Most estimators collapse all uncertainty modes into a single confidence score, preventing reliable reasoning about when to allocate more compute or adjust inference. W e introduce Uncertainty-Guided Inference-Time Selection, a lightweight inference time framework that disentangles aleatoric (data-driven) and epistemic (model-driven) uncertainty directly in deep feature space. Aleatoric uncertainty is estimated using a regularized global density model, while epistemic uncertainty is formed from three complementary components that capture local support deficiency, manifold spectral collapse, and cross-layer feature inconsistency. These components are empirically orthogonal and require no sampling, no ensembling, and no additional forward passes. W e integrate the decomposed uncertainty into a distribution free conformal calibration procedure that yields significantly tighter prediction intervals at matched coverage. Using these components for uncertainty guided adaptive model selection reduces compute by approximately 60 percent on MOT17 with negligible accuracy loss, enabling practical self regulating visual inference. Additionally, our ablation results show that the proposed orthogonal uncertainty decomposition consistently yields higher computational savings across all MOT17 sequences, improving margins by 13.6 percentage points over the total-uncertainty baseline.

The novel Bayesian loss described in formula 7 can be computed in closed form. For vector datasets, all models share an architecture of 3 linear layers with Relu activation. For PostNet, we used a 1D batch normalization after the encoder. All metrics have been scaled by 100 . We obtain numbers in [0, 100] for all scores instead of [0, 1].

GNN that is sensitive to various distribution shifts.

Based on R1's comments we also evaluated the models based on mutual Theoretically, the two metrics bring similar information [C]. For these reasons, we decided to use APR. We attribute the strong performance of PostNet to the dim. Similar conclusions have been drawn in [E]. In our paper we use 5 random splits (60%, 20%, 20%).

The novel Bayesian loss described in formula 7 can be computed in closed form. For vector datasets, all models share an architecture of 3 linear layers with Relu activation. For PostNet, we used a 1D batch normalization after the encoder. All metrics have been scaled by 100 . We obtain numbers in [0, 100] for all scores instead of [0, 1].

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic perspective and developing a suitable analog to data processing inequality to quantify information throughout the model's layers. In contrast to non-graph domains, information about the node-level prediction target can increase with model depth if a node's features are semantically different from its neighbors. Therefore, on heterophilic graphs, the latent embeddings of an MPNN each provide different information about the data distribution - different from homophilic settings. This reveals that considering all node representations simultaneously is a key design principle for epistemic uncertainty estimation on graphs beyond homophily. We empirically confirm this with a simple post-hoc density estimator on the joint node embedding space that provides state-of-the-art uncertainty on heterophilic graphs. At the same time, it matches prior work on homophilic graphs without explicitly exploiting homophily through post-processing.

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or only distinguish between structure-aware and structure-agnostic uncertainty without combining them into a single measure. We propose GEBM, an energy-based model (EBM) that provides high-quality uncertainty estimates by aggregating energy at different structural levels that naturally arise from graph diffusion. In contrast to logit-based EBMs, we provably induce an integrable density in the data space by regularizing the energy function. We introduce an evidential interpretation of our EBM that significantly improves the predictive robustness of the GNN. Our framework is a simple and effective post hoc method applicable to any pre-trained GNN that is sensitive to various distribution shifts. It consistently achieves the best separation of in-distribution and out-of-distribution data on 6 out of 7 anomaly types while having the best average rank over shifts on \emph{all} datasets.