The cerebellum is thought to help detect and correct errors between intended and executed commands(1,2) and is critical for social behaviours, cognition and emotion 3 Computations for motor control must be performed quicklyto correct errors in real time and should be sensitive to small differences between patterns for fine error correction while being resilient to noise(7). Influential theories of cerebellar information processing have largely assumed random network connectivity, which increases the encoding capacity ofthe network's first layer(8-)(13). However, maximizing encoding capacity reduces the resilience to noise(7). To understand how neuronal circuits address this fundamental trade-off, we mapped the feedforward connectivity in the mouse cerebellar cortex using automated large-scale transmission electron microscopy and convolutional neural network-based image segmentation. We found that both the input and output layers ofthe circuit exhibit redundant and selective connectivity motifs, which contrast with prevailing models. Numerical simulations suggest that these redundant, non-random connectivity motifs increase the resilience to noise at a negligible cost to the overall encoding capacity. This work reveals how neuronal network structure can support a trade-off between encoding capacity and redundancy, unveiling principles of biological network architecture with implications for the design of artificial neural networks.