arXiv:2604.09288v1 [cs.LG] 10 Apr 2026
Are Independently Estimated View Uncertainties Comparable? Unified Routing for Trusted Multi-View Classification Yilin Zhang
Cai Xu
Haishun Chen
Xidian University Xi’an, China [email protected]
Xidian University Xi’an, China [email protected]
Xidian University Xi’an, China [email protected]
Ziyu Guan
Wei Zhao
Xidian University Xi’an, China [email protected]
Xidian University Xi’an, China [email protected]
Abstract
not only make correct predictions, but also be able to dynamically assess which views are more trusted for the current sample. To this end, recent trusted multi-view learning methods [6, 10, 25, 34] are largely built on evidential learning [3, 27] and subjective logic [16, 28]. A typical paradigm is shown in Fig. 1(a), which let each view-specific branch produce non-negative class evidence, convert it into an uncertainty-aware opinion, and then fuse these opinions according to their branch-wise uncertainty. This line of work is attractive because it is modular, compatible with heterogeneous encoders, and naturally provides an interpretable fusion process through uncertainty-aware weighting. However, it also relies on an assumption that is rarely questioned explicitly: the evidence and self-assessed uncertainty from different views are treated as directly comparable across branches. We find that this assumption is in fact fragile, and it arises from two sources: (1) Data-level heterogeneity. Different views often reside in different feature spaces and exhibit different signal-tonoise ratios, statistical complexity, and levels of semantic abstraction, which naturally induce different evidence distributions. (2) Model-level heterogeneity. Each branch is trained primarily to improve its own classification objective, typically by increasing the evidence assigned to the ground-truth class and suppressing other classes. Such supervision encourages per-branch correctness, but places no explicit constraint on the absolute strength of evidence across views [35]. Moreover, different architectural choices can further amplify this mismatch. Therefore, features of the same quality may still yield evidence with significantly different strengths. A toy experiment, as shown in Fig. 1(b), demonstrates that for the same input features, simply changing the depth of one branch can lead to significant differences in evidence strength and induce different uncertainty values. This issue becomes particularly critical in trusted multi-view fusion, because subjective-logic uncertainty is directly tied to total evidence strength. When the uncertainty used for fusion weighting is dominated by branch-dependent scale rather than true samplewise reliability, it is meaningful only within each branch and loses fairness as a cross-view arbitration signal, as shown in Fig. 1(c). Therefore, the challenge is not merely how to estimate uncertainty within each branch, but how to perform fair cross-view arbitration when evidence scales are not directly comparable. This observation calls for a rethinking of the design principle of trusted multi-view fusion. If raw cross-view evidence cannot
Trusted multi-view classification typically relies on a view-wise evidential fusion process: each view independently produces class evidence and uncertainty, and the final prediction is obtained by aggregating these independent opinions. While this design is modular and uncertainty-aware, it implicitly assumes that evidence from different views is numerically comparable. In practice, however, this assumption is fragile. Different views often differ in feature space, noise level, and semantic granularity, while independently trained branches are optimized only for prediction correctness, without any constraint enforcing cross-view consistency in evidence strength. As a result, the uncertainty used for fusion can be dominated by branch-specific scale bias rather than true sample-level reliability. To address this issue, we propose Trusted Multi-view learning with Unified Routing (TMUR), which decouples view-specific evidence extraction from fusion arbitration. TMUR uses view-private experts and one collaborative expert, and employs a unified router that observes the global multi-view context to generate sample-level expert weights. Soft load-balancing and diversity regularization further encourage balanced expert utilization and more discriminative expert specialization. We also provide theoretical analysis showing why independent evidential supervision does not identify a common cross-view evidence scale, and why unified global routing is preferable to branch-local arbitration when reliability is sample-dependent. Extensive experiments on 14 datasets and comparisons with 15 recent baselines demonstrate that TMUR consistently improves both classification performance and reliability. The code will be released upon publication.
Keywords Trusted Multi-view Classification, Uncertainty-aware Deep Learning, Evidential Deep Learning.
1
Introduction
Multi-view classification [17, 22, 36] aims to improve prediction by integrating complementary information from multiple views. In many real-world scenarios, different views may exhibit distinct noise levels [32], semantic granularity, or even conflicting clues [11] for the same sample, causing their quality to vary dynamically across samples. As a result, a reliable multi-view model should 1
Are Independently Estimated View Uncertainties Comparable?
(a) Conventional assumption 𝑢1
𝒆1 𝑢2
Text Classifier
Fusion
Audio Classifier
k =1
(e1k + 1)
=
𝒆
Branch 1 (deeper)
K
𝑢3 Class-wise Evidence 𝒆3
Weighted by Self-assessed Uncertainty
𝑢1
1
𝒆2
View 2
View 3
Reliability Diagram on Caltech K K
K k =1
(e + 1) 2 k
= 𝑢2
Accuracy
Image Classifier
View 1
(c) What it causes in practice
(b) Why the assumption fails
Same uncertainty, Different accuracy
𝒆2
Branch 2 (shallow)
Uncertainy
Same input features, different evidence scale induce different uncertainty values
Real multi-view data show inconsistent reliabllity across views
Figure 1: (a) Conventional trusted multi-view fusion uses branch-local self-assessed uncertainty for weighting. (b) However, heterogeneous branches can produce different evidence scales, so even the same input may yield different uncertainty values. (c) On Caltech dataset, different views show inconsistent reliability under the same uncertainty level. This suggests that branch-local uncertainty is not directly comparable across views and may be unreliable for cross-view arbitration.
2 Related Work 2.1 Multi-View Learning
be compared reliably in magnitude, then fusion weights should no longer be determined solely by each branch’s own uncertainty. Instead, they should be assigned by an independent arbitration module that has access to the global multi-view context. Motivated by this, we propose Trusted Multi-view learning with Unified Routing (TMUR), a framework that explicitly decouples viewspecific evidence extraction from fusion arbitration. Specifically, TMUR equips each view, together with one global view, with its own expert network, and employs a unified router that observes the global multi-view context to generate sample-wise weights over these experts. In this way, fusion authority is no longer inferred only from branch-local uncertainty, but is instead determined through global, sample-aware routing. This design preserves the trusted nature of evidential prediction while mitigating the fusion bias induced by raw cross-view evidence-scale mismatch. We also provide a theoretical analysis explaining why independent evidence supervision cannot determine a universal evidence scale across views, and when view reliability depends on the sample, global dynamic routing is better grounded than branch-local self-weighting. In summary, this work makes the following contributions:
Multi-view learning aims to exploit complementary yet heterogeneous views for stronger prediction. Recent work improves multiview reasoning through stronger cross-view alignment [21], trustaware pairwise modeling [26], and uncertainty-refined representation learning [12]. In the classification setting, trusted multi-view methods such as TMC [9] and its dynamic evidential extension [10] formulate the problem through view-wise evidence extraction and decision-level fusion. Subsequent studies further enhance this line by modeling inter-view conflict [34], leveraging trust-aware learning under conflicting views [25], introducing fuzzy evidence for reliable classification [6], addressing ambiguity and debiasing in open-set settings [7], and incorporating expert knowledge constraints [20]. These efforts clearly demonstrate the importance of reliability-aware multi-view learning. Our work follows this trusted multi-view learning line, but focuses on a different bottleneck: whether the evidence produced by different branches is numerically comparable enough to support direct fusion.
• We identify cross-view evidence-scale incomparability as an important yet underexplored bottleneck in trusted multi-view classification, and trace it to both data-level and model-level heterogeneity. • We propose TMUR, a unified-routing framework that decouples evidential prediction from fusion arbitration and reduces scale-induced bias in cross-view fusion. • We provide theoretical analysis clarifying why independent evidential supervision cannot guarantee cross-view evidence comparability, and why dynamic global routing is preferable when view reliability is sample-dependent. • We validate TMUR on extensive multi-view benchmarks, reducing average ECE by 8.27 points and achieving consistently strong classification performance.
2.2
Evidential Fusion and Subjective Logic
Evidential Deep Learning maps network outputs to Dirichlet parameters and provides a natural interface for predictive uncertainty [27], with later extensions modeling richer forms of evidential uncertainty [18]. In multi-view settings, these outputs are often combined through subjective logic or Dempster–Shafer style fusion [16, 28]. A related line estimates branch quality from uncertainty, total evidence, calibration, or belief discrepancy, and then reweights the resulting opinions accordingly [1, 7, 8, 10, 30]. However, these signals are still generated independently by each branch, so their magnitudes can remain entangled with branch-specific data and model biases rather than true sample-level reliability. In other words, reweighting branch-local opinions by branch-local 2
Are Independently Estimated View Uncertainties Comparable?
Í Let Dirichlet strength 𝑆 = 𝐾𝑗=1 𝛼 𝑗 . The corresponding predictive probability and subjective-logic uncertainty are 𝐾 𝛼𝑘 𝑢= . (3) 𝑝𝑘 = , 𝑆 𝑆 Equivalently, the associated opinion can be written as O = (𝒃, 𝑢) with belief masses 𝑒𝑘 𝑏𝑘 = , 𝑘 = 1, . . . , 𝐾 . (4) 𝑆 This formulation makes the uncertainty directly depend on the total evidence magnitude. As a result, if different views produce evidence on different numerical scales, then their induced uncertainties need not be directly comparable across views, even when their semantic support patterns are similar.
quality estimates does not by itself make cross-view evidence numerically comparable. Classical evidence theory has long warned that fusion behavior becomes unreliable when the compatibility assumptions behind the combination rule are not justified [37]. Our method is motivated by this gap: instead of continuing to infer fusion authority directly from branch-local evidence quality, we delegate arbitration to a separate global router.
2.3
Dynamic Routing and Expert-Based Arbitration
Sample-dependent fusion has a long history in early expert-routing models [15] and modern routing architectures [29]. In multimodal learning, dynamic fusion has been used to adapt fusion weights to changing modality quality or sample context [38], and predictive fusion methods also exploit sample-wise uncertainty signals to guide fusion decisions [1]. At the same time, recent theory shows that dynamic fusion is not automatically robust: poorly designed weighting rules can even exacerbate modality greediness [4]. This makes the arbitration mechanism itself a first-class design issue. Recent routing-based expert models further show that expert specialization is useful across diverse multi-view or multimodal applications, including multimodal interaction modeling [33], molecular property prediction [31], time-series forecasting [14], and multi-view clustering [39]. Our use of routing is different. We introduce a unified router not as a generic capacity-expansion module, but as a dedicated arbitration mechanism that reduces the dependence of fusion authority on direct comparison of raw view-wise evidence.
3
3.2
Unified Routing and Evidential Fusion
To address this issue, TMUR explicitly separates two roles that are often entangled in existing trusted multi-view fusion methods: view-wise evidence extraction and cross-view fusion arbitration. The first role is to let each view-specific branch produce trusted evidence while preserving its own semantics. The second role is to decide, under the joint multi-view context of the current sample, how much each expert should contribute to the final decision. Based on this separation, TMUR maintains an expert pool composed of 𝑉 private experts and one collaborative expert, and introduces a unified router that assigns sample-wise fusion weights from the joint multi-view context. The overall architecture is shown in Fig. 2. 3.2.1 Router and Experts Settings. Specifically, We first map all views into a dimension-aligned space:
Method
𝒉 (𝑣) = LN(𝑃 𝑣 (𝒙 (𝑣) )),
We propose a unified-routing framework for trusted multi-view classification. The core principle is to decouple view-wise evidence extraction from multi-view fusion process. Instead of letting each view-specific branch explicitly determine its own fusion authority through its local evidence magnitude or uncertainty, we assign this role to a specialized router that observes the joint multi-view context. In this way, the model retains the advantages of trusted multi-view learning, dynamic fusion and uncertainty awareness, while avoiding direct reliance on the comparability of raw crossview evidence strengths.
𝑯 = [𝒉 (1) ; 𝒉 (2) ; · · · ; 𝒉 (𝑉 ) ].
Problem Definition
(1)
where 𝒙𝑛(𝑣) ∈ R𝑑 𝑣 is the feature of the 𝑣-th view of the 𝑛-th sample, and 𝑦𝑛 ∈ {1, . . . , 𝐾 } is its class label. For simplicity, we omit the sample index 𝑛 below when no confusion arises. In trusted multi-view learning [5, 23], each branch is expected to produce both class evidence and an uncertainty estimate. Following evidential learning, a predictor outputs a non-negative evidence vector 𝒆 ∈ R𝐾≥0 , from which the Dirichlet parameters are defined as: 𝜶 = 𝒆 + 1.
(6)
𝑣 = 1, . . . , 𝑉 ,
(7)
while the collaborative expert receives the concatenated multi-view representation, 𝒛 (𝑉 +1) = 𝐸𝑉 +1 (𝑯 ). (8) This design allows the private experts to express view-specific evidence, while the collaborative expert may captures complementary cues that emerge only after combining multiple views. To provide the router with richer cross-view context, we further construct interaction-enhanced features through cross-view attention: 𝒉˜ (𝑣) = Attn 𝒉 (𝑣) , {𝒉 ( 𝑗 ) }𝑉 , {𝒉 ( 𝑗 ) }𝑉 , (9)
We consider a 𝑉 -view classification problem with 𝐾 classes. The training set is denoted by: 𝑁 D = {(𝒙𝑛(1) , 𝒙𝑛(2) , . . . , 𝒙𝑛(𝑉 ) , 𝑦𝑛 )}𝑛=1 ,
(5)
The expert pool contains 𝑉 private experts and one collaborative expert. Each expert is implemented as a MLP. The 𝑣-th private expert receives only the aligned feature of the 𝑣-th view, 𝒛 (𝑣) = 𝐸 𝑣 (𝒉 (𝑣) ),
3.1
𝑣 = 1, . . . , 𝑉 ,
where 𝑃 𝑣 (·) is a view-specific projection layer and LN(·) denotes LayerNorm. This step improves cross-view feature compatibility while retaining view-specific information. We then concatenate the aligned view features as:
𝑗=1
𝑗=1
where the query is the aligned feature of the current view and the keys and values are the aligned features from all views. We then concatenate the enhanced features as: 𝒈 = [𝒉˜ (1) ; 𝒉˜ (2) ; · · · ; 𝒉˜ (𝑉 ) ]. (10)
(2) 3
Are Independently Estimated View Uncertainties Comparable?
Private Expert 1
𝒉(2)
Private Expert 2
𝒉(1)
⋮
⋮
𝒉(V)
Private Expert V
𝒉(2)
𝑯
Collabrative Expert
𝓞 𝑓𝑢𝑠𝑒𝑑
𝒆𝑓𝑢𝑠𝑒𝑑 = 𝜋𝑖 𝒆(𝑖)
𝑏3
View-Specific Projection
(2)
𝒉
𝑊𝑄
𝑸
𝑊𝐾 𝑲
⋮ 𝒉(V)
Data flow Training loss
𝑊𝑉
𝑏2
Fused Opinion
𝑽
෩ (1) 𝒉
Add
෩ (2) 𝒉 ෩ (V) 𝒉
𝓛𝑏𝑎𝑙
Router
⋮
𝒉(1)
𝑏1
⋮
𝒉(V)
Cross-View Attention
View V
𝑢 Expert-specific Opinions
Unified Awareness Routing
Aligned View Features
Projector V
𝑗=1
⋮
𝑖
⋮
⋮
𝐾
𝑘=1
𝜶(𝒊) = 𝒆(𝒊) + 1
⋮
LayerNorm
Projector 2
𝐾
𝓛𝑐𝑙𝑠 = 𝑦𝑗 𝜓( 𝛼𝑗(𝑖) ) − 𝜓(𝛼𝑘(𝑖) )
⋮
View 1
𝓛𝑑𝑖𝑣 Evidential Head
𝒉(1) Projector 1
View 2
Unified Evidential Fusion
Evidence Expert Prediction Pool
View Alignment
⋮ Expert weights 𝝅
Prevent Weight Collapse
Enhanced Features
Figure 2: Overview of TMUR. Aligned per-view features are sent to view-private experts for view-specific evidence extraction, while their concatenation is processed by a collaborative expert for joint multi-view evidence. In parallel, a unified router performs router-side cross-view interaction and predicts sample-wise expert weights from the global multi-view context. The final prediction is obtained by weighted evidence aggregation, so fusion authority is assigned by the router rather than by directly comparing branch-local evidence or uncertainty. These enhanced features are used to form the routing context, whereas the private experts still operate on their own aligned view features. In this way, cross-view interaction affects how experts are weighted, rather than replacing the view-specific evidence produced by the private experts themselves. Each expert outputs a non-negative evidence vector through an evidential classification head:
The final fused evidence is obtained by weighted aggregation: 𝒆 fused =
(14)
The corresponding fused opinion is denoted by O fused = (𝒃 fused, 𝑢 fused ),
𝑖 ∈ {1, . . . , 𝑉 + 1},
(11) 𝑏𝑘fused =
where 𝜙 (·) is a non-negative activation function. We use a softplusbased implementation in practice. The corresponding Dirichlet paÍ𝐾 rameters are 𝜶 (𝑖 ) = 𝒆 (𝑖 ) + 1. Let 𝑆 (𝑖 ) = 𝑘=1 𝛼𝑘(𝑖 ) . Then the opinion associated with expert 𝑖 is denoted by O
𝜋𝑖 𝒆 (𝑖 ) .
𝑖=1
(15)
where
𝒆 (𝑖 ) = 𝜙 (𝒛 (𝑖 ) ),
(𝑖 )
𝑉 +1 ∑︁
= (𝒃
(𝑖 )
,𝑢
(𝑖 )
).
𝑅(𝒈) ∈ R𝑉 +1, 𝜏
, 𝑆 fused
𝑢 fused =
𝐾 .
(16)
𝑆 fused
The predictive class probabilities can still be obtained from the fused Dirichlet mean: 𝑝𝑘fused =
𝛼𝑘fused
. (17) 𝑆 fused This fusion mechanism preserves the evidential output form while reassigning the arbitration role. Existing trusted multi-view fusion methods often let each branch both produce evidence and implicitly influence its own fusion weight through branch-local uncertainty. In contrast, TMUR keeps evidence generation inside the experts and lets a unified router assign fusion authority from the joint multi-view context. Consequently, the final weights are guided primarily by sample-level cross-view context, which reduces their dependence on branch-specific evidential scale.
(12)
3.2.2 Router-Driven Evidential Fusion. If raw evidential magnitude is not a reliable cross-view arbitration signal, then fusion weights should not be inferred directly from branch-local evidence or uncertainty alone. Instead, they should be assigned by a dedicated routing mechanism that can observe all views jointly. Based on the enhanced multi-view context 𝒈, we compute the sample-wise expert weights as: 𝝅 = softmax
𝑒𝑘fused
3.3
(13)
Training Objective
Our training objective is composed of several complementary terms that respectively supervise the fused prediction, maintain expert discriminability, and regularize the routing behavior.
where 𝑅(·) denotes the routing network and 𝜏 is the routing temperature. 4
Are Independently Estimated View Uncertainties Comparable?
4
Fused evidential classification loss. We take the fused output as the primary supervision target and optimize it with the evidential digamma loss [2]: # " 𝐾 ! 𝐾 ∑︁ ∑︁ fused fused Lfused = 𝑦𝑘 𝜓 𝛼𝑗 − 𝜓 𝛼𝑘 , (18) 𝑗=1
𝑘=1
where 𝜓 (·) is the digamma function and 𝒚 is the one-hot label vector.
4.1
Auxiliary expert supervision. Although the final prediction is produced after fusion, each expert should still learn to generate meaningful class evidence. We therefore apply the same evidential supervision to every expert: " 𝐾 ! # 𝑉 +1 𝐾 ∑︁ 1 ∑︁ ∑︁ Lview = 𝑦𝑘 𝜓 𝛼 𝑗(𝑖 ) − 𝜓 𝛼𝑘(𝑖 ) . (19) 𝑉 + 1 𝑖=1 𝑗=1
𝜶 = 𝒆 + 1,
𝑢=
𝛼𝑘 ,
𝒆(𝑡) = 𝑡 𝒓,
𝐾 . 𝑆
(25)
𝑡 > 0.
(26)
Then 𝜶 (𝑡) = 1 + 𝑡 𝒓, where 𝑅 =
𝐵
𝑢 (𝑡) =
𝐾 , 𝐾 + 𝑡𝑅
(27)
Í𝐾
𝑘=1 𝑟 𝑘 .
(20) Theorem 4.1 (Scale changes uncertainty without changing support direction). For the above family,
𝑏=1
be the average routing weight of expert 𝑖 over a mini-batch of size 𝐵, and define the routing concentration as ∑︁ ¯ = Conc( 𝝅) 𝜋¯𝑖2 . (21)
𝑑 𝑢 (𝑡) 𝐾𝑅 =− < 0. 𝑑𝑡 (𝐾 + 𝑡𝑅) 2
(28)
Moreover, if 𝑟 𝑦 > 𝑅/𝐾 for the ground-truth class 𝑦, then the predictive probability of the true class increases with 𝑡 as well. Therefore, along the same class-support pattern, increasing the evidence scale decreases the induced uncertainty even though the underlying support direction is unchanged.
𝑖
The load-balancing loss is 𝜌 , 0 , 𝑉 +1
𝐾 ∑︁
Thus, uncertainty is inversely proportional to the total evidence scale. Consider a fixed non-negative support pattern 𝒓 ∈ R𝐾≥0 and define a one-parameter evidence family
Load-balancing regularization. Since multi-view data can contain persistently strong and weak views, we do not force the router to use all experts equally. Instead, we only penalize excessive concentration of expert usage within a mini-batch, so that routing remains adaptive while avoiding collapse. Let
¯ − Lbal = max Conc( 𝝅)
𝑆=
𝑘=1
This auxiliary supervision stabilizes expert learning and prevents the router from compensating for poorly trained experts.
1 ∑︁ 𝜋𝑏,𝑖 𝐵
Why branch-local uncertainty is scale-sensitive
For an expert outputting non-negative evidence 𝒆 ∈ R𝐾≥0 , define
𝑘=1
𝜋¯𝑖 =
Theoretical Analysis
This section formalizes two points that directly support our design. First, branch-local uncertainty is scale-sensitive: changing evidence magnitude changes subjective-logic uncertainty even when the underlying class-support pattern is unchanged. Second, when optimal fusion authority depends on joint cross-view context, branch-local self-weighting is fundamentally limited, whereas a unified router can exploit the required joint information.
(22)
Proof. The expression for 𝑢 (𝑡) follows directly from the Dirichlet definition, and differentiating with respect to 𝑡 gives the stated derivative. If 𝑟 𝑦 > 𝑅/𝐾, the predictive probability of the true class is also increasing in 𝑡. □ Theorem 4.1 explains why branch-local uncertainty is vulnerable to scale bias. Two branches may encode essentially the same relative class preference, yet the one with a larger evidence scale will appear less uncertain and hence more trusted.
where 𝜌 > 1 controls the tolerated concentration. Expert diversity regularization. Because the private experts are optimized jointly, they may still drift toward redundant hidden representations. To encourage specialization, we regularize their hidden features to be decorrelated. Let 𝒛ˆ (𝑣) be the ℓ2 -normalized hidden feature of private expert 𝑣. We define 2 ∑︁ 2 Ldiv = 𝒛ˆ (𝑖 )⊤ 𝒛ˆ ( 𝑗 ) . (23) 𝑉 (𝑉 − 1) 1≤𝑖< 𝑗 ≤𝑉
4.2
Why unified routing is preferable to branch-local self-weighting
The squared cosine form penalizes both positive and negative alignment, thereby encouraging different private experts to capture different view-conditioned directions. The overall training objective is
Let L𝑥 (𝒘) denote the sample-wise fusion loss as a function of the expert-weight vector
L = Lfused + 𝜆Lview + 𝛽Lbal + 𝛾 Ldiv,
where Δ𝑉 is the probability simplex over the 𝑉 + 1 experts. Define
𝒘 ∈ Δ𝑉 ,
(24)
(29)
the oracle routing rule where 𝜆, 𝛽, and 𝛾 control the strengths of auxiliary expert supervision, load balancing, and diversity regularization, respectively.
𝒘 ★ (𝑥) = arg min L𝑥 (𝒘). 𝒘 ∈Δ𝑉
5
(30)
Are Independently Estimated View Uncertainties Comparable?
Table 1: Five-seed benchmark accuracy on the first seven reported datasets. Each entry reports mean ± standard deviation over five seeds. Method names include citation tags, while the ‘References’ column lists venue and year.
Method
Ref.
HandWritten
Scene
LandUse
NUS
Caltech-6V
PIE
WebKB
TMC [9] TMDLO [24] ETMC [10] RCML [34] ETF [25] FUML [6] TMCEK [20] TUNED [13] TEF [19] SAEML [35] RTMC [40] RCMCL [11]
ICLR’21 AAAI’22 PAMI’23 AAAI’24 ICML’25 ICML’25 ICML’25 AAAI’25 ICLR’25 MM’25 WWW’25 PAMI’26
98.00±0.88 97.20±1.03 98.30±0.48 98.00±0.79 96.65±1.12 98.90±0.54 98.30±0.84 98.90±0.34 98.80±0.51 98.80±0.53 84.55±1.61 97.15±1.06
75.76±0.95 66.87±2.97 78.10±1.14 76.03±1.35 68.21±0.79 80.65±1.03 77.37±1.20 78.15±0.69 78.00±0.48 79.67±1.42 68.92±1.31 70.81±1.37
60.95±2.25 52.67±3.36 65.48±1.27 65.86±1.72 19.52±8.86 76.62±1.24 70.10±1.18 72.95±1.80 80.48±1.41 74.05±1.23 54.38±0.36 45.24±1.15
44.70±0.36 43.09±0.42 48.53±0.34 44.43±0.28 44.12±0.69 48.07±0.34 43.20±0.32 43.35±0.31 47.14±0.52 42.94±0.25 35.12±0.69 37.75±0.28
93.72±0.30 86.15±2.42 94.06±0.47 94.60±0.38 93.97±0.48 95.61±0.37 95.40±0.51 95.15±0.75 94.85±0.28 93.81±0.51 94.60±0.33 94.14±0.70
91.32±2.43 73.09±1.89 94.85±1.14 95.29±1.10 95.59±1.40 96.91±1.35 97.79±0.93 89.56±2.56 97.65±1.27 95.88±1.78 92.79±1.99 96.18±1.18
82.44±2.84 83.41±2.84 82.93±2.67 82.93±2.67 80.49±3.09 72.20±18.09 85.37±2.67 80.00±2.39 84.88±2.39 84.88±2.39 78.54±2.39 81.95±2.49
NLC [36] MAMC [21] BCM [17]
AAAI’25 ICLR’25 MM’25
98.30±0.73 98.75±0.47 99.00±0.42
80.38±1.56 81.50±0.70 80.71±0.60
70.29±1.15 79.33±0.59 78.81±1.86
47.85±0.49 48.14±0.34 47.25±0.46
92.34±0.81 96.03±0.30 94.35±0.84
89.71±2.42 97.06±1.04 94.56±1.95
71.71±9.58 84.39±1.19 85.37±3.09
TMUR
Ours
99.10±0.46
82.88±1.36
80.48±0.78
50.07±0.26
96.69±0.36
97.94±0.86
88.29±0.98
5 Experiments 5.1 Experimental Setup
Suppose branch-local self-weighting rules can only access local statistics 𝒔 (𝑥), such as branch-wise evidence or uncertainty, and therefore take the form 𝒘local (𝑥) = 𝜓 (𝒔 (𝑥)).
Dataset. We evaluate TMUR on fourteen public multi-view classification datasets1 : HandWritten, Scene, LandUse, NUS, Caltech6V, PIE, WebKB, Caltech, UCI, CUB, Animal, MSRCV1, BBC, and Leaves. Detailed dataset statistics, view descriptions are deferred to the appendix.
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By contrast, a unified router can access a joint representation 𝒈(𝑥) and output 𝒘global (𝑥) = 𝜙 (𝒈(𝑥)).
Compared methods. We compare TMUR with two groups of baselines. The trusted baselines include TMC [9], TMDLO [24], and ETMC [10], which formulate multi-view predictions as evidence or opinions and perform uncertainty-aware fusion. They also include more recent trusted methods for conflict handling and reliability modeling, including RCML [34], ETF [25], FUML [6], and RCMCL [11], which focus on conflict-aware aggregation, trust discounting, fuzzy uncertainty modeling, or robust collaborative learning under conflictive views. In addition, we compare with recent refinements of trusted fusion, including TMCEK [20], TUNED [13], TEF [19], SAEML [35], and RTMC [40], which introduce expert knowledge constraints, feature-neighborhood dynamics, evolutionary fusion architecture search, strength-adaptive evidence weighting, and a refined treatment of confusion and ignorance, respectively. The non-trusted baselines include NLC [36], which addresses noisy-label multi-view classification via label calibration, MAMC [21], which combines multi-scale alignment with expanded decision boundaries, and BCM [17], which performs multi-view classification in Hamming space with a bit-level calibration mechanism.
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Theorem 4.2 (Branch-local self-weighting has an irreducible information gap). Assume that for each sample 𝑥, the fusion loss L𝑥 (𝒘) is 𝜇-strongly convex on Δ𝑉 for some 𝜇 > 0. Let Wlocal := {𝒘 (𝑥) = 𝜓 (𝒔 (𝑥))}
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denote the class of branch-local self-weighting rules. Then 𝜇 E[L𝑥 (𝒘 (𝑥))] −E L𝑥 (𝒘 ★ (𝑥)) ≥ E Var 𝒘 ★ (𝑥) | 𝒔 (𝑥) . 2 (34) In particular, if the optimal authority assignment depends on crossview relations that are not recoverable from branch-local statistics alone, then every branch-local self-weighting rule incurs a strictly positive irreducible excess risk. inf
𝒘 ∈ Wlocal
Proof sketch. Strong convexity lower-bounds excess loss by squared distance to the oracle weight 𝒘 ★ (𝑥). Among all rules measurable with respect to 𝒔 (𝑥), the best predictor of 𝒘 ★ (𝑥) under squared loss is the conditional expectation, and the corresponding minimum residual is the conditional variance. Therefore, if 𝒘 ★ (𝑥) is not measurable from branch-local statistics alone, branch-local self-weighting necessarily leaves a positive irreducible gap. □
Implementation details. All experiments are conducted on NVIDIA RTX 4090 GPUs using PyTorch 2.2.2. Following our benchmark protocol, every method is evaluated with five fixed random 1 https://github.com/JethroJames/Awesome-Multi-View-Learning-Datasets
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Are Independently Estimated View Uncertainties Comparable?
Table 2: Calibration results on trusted multi-view classification methods (ECE%, lower is better). Method
Ref.
LandUse
PIE
TMC [9] TMDLO [24] ETMC [10] RCML [34] TEF [19] TMCEK [20] TUNED [13] SAEML [35] RTMC [40] RCMCL [11]
ICLR’21 AAAI’22 PAMI’23 AAAI’24 ICLR’25 ICML’25 AAAI’25 MM’25 WWW’25 PAMI’26
13.34±2.13 27.16±4.29 8.69±2.60 64.90±0.81 8.13±5.73 62.25±4.67 48.83±0.67 9.83±1.71 72.39±1.70 51.09±4.38
46.07±1.74 40.29±2.33 23.21±2.39 26.71±2.62 40.03±3.55 41.78±1.53 58.64±1.61 51.92±1.91 10.83±2.06 24.58±2.18 61.33±1.97 58.32±0.99 55.69±1.17 52.62±1.14 12.45±0.99 16.62±1.22 59.47±1.32 47.88±0.36 52.62±1.38 35.62±1.16
TMUR
Ours
5.36±1.66
6.87±1.69 7.35±0.94 52.50±3.93 12.01±4.44
Animal
Caltech-6V
Leaves
74.50±0.53 8.91±2.95 43.31±7.20 58.25±2.28 32.36±11.21 25.60±1.09 84.49±1.53 21.56±6.58 23.93±10.13 87.05±1.80 38.95±4.01 51.11±2.23 70.47±4.63 47.51±8.00 24.91±0.52 92.16±0.73 28.62±5.77 54.89±2.00 81.17±1.55 31.17±2.90 64.18±1.24 60.35±4.20 10.11±3.12 30.68±0.71 90.69±1.98 47.41±3.69 81.50±0.97 86.92±1.12 42.86±3.71 60.70±0.71
6.43±4.11 18.16±2.05 7.76±3.54 47.07±1.47 9.21±2.02 54.25±4.19 52.09±1.42 5.01±1.10 87.16±0.34 42.15±1.99
87.56±2.59 50.23±1.91 87.74±3.86 90.43±1.15 72.84±1.71 93.83±0.67 84.56±1.52 66.96±1.17 84.50±2.54 93.61±0.72
7.55±5.23
44.43±8.60
Density
FUML
RCML
TMC
SAEML
Ours
PIE
R1 R2
92.89 82.35
93.38 89.95
88.73 81.86
93.87 84.80
96.08 91.67
R1 R2
67.41 69.12
61.32 63.43
68.75 71.16
69.75 73.39
71.39 74.99
LandUse Caltech-6V WebKB
R1 R2 R1 R2 R1 R2
45.40 42.14 94.70 93.17 64.23 61.79
57.62 54.68 94.56 94.98 81.30 77.24
52.78 56.90 93.93 93.86 82.11 79.67
49.29 52.78 92.89 88.15 81.30 78.86
4
0 0.0
10
5
0.2
0.4
0.6
0.8
Uncertainty
0 0.0
1.0
0.2
(c) HandWritten
63.97 65.16
20
95.33 94.84
0.8
1.0
In-Distribution OOD (σ=0.1) OOD (σ=1) OOD (σ=10)
4
10
3 2 1
5
86.18 86.99
0.6
(d) Caltech101-6V
15
0 0.0
0.4
Uncertainty
5
In-Distribution OOD (σ=0.1) OOD (σ=1) OOD (σ=10)
25
0.2
0.4
0.6
Uncertainty
0.8
1.0
0 0.0
0.2
0.4
0.6
Uncertainty
0.8
1.0
Figure 3: Uncertainty distributions of TMUR under increasing Gaussian perturbation on four datasets. As the noise level increases from 𝜎 = 0.1 to 𝜎 = 1 and 𝜎 = 10, the predicted uncertainty shifts upward, demonstrating that TMUR remains uncertainty-aware under degraded inputs.
seeds, and the reported accuracy is the mean ± standard deviation over the five runs. We use Adam with an initial learning rate of 10−3 , cosine learning-rate decay, and a fixed batch size of 128. The auxiliary expert-supervision weight 𝜆 is fixed to 0.3 on all datasets, while the load-balancing and diversity weights 𝛽 and 𝛾 are selected per dataset; their final values are reported in the appendix.
5.2
6
In-Distribution OOD (σ=0.1) OOD (σ=1) OOD (σ=10)
15
2
Density
Scene
(b) WebKB In-Distribution OOD (σ=0.1) OOD (σ=1) OOD (σ=10)
8
Methods
Ratio
9.79±5.73
(a) Scene
Table 3: View Strength Variation Experiments. The view strength in the multi-view dataset is randomly rescaled.
Dataset
WebKB
Density
Scene
Density
HandWritten
overall pattern: TMUR remains highly competitive and achieves the best or tied-best performance on six datasets, indicating that the proposed routing mechanism improves accuracy without sacrificing generality across diverse multi-view benchmarks. Accuracy alone is insufficient for trustworthy multi-view learning; the fused prediction should also remain well calibrated. Table 2 therefore compares ECE on eight representative datasets against trusted baselines. TMUR achieves the lowest ECE on six of the eight datasets, namely HandWritten, Scene, LandUse, PIE, Animal, and Leaves, and remains competitive on the remaining two datasets. Averaged over all eight datasets, TMUR reduces ECE from 26.50% achieved by the strongest baseline SAEML to 18.23%, yielding an absolute improvement of more than 8 ECE points. These results are important because they show that our gains are not merely due to
Main Results
Table 1 reports the current five-seed accuracy results on seven representative datasets, with each entry shown as mean ± standard deviation. To keep the comparison readable under the enlarged baseline set, the methods are separated into trusted baselines, nontrusted baselines, and our model, with horizontal rules marking the three groups. The remaining are reported in appendix. TMUR achieves the best or tied-best accuracy on all of the seven datasets in Table 1, including LandUse21, NUS, PIE, Caltech1016V, and WebKB. In particular, the gains on NUS and WebKB are clear, suggesting that unified routing is especially helpful when the reliability of different views varies substantially across samples. The appendix results on the remaining seven datasets show the same 7
Are Independently Estimated View Uncertainties Comparable?