Socrates Loss: Unifying Confidence Calibration and Classification by Leveraging the Unknown

Deep neural networks, despite their high accuracy, often exhibit poor confidence calibration, limiting their reliability in high-stakes applications. Current ad-hoc confidence calibration methods attempt to fix this during training but face a fundamental trade-off: two-phase training methods achieve strong classification performance at the cost of training instability and poorer confidence calibration, while single-loss methods are stable but underperform in classification. This paper addresses and mitigates this stability-performance trade-off. We propose Socrates Loss, a novel, unified loss function that explicitly leverages uncertainty by incorporating an auxiliary unknown class, whose predictions directly influence the loss function and a dynamic uncertainty penalty. This unified objective allows the model to be optimized for both classification and confidence calibration simultaneously, without the instability of complex, scheduled losses. We provide theoretical guarantees that our method regularizes the model to prevent miscalibration and overfitting. Across four benchmark datasets and multiple architectures, our comprehensive experiments demonstrate that Socrates Loss consistently improves training stability while achieving more favorable accuracy-calibration trade-off, often converging faster than existing methods.

AnchorGK: Anchor-based Incremental and Stratified Graph Learning Framework for Inductive Spatio-Temporal Kriging

Spatio-temporal kriging is a fundamental problem in sensor networks, driven by the sparsity of deployed sensors and the resulting missing observations. Although recent approaches model spatial and temporal correlations, they often under-exploit two practical characteristics of real deployments: the sparse spatial distribution of locations and the heterogeneous availability of auxiliary features across locations. To address these challenges, we propose AnchorGK, an Anchor-based Incremental and Stratified Graph Learning framework for inductive spatio-temporal kriging. AnchorGK introduces anchor locations to stratify the data in a principled manner. Anchors are constructed according to feature availability, and strata are then formed around these anchors. This stratification serves two complementary roles. First, it explicitly represents and continuously updates correlations between unobserved regions and surrounding observed locations within a graph learning framework. Second, it enables the systematic use of all available features across strata via an incremental representation mechanism, mitigating feature incompleteness without discarding informative signals. Building on the stratified structure, we design a dual-view graph learning layer that jointly aggregates feature-relevant and location-relevant information, learning stratum-specific representations that support accurate inference under inductive settings. Extensive experiments on multiple benchmark datasets demonstrate that AnchorGK consistently outperforms state-of-the-art baselines for spatio-temporal kriging.