Singularity is actually a property of the parameter function map, not the data distribution. The RLCT is defined in terms of the loss function/reward and the parameter function map. See definition 1.7 of the grey book for the definition of singular, strictly singular, and regular models.
Edit: To clarify, you do need the loss function & a set of data (or in the case of RL and the human brain, the reward signals) in order to talk about the singularities of a parameter-function map, and to calculate the RLCT. You just don’t need them to make the statement that the parameter-function map is strictly singular.
Singularity is actually a property of the parameter function map, not the data distribution. The RLCT is defined in terms of the loss function/reward and the parameter function map. See definition 1.7 of the grey book for the definition of singular, strictly singular, and regular models.
Edit: To clarify, you do need the loss function & a set of data (or in the case of RL and the human brain, the reward signals) in order to talk about the singularities of a parameter-function map, and to calculate the RLCT. You just don’t need them to make the statement that the parameter-function map is strictly singular.
Oops, you’re entirely right.