Figure 6. Auditory cortical responses are more reverberation invariant than adaptation-free simulated neural responses.

Pearson’s correlation coefficient (${\displaystyle \mathrm{C}\mathrm{C}}$) was computed between the neural response-over-time (trial-averaged spike count in 10ms time bins) to natural sounds presented in two different reverberant conditions. The correlations for each cortical unit were then compared with the correlation coefficient for the unit’s corresponding LNP model. A positive difference between these correlations indicates that the real neuron is more invariant to reverberation than its LNP simulation, suggesting that adaptation may help in removing the effects of reverberation. (A-C) Each histogram plots the distribution over units of difference between the correlation coefficient for the recorded neural response-over-time (${\displaystyle {\mathrm{C}\mathrm{C}}_{\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{r}\mathrm{o}}}$) and that for the corresponding simulated response-over-time (${\displaystyle {\mathrm{C}\mathrm{C}}_{\mathrm{s}\mathrm{i}\mathrm{m}}}$; LNP simulations as described in Figure 4). (A) ${\displaystyle \mathrm{C}\mathrm{C}}$ difference between recorded and simulated cortical units for the small and anechoic rooms (median difference = 0.016; Z = 6.0; p = 1.5 x 10^-9). (B) ${\displaystyle \mathrm{C}\mathrm{C}}$ difference for the large and anechoic rooms (median difference = 0.012; Z = 6.9; p = 7.2 x 10^-2). (C) ${\displaystyle \mathrm{C}\mathrm{C}}$ difference for the large and small rooms (median difference = 0.036; Z = 13.0; p = 1.0 x 10^-40). Asterisks indicate the significance of Wilcoxon signed-rank tests: ${\displaystyle {}^{\ast \ast \ast \ast }p<0.0001}$.

Figure 6—figure supplement 1. The estimated cochleagrams produced by the dereverberation model are more reverberation invariant than the original cochleagrams.

To assess reverberation invariance, we measured and compared the correlation coefficients (${\displaystyle \mathrm{C}\mathrm{C}}$s) between corresponding rows of different cochleagrams. (A) We define ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{g}{\mathrm{e}}_{\mathrm{e}\mathrm{s}\mathrm{t}},\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{e}\mathrm{s}\mathrm{t}}{)}_{\mathrm{i}}}$ as the correlation coefficient between row i (i.e. a single frequency channel) of the estimated cochleagram produced by the dereverberation model trained on small room data, and row i of the anechoic cochleagram of the original sound. This is a measure of the similarity of row i of these two cochleagrams. To provide a baseline for comparison, we measure ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l},\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{h}{)}_{\mathrm{i}}}$, the correlation coefficient between row i of the cochleagram of the small room sound, and row i of the anechoic cochleagram. We then plot a histogram of ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{e}\mathrm{s}\mathrm{t}},\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{h}{)}_{\mathrm{i}}-\mathrm{C}\mathrm{C}(\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l},\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{h}{)}_{\mathrm{i}}}$ for all 30 values of i, corresponding to each of the 30 model kernels. We find that the resulting values are consistently above zero (median difference = 0.067; Z = 4.8; p = 1.7 × 10^-9), indicating that ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{e}\mathrm{s}\mathrm{t}},\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{h})}$ is consistently larger than ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l},\mathrm{a}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{h})}$. Thus, the similarity between the dereverberated cochleagram and the anechoic sound is greater than the similarity between the original echoic cochleagram and the anechoic sound. This suggests that the dereverberation model has successfully removed some effects of reverberation from the input cochleagrams, making its outputs more invariant to reverberation. (B) As for A, but for the large room. Median difference = 0.092; Z = 4.8; p = 1.7 × 10^-9. (C) As for A-B, but comparing the ${\displaystyle \mathrm{C}\mathrm{C}}$ of small and large room cochleagrams, ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e},\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l}{)}_{\mathrm{i}}}$ to those of their corresponding model kernel estimates, ${\displaystyle \mathrm{C}\mathrm{C}(\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{g}{\mathrm{e}}_{\mathrm{e}\mathrm{s}\mathrm{t}},\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{e}\mathrm{s}\mathrm{t}}{)}_{\mathrm{i}}}$. Positive values indicate that the dereverberation model makes the cochleagrams of the two rooms more similar and hence more invariant to reverberation. Median difference = 0.037; Z = 4.8; p = 1.7 × 10^-9. Asterisks indicate the significance of Wilcoxon signed-rank tests: ****P<0.0001.