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Dissociable changes in temporal precision and causal expectations following perceptual training

Haocheng ZhuiD, Shizhong Cai, Jingci Lang, Xiaole Liu, Aijun WangiD

Abstract

A common behavioral gain does not necessarily reflect a common learning mechanism. Perceptual learning may sharpen sensory evidence without updating higher-level expectations about its causes. Across three experiments, we examined audiovisual binding and its plasticity in children with ADHD and typically developing children. Children with ADHD were more susceptible to the sound-induced flash illusion (Experiment 1) and showed markedly flatter temporal tuning of it (Experiment 2), yet conventional temporal binding window (TBW) estimates did not distinguish the groups, behavior alone could not localize the difference. Following six days of simultaneity-judgment training, both groups became comparably less susceptible to the illusion. A temporally explicit two-dimensional Bayesian causal inference model, however, revealed sharply different latent changes. Typically developing children reduced their causal prior expectation that auditory and visual signals shared a common cause. Children with ADHD showed no corresponding prior recalibration but instead exhibited a marked reduction in temporal uncertainty, indicating more precise perceptual evidence that did not propagate to the slower, more abstract estimate of environmental causal structure. Thus, perceptual learning converged at the behavioral level while diverging computationally. These findings argue against unitary accounts of multisensory plasticity and show how the same perceptual endpoint can conceal adaptation at different levels of the inferential hierarchy.

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Claude Opus 5.5 · xhigh effort · 7 Nov 2026 · from the full text of version 1 (13 Sept 2026) · CC BY 4.0

Simultaneity-judgment training reduced flash-illusion susceptibility similarly in children with and without ADHD; Bayesian modelling showed lower common-cause prior in typical children versus lower temporal uncertainty in ADHD.

Illusion rates and temporal binding window width drop whether sensory timing becomes sharper or the expectation that sight and sound share a cause weakens, so behavior alone cannot say which changed. Prior modelling had already separated these components in principle; this work reports one training protocol moving different components in different groups of children while their behavioral gains matched.

Key results

  1. SuggestedIn the two-dimensional Bayesian causal inference model of the illusion, training lowered the common-cause prior (pcommon) only in typically developing (TD) children and lowered temporal uncertainty (σt) only in children with ADHD.

    pcommon: TD 0.637 to 0.379 (pHolm = .021), ADHD 0.631 to 0.630 (pHolm = 1.000); group difference in change t(47.23) = 2.33, pHolm = .048. σt: ADHD 228.86 to 110.19 ms (reduction 118.67 ms, pHolm = .006), TD 114.10 to 115.49 ms; group difference t(42.76) = −2.31, pHolm = .048. Visual-to-auditory noise ratio unchanged in both groups. · 3.3.2. Computational modelling

  2. ShownAfter six training sessions, fission-illusion susceptibility fell by a similar amount in both groups, without reliable narrowing of individually fitted simultaneity windows or any gain in temporal-order accuracy.

    Mean fission rate TD 0.49 to 0.33 (change −0.16, 95% CI [−0.29, −0.03], p = .017, dz = −0.49); ADHD 0.54 to 0.40 (−0.14, p = .016, dz = −0.54); Group × Time t(47.79) = 0.23, p = .82. Simultaneity window change TD −40 ms (p = .593), ADHD 55 ms (p = .648); temporal-order judgment accuracy unchanged (p = .532 and p = .842). · 3.3.1. Behavioural results

  3. ShownChildren with ADHD showed a flatter decline of the fission illusion as audiovisual asynchrony grew, while standard temporal binding window (TBW) width estimates did not differ between groups.

    Group × asynchrony interaction F(4.21, 243.94) = 6.96, p = 1.76 × 10^−5; slope −0.038 vs −0.131 per 100 ms (ADHD vs TD), t(50.84) = 3.81, p = 0.0004, d = 0.98; far-minus-near attenuation −0.064 vs −0.260, d = 1.05. TBW₈₀ 330.83 vs 253.80 ms, p = 0.096; Gaussian width 170.88 vs 177.70 ms, p = 0.839; n = 30 per group. · 3.2. Experiment 2

  4. ShownChildren with ADHD were more susceptible to the fission illusion (one flash, two beeps) but not the fusion illusion, with no group difference in signal-detection sensitivity or control-condition accuracy.

    Fission rate 0.857 vs 0.771 (ADHD vs TD), t(39.63) = 2.25, p = 0.030, d = 0.60; Mann-Whitney p = 0.021. Fusion 0.695 vs 0.712, p = 0.774. Group × illusion-type interaction p = 0.056. Fission d′ 2.27 vs 2.00, p = 0.352; n = 28 per group. · 3.1. Experiment 1

  5. ShownOf five candidate causal inference architectures, the Standard 2D model (free pcommon, visual noise, σt and latency) was most often preferred by Bayesian information criterion (BIC), though preference varied across children.

    Lowest BIC in 50% of 100 participant-time cells (alternatives 12%, none, 16%, 22%); in the top three ranks in 90% of cells; favoured in exact sign tests over each alternative, e.g. 78 vs 22 cells (pHolm = 4.77 × 10^-8) and 88 vs 12 cells (pHolm = 7.65 × 10^-15). · 3.3.3. Model Comparison

Methods, data and reproducibility

Three experiments compared children with ADHD and typically developing children on the sound-induced flash illusion (SIFI): at synchrony, across audiovisual asynchronies, and before and after six daily sessions of adaptive simultaneity-judgment training. A two-dimensional Bayesian causal inference model fitted per child and session separated the common-cause prior from temporal and visual numerosity noise.

  • Experiment 1: children with clinically diagnosed (DSM-5), medication-naive ADHD and typically developing children; sound-induced flash illusion task, 120 trials · human · n = 56 (28 ADHD, 28 TD)
  • Experiment 2: children with ADHD and typically developing children; fission-illusion task across 10 audiovisual onset asynchronies, 480 trials · human · n = 60 (30 ADHD, 30 TD)
  • Experiment 3: children with ADHD and typically developing children; pre/post illusion, simultaneity-judgment and temporal-order-judgment tasks around six adaptive training sessions · human · n = 50 completers (23 ADHD, 27 TD); 60 enrolled, 10 withdrew
Methods & tools
Presentation (Neurobehavioral Systems), G*Power 3.1.9, MATLAB R2025b, BCI Toolbox, Bayesian Adaptive Direct Search (BADS), Python, NumPy, SciPy, pandas, Matplotlib, Combined Raven's Test, DSM-5
Code
https://github.com/evans1112/ADHD_perceptual_learninghttps://github.com/acerbilab/bads
Data & accessions
https://github.com/evans1112/ADHD_perceptual_learning
Software & environment
MATLAB R2025b for model fitting; Python 3.7 with NumPy, SciPy, pandas and Matplotlib for statistics and figures; no library versions, requirements file or container stated.
Reproducibility gaps
Evidence integrals, estimator equations, full alternative-model specifications and identifiability/parameter-recovery analyses are deferred to Supplementary Methods and Figure S1, which are not in this text.
Limitations (6)
  • No untrained or active control group, so retesting, task familiarity or stimulus exposure could explain pre-post changes; effects are described as training-related rather than shown to be training-induced. · stated by the authors
  • The σt interaction could reflect regression toward the mean, since the group with higher baseline σt showed the larger decrease; the prior effect is not exposed to this because baseline pcommon did not differ between groups. · stated by the authors
  • Decision strategies were assigned by best-fitting model per child and session; frequent switching (19 of 27 TD, 16 of 23 ADHD) may reflect near-equal model evidence, so individual strategy labels are uncertain. · stated by the authors
  • SJ and SIFI estimates of pcommon and σt did not correlate (r = .12 and .02), suggesting task-dependent parameters, but this test is limited by parameter reliability and treats repeated observations from one child as independent. · stated by the authors
  • Small training samples (23 ADHD and 27 TD completers) and both focal Group × Time interactions only just pass Holm correction (pHolm = .048). · noted in this summary
  • The prior-versus-precision split rests on the illusion model: the separately fitted simultaneity-judgment model showed no corrected pcommon change (TD pHolm = .053) or group difference (pHolm = .398), and recovery analyses are not in this text. · noted in this summary

Who should read:Read this if you model multisensory causal inference or perceptual learning and want a worked case where matched behavioral gains in children with and without ADHD map onto different latent parameter changes.

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