We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which we identify with the universal Marchenko-Pastur distribution. Applying the Functional Renormalization Group to the two-dimensional Model A, we demonstrate that the noise-to-signal ratio acts as a physical temperature, where the signal emerges as ordered domains within a thermalized background of fluctuations. Using the exact Onsager solution as a benchmark, we show that this approach identifies critical thresholds with an error below 4%, significantly outperforming standard information-theoretic metrics such as the Kullback-Leibler divergence. Our results provide a universal strategy for resolving structures in complex datasets near criticality, bridging the gap between statistical mechanics and statistical inference.

翻译：我们建立了高噪声条件下异常检测与非平衡场论重整化群流之间的对应关系。通过证明相互作用非平衡系统中相变检测可映射到高斯不动点附近有效平衡场论的研究（我们将其与通用Marchenko-Pastur分布相关联），为该框架提供了物理基础。将泛函重整化群应用于二维模型A，我们论证了噪声信号比可视为物理温度，其中信号在热化涨落背景中呈现为有序域。以精确Onsager解为基准，我们证明该方法识别临界阈值的误差低于4%，显著优于Kullback-Leibler散度等标准信息论指标。我们的研究结果为临界点附近复杂数据集中结构解析提供了通用策略，弥合了统计力学与统计推断之间的鸿沟。