TRANSFORMER-BASED PROBABILISTIC MODELING OF PARKINSON’S DISEASE EYE MOVEMENTS FROM SACCADE-INDUCED OPTICAL FLOW

This study investigates whether saccades in Parkinson’s disease (PD) originate from a different action distribution compared to healthy controls. Participants were allowed to freely view videos with their head position stabilized using a chin rest. Unlike traditional deterministic control models, where a specific state corresponds to a single optimal action, we employ a probabilistic inverse optimal control framework (Rothkopf), in which behavior is characterized by a distribution over actions influenced by internal costs and sensorimotor factors uncertainty. We trained a Transformer model that encodes saccade-induced optical-flow patches, integrates them with a causal temporal Transformer, and predicts a Gaussian mixture over instantaneous saccadic velocity, yielding mixture weights (π), component means (μ), and variances (σ) as latent velocity regimes. A distance-to-goal signal was early-fused as an additional cue. The inferred velocity densities were predominantly unimodal; however, their structure varied across different groups. Trials involving PD exhibited a higher relative uncertainty (σ/|μ|) around the peak velocity and demonstrated increased mixture entropy, which is consistent with more variable action selection. At peak velocity, probability mass shifted across mixture components in PD, and component-mean distributions were more concentrated, suggesting a narrower set of effective velocity regimes. Within comparable peak-velocity ranges, group differences in component means persisted, indicating a distributional shift beyond simple amplitude differences. Model uncertainty was only weakly related to prediction error, supporting the interpretation that elevated uncertainty reflects intrinsic trial-to-trial motor variability rather than model unfamiliarity. These results motivate mixture-based oculomotor biomarkers that quantify changes in the full action distribution rather than relying on single summary statistics.