A complete neuroscience requires multi-level theories that address phenomena ranging from higher-level cognitive behaviors to activities within a cell. Unfortunately, we don't have cognitive models of behavior whose components can be decomposed into the neural dynamics that give rise to behavior, leaving an explanatory gap. Here, we decompose SUSTAIN, a clustering model of concept learning, into neuron-like units (SUSTAIN-d; decomposed). Instead of abstract constructs (clusters), SUSTAIN-d has a pool of neuron-like units. With millions of units, a key challenge is how to bridge from abstract constructs such as clusters to neurons, whilst retaining high-level behavior. How does the brain coordinate neural activity during learning? Inspired by algorithms that capture flocking behavior in birds, we introduce a neural flocking learning rule to coordinate units that collectively form higher-level mental constructs ("virtual clusters"), neural representations (concept, place and grid cell-like assemblies), and parallels recurrent hippocampal activity. The decomposed model shows how brain-scale neural populations coordinate to form assemblies encoding concept and spatial representations, and why many neurons are required for robust performance. Our account provides a multi-level explanation for how cognition and symbol-like representations are supported by coordinated neural assemblies formed through learning.