In systems neuroscience, a neural population's 'intrinsic dimension' is the minimal number of continuous latent variables needed to parametrize its activity manifold (Jazayeri & Ostojic 2021)

Jazayeri & Ostojic, "Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity" (arXiv:2107.04084, 2021), give the field's working definition inside a formal aside: "The intrinsic dimension is the minimal number of continuous variables needed to parametrize the manifold." The object being measured is the manifold traced out by population firing-rate activity in an N-dimensional neuron-by-neuron state space — not the weights or connectivity of the circuit.

The definition is sharpened by two contrasts drawn in the same passage. It is distinct from the space's raw ambient dimensionality (the number of neurons, N) and from the manifold's embedding dimensionality (how many Euclidean dimensions the manifold occupies once curvature and warping are accounted for). Each independent parametrizing variable is a latent variable: "we call the number of independent variables the intrinsic dimension, and we refer to each independent variable describing the neural activity as a latent variable."

This is the same category of construction underlying the "intrinsic manifold" of motor cortex in claim-sadtler-2014-within-manifold-bci-learning-fast-outside-resists — a low-dimensional subspace of population activity. It is also, by type, the same kind of object as the representation-space intrinsic dimension of a deep network's activations (claim-ansuini-2019-two-intrinsic-dimensions-representation-vs-weight-space), and thereby a different kind of object from the weight-space intrinsic dimension of an LLM fine-tuning objective (claim-li-2018-intrinsic-dimension-objective-landscape-codimension-parameter-space, claim-aghajanyan-2020-fine-tuning-low-intrinsic-dimension). The distinction is the pivot the vault tracks at entity-intrinsic-dimension and observation-low-dimensional-subspace-constrains-adaptation-brains-and-nets; whether the recurrence across these domains is one object or three analogies is the open question-low-dimensional-subspace-one-object-or-analogy.