SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional assumptions, we propose Hyperspherical Confidence Mapping (HCM), a simple yet principled framework for sampling-free and distribution-free uncertainty estimation. HCM decomposes outputs into a magnitude and a normalized direction vector constrained to lie on the unit hypersphere, enabling a novel interpretation of uncertainty as the degree of violation of this geometric constraint. This yields deterministic and interpretable estimates applicable to both regression and classification. Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment. Our results highlight the power of geometric structure in uncertainty estimation and position HCM as a versatile alternative to conventional techniques.

LLM-based multi-agent systems (MAS) have attracted growing attention for improving reasoning through interaction among multiple agents. In this work, we focus on parallel multi-agent reasoning systems, where several agents solve the same problem over multiple rounds and aggregate their outputs into a final answer. Despite their strong reasoning performance, uncertainty estimation for such systems remains underexplored: the reliability of a MAS depends not only on individual generations, but also on how agents interact and evolve across rounds. We propose SAUCE (Sequential Agent Uncertainty through Consensus Evolution), a lightweight, training-free uncertainty estimator that formulates MAS uncertainty as sequential inference over a latent system-level belief. SAUCE aggregates round-level agreement and generation-uncertainty signals through a filtering-style update. Across five backbones, five benchmarks, and two MAS protocols, SAUCE improves misclassification detection, selective prediction, and calibration over a broad set of uncertainty estimation baselines, including standard log-likelihood-based methods and MAS-specific estimators.

Causal perception occurs when agents with competing Structural Causal Models (SCMs) of the same system infer different probability distributions, including the hypothetical distributions implied by each agent's SCM under the same set of interventions. It shapes how agents reason about the system and how they perceive its fairness. Causal perception is a promising probabilistic framework, but it has remained purely theoretical. This work provides the first implementation of the causal perception framework of Álvarez and Ruggieri (2025). We operationalize structural (agents disagree on the causal graph) and parametrical (agents agree on the causal graph but disagree on its weights) causal perception. We design algorithms for computing interventional and counterfactual distributions and propose suitable distance measures to quantify the disagreement. Using the German Credit dataset, we illustrate how causal perception affects accuracy and fairness in a multi-expert decision setting. We show that the perception verdict is sensitive to the choice of distance metric and threshold. We also show that causal perception changes fairness assessments and threshold-based decisions. Bias proves situated with respect to the agent's SCM, demonstrating that competing worldviews in fairness problems cannot be ignored.