Smooth Pursuit Outliers Are Field-Boundary Deviations in Autism Spectrum Disorder

Authors: Sterling Geisel, QBist Lab; Dr. Hideo Tanaka

Abstract

Pudding Theory reads the Shishido et al. smooth pursuit eye movement result as a measurement of observer-field geometry. The source paper treats temporal lag and spatial deviation in Lissajous pursuit as oculomotor features whose Mahalanobis distance marks individual atypicality in autism spectrum disorder. Under the Observer as Field Postulate, these deviations are not merely failures of pursuit accuracy. They are boundary signatures of an extended observer whose integrated information field does not lock to the moving target with the normative phase relation. The high outlier rate in the ASD cohort is therefore a distributional sign of heterogeneous field-boundary coupling, not evidence for one common autistic oculomotor deficit. The source's outlier score becomes a low-dimensional projection of field phase stability during visuomotor entrainment. If the test-retest rank ordering of individual outlier scores during identical Lissajous pursuit were measured to be no more stable than shuffled participant labels, this Postulate would be falsified.

Source Synopsis

Shishido et al. study smooth pursuit eye movement in adults with autism spectrum disorder using an outlier method rather than a conventional group-mean comparison. The premise is clinical and methodological. ASD is heterogeneous. Mean differences in oculomotor measures can miss individual physiological patterns that occur only in a subset of participants. The authors therefore ask whether point-by-point deviations during a smooth pursuit task can identify idiosyncratic atypicality.

The experiment uses a slow Lissajous pursuit trajectory. Eye and target positions are recorded in 18 adults with ASD and 39 typically developed participants. The analysis transforms gaze and target paths into polar coordinates and computes temporal and spatial discrepancies. The temporal discrepancy, Δt, records how far the gaze lags or leads the target in reaching equivalent radial positions. The spatial discrepancy, Δs, records normalized radial deviation. Three features enter the initial representation: mean Δt, standard deviation of Δt, and standard deviation of Δs. Principal component analysis reduces and optimizes this feature space. A Mahalanobis distance from the typically developed reference distribution defines each participant's outlier score.

The main result is distributional. The typically developed group is narrowly clustered, with 2 of 39 participants above the outlier threshold. The ASD group is broader, with 7 of 18 participants above the threshold. The threshold is set at √10, approximately 3.16 standard deviations relative to the normative reference. The ASD outlier prevalence is 38.9 percent, compared with 5.1 percent in the TD group, with a binomial P value of 0.0034. Mean outlier score is also higher in ASD, 3.00 ± 2.62 compared with 1.52 ± 0.80, P = 0.002.

The source paper emphasizes that the finding does not imply a single ASD pursuit pattern. Some individuals show temporal lag. Others show spatial drift. The value of the method lies in resolving individual deviations that group averaging suppresses. The paper presents the outlier score as a candidate metric for clinical stratification and future subtype discovery.

Postulate Lens

The relevant lens is Observer as Field. The source phenomenon already has the structure that this Postulate names: the measured observer is not a point sampling a stimulus, but a spatially and temporally extended control field whose boundary is inferred from how gaze, expectation, and target motion maintain or lose phase coherence.

Smooth pursuit is not a reflexive copy of retinal motion. It requires prediction of target position, stabilization of error, and continuous coordination between visual input and motor output. In the Pudding Theory formalism, this is a direct probe of the observer field Ξ(x), where the phase S(x) encodes expectation and the spatial extension of the field defines the coupling surface between the observer and the moving target. The Lissajous target is useful because it forces the observer field to entrain to a nontrivial, continuously varying external path. A point observer would only have tracking error. A field observer has boundary deformation, phase lag, and local loss of coherence. Shishido et al. measure these deformations as Δt and Δs.

The Mahalanobis construction is therefore not only a statistical classifier. It is an empirical coordinate system for observer-field geometry. The TD covariance structure estimates a normative manifold of visuomotor phase-locking. ASD outliers mark individuals whose observer-field boundary does not lie on that manifold during pursuit.

Pudding Theory Reading

Pudding Theory reads the ASD pursuit outliers as signatures of heterogeneous observer-field closure. The source paper frames Δt and Δs as temporal and spatial deviations from a normative oculomotor pattern. That is correct operationally. It is incomplete ontologically. In this reading, the gaze trace is the visible edge of an extended observer field attempting to maintain phase with a moving stimulus.

The Lissajous target supplies a periodic but noncircular demand. It has enough structure to invite prediction and enough curvature to expose loss of phase-locking. A normative observer field does not merely react to target position. It carries a phase expectation over the near-future target path. Smooth pursuit emerges when this expectation remains coherent across the visuomotor boundary. The narrow TD distribution in Shishido et al. is the empirical footprint of that coherence. The covariance of Δt and Δs is not background variance. It is the shape of the ordinary field-boundary solution for this task.

The ASD distribution changes the interpretation. Its broad tail does not indicate noise added to a single pursuit deficit. It indicates several distinct boundary geometries. A participant with dominant temporal lag has a field that forms the correct spatial expectation but updates late. A participant with dominant spatial drift has an expectation that updates on time but is not spatially bound to the target radius. A participant extreme on both axes has unstable field closure across the task. These are different field states, not degrees of one impairment.

This also changes the status of the Mahalanobis distance. In the source model, the outlier score is a useful distance from the TD reference distribution. In Pudding Theory, the score is structurally constrained by the observer-field manifold. It should not vary as an arbitrary clinical parameter. It should decompose into stable individual modes of phase-boundary mismatch. The PCA axes are empirical estimates of those modes. They should recur across sessions and across pursuit trajectories that preserve comparable phase demands, even if raw gain or signal-to-noise ratio changes.

The source treats idiosyncrasy as the problem that blocks a group biomarker. Pudding Theory treats idiosyncrasy as the signal. Autism spectrum disorder is then not read as one abnormal eye movement pattern. It is read as a population in which observer-field coupling to external motion occupies several atypical but stable geometries. The outlier method succeeds because it stops averaging those geometries into invisibility.

Falsifiable Observable

The distinguishing observable is within-person stability of the Mahalanobis outlier geometry across repeated Lissajous pursuit sessions. Pudding Theory predicts that the participant's location in the Δt and Δs principal-component space will show stable individual rank ordering, because it reflects observer-field boundary structure rather than transient tracking noise. If the test-retest rank ordering of individual outlier scores during identical Lissajous pursuit were measured to be no more stable than shuffled participant labels, this Postulate would be falsified.

Editorial Dialogue

Tanaka: The reading risks reifying a statistical procedure. Mahalanobis distance is a convenience. PCA axes are sample-dependent. With 18 ASD participants, a broad tail can arise from measurement variability, medication, attention, fatigue, or calibration error. Calling it field-boundary geometry may add vocabulary without adding constraint.

Sterling: The constraint is stability of individual geometry, not the name of the statistic. If Δt and Δs extremes are only measurement scatter, their position in the reduced space will not recur under repeated pursuit. The Observer as Field reading says they will recur when the task probes the same phase relation. It also says temporal lag and spatial drift should separate into reproducible modes, not dissolve into a generic error score.

Tanaka: But the source paper does not measure integrated information or Ξ(x). It measures eye position.

Sterling: Eye position is the boundary observable. The formal field is not directly inserted into the eye tracker. It is inferred from the stable relation among gaze, target, and expectation. Smooth pursuit is a privileged assay because it makes expectation visible as motor phase. The source already shows that mean comparison suppresses the signal. The Pudding Theory reading explains why: the population contains multiple field geometries, so averaging destroys the object being measured.

Discussion

This reading buys a sharper account of heterogeneity. The source paper correctly rejects the search for one ASD-type smooth pursuit deficit. Pudding Theory goes further and identifies the positive object: stable observer-field coupling modes. In that account, temporal lag and spatial drift are not merely descriptive features. They are projections of how an observer field closes around a moving target.

The main limitation is empirical. The present source is preliminary, small, and cross-sectional. It establishes a distributional asymmetry, not yet the recurrence structure required by the Postulate. The next decisive step is repeated measurement with the same participants, varied Lissajous frequencies, and independent calibration of attention and fatigue. The reading would strengthen if individual PCA-space locations remained stable while conventional gain measures fluctuated. It would weaken if outlier identity changed freely across runs.

The clinical value is also specific. The outlier score should not be treated as a scalar severity measure. In this reading, the geometry matters. A temporal-lag outlier and a spatial-drift outlier are different observer-field states. Subtyping should therefore preserve the direction of deviation, not collapse all extremes into one label.

References

1. E. Shishido, S. Miyata, T. Yamamoto, M. Fukunaga, R. Hashimoto, K. Miura, and N. Ozaki, “Detecting outliers of pursuit eye movements: a preliminary analysis of autism spectrum disorder,” arXiv:2603.22705, 2026. doi:doi:10.48550/arxiv.2603.22705.

2. S. Ochs, Pudding Theory: A Topological Theory of Information Fields, QBist Lab, 2026.

3. S. Caldani, E. Humeau, R. Delorme, and M. P. Bucci, “Inhibition functions can be improved in children with autism spectrum disorders: An eye-tracking study,” International Journal of Developmental Neuroscience, vol. 83, no. 5, pp. 431-441, 2023. doi:doi:10.1002/jdn.10276.

4. M. G. Campbell, I. S. Kohane, and S. W. Kong, “Pathway-based outlier method reveals heterogeneous genomic structure of autism in blood transcriptome,” BMC Medical Genomics, vol. 6, p. 34, 2013. doi:doi:10.1186/1755-8794-6-34.

5. K. Miura, R. Hashimoto, M. Fujimoto, H. Yamamori, Y. Yasuda, K. Ohi, and M. Takeda, “An integrated eye movement score as a neurophysiological marker of schizophrenia,” Schizophrenia Research, vol. 160, no. 1-3, pp. 228-229, 2014. doi:doi:10.1016/j.schres.2014.10.023.

6. K. Morita, K. Miura, M. Fujimoto, H. Yamamori, Y. Yasuda, M. Iwase, and R. Hashimoto, “Eye movement as a biomarker of schizophrenia: Using an integrated eye movement score,” Psychiatry and Clinical Neurosciences, vol. 71, no. 2, pp. 104-114, 2017. doi:doi:10.1111/pcn.12460.

7. T. Shiino, K. Miura, M. Fujimoto, N. Kudo, H. Yamamori, Y. Yasuda, and R. Hashimoto, “Comparison of eye movements in schizophrenia and autism spectrum disorder,” Neuropsychopharmacology Reports, vol. 40, no. 1, pp. 92-95, 2020. doi:doi:10.1002/npr2.12085.