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Network features found in the brain may help implement more efficient and robust neural networks. Spiking neural networks (SNNs) process spikes in the spatiotemporal domain and can offer better energy efficiency than deep neural networks. However, most SNN implementations rely on simple point neurons that neglect the rich neuronal and dendritic dynamics. Herein, a bio‐inspired columnar learning network (CLN) structure that employs feedforward, lateral, and feedback connections to make robust classification with sparse data is proposed. CLN is inspired by the mammalian neocortex, comprising cortical columns each containing multiple minicolumns formed by interacting pyramidal neurons. A column continuously processes spatiotemporal signals from its sensor, while learning spatial and temporal correlations between features in different regions of an object along with the sensor's movement through sensorimotor interaction. CLN can be implemented using memristor crossbars with a local learning rule, spiking timing‐dependent plasticity (STDP), which can be natively obtained in second‐order memristors. CLN allows inputs from multiple sensors to be simultaneously processed by different columns, resulting in higher classification accuracy and better noise tolerance. Analysis of networks implemented on memristor crossbars shows that the system can operate at very low power and high throughput, with high accuracy and robustness to noise.