Incorporating Midbrain Adaptation to Mean Sound Level Improves Models of Auditory Cortical Processing

Abstract

Adaptation to stimulus statistics, such as the mean level and contrast of recently heard sounds, has been demonstrated at various levels of the auditory pathway. It allows the nervous system to operate over the wide range of intensities and contrasts found in the natural world. Yet current standard models of the response properties of auditory neurons do not incorporate such adaptation. Here we present a model of neural responses in the ferret auditory cortex (the IC Adaptation model), which takes into account adaptation to mean sound level at a lower level of processing: the inferior colliculus (IC). The model performs high-pass filtering with frequency-dependent time constants on the sound spectrogram, followed by half-wave rectification, and passes the output to a standard linear-nonlinear (LN) model. We find that the IC Adaptation model consistently predicts cortical responses better than the standard LN model for a range of synthetic and natural stimuli. The IC Adaptation model introduces no extra free parameters, so it improves predictions without sacrificing parsimony. Furthermore, the time constants of adaptation in the IC appear to be matched to the statistics of natural sounds, suggesting that neurons in the auditory midbrain predict the mean level of future sounds and adapt their responses appropriately.

Significance statement: An ability to accurately predict how sensory neurons respond to novel stimuli is critical if we are to fully characterize their response properties. Attempts to model these responses have had a distinguished history, but it has proven difficult to improve their predictive power significantly beyond that of simple, mostly linear receptive field models. Here we show that auditory cortex receptive field models benefit from a nonlinear preprocessing stage that replicates known adaptation properties of the auditory midbrain. This improves their predictive power across a wide range of stimuli but keeps model complexity low as it introduces no new free parameters. Incorporating the adaptive coding properties of neurons will likely improve receptive field models in other sensory modalities too.

Keywords: adaptation; auditory cortex; inferior colliculus; mean sound level; model; spectrotemporal receptive field.

Figure 1.

Two models of the stimulus–response relationship for auditory neurons. A, Standard LN model. The log-spectrogram of the sound waveform, X_tf, is operated on by a linear kernel, k_fh, and sigmoid output nonlinearity to produce a model, ŷ_t, of the neuronal response. B, The IC Adaptation model augments the LN model by adding a nonlinear transform of the spectrogram. The dashed arrows indicate the alternative processing paths for the Standard LN and IC Adaptation models. The nonlinear transform consists of high-pass filtering each frequency band of the spectrogram by subtracting the convolution of that frequency band with an exponential filter with time constant τ (shown by the vertical line), followed by half-wave rectification. The resulting modified spectrogram, X_tf^IC, is then used as an alternative input to the standard LN model.

Figure 2.

Time constants of adaptation to stimulus mean observed by Dean et al. (2008) in the guinea pig IC. The x-axis shows the characteristic frequency of each IC unit, and the y-axis shows the time constant of an exponential fit to the adaptation curve for the corresponding unit. The line is our regression fit to these data (Eq. 4).

Figure 3.

Comparison of the ability of the standard LN model and the IC Adaptation model to predict neural responses to natural sounds. A, B, Scatterplots showing the correlation coefficients between model predictions and actual neural responses (BigNat dataset). The x-axis shows performance of the standard LN model, the y-axis shows performance of the IC Adaptation model, and colors indicate the NR of each unit. A, Raw correlation coefficient CC_raw. B, Normalized correlation coefficient CC_norm. C, Scatterplot showing how the difference in CC_norm between the two models varies with NR. The solid line is a linear regression, and the shaded area shows the 95% confidence intervals on the regression.

Figure 4.

A, Comparison of the LN and IC Adaptation models for several stimulus classes, when models are trained and tested on the same stimulus class (dots show the mean of the within-class predictions for all units). B, Percentage improvement in mean model performance between the LN and IC Adaptation models, ΔCC_norm^′, when models are trained (rows) on one stimulus class and tested (columns) on another (cross-class predictions; Comparison dataset only). C, Difference between prediction performance of control models with fixed time constants (τ^med, τ^min, and τ^max) and without half-wave rectification, compared with the LN model for each stimulus class (colors as in Fig. 4A).

Figure 5.

A, Autocorrelation of the spectrogram of an ensemble of natural sounds. The black lines indicate the point where the autocorrelation has decreased to 1/e. B, Optimal time constants for predicting the mean sound level of natural sounds in a window of length T_av ms into the future. This is plotted as a function of the window size, for frequency bands centered on a low value (70 Hz; red line) and a high value (20 kHz; blue line). Lines indicate mean, error bars show SEM, and shaded regions indicate entire range. C, Optimal time constants for prediction of the mean level of natural stimuli in each frequency band. The shaded region indicates the range of time constants in that frequency band; the solid line indicates the middle of the range. The dots indicate time constants observed in guinea pig IC by Dean et al. (2008), and the dashed line is the linear regression of those time constants against log(frequency).