Fig. 6: Different slice types capture latent variables with distinct geometric properties.

Neuron-slicing component: example of two neuron-slicing components visualized in neural activity space. The latent activity is embedded in a 2D subspace, but their trajectories within that subspace are unconstrained. Time-slicing component: example of two time-slicing components. These are also embedded within a 2D subspace, but that subspace may vary over trials. Within each latent subspace, the latent trajectories have similar shape as they are constrained to linear combinations of a few characteristic temporal weights. Trial-slicing component: the trial-slicing components are not constrained to any subspace, as the neural encodings may change at every time point. These components describe linear combinations of a few potentially high-dimensional latent trajectories such as neural sequences. Note that, here, only one component is shown for clarity. In this case, the latent trajectory is simply re-scaled on each trial. Reconstruction: after summing these components, the full latent trajectories are not necessarily limited by any of the geometric constraints that characterize individual slice types.