The Rao detector provides asymptotically optimal signal detection when you know the noise distribution exactly. In practice — radar, gravitational waves, industrial sensors — you rarely do. The noise is non-Gaussian, its statistics shift, and deriving the optimal test statistic by hand becomes intractable. The LRao detector sidesteps this by training a compact neural network on noise-only data to learn a transformation that maps the observed noise into a representation where the Rao framework applies optimally. The network never sees the signal; it learns only the structure of the noise.

This separation is the key architectural choice. By confining the learning to the noise model and leaving the detection logic to classical theory, the approach remains interpretable and retains the asymptotic guarantees of the Rao framework. The neural network is not a black-box detector — it is a learned preprocessing step that reshapes an intractable problem into a tractable one. On real magnetic sensor data, the improvement over conventional methods is substantial.

The broader principle: when a well-understood theoretical framework fails because its assumptions do not hold, learning the transformation that restores those assumptions can be more powerful — and more trustworthy — than learning the entire solution from scratch.

(arXiv:2603.01737)