arXiv:2602.14251v1 Announce Type: cross Abstract: Tabular anomaly detection is often handled by single detectors or static ensembles, even though strong performance on tabular data typically comes from heterogeneous model families (e.g., tree ensembles, deep tabular networks, and tabular foundation models) that frequently disagree under distribution shift, missingness, and rare-anomaly regimes. We propose MAD, a Multi-Agent Debating framework that treats this disagreement as a first-class signal and resolves it through a mathematically grounded coordination layer. Each agent is a machine learning (ML)-based detector that produces a normalized anomaly score, confidence, and structured evidence, augmented by a large language model (LLM)-based critic. A coordinator converts these messages into bounded per-agent losses and updates agent influence via an exponentiated-gradient rule, yielding both a final debated anomaly score and an auditable debate trace. MAD is a unified agentic framework that can recover existing approaches, such as mixture-of-experts gating and learning-with-expert-advice aggregation, by restricting the message space and synthesis operator. We establish regret guarantees for the synthesized losses and show how conformal calibration can wrap the debated score to control false positives under exchangeability. Experiments on diverse tabular anomaly benchmarks show improved robustness over baselines and clearer traces of model disagreement

arXiv:2602.13021v2 Announce Type: replace-cross Abstract: Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity.