A Mathematical Model of Reliability-Dependent Sensory Reweighting in Quiet Standing
- 1Kyushu Institute of Technology
Abstract
Human quiet standing relies on vestibular, proprioceptive, and visual information whose contributions change with sensory context. Dynamic posturography characterizes this reweighting through responses to visual-scene and support-surface perturbations, but a compact mathematical account of how sensory reliability propagates from state estimation to postural action remains incomplete. We develop a minimal quiet-standing model in which sensory reliability is encoded by channel-specific precision parameters that weight sensory prediction errors. A one-link inverted pendulum receives vestibular, proprioceptive, and visual observations, estimates posture using an active-inference variational free-energy objective over temporally embedded states, and selects ankle torque by minimizing the same free-energy form under an upright sensory goal. Changes in sensory conditions enter the model only through the relative channel precisions; body dynamics, the action optimizer, and the upright goal prior are held fixed. A fixed-point analysis yields closed-form predictions: the perturbation-induced belief bias, each channels state-update contribution, and the resulting posture shifts are set by relative channel precisions, with a stability condition on the upright goal. Closed-loop simulations confirmed these predictions: reducing an unreliable channels precision reduced perturbation-driven postural shifts by approximately 82%, as predicted, with a matching decrease in that channels state-update contribution, identifying belief updating as the mechanism of reweighting. A graded reliability-to-precision mapping monotonically controlled sensory contribution, and reweighting required relative, channel-selective precision changes rather than a global reduction. These results provide a compact mathematical account of postural sensory reweighting as relative, context-selective precision control in a closed-loop multisensory system.
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BibTeX
@misc{kobayashi2026mathematical,
title = {{A Mathematical Model of Reliability-Dependent Sensory Reweighting in Quiet Standing}},
author = {J. Kobayashi},
howpublished = {bioRxiv},
year = {2026},
month = jun,
doi = {10.64898/2026.06.23.733972},
url = {https://www.biorxiv.org/content/10.64898/2026.06.23.733972v3},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - A Mathematical Model of Reliability-Dependent Sensory Reweighting in Quiet Standing
AU - J. Kobayashi
PY - 2026
DA - 2026/06/23
PB - bioRxiv
DO - 10.64898/2026.06.23.733972
UR - https://www.biorxiv.org/content/10.64898/2026.06.23.733972v3
AB - Human quiet standing relies on vestibular, proprioceptive, and visual information whose contributions change with sensory context. Dynamic posturography characterizes this reweighting through responses to visual-scene and support-surface perturbations, but a compact mathematical account of how sensory reliability propagates from state estimation to postural action remains incomplete. We develop a minimal quiet-standing model in which sensory reliability is encoded by channel-specific precision parameters that weight sensory prediction errors. A one-link inverted pendulum receives vestibular, proprioceptive, and visual observations, estimates posture using an active-inference variational free-energy objective over temporally embedded states, and selects ankle torque by minimizing the same free-energy form under an upright sensory goal. Changes in sensory conditions enter the model only through the relative channel precisions; body dynamics, the action optimizer, and the upright goal prior are held fixed. A fixed-point analysis yields closed-form predictions: the perturbation-induced belief bias, each channels state-update contribution, and the resulting posture shifts are set by relative channel precisions, with a stability condition on the upright goal. Closed-loop simulations confirmed these predictions: reducing an unreliable channels precision reduced perturbation-driven postural shifts by approximately 82%, as predicted, with a matching decrease in that channels state-update contribution, identifying belief updating as the mechanism of reweighting. A graded reliability-to-precision mapping monotonically controlled sensory contribution, and reweighting required relative, channel-selective precision changes rather than a global reduction. These results provide a compact mathematical account of postural sensory reweighting as relative, context-selective precision control in a closed-loop multisensory system.
ER -