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, 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: Adaptive Residual Kalman Smoother that provably operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

Finding unexpected problems or anomalies in data streams from complex systems like spacecraft or factories is crucial for safety. AI models typically do this by learning what "normal" data looks like and flagging large errors as anomalies. However, the standard rules these models use assume their everyday errors are just harmless, random noise. In reality, these errors are messy and unpredictable, making it hard for the system to tell a real crisis from a harmless computer glitch. To fix this, we created COGNOS, a universal upgrade framework. First, we change how the model trains, strictly forcing its baseline errors to perfectly mimic pure, random "white noise". Once this background noise is mathematically purified, we introduce a smart filter acting as a "circuit breaker". Because the background is now entirely predictable, this filter can instantly and accurately detect when a genuine anomaly breaks through the noise. COGNOS consistently boosts the reliability of many existing AI anomaly detectors. It achieves this without needing new, complex designs, making it much easier to safely monitor the critical infrastructure we rely on every day.