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

Ana Carolina Filipe; Rui Ponte Costa; Cláudia Soares

cs.LGSep 24, 2026

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

Authors: Ana Carolina Filipe, Rui Ponte Costa, Cláudia Soares

Organizations: Department of Computer Science, NOVA School of Science and Technology, Caparica, Portugal · Centre for Neural Circuits and Behaviour, University of Oxford

Abstract

Robust control under delayed sensory feedback remains a key challenge in both robotics and neuroscience. Classical cerebellar models explain delay compensation through forward prediction but fail to account for fast online corrections and rapid adaptation observed in biological systems. We propose a cerebellum-inspired control framework that combines multiplexed predictive representations with internal feedback. By jointly encoding kinematic variables and task-relevant error signals, the model enables accurate online correction despite delayed feedback. Furthermore, incorporating feedback within the cerebellar loop significantly accelerates adaptation, reducing learning time by an order of magnitude. Our results show that single-signal predictions are insufficient under delay, while multiplexing and feedback together provide a unified mechanism for online control and rapid learning.

Figures & tables

Figure 1: Model architecture and learning mechanism. (A) Schematic of the proposed cortico-cerebellar model. (B) The cerebellar module learns through temporally specific, error-driven plasticity consistent with experimental observations. In particular, the discrepancy between the cerebellar prediction $c$ and delayed behavioral variables (120 ms) drives synaptic updates via climbing fiber signals at the parallel fibre–Purkinje cell synapses.

Figure 2: Multiplexed representations are required for robust online error correction. (A) Experimental reaching behavior: Hand trajectories across three learning phases: baseline (initial 30 trials), early adaptation (first 10 perturbation trials), and late adaptation (final 30 trials of a 150-trial epoch). Trajectories are color-coded by target direction. Data adapted from [ 20 ] . (B) Single-variable predictive models: Model predictions on the test set across all phases. Performance is invariant regardless of whether the cerebellar (cb) module predicts velocity, position, or position error independently; notably, single-variable models fail to exhibit corrective re-aiming. (C) Multiplexed model: When the cerebellum integrates velocity, position, and position error, the system successfully reproduces the characteristic re-aiming behavior observed during early biological adaptation. (D) Direct feedback baseline: Performance in the absence of the cerebellar module, where control is driven exclusively by the delayed position error signal, resulting in systematic instability and poor target acquisition.

Model architecture		Takeoff error (deg)			Task error(along traj., lateral) (cm)
Cerebellum prediction	Sensory feedback	Baseline	Early adap.	Late adap.	Baseline	Early adap.	Late adap.
v	–	$0_{\pm 1}$	$28_{\pm 4}$	$0_{\pm 2}$	$(1_{\pm 0.4},\,0_{\pm 0.8})$	$(1.5_{\pm 0.5},\,2.2_{\pm 0.8})$	$(1.1_{\pm 1},\,0_{\pm 0.5})$
p	–	$0_{\pm 1}$	$30_{\pm 5}$	$0_{\pm 2}$	$(0.8_{\pm 0.6},\,0_{\pm 0.5})$	$(1_{\pm 1},\,2.2_{\pm 0.8})$	$(0.8_{\pm 1},\,0_{\pm 0.5})$
pe	–	$0_{\pm 0.5}$	$30_{\pm 3}$	$0_{\pm 0.5}$	$(0_{\pm 0.3},\,0_{\pm 0.1})$	$(0_{\pm 0.3},\,1.5_{\pm 0.9})$	$(0_{\pm 0.3},\,0_{\pm 0.3})$
v + p + pe	–	$0_{\pm 0.5}$	$29_{\pm 2}$	$0_{\pm 0.5}$	$(0_{\pm 0.2},\,0_{\pm 0.1})$	$(0.1_{\pm 0.2},\,0.3_{\pm 0.2})$	$(0_{\pm 0.1},\,0_{\pm 0.1})$
–	pe	$0_{\pm 2}$	$30_{\pm 5}$	$3_{\pm 2}$	$(1.8_{\pm 0.5},\,0_{\pm 0.5})$	$(2.7_{\pm 1},\,3.5_{\pm 1.8})$	$(1.5_{\pm 0.6},\,0_{\pm 0.6})$

Table 1: Performance of different cerebellar prediction and sensory feedback architectures across adaptation stages. Results are averaged across 3 seeds. Takeoff error is reported in angular deviation (deg), while task error is decomposed into directional and lateral components relative to the movement trajectory (cm). Values are reported as mean ±std .

Figure 3: Error-driven adaptation dynamics. (A) Model architecture with delayed sensory feedback to the cerebellum. (B) Take-off angle error across baseline (white) and adaptation (blue) phases. (C) Task error (endpoint angular error) during early (first 10 trials) and late (last 30 trials) adaptation, comparing models and experimental data.

Figure 4: Cortical dynamics under different feedback architectures. (A) Model variant with both cerebellar feedback and direct delayed sensory input to the RNN. (B) Average change in RNN activity across time, computed from population activity $r(t)$ obtained by averaging hidden-unit activity across neurons and trials; and comparison with experimental recordings [ 20 ] . Neural population activity is obtained by averaging firing rates across neurons, and both model and data are aligned to movement onset (Go cue) for temporal comparison.

Figure 5: Error-dependent feedback dynamics and adaptation performance. (A) Feedback-related activity change measured 800 ms after the go cue across baseline and adaptation phases. (B) Task error across trials for models without sensory feedback (blue), with cerebellar feedback (orange), and with direct sensory feedback to the RNN (green).

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Teaching signal synchronization in deep neural networks with prospective neurons

Nicolas Zucchet, Qianqian Feng, Axel Laborieux, Friedemann Zenke+2

Computer Science Department, ETH Zürich · Gatsby Computational Neuroscience Unit, University College London · Friedrich Miescher Institute for Biomedical Research+3

Synaptic Plasticity Neurons

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Working memory requires the brain to maintain information from the recent past to guide ongoing behavior. Neurons can contribute to this capacity by slowly integrating their inputs over time, creating persistent activity that outlasts the original stimulus. However, when these slowly integrating neurons are organized hierarchically, they introduce cumulative delays that create a fundamental challenge for learning: teaching signals that indicate whether behavior was correct or incorrect arrive out-of-sync with the neural activity they are meant to instruct. Here, we demonstrate that neurons enhanced with an adaptive current can compensate for these delays by responding to external stimuli prospectively -- effectively predicting future inputs to synchronize with them. First, we show that such prospective neurons enable teaching signal synchronization across a range of learning algorithms that propagate error signals through hierarchical networks. Second, we demonstrate that this successfully guides learning in slowly integrating neurons, enabling the formation and retrieval of memories over extended timescales. We support our findings with a mathematical analysis of the prospective coding mechanism and learning experiments on motor control tasks. Together, our results reveal how neural adaptation could solve a critical timing problem and enable efficient learning in dynamic environments.

Abstract

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