COGNOS: Universal Enhancement for Time Series Anomaly Detection via Constrained Gaussian-Noise Optimization and Smoothing

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores with a poor signal-to-noise ratio, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: a Kalman Smoothing Post-processor that provably operates as a statistically optimal estimator to denoise the raw anomaly scores. The synergy between these two components allows COGNOS to robustly separate the true anomaly signal from random fluctuations. Extensive experiments demonstrate that COGNOS is highly effective, delivering an average F-score uplift of 57.9% when applied to 12 diverse backbone models across multiple real-world benchmark datasets. Our work reveals that directly regularizing output statistics is a powerful and generalizable strategy for significantly improving anomaly detection systems.