Fig. 1: Manifold alignment with dynamics can stabilize representations of neural activity despite changes in recording conditions.

We begin with a supervised training dataset containing neural activity and corresponding behavior from an initial recording session (Day 0). For a 3-electrode example (electrodes E₁, E₂, E₃), population activity exhibits an underlying manifold structure in a 3-D neural state space in which each axis corresponds to the firing rate from a given electrode. The evolution of population activity in time exhibits consistent dynamics (vector field). The relationship between manifold activity and behavior, for simple linear decoding of a hypothetical 1-D behavioral variable, is represented by a Decoding axis, which is assumed to be consistent over time. In a subsequent recording session (Day K), instabilities lead to changes in the recorded neural population, and the Day K activity (E₁', E₂', E₃') has a different relationship to the underlying manifold, dynamics, and decoding axis (schematized by a rotation). With NoMAD, our goal is to learn a mapping from the Day K neural activity to the original manifold and dynamics in an unsupervised manner. This allows the original decoding axis to be applied to accurately decode behavior.