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

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.

Deploying learned control policies on low-cost robotic platforms introduces transport latencies and noisy motor feedback that systematically widens the sim-to-real gap. The chasm of simulation to deployment in hardware lies in the delay of the actuator reaching the commanded position. On platforms such as the Mini Pupper 2, a measured >50 ms transport delay transforms the locomotion task from a standard Markov decision process into a partially observable one. In this paper, we take a biologically inspired approach of handling noisy and delayed feedback to close the sim-to-real gap, thereby expanding the capability of reinforcement learning on cost-constrained hardware. Using a low-cost quadrupedal hardware platform, we find that using a forward model of the average actuator delay, paired with a time-aware neural network results in robust locomotion. Additionally, our time-aware neural network learned a central pattern generator (CPG): a self-sustaining rhythmic gait that is robust to +320 ms latency perturbations, mirroring the CPGs found in the spinal cords of vertebrates. We posit that temporal self-organization may be a general strategy for cost-constrained locomotion.

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.