Precision-weighted updating shows cross-task consistency as a bounded computational marker when precision gain is sufficiently large

Technical Summary: Precision-weighted updating shows cross-task consistency as a bounded computational marker when precision gain is sufficiently large

Problem Statement
Computational psychiatry seeks to replace syndromal labels with generative parameters (e.g., learning rates, precision weights) that serve as transdiagnostic markers or endophenotypes. However, a critical tension exists: parameters estimated within a single experimental task are often treated as portable traits, yet they may be "task-bound regression weights" rather than stable biological quantities. The paper addresses whether a specific precision-weighting coefficient ($\gamma$) within the CPSP-8 model (a three-layer threat-dissociation framework) generalizes across distinct risk-taking tasks (Balloon Analogue Risk Task [BART] and Columbia Card Task [CCTHot]) and a behavioral probe, or if it is merely an artifact of the specific task graph. The study specifically investigates the identifiability and cross-task consistency of $\gamma$ compared to other decision parameters (threat, baseline, initial learning rate $\alpha_0$, inverse temperature $\beta$, value gain $v_{gain}$) and the theoretical Ornstein-Uhlenbeck (OU) threat layer.

Methodology
The study utilized secondary analysis of de-identified data from three OpenNeuro datasets:

1. D1 (BART): $N=173$ (124 controls, 49 schizophrenia) from ds000030.
2. D5 (CCTHot): $N=104$ from ds004636.
3. D2 (HierPrior): $N=43$ from ds008083, providing a behavioral probe for $\gamma$.

Model Architecture:
The author employed CPSP-8, a model comprising:

• Layer 1 (Theoretical): A continuous-time Ornstein-Uhlenbeck (OU) process for latent threat state ($z_t$) and a dissociation drift. These parameters ($\theta, \sigma_{ou}, \kappa, \lambda, onset$) were frozen at group means derived from prior recovery simulations (where $\theta$ recovery was $r < 0.3$) to prevent narrating unidentifiable dynamics as patient-specific traits.
• Layer 2 (Decision): A precision-gated delta-rule. The learning rate $\alpha_t$ is modulated by a precision-weighting coefficient $\gamma$ based on squared prediction errors ($PE_t^2$) relative to Bernoulli uncertainty.
• Layer 3: RT modeling via a log-normal approximation of a Wald process.

Analytical Procedure:
The core analysis used Hierarchical Transfer Cross-Validation (HTCV), preregistered before results were viewed. Unlike standard leave-one-subject-out CV, HTCV tests the exchangeability of group-level posterior means across tasks.

• Consistency Criterion: A parameter is considered consistent across tasks if the 95% Highest Density Interval (HDI) of the difference between task means ($\Delta = \mu_{TaskA} - \mu_{TaskB}$) contains zero.
• Hypotheses:
  • H1: All non-$\gamma$ decision parameters are consistent across BART and CCT.
  • H2: $\gamma$ is consistent across BART, CCT, and the HierPrior probe.
  • H3: The OU layer is untestable under the freeze.
  • H4: CPSP-8 is not worse than dedicated models (Random Walk, Logistic Regression, DDM, simplified HGF-2) on choice and RT.
• Post-Review Diagnostics: Included ROPE (Region of Practical Equivalence) checks, a conjugate MAP+SE sensitivity grid (36 variations of priors and pooling), WAIC/LOO-IC model comparison, and demographic propensity score weighting (IPW).
• Identifiability Checks: Virtual-subject simulations (D1d, D1e) tested parameter recovery ($r$) and family-level separability (Bayes Factors) between the precision-gated model and a Random Walk (RW) limit ($\gamma=0$).

Key Results

1. H1 Failed (Task Specificity): All non-$\gamma$ decision parameters ($\text{threat}, \text{baseline}, \alpha_0, \beta, v_{gain}$) showed significant differences between BART and CCT (95% HDIs excluded zero). For example, $\beta$ (inverse temperature) was 1.769 in BART vs. 0.001 in CCT. The author interprets this not as a fitting failure, but as evidence that these parameters act as "mode switches" adapting to specific task structures (e.g., hidden hazard vs. explicit probabilities).
2. H2 Conditionally Supported (Pipeline-Sensitive Consistency): Under the preregistered NUTS HDI rule, the precision-weighting coefficient $\gamma$ was the only parameter where the 95% HDI of the difference between BART and CCT contained zero ($\Delta = 0.3835$, HDI $[-0.0084, 0.7826]$). This consistency held across all three contrasts (BART-CCT, BART-EEG, CCT-EEG) under this specific rule.
   • Critical Limitations: The paper explicitly states this result is not robust across pipelines. The consistency fails on a conjugate MAP+SE grid (0/36 cells contained zero), is not ROPE equivalence (HDI overlaps but is not contained within ROPE), and WAIC/LOO favored task-specific $\gamma$ models over a shared-$\gamma$ model ($\Delta$WAIC = 146.6). Consequently, $\gamma$ is described as a "bounded, pipeline-sensitive cross-task scalar" rather than a stable marker.
3. H3 Confirmed (Unidentifiable OU): The OU layer parameters remained frozen because virtual-subject recovery simulations showed Pearson correlations $r < 0.3$ for $\theta$, rendering them unidentifiable in these tasks.
4. H4 Failed (Predictive Performance): CPSP-8 did not outperform dedicated models. Random Walk (RW) and Logistic Regression outperformed CPSP-8 on choice RMSE; DDM outperformed on RT RMSE.
5. Identifiability and Separability:
   • $\gamma$ was recoverable at the individual level with 960 trials (median $r \approx 0.66$).
   • Family Separability: The model could distinguish the precision-gated mechanism from a Random Walk ($\gamma=0$) only when the true $\gamma$ was sufficiently large. Separability was achieved at $\gamma \ge 1.0$ with $\ge 960$ trials (or $\gamma \ge 1.5$ with 480 trials). At $\gamma \le 0.5$ or $\gamma=0$, the model was family-inseparable from RW (Bayes Factors near 1).

Significance and Claims
The paper claims a modest, bounded contribution to computational psychiatry:

• $\gamma$ is a Bounded Scalar, Not a Biomarker: The precision-weighting coefficient $\gamma$ demonstrates cross-task consistency only under specific conditions (sufficiently large gain, sufficient trial counts, and a specific NUTS fitting pipeline). It fails robustness checks (conjugate grid, WAIC) and is not a diagnostic biomarker for schizophrenia (as $\gamma$ did not differ by diagnosis in the BART sample; $\beta$ did, but $\beta$ failed cross-task consistency).
• Mechanism vs. Architecture: The study distinguishes between "portable" parameters and "mode switches." The failure of H1 indicates that many decision parameters are context-dependent. The conditional success of H2 suggests that precision weighting is a candidate for a computational endophenotype only when the "precision gain" is large enough to be distinguishable from a simple learning rate and the fitting pipeline is fixed.
• Honesty Constraints: The author emphasizes that freezing the OU layer and acknowledging the inability to separate $\gamma$ from RW at low values are "honesty constraints." They argue against narrating unidentified dynamics as patient-specific traits.
• Methodological Rigor: The study reinforces the necessity of hierarchical transfer validation and parameter recovery checks, showing that a parameter can appear consistent across tasks under a Bayesian HDI rule while failing in other robustness checks (ROPE, conjugate grid, WAIC), highlighting the pipeline sensitivity of computational phenotypes.

In conclusion, the paper asserts that while precision-weighted updating ($\gamma$) shows promise as a cross-task computational marker, its utility is strictly bounded by the magnitude of the gain, the trial count, and the fitting pipeline. It should not be interpreted as a definitive clinical diagnostic tool or a heritable endophenotype without further validation involving neural anchors and familial designs.