Identifying aligned tensor decompositions across heterogeneous neural datasets

Large-scale neural recordings increasingly span many sessions, brain regions and animals, but differences in neuronal sampling make it difficult to identify and interpret shared patterns. We introduce Neuralign, a tensor- based model that jointly aligns and decomposes recordings into components, each pairing a shared temporal pattern with its expression in individual trials and neurons, without requiring matched neurons, matched trials or behavioural labels. In simulations, pooling recordings improved recovery of shared components; in recurrent networks, Neuralign distinguished related from distinct task solutions. In the macaque motor cortex, label-free components recovered the ring-like organisation of reach directions. Across 93 brain-wide mouse recordings, Neuralign discovered a single component that isolated the response to inhibition of the anterior lateral motor cortex (ALM). A reference learned from correct, uninhibited trials revealed inhibition-related activity outside the choice direction on error trials, most strongly in the ALM and thalamus. Neuralign provides an interpretable framework for studying the shared structure of large neural datasets, linking shared patterns to individual trials and recorded populations.