Table 1. Definition of statistical measures.

Time-averaged information ≡ 〈I〉t

Difference in mean spike count between task epochs $\equiv {\langle N_{adapt}\rangle }_{trials}-{\langle N_{repet}\rangle }_{trials}$

Normalized absolute difference in mean spike count between task epochs $\equiv \frac{\left|{\langle N_{adapt}\rangle }_{trials}-{\langle N_{repet}\rangle }_{trials}\right|}{{\langle N_{adapt}\rangle }_{trials}+{\langle N_{repet}\rangle }_{trials}}$

Optimal timing sensitivity $q_{opt}\equiv mean\left(\underset{q}{\text{argmax}}\left({\langle I\rangle }_t\right)\right)$

Optimal distinction degree between units $k_{opt}\equiv mean\left(\underset{k}{\text{argmax}}\left({\langle I\rangle }_t\right)\right)$

Temporal structure related gain of information $\equiv \frac{\underset{q}{\text{max}}\left({\langle I\rangle }_t\right)-{\langle I_{q=0}\rangle }_t}{{\langle I_{q=0}\rangle }_t}$

Fano factor estimate $F\equiv \frac{{\text{var}}_{estim}\left(C_t\right)}{\langle C_t\rangle }=\frac{\frac{{\displaystyle {\sum }_{i=1}^{n_{trials}}{\left(C_t^i-\langle C_t\rangle \right)}^2}}{\left(n_{trials}-1\right)}}{\langle C_t\rangle }$, where C t is the random variable counting the number of spikes fired by a neuron in a given analysis windows during one task-epoch, and $C_t^i$ is its realization in a given trial among the n trials available trials.

Gain in the pair relative to the best single unit $\equiv \frac{\underset{q,k}{\text{max}}\left({\langle I^{pair}\rangle }_t\right)-\underset{cells,q}{\text{max}}\left({\langle I^{single}\rangle }_t\right)}{\text{max}\left(\underset{q,k}{\text{max}}\left({\langle I^{pair}\rangle }_t\right),\underset{cells,q}{\text{\hspace{0.17em}max}}\left({\langle I^{single}\rangle }_t\right)\right)}$

Information imbalance between two units $\equiv \frac{\left|\underset{q}{\text{max}}\left({\langle I^{cell1}\rangle }_t\right)-\underset{q}{\text{max}}\left({\langle I^{cell2}\rangle }_t\right)\right|}{\text{max}\left(\underset{q}{\text{max}}\left({\langle I^{cell1}\rangle }_t\right),\underset{q}{\text{max}}\left({\langle I^{cell2}\rangle }_t\right)\right)}$

For pairs with k opt = 0: Information gain when not distinguishing between neurons $\equiv \frac{\underset{q}{\text{max}}\left({\langle I_{k=k_{opt}=0}^{pair}\rangle }_t\right)-\underset{q}{\text{max}}\left({\langle I_{k=k\text{max}=2}^{pair}\rangle }_t\right)}{\underset{q}{\text{max}}\left({\langle I_{k=k_{opt}=0}^{pair}\rangle }_t\right)}$

Between-neuron spike coincidence index $\equiv \text{max}\left(P_{adapt}^{intra},P_{repet}^{intra}\right)-P^{inter}$, where P is the proportion of trials for which between-neuron spike-matching(s) did impact the Victor and Purpura distance $d_{q_{opt},k_{opt}}$, for the analysis window that maximizes I pair.

The angle brackets denote averaging; t denotes time average over the ensemble of analysis windows beginning 1 ms after the feedback and ending from 100 ms to 1 s (by steps of 100 ms). Information values I were always normalized and bias corrected unless mentioned. We therefore simply refer to them as “information” throughout the text. “adapt” stands for behavioral adaptation task epochs (either errors or first reward); “repet” stands for repetition task epoch. N is the spike count in a window between 1 and 1,000 ms after feedback onset. $\underset{y}{\text{argmax}\left(f\left(y\right)\right)}$ is the point y_o of the argument y for which the function f attains its maximum value.