Error- and Prediction-Driven Motor Learning in the Cortico-Cerebellar Loop

1 Introduction

• Classical predictive models do not fully explain how biological systems achieve both rapid online corrections and stable trial-by-trial adaptation.Experimental findings indicate that cerebellar outputs multiplex kinematics and performance errors, while motor cortex exhibits distinct feedforward and feedback dynamics.Source: §1 · pp. 1–2
• The central question is how delayed sensory feedback should be routed and represented in cortico-cerebellar circuits to support stable control and rapid adaptation.The challenge matters because sensory delays can degrade performance and hinder both online correction and learning.Source: §1 · pp. 1–2
• The proposed recurrent neural network adds a cerebellum-inspired module integrating delayed sensory feedback, and multiplexed cerebellar outputs improve online correction.Routing delayed feedback through the cerebellar loop can facilitate faster, more stable adaptation and reproduce key experimentally observed neural population patterns.Source: §1 · p. 2
• The framework treats cerebellar processing as transforming delayed sensory signals into effective feedback, unifying predictive control and error-driven learning.Figure 1 describes temporally specific, error-driven plasticity in which prediction discrepancies with delayed behavioral variables drive synaptic updates.Source: §1 · p. 2, Figure 1 · p. 2

2 Related Work

• Cerebellar forward models have been proposed to predict sensory consequences and enable error-driven adaptation, while behavior combines rapid error correction with slower internal-model updates.The cited accounts include for forward models and for multiple adaptation timescales.Source: §2 · p. 3
• Motor-cortex population dynamics include dual-phase responses associated with feedforward and feedback processes, and recurrent networks model such dynamics and realistic motor behavior.Some RNN approaches provide sensory feedback directly to cortical units for online correction.Source: §2 · p. 3
• Cerebellum-inspired modules have provided predictive mappings and corrective signals, but delayed-feedback routing remains unclear; this work compares cortical and cerebellar feedback routes.The authors report that cerebellar-mediated feedback better captures behavioral adaptation and neural dynamics.Source: §2 · p. 3

3.1 Task

• A synthetic instructed-delay centre-out task samples start and target positions uniformly, uses variable holds, and tests a 30° visuomotor rotation.The hold period ranges from 1.2 to 1.7 seconds.Source: §3.1 · p. 3

3.2 Network Architecture

• The cortical RNN maps state to hand velocity; the cerebellum receives delayed cortical activity and sensory error, returns corrective feedback, and position is integrated from velocity.The delayed sensory-feedback signal is fixed at 120 ms unless otherwise stated.Source: §3.2 · pp. 3–4

3.3 Adaptation and Learning

• Cortical adaptation uses local eligibility traces and trial-end recurrent-weight updates, while cerebellar targets vary across velocity, position, position-error, or multiplexed signals.Cerebellar learning uses delayed feedback as its teaching signal; mossy-fibre weights remain fixed.Source: §3.3 · pp. 4–5

3.4 Training Procedure

• Training first held cortical feedback projections fixed for 100 epochs, then enabled cortical adaptation and cerebellar learning together for 500 epochs.Simulations used 10-ms steps and a 50-ms time constant; cortical traces accumulated online and updates were applied after each trial.Source: §3.4 · p. 5

4.1 Multiplexing Enables Online Compensation for External Perturbations

• Only the multiplexed model reproduced rapid online re-aiming; single-variable predictions failed to redirect movements, while delayed-error-only control was unstable and acquired targets poorly.The multiplexed module combines position, velocity, and position error; it maintained low directional and lateral errors across adaptation phases.Source: §4.1 · pp. 5–6, Figure 2 · p. 6, Table 1 · p. 7

4.2 Error-Based Feedback Enables Rapid Trial-by-Trial Adaptation

• Delayed cerebellar sensory feedback yielded lower endpoint error during early adaptation while preserving gradual take-off-error reduction, with both models reaching near-zero late task error.Without cerebellar sensory input, take-off error fell faster, an adjustment described as less biologically realistic.Source: §4.2 · pp. 7–8, Figure 3 · p. 8

4.3 Sensory Feedback Shapes Dual-Phase Cortical Dynamics

• Models with sensory feedback reproduced the late feedback-related cortical activity peak, and cerebellar routing alone sufficed without direct sensory input to the cortical RNN.The no-feedback model showed only an early peak.Source: §4.3 · p. 9, Figure 4 · p. 9

4.4 Error-Dependent Modulation of Feedback Dynamics

• Cerebellar feedback activity rose transiently during early adaptation and declined as errors fell, while direct-feedback activity persisted across phases; cerebellar feedback also produced smoother, more stable error reduction.Direct sensory feedback to the RNN produced less stable learning dynamics with increased variability.Source: §4.4 · p. 10, Figure 5 · p. 10

• The cortico-cerebellar model produces rapid trial-by-trial error reduction, slower adaptation of movement initiation, and dual-phase cortical dynamics.Source: §5 · p. 11
• Models without delayed feedback or with direct cortical sensory input show overly rapid adaptation, persistent feedback activity, or unstable learning dynamics.The proposed model captures error-dependent gating of feedback, consistent with theories of cerebellar forward models and prediction error minimization.Source: §5 · p. 11
• The authors propose modularly separating instantaneous, predictive error correction from a feedforward controller as a bio-inspired approach to latency in adaptive systems.They identify robotics and deep reinforcement learning as settings where feedback delays can cause overcorrections or degraded performance.Source: §5 · p. 11