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

TL;DR

COGNOS is a universal framework that improves time series anomaly detection by enforcing Gaussian noise regularization and applying adaptive smoothing to produce more reliable anomaly scores.

Contribution

It introduces a novel Gaussian-White Noise Regularization and an Adaptive Residual Kalman Smoother to enhance reconstruction-based TSAD methods.

Findings

Consistently improves performance of state-of-the-art backbones.

Creates statistically sound residuals for anomaly detection.

Validates effectiveness across multiple benchmarks.

Abstract

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 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.