As deviations from what is expected, anomalies are typically seen as an obstruction to making good predictions or an impulse to revise the predictive framework. Here, we consider a different possibility—that anomalies, particularly those related to cognitive processing, may be a valuable source of diagnostic information. More specifically, we hypothesize that the extent to which the prechoice information search has been atypical (anomalous) can be used to reverse-infer important latent features of the decision process. For instance, based on atypicalities in how juries examine courtroom evidence, can we infer if they were biased by media reports; or if financial traders browsed public stock market data in a way sufficiently unusual to indicate access to insider information? In our preregistered experiment, participants viewed expert opinions about financial stocks, before deciding whether to invest and get paid according to the subsequent market return, adjusted by an independent random amount. We used eye-tracking and machine-learning dimensionality reduction and anomaly detection techniques to measure the extent to which eye-movements while viewing opinions were idiosyncratic/anomalous. We found that nudging participants by disclosing the return adjustment value beforehand (thus giving them “privileged information”) made their patterns of subsequently viewing opinions more idiosyncratic. With those idiosyncrasies as potential markers of top-down attentional control, we demonstrated a reverse-inference of motivation and prior knowledge from attention, predicting if people were nudged in a particular direction based on how idiosyncratically they then searched for information.