Penetrating flexible electrode arrays can simultaneously record thousands of individual neurons in the brains of live animals. However, it has been challenging to spatially map and longitudinally monitor the dynamics of large three-dimensional neural networks. Here we show that optimized ultraflexible electrode arrays distributed across multiple cortical regions in head-fixed mice and in freely moving rats allow for months-long stable electrophysiological recording of several thousand neurons at densities of about 1,000 neural units per cubic millimetre. The chronic recordings enhanced decoding accuracy during optogenetic stimulation and enabled the detection of strongly coupled neuron pairs at the million-pair and millisecond scales, and thus the inference of patterns of directional information flow. Longitudinal and volumetric measurements of neural couplings may facilitate the study of large-scale neural circuits.