Dynamic Expert Metric Loss in Collaborative Perception

• The paper demonstrates DEML’s main contribution is to regularize dynamically generated experts by promoting both diversity and consistency with the fused feature.
• Dynamic Expert Metric Loss is a regularization term within CoBEVMoE that enforces separation between heterogeneous agent-specific outputs while anchoring them to a collaborative feature representation.
• Empirical evidence shows that incorporating DEML improves segmentation and detection benchmarks, confirming its role in enhancing multi-agent collaborative perception.

Dynamic Expert Metric Loss (DEML) is a regularization loss introduced in the CoBEVMoE framework for collaborative perception in Bird’s Eye View space. In that setting, CoBEVMoE incorporates a Dynamic Mixture-of-Experts (DMoE) architecture in which each expert is dynamically generated based on the input features of a specific agent, and DEML is used to promote diversity among expert outputs while ensuring their consistency with the fused feature. The loss is therefore designed to preserve heterogeneous, agent-specific information without disconnecting expert outputs from the shared collaborative representation, and it is optimized jointly with the downstream task loss (Kong et al., 21 Sep 2025).

1. Placement within collaborative perception

Collaborative perception aims to extend sensing coverage and improve perception accuracy by sharing information among multiple agents. Because agents differ in viewpoints and spatial positions, they often acquire heterogeneous observations rather than redundant measurements. The CoBEVMoE framework was proposed to address this setting in the Bird’s Eye View domain, with an explicit emphasis on modeling both feature similarity and heterogeneity across agents through DMoE (Kong et al., 21 Sep 2025).

Within this framework, DEML serves as the loss component that regularizes the expert representations. Its function is not to replace feature fusion, but to constrain how expert outputs relate both to one another and to the fused feature. This positioning is central: the DMoE architecture provides agent-conditioned experts, while DEML shapes the geometry of the resulting expert feature space.

2. Motivation and design objective

The stated motivation for DEML is that, although the DMoE module effectively captures heterogeneous agent features, the extracted features may still lack sufficient regularization, potentially resulting in suboptimal performance. In collaborative perception, this is consequential because different agents may hold complementary, non-overlapping observations, and a weakly constrained MoE can allow agent-specific features to collapse or become too similar (Kong et al., 21 Sep 2025).

DEML is therefore introduced to address three linked objectives. First, it prevents representational collapse by discouraging experts from producing overly similar outputs. Second, it encourages experts to extract unique, agent-specific information. Third, it aligns expert features with the joint fused representation so that diversity does not come at the expense of semantic consistency. In the paper’s formulation, the intended effect is improved discriminability of the fused representation.

A useful clarification follows directly from the formulation: DEML is not only a diversity term. It also contains an explicit closeness term to the fused feature. Any description of DEML as merely “pushing experts apart” is incomplete, because the loss simultaneously enforces inter-expert separation and anchor consistency.

3. Mathematical formulation

For each expert $k$, DEML constructs a triplet in which the anchor is the self-attention fused feature $\mathbf{F_c}$, the positive is the corresponding expert output $\mathbf{E}_k$, and the hard negative is the most similar output from another expert, selected by the minimum mean squared error among the remaining experts (Kong et al., 21 Sep 2025):

$T_k = (\mathbf{F_c}, \mathbf{E}_k, \mathbf{E}_j),$

$$\mathbf{E}_j = \arg\min_{i \neq k} \mathrm{MSE}(\mathbf{E}_i, \mathbf{E}_k).$$

The positive and negative distances are squared $L_2$ distances normalized by the feature dimensionality $D$:

$$d_{\text{pos}}^k = \frac{1}{D}\|\mathbf{E}_k - \mathbf{F_c}\|_2^2,$$

$$d_{\text{neg}}^k = \min_{j \neq k}\frac{1}{D}\|\mathbf{E}_k - \mathbf{E}_j\|_2^2.$$

The per-expert triplet term is then

$$\mathcal{L}_{\text{triplet}}^k = \max\big(0, d_{\text{pos}}^k - d_{\text{neg}}^k + m\big),$$

where $\mathbf{F_c}$0 is the margin hyperparameter.

The total DEML aggregates the anchor-consistency term and the triplet term across experts, with balancing factor $\mathbf{F_c}$1, and normalizes by the number of valid experts $\mathbf{F_c}$2:

$\mathbf{F_c}$3

Training uses DEML as an auxiliary regularizer added to the task objective:

$\mathbf{F_c}$4

This decomposition makes the role of each term explicit. The $\mathbf{F_c}$5 component keeps each expert close to the fused feature, while the triplet component enforces a margin between an expert and its hardest competing expert.

4. Functional role in DMoE

Within CoBEVMoE, each agent gets an expert specialized on its own features. DEML regularizes these experts in two complementary ways. By using $\mathbf{F_c}$6, it keeps each expert output close to the fused representation and therefore tied to the collaborative perceptual objective. By using the hard-negative triplet term, it explicitly pushes experts apart, so that they learn unique, agent-specific cues rather than redundant encodings (Kong et al., 21 Sep 2025).

The resulting representation geometry is intended to retain unique, complementary features from each agent, in contrast to fusion mechanisms that average out or over-smooth perceptual differences. The paper describes this as alleviating feature redundancy and improving discriminability, with downstream benefits for segmentation and detection. A plausible implication is that DEML acts as a structural regularizer on the expert manifold: it constrains both the centroid-seeking tendency toward the fused feature and the repulsive tendency required for heterogeneity preservation.

The “dynamic” aspect of DEML should also be interpreted in the context of CoBEVMoE’s DMoE architecture. In this framework, each expert is dynamically generated based on the input features of a specific agent. DEML regularizes the outputs of these dynamically generated experts; it is not presented as a separate reinforcement-learning controller that changes loss parameters over time.

5. Empirical evidence and ablation findings

The CoBEVMoE experiments on the OPV2V and DAIR-V2X-C datasets report state-of-the-art performance, with an improvement of $\mathbf{F_c}$7 IoU for Camera-based BEV segmentation on OPV2V and $\mathbf{F_c}$8 AP@50 for LiDAR-based 3D object detection on DAIR-V2X-C. These results are presented as evidence that expert-based heterogeneous feature modeling is effective in multi-agent collaborative perception (Kong et al., 21 Sep 2025).

The ablation study isolates DEML’s contribution. For Vehicle, Drivable Area, and Lane, the baseline CoBEVT scores are 60.4, 61.2, and 48.8. Adding Vanilla MoE yields 60.8, 61.2, and 49.1. Replacing this with DMoE gives 61.3, 61.6, and 50.1. Adding DEML on top of DMoE yields 61.9, 61.8, and 50.5. The reported pattern is that Vanilla MoE provides only a small boost, DMoE provides a moderate improvement, and DMoE plus DEML provides the largest final gain, particularly in Vehicle and Lane.

The hyperparameter analysis further constrains the interpretation. With no regularization, $\mathbf{F_c}$9, Vehicle IoU is 61.3. A moderate DEML weight, $\mathbf{E}_k$0, gives the best result, 61.9. When $\mathbf{E}_k$1, performance drops. This indicates that DEML is most effective when used with moderation rather than as a dominant training signal. The qualitative analysis associated with Figure 1 reports that different experts focus on distinct spatial patterns, which the paper treats as visual confirmation of expert diversity.

6. Relation to adjacent expert-loss and metric-aware loss research

DEML belongs to a broader family of objectives that attempt to improve specialization or task alignment by modifying the loss seen by experts or by the model as a whole. A related but distinct example appears in a time-series forecasting MoE framework that integrates expert-specific losses directly into the objective,

$\mathbf{E}_k$2

so that each expert receives direct gradient updates from its own prediction error rather than only through the gating mechanism. In that setting, ablation with $\mathbf{E}_k$3 worsens MAE from 6.99 to 8.12 and RMSE from 14.58 to 15.40, and the paper interprets this as evidence that integrating expert-specific losses improves forecasting performance (Mahtout et al., 11 May 2026).

This suggests a broader research pattern: expert architectures often require explicit loss-level mechanisms to avoid weak specialization, expert collapse, or diluted gradients. DEML addresses that concern through a metric-style regularizer over expert outputs, whereas the time-series MoE addresses it through direct expert-specific prediction losses.

A second adjacent line of work is Adaptive Loss Alignment, which studies the loss-metric mismatch and meta-learns an adaptive loss function to optimize the evaluation metric directly. That framework formulates the problem as reinforcement-learning-based meta-learning, updating loss parameters according to validation-metric rewards and showing improvements in classification and metric learning (Huang et al., 2019). DEML differs in scope and mechanism. It is not a general-purpose controller for dynamically modifying loss parameters across tasks; it is a task-specific regularization term for DMoE expert outputs in collaborative perception.

Taken together, these comparisons place DEML within a larger shift away from treating the loss as a fixed, purely global surrogate. In DEML, that shift is expressed through explicit regularization of inter-expert geometry and fused-feature consistency, tailored to heterogeneous multi-agent perception.