React or Predict? A Spectral Rule for Wireless Threshold Detection

What the math gives to ML

The paper provides a constructive criterion for deciding whether forward prediction can add information to a threshold detector: lookahead is structurally redundant when the threshold direction is a left eigenvector of the dynamics with a nonnegative eigenvalue. This distinguishes a dynamical obstruction from a poor predictor or noisy channel, rather than requiring blind horizon search. The criterion can be transplanted to state-space neural networks and learned world models that trigger events, alarms, or early exits, by activating multi-step prediction only when the readout direction is rotated or sign-changing by the learned transition operator. The covariance-normalized score additionally provides a principled confidence signal for predicted threshold crossings.