Abstract
The brain constructs distributed representations of key low-dimensional variables. These variables may be external stimuli or internal constructs of quantities relevant for survival, such as a sense of one's location in the world. We consider that the high-dimensional population-level activity vectors are the fundamental representational currency of a neural circuit, and these vectors trace out a low-dimensional manifold whose dimension and topology matches those of the represented variable. This manifold perspective -- applied to the mammalian head direction circuit across rich waking behaviors and sleep -- enables powerful inferences about circuit representation and mechanism, including: Direct visualization and blind discovery that the network represents a one-dimensional circular variable across waking and REM sleep; fully unsupervised decoding of the coded variable; stability and attractor dynamics in the representation; the discovery of new dynamical trajectories during sleep; the limiting role of external rather than internal noise in the fidelity of memory states; and the conclusion that the circuit is set up to integrate velocity inputs according to classical continuous attractor models.
