Neuralign puts neural recordings from different sessions into one tensor decomposition, sharing a time course while estimating trial and neuron weights per session

Multi-session neural recordings can now be decomposed jointly without first assuming that the same neurons were tracked, and without first compressing each session into a common space and decomposing afterwards. Tensor component analysis previously needed the same neurons tracked across sessions to correspond components, which is difficult within an animal and impossible between animals; aligning first and decomposing second fixed the correspondence between recordings before the components were estimated. On simulated recordings with known generating factors, Neuralign's mean factor-match score rose from 0.730 with two sessions to 0.860 with 12 sessions, with little further gain at 24 and 36 sessions, and it exceeded per-session TCA and jointly fitted SRM and Hyperalignment at every cohort size.

Each component pairs one temporal factor shared across sessions with trial and neuron factors estimated separately for each session, and the shared time course establishes a common identity across recordings. Neuron factors are coupled through a shared mixing matrix: a session-specific orthogonal projection maps the shared component geometry onto that session's recorded neurons, and session gains scale each component's strength in that session, with the coupling imposed as a soft penalty that lets session-specific variation remain. On 36 macaque motor cortex sessions from three macaques with simultaneous M1 and PMd recordings, the two components most informative about reach direction in a label-free rank-6 fit arranged trials in a ring matching the eight-target layout, and the same fit's session gains grouped recordings by animal.

In the brain-wide mouse data, one unsupervised component carried the ALM inhibition response on its own, and that response remained detectable outside the dominant choice direction on error trials. SRM and Hyperalignment return a common space but do not explicitly factor each shared motif into temporal, trial and neuronal contributions, and did not isolate the inhibition signal into a single component. Across 93 recordings from 19 mice, a linear discriminant on component C5's trial factors alone classified inhibition in held-out sessions with balanced accuracy 0.647 ± 0.019 against chance 1/3; under the same protocol SRM and Hyperalignment reached 0.3542 ± 0.0034 and 0.3336 ± 0.0002. On error trials, late-delay inhibition decoding reached ROC AUC 0.685 ± 0.011 in the nine-dimensional choice-residual subspace versus 0.548 ± 0.005 along the choice direction.

The demonstrated scope covers simulated recordings with known generating factors, three low-rank recurrent networks, 36 macaque motor cortex sessions, and 93 brain-wide recordings from 19 mice; decoder transfer was evaluated within jointly fitted cohorts. The authors state that aligning new recordings to a fixed reference remains an important next test, with direct relevance to stabilising brain–computer interfaces.

Component interpretation requires stability across fits, and conditional uniqueness results for tensor decompositions do not establish identifiability of the complete coupled model. In label-free fits, a component's session-gain and trial-factor signs can be exchanged within a recording without changing the loss, so signed comparisons across recordings depend on an explicit convention. Decoder transfer did not significantly improve across animals. The method assumes a common time axis and shared temporal profiles, trial factors capture amplitude rather than timing, and robustness to latency variability remains to be tested; the simulations were generated under these assumptions.