Figure 6.
*A*, Input nonlinearity model **w**^{tf} ⊗ **w**^{l} for a neuron in mouse auditory cortex. Left, The time-frequency component **w**^{tf} of the model. The average SE of the weights of **w**^{tf} across time-frequency bins is shown by the error bar at the 0 position of the color bar. The SE of the peak weight is shown at the top of the bar; the error at the minimum is shown at the bottom of the bar. Units are spikes/s. Center, The sound level component of the model. The 1 SD error bars are shown as a gray area. All error bars were calculated by bootstrap methods. This graph has been normalized and thus has no units. Right, Predictive power of the STRF model and all the possible configurations of the input nonlinearity model. The white bars show the predictive power of the regularized models on the training data and the black bars show the predictive power on cross-validation data. For this neuron, the **w**^{tf} ⊗ **w**^{l} model has the highest predictive power, and indeed, the **w**^{tf} receptive field can be seen to be inseparable, because the peak excitation (at a 20 ms lag time) occurs at a lower frequency than the peak suppression (at a 60 ms lag time). *B*, For comparison, the STRF estimated on the same data, which in this case differs little from **w**^{tf}. *C*, Various **w**^{l} from the population. Gray areas indicate 1 SE. *D*, Number of cells whose **w**^{l} fits are best approximated by each of five idealized shapes. The shapes were chosen by hand to reflect the variety of shapes of **w**^{l} derived from the data. Similarity between the actual **w**^{l} and the idealized shape is defined to be the normalized dot product between the graphs. No nonmonotonic shapes were observed, but this may be a result of the sound level range used in the experiments, or of the inequivalence between **w**^{l} and the rate-level function. The smoothed ramp shape was the most common. *E*, Example of a cell for which **w**^{tf} of the input nonlinearity model is different from the STRF. The difference is shown in the fourth panel; the color code is the same in all panels. The third panel shows **w**^{l} for the input nonlinearity model (solid), and the fixed input scaling function that is assumed for all STRF models (dashed). (This function, which is linear in sound pressure, was found to produce better STRF results across the population of cells than a linear function in dB.) The **w**^{tf} receptive field shows a peak response at a larger lag time than suggested by the STRF. The predictive power of the input nonlinearity model was 1.6 times that of the STRF model, on both training and cross-validation data.