Cerebellum-inspired neural network of supervised learning with tensor-based sparse coding for multi-class classification

Under the Marr-Ito-Albus framework, the cerebellum performs supervised learning in Purkinje cells upon the unsupervised sparse representations generated within granule cells, contributing fundamentally to associative learning in motor control. However, the specific mechanisms through which cerebellar circuitry and plasticity rules enable supervised learning, and properties of the sparse coding induced by cerebellar architectural constraints, remain poorly characterized. To address this, we first established a sparse coding mechanism inspired by anatomical and physiological properties of the granular layer, including input-sharing connectivity from mossy fibers, Golgi-cell-mediated localized feedback inhibition for winner-take-all sparsification, and activity-dependent bias adjustments. This sparse coding, implemented via efficient tensor-based computations, preserves local neighborhood structures as revealed in a geometric interpretation. Furthermore, we demonstrated that error signals transmitted via climbing fibers to Purkinje cells, integrated with intrinsic plasticity, drive efficient learning of the sparse representations for multi-class classification, leading to accurate population coding for judgments in the cerebellar nuclei. The resultant cerebellum-inspired neural network model achieved a test accuracy of 90.50±0.10% on Fashion-MNIST, performance comparable to a backpropagation-trained single-hidden-layer feedforward neural network, while providing more than 5× computational acceleration. The model further exhibited proof-of-principle closed-loop control capability in simplified motor tasks, including balancing a cart-attached pole and controlling a robotic arm to reach targets. Our study delineates cerebellum-inspired sparse coding and supervised learning mechanisms, and demonstrates robust performance of the cerebellum-inspired neural network across multiple task domains. These results suggest that cerebellum-inspired architectures would provide useful design principles for lightweight neural networks in resource-limited and latency-critical applications.Author summary: We established a cerebellum-inspired computational framework incorporating random-feature-based sparse coding and climbing-fiber-driven supervised learning mechanisms. The granular-layer-inspired architecture, combined with an unsupervised learning technique, exhibits robust feature representation capabilities, enabling performance comparable to fully supervised three-layer artificial neural networks trained via backpropagation, while providing substantial computational acceleration. By integrating intrinsic plasticity and population coding, the Purkinje cells and the cerebellar nuclei are modeled as a linear multi-class classifier trained with instructive error signals from the climbing fibers, which demonstrates high learning efficiency and stability when processing sparse representations from the upstream granular layer. Implemented using tensor-based operations, the cerebellum-inspired neural network demonstrates proof-of-principle supervised learning capabilities in observation-action mapping, suggesting potential applications as a lightweight module in dynamic control systems.