Investigating the representation of uncertainty in neuronal circuits
Fig 3
IC and OT models approximate the ideal observers.
(A) Schematic model of IC. Sounds reaching the two ears are first convolved with bandpass filters, then delayed, then cross-correlated at several delays, and lastly rectified to obtain tuning curves to ITD. (B) Average KL divergence between the posterior distribution computed by the ideal observer and the posterior decoded from the model population activity before (dashed line) and after (continuous) rectification. KL was normalized to the KL between the ideal observer posterior and the priors. Shaded areas represent s.e.m. Note that the pre-rectification KL divergence differs from 0 purely due to the fact that we cannot exactly decode from a finite amount of training examples. (C) Schematic model of OT. Outputs of the IC model are first combined across frequency bands and divided by the signal energy. Then, the outputs are passed through a static nonlinearity, filtered and rectified; these operations are equivalent to a non-linear filtering stage. The color of the units indicates their frequency preference (low: red, mid: blue, high: green). (D) Same as (B) but for the OT model activity, after rectification. (E) Example posterior distribution in one trial with true ITD = -145 and BC = 0.1, for the post-marginalization ideal observer (dashed pink line) and the reconstruction from the output of the OT model population (continuous black). (F) Same as (E), but with BC = 0.4. Note that the small secondary peak around ITD = 200 is present only in the reconstruction, not in the ideal observer’s posterior.