A RECURRENT CIRCUIT SUPPORTING BOTH LOW- AND HIGH-DIMENSIONAL POPULATION DYNAMICS

During behavior, neural population activity typically unfolds as trajectories in a high-dimensional space, whose geometry reflects the computations implemented by the network. Analyses of neural recordings have recently exposed two conflicting phenomena. In many cases, trajectories appear to be confined to low-dimensional manifolds, i.e. stable patterns shaped by circuit connectivity and inputs, which stabilize the dynamics and facilitate reliable readout by downstream regions. Yet recent large-scale recordings revealed that the effective dimensionality of neural activity seems to be increasing as more neurons and conditions are sampled. How structured low-dimensional dynamics are embedded within such high-dimensional circuits remains unclear.
Here we develop a computational framework to explicitly construct low-dimensional dynamics within high-dimensional recurrent neural networks. We design networks with structured recurrent connectivity that constrains activity to evolve within a low-dimensional subspace embedded in a larger neural state space. The network can generate low-dimensional dynamics, with population activity evolving along a small number of dominant modes over time. Although dynamics are locally low-dimensional, their evolution over time spans a higher-dimensional region of the state space, consistent with experimental observations that high-dimensional latent dimensions can be revealed as neural activity evolves or is perturbed.
As a result, low-dimensional population dynamics produce activity patterns that appear high-dimensional when analyzed in terms of task variables or decoding axes. This misalignment leads to a dissociation between the dimensionality of the recurrent dynamics and the apparent dimensionality of task-related neural activity. Structured low-dimensional dynamics and high-dimensional neural representations can therefore coexist within the same network.