with more severe degradation and effectively integrates the understanding of image content (i.e., where enhancement is most needed) into the model learning process.\n\n# 9jD7 W2\n&emsp;&emsp;Thank you very much for your suggestion. We have added a new ablation study to evaluate the effectiveness of the novel components ADPT and HODMMD in the framework. In particular, we have added new experiments to compare the performance of different methods on fusion strategies.\n\n&emsp;&emsp;To verify the indispensability of the ADPT and HODMMD modules, we perform ablation studies on the image classification task of the CIFAR-10 dataset with the architecture of ResNet-18:\n|Dataset|Methods|Accuracy|\n|-|-|-|\n||$w/o$ ADPT|94.56%|\n|CIFAR-10|$w/o$ HODMMD|93.55%|\n||Ours|**95.61%**|\n\n&emsp;&emsp;In addition, we have added the following experiments to verify the effectiveness of the proposed method:\n|Dataset|Methods|Accuracy|\n|-|-|-|\n||Replacing the HODMMD with the Euclidean distance|94.31%|\n|CIFAR-10|Building BBAs via evident neural networks[1]|94.57%|\n||Ours|**95.61%**|\n\n&emsp;&emsp;The above experiments indicate that the model performance decreases to 94.56% when the ADPT module is removed. This shows that ADPT can use the prior information of the data to better address uncertainty information through nonuniform splitting, thereby significantly improving the classification accuracy. The accuracy of the model decreased by 2.06% after the HODMMD module was removed, and the accuracy of the model decreased by 1.3% when the Euclidean distance was used to replace HODMMD, which indicates that our method can more accurately capture the nonlinear difference between complex data distributions, thereby more effectively assessing the conflict between evidence and more reliable fusion decisions. Moreover, in the LLIE task, we introduced the TTS to the baseline method, and the effectiveness of our method was verified through the improvement in performance.\n> [1] Tong, Z., Xu, P., & Denoeux, T. (2021) An evidenced classifier based on dempster-shafer theory and deep learning. Neurocomputing 450:275–293.\n\n# 9jD7 W3\n&emsp;&emsp;Thank you very much for your suggestion. We have added relevant experiments to supplement the sensitivity discussion of key hyperparameters and the analysis of model complexity.\n\n&emsp;&emsp;**(1) Sensitivity of hyperparameters**\n\n&emsp;&emsp;First, we added a numerical experiment as follows:\n$$\n\\widehat{m_1}:\\widehat{m_1}(\\{\\theta_1\\})=\\frac{3}{20},\\widehat{m_1}(\\{\\theta\n  _2\\})=\\frac{1}{4},\\widehat{m_1}(\\{\\theta_1,\\theta_2\\})=\\frac{3}{10},\\widehat{m_1}(\\{\\theta_3\\})=\\frac{1}{10},\\widehat{m_1}(\\{\\theta_1,\\theta_3\\})=\\frac{1}{5};\\\\\n  \\widehat{m_2}:\\widehat{m_2}(\\{\\theta_1\\})=\\frac{1}{4},\\widehat{m_2}(\\{\\theta_2\\})=\\frac{3}{20},\\widehat{m_2}(\\{\\theta_1,\\theta_2\\})=\\frac{1}{5},\\widehat{m_2}(\\{\\theta_3\\})=\\frac{1}{5},\\widehat{m_2}(\\{\\theta_1,\\theta_3\\})=\\frac{1}{5}.\n$$\n&emsp;&emsp;By fixing the kernel bandwidth $\\sigma=0.5$, we tested the variation in HODMMD in the range of [1,6], and the variation values of the mass function and HODMMD were plotted as a line graph. As $\\tau$ increases, the value of the mass function of the uncertainty information gradually decrease is assigned to the mass function represents a single category, and the HODMMD value also decreases. In addition, $\\tau=1$ was fixed, and the variation of HODMMD in the range of [0.05, 10] for $\\sigma$ was tested. When $\\sigma $ is between [0.05, 0.1], the HODMMD rapidly decreases, and when $\\sigma$ is between [0.1, 2], it tends to increase and eventually stabilizes.\n\n&emsp;&emsp;Second, in the classification and LLIE tasks, $\\tau$ controls the degree of nonuniform splitting. We tested the effect on task accuracy when $\\tau$ was {1,2,3,4,5,6}. The results show that when $\\tau=5$, the model performance remains stable and optimal. Similarly, for $\\sigma$, we took the interval as 0.1 to test the effect on task accuracy between [0.1, 2]. The results show that when $\\sigma=0.5$, the model performance remains stable and optimal. In summary, we fix $\\tau=5$ and $\\sigma=0.5$.\n\n&emsp;&emsp;**(2) Complexity analysis of the model**\n\n&emsp;&emsp;We have added parameter (M), FLOPs (G) and FPS comparisons with the baseline method on the LLIE task. The results are shown in the table below. Notably, LGS is an application of our thoughts in LLIE, which is a specific application to a task. To avoid confusion, we unify LGS as the “targeted training strategy (TTS)” in the third contribution.\n|Methods|Param(M)|FLOPs(G)|FPS|\n|-|-|-|-|\n|SNR|4.01|26.35|1.175|\n|SNR-TTS|5.07|37.56|1.172|\n|LLFlow-L|37.68|287|0.813|\n|LLFlow-L-TTS|38.74|298.21|0.812|\n|LLFlow-S|4.97|37.86|0.943|\n|LLFlow-S-TTS|6.03|49.07|0.942|\n|Retinexformer|1.61|15.57|1.724|\n|Retinexformer-TTS|2.67|26.78|1.718|\n\n&emsp;&emsp;The results indicate that the complexity and time of the model both increase after the introduction of the TTS. However, considering the improvement in model performance, this increase is within the acceptable range, which proves the actual application efficiency of our method.\n\n# 9jD7 W4\n\n&emsp;&emsp;Thank you very much for your suggestion. In the LLIE task, after we introduced the TTS, some SSIM indicators decreased. We have added an analysis and explanation of these negative results to perform a more balanced and complete evaluation of the impact of the proposed method.\n\n&emsp;&emsp;In combination with the supplemental experiments, the introduction of TTS consistently improves the performance in all but a few cases (e.g., LLFLow-L and LLFLow-S on the LOL-v1 dataset). The core of this strategy is to guide the model to focus on the most severely degraded areas in the image. This strategy greatly improves the detail recovery and noise suppression in these key areas, thereby significantly reducing the pixel-level error, which directly reflects the increase in the PSNR. However, the TTS may slightly change the local statistical characteristics of the image. For example, to restore textures obscured by noise, some noise patterns may be amplified during the learning process, resulting in a slight loss of structural information. Importantly, from the comparison of the visual effects in Figure 4, after the introduction of the TTS in the baseline method, the subjective quality of the image was better, and the overall performance tended to increase, which verified the effectiveness of the proposed method."}, {"review_id": "DFJVC7GklU", "reviewer": "Reviewer_kSLV", "summary": "This paper aims to address the limitations in model performance that arise from insufficient prior information, imbalanced data distribution, and conflicting evidence fusion in Dempster-Shafer Evidence Theory (DSE). The main contribution of this work is a novel learning strategy that combines a non-uniform splitting mechanism with Hilbert space mapping. This approach enables prior knowledge fusion through dynamic basic belief assignments（BBAs） guided by data-driven diffusion factors, resolves nonlinear conflicts using Hilbert space feature mapping, and incorporates targeted training strategies to enhance the learning of critical features. Ultimately, it facilitates effective modeling of uncertain information, thereby improving performance in both classification tasks and image enhancement applications. Experimental results show that the proposed method outperforms existing approaches in these domains and provides new insights into the modeling of uncertain information.", "questions": "1. There is some confusion in the content presentation. The proposed method is referred to as a \"dynamic learning strategy\" in the section title, a \"fusion framework\" in the abstract, and a \"learning guidance strategy\" in the main text. Additionally, the plug-and-play descriptions of LGS and ADPT are somewhat ambiguous and may cause confusion. Consistent terminology should be used for clarity.\n2. key implementation details—such as the Gaussian kernel bandwidth in HODMMD and iteration settings in ADPT—are insufficiently described; clarification on whether they are empirically or systematically determined is needed.\n3. The third contribution mentioned in the paper is the design of a targeted training strategy. It is, however, unclear whether this refers to the collaborative decision optimization described in Section 3.4 or the loss function introduced in Section 4.4. If the loss in Section 4.4 is indeed part of the proposed method, it should be moved to Section 3 for better organizational clarity.\n4. Compared to other methods such as DMA, this work takes into account the importance and differences among information sources in its relevance measurement. However, the experimental validation lacks a comparison with existing methods in terms of uncertainty modeling. Additionally, there is insufficient comparative analysis — such as against the Dempster's rule or Euclidean distance — for BBAs fusion. Further experiments are needed to substantiate the effectiveness of HODMMD.\n5. It would be helpful to evaluate the method on larger datasets (e.g., SID, SMID) and compare it with recent models like Retinexformer, especially for important region focusing. In addition, its performance in other domains is worth exploring.", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: 1. This article proposes a non-uniform splitting mechanism that dynamically assigns weights based on the prior information of different subset importance to handle uncertainty and conflict information, achieving more efficient and flexible uncertainty modeling. 2. The high-order dynamic maximum mean difference (HODMMD) is used to map the data to Hilbert space for calculation, to reducing the conflict \nduring the fusion process of different BBAs. 3. The method can be used as a plug-and-play module for focusing on important areas and has been validated in the field of low light image enhancement. \nWeaknesses: 1. The paper provides a solid theoretical foundation but lacks sufficient experimental validation. 2. The organization and presentation of content could be improved to enhance readability and logical flow. 3. Several parts of the paper suffer from unclear expressions, especially in the descriptions of the methodology and experimental procedures. These sections need clarification and refinement for better understanding.", "was_revised": false, "final_justification": "", "rebuttal": "# kSLV S1-3\n&emsp;&emsp;Thank you very much for your opinion. We propose a dynamic learning strategy based on a nonuniform splitting mechanism and Hilbert space mapping to effectively process uncertain information. The validity of the method is also illustrated by numerous experiments.\n# kSLV W1\n&emsp;&emsp;Thank you very much for your suggestion and for affirming the theoretical basis of this work. We have performed supplementary experiments on the basis of your suggestion. First, experiments targeting uncertainty modelling and BBA fusion strategies were added (Q4). Second, experiments were conducted on larger datasets (Q5). Third, sensitivity experiments for hyperparameters were added (Q2).\n# kSLV W2\n&emsp;&emsp;Thank you very much for your suggestion; we have comprehensively reviewed the papers. First, we standardized the terminology in the full text to ensure the consistency of the core concepts (Q1). Second, we reorganized the structure of the paper to make the logic clearer and more coherent (Q3).\n# kSLV W3\n&emsp;&emsp;Thank you very much for your suggestion. We have checked and reorganized the individual expressions in the paper and have reviewed and modified the entire method chapter and experimental chapter. First, we rewrote the iterative procedure of ADPT in more precise language. Second, we reviewed the description of the experimental results. Third, the application of the proposed method to the LLIE task is described in more detail.\n# kSLV Q1\n&emsp;&emsp;Thank you very much for your suggestion. We have reviewed all the concepts and content in the paper and have revised some confusing expressions as follows:\n\n&emsp;&emsp;(1) We changed “a fusion framework based on a nonuniform splitting mechanism and Hilbert space mapping” to “a dynamic learning strategy based on a nonuniform splitting mechanism and Hilbert space mapping (DNHFrame)”. We strengthened and unified the presentation.\n\n&emsp;&emsp;(2) ADPT is a part of DNHFrame. LGS is a specific application of DNHFrame in combination with a loss function in the LLIE task. The idea is to use the proposed DNHFrame to calculate the degradation degree weights of different regions in the image ($I_{pro}$) to train an existing LLIE network (Eq. 15, 16). To avoid confusion, we unify LGS as the targeted training strategy (TTS).\n\n&emsp;&emsp;(3) DNHFrame is a plug-and-play module that can be conveniently integrated into various existing LLIE models to optimize their training process by providing bootstrap weights without changing the network structure of these models themselves.\n\n# kSLV Q2\n&emsp;&emsp;Thank you very much for your suggestion. In the experiments, the kernel bandwidth in HODMMD and the iteration settings in ADPT were obtained through empirical methods. In addition, we added new numerical experiments and hyperparameter sensitivity experiments to illustrate the kernel bandwidth and the iteration settings and performed a detailed experimental analysis.\n\n&emsp;&emsp;**(1) Classification and LLIE experiment**\n\n&emsp;&emsp;For the classification and LLIE tasks, the kernel bandwidth and the iteration settings were based on experimental observations. We tested the effect on task accuracy when $\\tau$ was {1,2,3,4,5,6} and when $\\sigma$ was taken at intervals of 0.1 between [0.1,2]. The results show that when $\\tau=5$ and $\\sigma=0.5$, the model performance remains stable and optimal.\n\n&emsp;&emsp;**(2) Numerical experiment**\n\n&emsp;&emsp;We added a numerical experiment as follows:\n$$\n\\widehat{m_1}:\\widehat{m_1}(\\{\\theta_1\\})=\\frac{3}{20},\\widehat{m_1}(\\{\\theta\n  _2\\})=\\frac{1}{4},\\widehat{m_1}(\\{\\theta_1,\\theta_2\\})=\\frac{3}{10},\\widehat{m_1}(\\{\\theta_3\\})=\\frac{1}{10},\\widehat{m_1}(\\{\\theta_1,\\theta_3\\})=\\frac{1}{5};\\\\\n  \\widehat{m_2}:\\widehat{m_2}(\\{\\theta_1\\})=\\frac{1}{4},\\widehat{m_2}(\\{\\theta_2\\})=\\frac{3}{20},\\widehat{m_2}(\\{\\theta_1,\\theta_2\\})=\\frac{1}{5},\\widehat{m_2}(\\{\\theta_3\\})=\\frac{1}{5},\\widehat{m_2}(\\{\\theta_1,\\theta_3\\})=\\frac{1}{5}.\n$$\n&emsp;&emsp;By fixing the kernel bandwidth $\\sigma=0.5$, the values of the variation in $\\tau$ in the mass function and HODMMD over the range [1, 6] were plotted on a line graph. As $\\tau$ increases, the value of the mass function of the uncertainty information gradually decrease, the HODMMD value also decreases. In addition, $\\tau=1$ was fixed, and the variation of HODMMD in the range of [0.05, 10] for $\\sigma$ was tested. When $\\sigma $ is between [0.05, 0.1], the HODMMD rapidly decreases, and when $\\sigma$ is between [0.1, 2], it tends to increase and eventually stabilizes.\n# kSLV Q3\n&emsp;&emsp;Thank you very much for your suggestion. In the third contribution mentioned in the paper, we designed the TTS, which refers to the application of the “DNHFrame” proposed in Section 4.4 to the LLIE task. To avoid confusion, we unify the LGS as the TTS.\n\n&emsp;&emsp;The proposed TTS divides the input image into multiple patches and then determines the initial probability distribution for the degree of degradation of each patch. A representation of the degree of degradation of the different regions $I_{pro}$ is generated after the ADPT module (Eq. 15), which weighted with the loss function of the original network to guide the training of the enhanced network (Eq. 16). Specifically, the network pays more attention to the image regions with more severe degradation and effectively integrates the understanding of image content (i.e., where enhancement is most needed) into the model learning process.\n\n&emsp;&emsp;We have moved the description of the specific implementation of our TTS in Section 4.4 to Section 3 to ensure that all the proposed methods are thoroughly described before the experimental section.\n# kSLV Q4\n&emsp;&emsp;Thank you very much for your suggestion. To examine the advantages of our method in uncertainty modelling and the effectiveness of the proposed BBA fusion method, we designed the following experiments on the CIFAR-10 dataset with the architecture ResNet-18 for the image classification task.\n\n&emsp;&emsp;**(1) Added comparison of different uncertainty modelling**\n|Dataset|Methods|Accuracy|\n|-|-|-|\n||Building BBAs via evident neural networks[1]|94.57%|\n|CIFAR-10|Using a uniform splitting mechanism[2]|94.56%|\n||Ours|**95.61%**|\n> [1] Huang, Y., Xiao , F., Cao , Z., & Lin, C.-T. (2023) Higher order fractal belief rényi divergence with its applications in pattern classification. IEEE Transactions on Pattern Analysis and Machine Intelligence.\n> \n> [2] Tong, Z., Xu, P., & Denoeux, T. (2021) An evidenced classifier based on dempster-shafer theory and deep learning. Neurocomputing 450:275–293.\n\n&emsp;&emsp;In addition, the method in [13] in the paper regards each neighboring point of the sample as evidence about the category to which the pattern belongs to construct BBAs. Method [58], which is based on the normal distribution, uses the relationship between the test data and the normal distribution model to construct BBAs. We compared these methods in uncertainty modelling, and the experimental results show the superiority of our method in uncertainty modelling over existing methods.\n\n&emsp;&emsp;**(2) Different BBAs fusion methods were added for comparison**\n|Dataset|Methods|Accuracy|\n|-|-|-|\n||Fusion via Dempster's combination rule|93.55%|\n|CIFAR-10|Replacing HODMMD with Euclidean distance|94.31%|\n||Ours|**95.61%**|\n\n&emsp;&emsp;The above experiments reveal that when simple Dempster's combination rule is used directly for fusion, that is, the HODMMD module is removed, the accuracy of the model decreases by 2.06%. The accuracy of the model decreased by 1.3% when the Euclidean distance was used to replace the HODMMD. This finding indicates that our method can more accurately capture the nonlinear difference between complex data distributions, thereby more effectively assessing the conflict between evidence.\n# kSLV Q5\n&emsp;&emsp;Thank you very much for your suggestion. We added experiments on the SID and SMID datasets to verify the effectiveness of the TTS by using the retinexformer as the baseline network and performed a detailed experimental analysis on the experimental results. In addition, we also considered the application of the proposed method in other fields.\n\n&emsp;&emsp;(1) Experimental supplementation\n|Dataset|SMID||SID||\n|-|-|-|-|-|\n||PSNR|SSIM|PSNR|SSIM|\n|Retinexformer|29.15|0.815|24.44|0.680|\n|Retinexformer-TTS|29.23|0.816|24.62|0.682|\n\n&emsp;&emsp;In combination with the supplemental experiments, the introduction of TTS consistently improves the performance in all but a few cases (e.g., LLFLow-L and LLFLow-S on the LOL-v1 dataset). The core of this strategy is to guide the model to focus on the most severely degraded areas in the image, thereby significantly reducing the pixel-level error. However, the TTS may slightly change the local statistical characteristics of the image, resulting in a slight loss of structural information. Importantly, from the comparison of the visual effects in Figure 4, after the introduction of the TTS in the baseline method, the subjective quality of the image was better, and the overall performance tended to increase, which verified the effectiveness of the proposed method.\n\n&emsp;&emsp;(2) The key to the method we propose is to address the uncertainty in the information. Our work prospects in other application areas are discussed in the conclusion paragraph. We propose DNHFrame enhances the interpretability of the decision. This will promote the application of deep learning technology in a wider range of fields. In addition to classification and LLIE, our ideas can be applied in all uncertainty tasks, for example, image segmentation (uncertainty of the object boundary) and automatic driving (uncertainty in the fusion of multisensor information). Owing to time constraints, this work requires a large amount of computing resources and time. We will continue to explore the performance of this method in other fields."}]

Author rebuttal:

Meta-review: as all the reviewers decide to accept this paper, i recommend to accept this paper. the authors should revise the paper based on the discussion.
Decision: Accept (poster)