We began by analyzing activity from animals with normal hearing. As a first step toward characterizing the neural code for speech at the network level, we determined whether there was shared variance across units that would allow us to reduce the dimensionality of the activity patterns. Previous work has shown that the correlations in IC activity are dominated by ‘signal’ (features of activity that are reproducible across repeated trials and, thus, convey acoustic information) rather than ‘noise’ (features of activity that vary from trial-to-trial and reflect intrinsic noise or fluctuations in brain state) (Figure 1b; Garcia-Lazaro et al., 2013).

Signal correlations were also dominant in our recordings: although signal variance (the covariance in activity across repeated trials) accounted for only 40% of the overall variance in activity, signal correlations accounted for 95% of the total correlation between units (Figure 1c). For a network operating in such a regime, with each neuron having more than half of its variance uncorrelated with that of its neighbors, there is limited scope for reducing the dimensionality of the full activity patterns. However, given the large signal correlations, it may be possible to identify a low-dimensional subspace in which the acoustic information represented by the signal is embedded.

We partitioned the recordings from each animal into two sets: a training set that was used to identify the principal components (PCs) of the activity (Figure 2a, step 1) and a test set with two repeated trials that was used to measure the variance that could be explained by each PC. To measure the total variance explained (Figure 2a, steps 2a–c), we projected the activity from test trial 1 onto the PCs, then reconstructed the original activity from the same trial using the PC projection and compared the reconstruction to the original activity. The overall dimensionality of the neural activity was high, as expected, with a large number of PCs required for the reconstruction to explain 95% of the total variance in the original activity (Figure 2b).

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To measure the signal variance explained (Figure 2a, step 3), we compared the same reconstructed activity to the original activity from test trial 2 (when using activity from one trial to reconstruct activity on another, only those features that reliably encode acoustic information across trials can be successfully reconstructed and, thus, only signal variance can be explained). The signal variance explained saturated quickly, indicating that the signal dimensionality was much lower than the overall dimensionality, with only a small number of PCs (between 5 and 10) required to explain 95% of the signal variance in the original activity (Figure 2c).

These results suggest that the acoustic information in IC activity is restricted to a low-dimensional subspace, which we term the neural signal manifold, and that PCA is able to identify the dimensions that define this manifold. To confirm that PCA preferentially identified the signal manifold, we computed the fraction of the variance explained by each PC that was signal rather than noise (measured as the covariance between the activity on the two test trials when projected onto each PC relative to the overall variance after the same projection) and verified that it decreased with each successive PC (Figure 2d).

If the signal manifold reflects something fundamental about auditory processing, then we should expect the activity within it, which we term the signal dynamics, to be similar across animals with the same hearing status. To measure the similarity of the signal dynamics across animals (Figure 2a, step 4), we projected the original activity for each animal onto its respective signal manifold and then determined how much of the variance in the activity from one animal could be explained by the activity from another (allowing for additional linear transformation). We found that the signal dynamics for different animals were remarkably similar, with the signal dynamics from one animal accounting for, on average, 96% of the variance in the signal dynamics from other animals (Figure 2e). This result gives us confidence that the signal manifold is indeed fundamental, and that our methods are sufficient to identify it robustly in individual animals.

We next sought to use analysis of the signal manifold to better understand the impact of hearing loss on the neural code for speech at the network level. We induced sloping mild-to-moderate sensorineural hearing loss (Figure 2—figure supplement 1) by exposing gerbils (n = 6) to broadband noise using established protocols (Armstrong et al., 2022; Suberman et al., 2011). After waiting at least 1 mo for the effects of the hearing loss to stabilize, we made neural recordings while presenting the same speech and noise sounds and then performed the same manifold learning.

The results for animals with hearing loss were similar to those for animals with normal hearing: the overall dimensionality of the neural activity was high (Figure 2f); the dimensionality of the signal manifold was low (Figure 2g; between 4 and 7 PCs required to explain 95% of the signal variance); and the signal dynamics were similar across animals (Figure 2h; 95% average variance explained), demonstrating again that the signal manifold is fundamental and robust. But the similarity between the signal dynamics of normal hearing animals and animals with hearing loss was much lower than that between animals with the same hearing status (Figure 2h and i; 78% average variance explained). This result indicates that the activity within the signal manifold of an animal with hearing loss is not linearly predictable from the activity within the signal manifold of a normal hearing animal and, thus, that the impact of hearing loss at the network level is a true nonlinear distortion that reshapes the neural code in a complex way.

To develop an understanding of exactly how hearing loss impacts signal dynamics, further investigation is required. However, traditional approaches to manifold learning such as PCA are limited by the fact that they can only be applied to existing recordings. To overcome this limitation, we designed a DNN that allowed us to identify the signal manifold within the framework of an encoding model that maps sound to neural activity (Figure 3a). If the DNN can be trained to replicate neural activity with high accuracy for a wide range of sounds, it can then be used to probe the effects of hearing loss on signal dynamics using new sounds as needed.

Figure 3

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The DNN first projects sound into a high-dimensional feature space using an encoder with a cascade of convolutional layers. It then reduces the dimensionality of its feature space through a bottleneck layer and uses a simple (i.e., not convolutional) linear readout to transform the activations in the bottleneck into the neural activity for each recorded unit. During training, the DNN learns to use the bottleneck to identify the low-dimensional feature space that captures as much of the explainable variance in the recorded neural activity as possible, that is, the signal manifold. (Note that the structure of the DNN is not meant to reflect the anatomy of the auditory system; it is simply a tool for identifying latent dynamics and predicting neural activity.)

Once trained, the DNN can be used to simulate neural activity for any sound, whether it was presented during neural recordings or not, with the activations in the bottleneck layer reflecting the underlying signal dynamics. This supervised approach to identifying the signal manifold also has the added advantage that it eliminates the residual noise that is inevitable with unsupervised methods such as PCA (Figure 3b). (See decreasing SNR with successive PCs in Figure 2d.).

The utility of the DNN rests, of course, on its ability to faithfully reproduce the recorded neural activity. We trained and tested a separate DNN for each animal (after partitioning the recordings into training and test sets as described above) and found that they performed with remarkable accuracy. The explainable variance explained for activity in the test set approached 100% for the units with highest explainable variance and was far beyond that achieved by a standard single-layer linear–nonlinear model (Figure 3c). We varied the size of the bottleneck layer and found that performance plateaued with more than eight channels for both normal hearing animals and those with hearing loss, consistent with the dimensionality of the signal manifold identified through PCA (Figure 3c).

We also assessed the similarity of the DNN-derived signal dynamics across animals by measuring how much of the variance in the bottleneck activations from one animal could be explained by the bottleneck activations from another (Figure 3d and e; allowing for additional linear transformation). We found that the signal dynamics for animals with the same hearing status were nearly identical (97% average variance explained for both normal hearing and hearing loss), while the similarity between the signal dynamics for animals with normal hearing and those with hearing loss was much lower (87% average variance explained). Thus, the signal manifold as identified by the DNN appears to have similar properties to that identified through PCA, with the added advantages of reduced residual noise and the ability to probe the signal dynamics using novel sounds.

To examine the degree to which the DNNs trained on speech were capable of predicting responses to other sounds, we compared recorded and DNN-generated responses to pure tones with different frequencies and intensities (Figure 3f). The DNNs performed well, explaining an average of 83% of the explainable variance in the recorded activity across animals. To further test the generality of the DNN models, we used transfer learning to test their ability to predict responses to new sounds for a new set of animals. If the DNN encoder really does capture transformations that are common to all animals with the same hearing status, then it should be possible to use a trained encoder from one animal to predict responses for a new animal after learning only a new linear readout (Figure 3g). For each of the DNN models trained on activity from one of the six normal hearing animals in our original dataset, we froze the encoder and retrained the linear readout for each of four new normal hearing animals. We initialized the readout weights for each unit in a new animal using the readout weights for a random unit from the original animal, and then optimized the weights using a relatively small sample (between 2 and 3.5 hr) of activity recorded from the new animal during the presentation of speech and moving ripples. We then used the new DNN model (the frozen encoder and the optimized readout) to predict responses from the new animal to sinusoidally amplitude modulated (SAM) broadband noise sounds with different modulation frequencies, modulation depths, and intensities. The new DNN models performed well, explaining an average of 85% of the explainable variance in the recorded activity across animals. While pure tones and SAM noise are only two of many possible sounds, these results provide encouraging evidence of the generality of the DNN models.

Before continuing our investigation of the neural coding of speech, we first used the DNN to examine the impact of hearing loss on the processing of basic acoustic features. To assess spectral processing, we presented the DNN for each animal with a stream of pure tones with different frequencies and intensities and extracted the activations from the bottleneck layer (Figure 4a; we set the dimensionality of the bottleneck layer to 8 for this and all subsequent analyses). The frequency response areas (FRAs) for individual bottleneck channels resembled those that are typically observed for individual neurons in the IC: some exhibited a clear preferred frequency at low intensities and broader tuning at high intensities, while others had more complex shapes (Figure 4b). For animals with hearing loss, elevated intensity thresholds were also evident.

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To visualize the signal dynamics, we applied PCA to the bottleneck activations (for each intensity separately) and projected the full dynamics onto the top two PCs, which explained more than 90% of the variance for these simple sounds (Figure 4c). For normal hearing animals, the paths traced by the dynamics within the signal manifold for different sounds, which we term trajectories, were distinct and formed an orderly arrangement, but with a clear change in geometry across intensities (Figure 4d). At low intensities, the trajectories for different frequencies were distinct across both PCs, each of which accounted for substantial variance (the percent of the variance in the signal dynamics explained by each PC at each intensity is indicated on each panel). But at high intensities, the trajectories for all frequencies were similar along the first PC, which accounted for the vast majority of the variance, and varied only along the second PC. These intensity-dependent changes in the geometry of the signal dynamics are consistent with the known effects of intensity on spectral tuning in IC neurons. At low intensities, tuning is narrow and, thus, different tone frequencies elicit distinct population activity patterns. But at high intensities, because tuning is broader, the population activity patterns elicited by different frequencies are less distinct.

For animals with hearing loss, the signal dynamics were dramatically different. At moderate intensity, only the lowest frequencies elicited any activation (as expected, given the larger elevation in intensity thresholds at high frequencies; Figure 2—figure supplement 1). At higher intensity, all tones elicited activation, but rather than forming an orderly arrangement within the manifold, the trajectories for different frequencies clustered into two groups, one for low frequencies and one for high frequencies. At the highest intensity, the trajectories for different frequencies became more distinct, but clear clustering remained. The increased similarity in the signal trajectories for different frequencies is consistent with the increased similarity of spectral tuning between individual IC neurons in animals with hearing loss (Barsz et al., 2007; Willott, 1986), but the clustering of dynamics within the signal manifold is an emergent network-level phenomenon that has not previously been observed.

To further analyze the dynamics and allow for direct comparisons across animals, we first turned to representational similarity analysis (RSA) (Kriegeskorte et al., 2008). RSA uses only the relative distances between trajectories within a manifold and, thus, does not require the dynamics for different animals to be aligned. The first step in RSA is to form a representational dissimilarity matrix (RDM) for each set of trajectories, with each entry in the RDM equal to one minus the point-by-point correlation between a pair of trajectories for two different sounds (Figure 4e, left).

The structure of the RDMs was consistent with the observations about the dynamics made above. For normal hearing animals, the RDMs had a diagonal symmetry with a smooth gradient, indicating that the similarity of the trajectories for two frequencies decreased gradually as the difference between the frequencies increased. For animals with hearing loss, the RDMs had a block structure, indicating that the trajectories formed two clusters (Figure 4e, center; note that RDMs are symmetric, so the lower half of the normal hearing RDM is shown with the upper half of the hearing loss RDM for comparison).

Because we were interested in identifying the effects of hearing loss beyond those related to audibility, we also compared the normal hearing RDMs at a given intensity to the hearing loss RDMs at the best intensity, that is, at whatever intensity resulted in the highest similarity to the normal hearing RDM for each pair of animals (measured as the point-by-point correlation between the RDMs). Amplification to the best intensity softened the block structure and shifted the transition between clusters to a lower frequency, but did not fully restore the diagonal structure present in the normal hearing RDMs (Figure 4e, right). Overall, the similarity between the RDMs for different normal hearing animals at moderate intensity (55 dB SPL) was high (0.91 ± 0.01; mean ± SEM; n = 15 pairwise comparisons; Figure 4f; for full details of all statistical tests, see Table 1). The similarity between the normal hearing and hearing loss RDMs at the same moderate intensity was much lower (0.59 ± 0.02; n = 36) and remained relatively low even at the best intensity (0.78 ± 0.02; n = 36).

The results of RSA are easy to interpret, but, because it uses only the relative distances between trajectories, it can be insensitive to distortions that impact the overall structure of the dynamics (e.g., a change in temporal dynamics that is common across all sound frequencies). To allow for direct comparisons of overall structure, we used canonical correlation analysis (CCA) (Dabagia et al., 2022). CCA identifies a series of linear projections, known as canonical components (CCs), that attempt to align two sets of dynamics such that the point-by-point correlation between trajectories after projection onto their respective CCs is maximized. The set of CCs for a given set of dynamics are required to be orthogonal to each other and to explain all of the variance in the original trajectories. CCA can also be extended to simultaneously align dynamics for an entire group of animals through multiway canonical correlation analysis (MCCA) (de Cheveigné et al., 2019).

The average dynamics after alignment via CCA exhibited phenomena that were similar to those that were evident for individual animals (Figure 4g). For normal hearing animals, the trajectories for different tone frequencies were distinct and formed an orderly arrangement with frequency-dependent variation across two dimensions at low intensities, while at high intensities the variation across frequencies was largely confined to the second CC. For animals with hearing loss, the trajectories for different frequencies clustered into two groups at moderate intensities and remained clustered, albeit more weakly, at high intensities. This clustering was also evident when a similar analysis was performed directly on recorded neural activity (Figure 4—figure supplement 1).

To measure the similarity between the dynamics for different animals after alignment via CCA, we used a weighted sum of the point-by-point correlations between the two sets of dynamics after projection onto each pair of CCs, with the weight for the correlation associated with each pair of CCs given by the average variance in the original dynamics that those CCs explained (see ‘Methods’ for equation). Overall, the similarity between the dynamics for different normal hearing animals at moderate intensity after alignment via CCA was extremely high (0.98 ± 0.01; n = 15; Figure 4h). The similarity between the aligned dynamics for normal hearing and hearing loss animals at the same moderate intensity was much lower (0.37 ± 0.02; n = 36) and remained below normal even when compared at the best intensity (0.88 ± 0.01; n = 36). Taken together, the RSA and CCA results suggest that hearing loss results in a fundamental disruption of spectral processing at the network level.

We next assessed temporal processing by performing a similar analysis on the bottleneck activations elicited by a stream of SAM broadband noise sounds with different modulation frequencies and intensities (Figure 5a). For these sounds, two dimensions were again enough to capture almost all of the variance in the full signal dynamics across all intensities (Figure 5b). For both normal hearing animals and those with hearing loss, the explicit tracking of envelope modulations in the signal dynamics decreased with increasing modulation frequency and increasing intensity (Figure 5c). But when compared at the same intensity, the dynamics for animals with hearing loss clearly differed from those for animals with normal hearing (Figure 5d and e).

Figure 5

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This was confirmed by RSA (Figure 5f), which indicated that while the similarity between normal hearing RDMs at moderate intensity (55 dB SPL) was extremely high (0.99 ± 0.01; n = 15), the similarity between normal hearing and hearing loss RDMs was lower (0.76 ± 0.01; n = 36). But when compared at the best intensity to eliminate differences related to audibility, the dynamics for animals with hearing loss became nearly identical to those for animals with normal hearing (Figure 5e), and this was reflected in the similarity between RDMs (0.99 ± 0.01; n = 36).

Comparing the similarity of the dynamics after alignment via CCA yielded similar results (Figure 5g). The similarity between the dynamics for different normal hearing animals at moderate intensity after alignment via CCA was high (0.97 ± 0.01; n = 15). The similarity between the aligned dynamics for normal hearing and hearing loss animals was much lower when compared at the same moderate intensity (0.44 ± 0.02; n = 36) but increased to normal levels when the comparison was made at the best intensity (0.95 ± 0.01; n = 36). Thus, it appears that hearing loss has little impact on temporal processing beyond that which results from decreased audibility.

We verified that this was also true for the processing of sounds with different modulation depths. We performed the same analysis on the bottleneck activations elicited by a stream of SAM noise sounds with different modulation depths and intensities (and a fixed modulation frequency of 30 Hz; Figure 5h). When compared at the best intensity, the signal dynamics for normal hearing animals and animals with hearing loss were nearly identical (Figure 5i), with the explicit tracking of envelope modulations decreasing with decreasing modulation depth. The overall similarity measured at the best intensity both by RSA (0.99 ± 0.01; n = 36; Figure 5j) and after alignment via CCA (0.96 ± 0.01; n = 36; Figure 5k) confirmed that the impact of hearing loss on temporal processing beyond that which results from decreased audibility was negligible.

Having established that the distortions in neural signal dynamics caused by hearing loss affect primarily spectral, rather than temporal, processing for simple sounds, we next returned to speech. We focused on consonants, which vary widely in their spectral properties and are the primary contributor to the perceptual deficits exhibited by people with hearing loss when listening to ongoing speech (Fogerty et al., 2012). We presented the DNN with a stream of isolated consonants (diphone syllables with the vowel removed), each uttered multiple times by multiple talkers (Figure 6a). The consonants can be divided into three broad groups: the vowel-like consonants (nasals and approximants), which are dominated by low frequencies; the plosives, which are broadband; and the fricatives, which are dominated by high frequencies (Figure 6b).

Figure 6

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For both normal hearing animals and animals with hearing loss, two dimensions were again sufficient to explain nearly all of the variance in the bottleneck activations (Figure 6c). For normal hearing animals, the dynamics elicited by different consonants followed distinct trajectories that were organized within the signal manifold according to consonant type (Figure 6d; the dynamics shown are the average across all instances of each consonant). For animals with hearing loss, only the vowel-like consonants elicited responses at moderate intensity (as expected, given the larger elevation in intensity thresholds at high frequencies; Figure 2—figure supplement 1). At higher intensities, all consonants elicited responses but the trajectories were not as distinct as with normal hearing and exhibited a clustering similar to that observed for pure tones (Figure 4d), which softened at the highest intensity.

The differences in the dynamics for normal hearing animals and those with hearing loss were evident in the RDMs (Figure 6e). When compared at a typical conversational intensity (60 dB SPL), the similarity between normal hearing RDMs was high (0.94 ± 0.01; n = 15), but the similarity between normal hearing and hearing loss RDMs was low (0.23 ± 0.02; n = 36). The normal hearing and hearing loss RDMs were much more similar when compared at the best intensity, though some differences remained (0.87 ± 0.01; n = 36).

Comparing the similarity of the dynamics after alignment via CCA yielded similar results (Figure 6f). The similarity between the dynamics for different normal hearing animals after alignment via CCA was high (0.96 ± 0.01; n = 15). The similarity between normal hearing and hearing loss animals when compared at the same conversational intensity was much lower (0.31 ± 0.02; n = 36) and increased when the comparison was made at the best intensity, but not to normal levels (0.77 ± 0.01; n = 36).

Given that hearing loss seems to impact primarily spectral processing, we investigated whether the distortions in the neural code for speech could be corrected by providing frequency-dependent amplification using a simulated hearing aid (Armstrong et al., 2022; Alexander and Masterson, 2015). We used the measured ABR threshold shifts for each animal to set the parameters for the amplification, which resulted in a gain of approximately 10 dB at low frequencies and 30 dB at high frequencies for speech at conversational intensity (Figure 2—figure supplement 1), and presented the same stream of consonants again after processing with the hearing aid. The frequency-dependent amplification was effective in reducing the distortion in the dynamics for animals with hearing loss. The overall similarity between normal hearing and hearing loss animals as measured by RSA was restored to normal levels (0.91 ± 0.01; n = 36; Figure 6e), and the similarity measured after alignment via CCA was also increased, though some residual distortion remained (0.86 ± 0.01; n = 36; Figure 6f). (Note that we did not record neural activity in response to speech through the simulated hearing aid; while we have no specific reason to doubt the accuracy of the DNN model for this class of sounds, the fact that it has not been explicitly validated should be considered.)

To evaluate the functional consequences of the remaining distortion, we turned to decoding. We trained a support vector machine to classify consonants based on the signal dynamics for each animal. For normal hearing animals, the decoder identified 55% of consonants correctly (±1%; n = 6; chance = 4.5%) when the consonants were presented at conversational intensity (Figure 6g). For animals with hearing loss, performance at the same intensity was lower (41 ± 1%; n = 6) but increased substantially at best intensity (47 ± 1%; n = 6), and increased further still with frequency-dependent amplification by the hearing aid (49 ± 1%; n = 6). Taken together, these results suggest that while amplification cannot completely restore the neural code for speech in quiet to normal, the residual distortions are relatively minor.

Given that the perceptual difficulties experienced by listeners with hearing loss are most pronounced in noisy environments, we expected that the addition of background noise to the speech would create larger distortions in the neural code. We presented the same consonant stream with added speech babble (background noise formed by adding together the voices of many different talkers; Figure 7a and b) at a speech-to-noise ratio of 3 dB, which is typical of real-world settings experienced by hearing aid users (Christensen et al., 2021). The addition of background noise increased the dimensionality of the signal dynamics relative to simple sounds or speech in quiet, especially at high overall intensities; three PCs were often required to capture more than 90% of the variance (Figure 7c). (Note that both the speech and the background noise contribute to the signal dynamics, which encode all incoming sounds without distinction.)

Figure 7

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For normal hearing animals, the signal dynamics for speech-in-noise and speech-in-quiet were nearly identical at the lowest intensities, but differed strongly at higher intensities (Figure 7d; the dynamics shown are the average across all instances of each consonant). For speech-in-noise at the highest intensity, there was a clear distinction between the first PC, which provided a clean reflection of each consonant (though not the same as for speech in quiet), and the other PCs, which were dominated by the background noise (despite averaging across all instances of each consonant with independent noise). The trends were similar for animals with hearing loss, though the background noise was reflected in the signal dynamics even more strongly.

When compared at the same high intensity (70 dB SPL), typical of a social setting, both RSA and CCA indicated strong effects of hearing loss on the signal dynamics for speech in noise (Figure 7e and f). The similarity between normal hearing RDMs was high (0.89 ± 0.02; n = 15), but the similarity between normal hearing and hearing loss RDMs was much lower (0.15 ± 0.03; n = 36). Amplification to best intensity increased the similarity between normal hearing and hearing loss RDMs (0.62 ± 0.02; n = 36), as did the frequency-weighted amplification provided by the hearing aid (0.56 ± 0.03; n = 36), but neither was sufficient to bring the similarity close to normal levels. For both forms of amplification, the similarity of the signal dynamics for speech in noise to those with normal hearing was much lower than for speech in quiet (best intensity: 0.62 vs. 0.87, n = 36; p<1e-10, paired t-test; hearing aid: 0.56 vs. 0.91, n = 36, p<1e-10, paired t-test). Comparing the similarity of the dynamics after alignment via CCA yielded similar results. The similarity between the dynamics for different normal hearing animals after alignment via CCA was high (0.92 ± 0.01; n = 15). The similarity between normal hearing and hearing loss animals when compared at the same intensity was much lower (0.49 ± 0.02; n = 36) and increased when the comparison was made at the best intensity (0.68 ± 0.01; n = 36) or after processing with the hearing aid (0.70 ± 0.02; n = 36), but remained well below normal levels. Again, for both forms of amplification, the similarity of the signal dynamics for speech in noise to those with normal hearing was much lower than for speech in quiet (best intensity: 0.68 vs. 0.77, n = 36; p<1e-6, paired t-test; hearing aid: 0.70 vs. 0.86, n = 36, p<1e-10, paired t-test).

Decoding the signal dynamics for each animal suggested that the distortions in the signal dynamics for speech in noise had functional consequences (Figure 7g). For normal hearing animals, the decoder identified 32% of consonants correctly (±1%; n = 6). For animals with hearing loss, performance at the same intensity was lower (15 ± 1%; n = 6) and remained well below normal levels both at the best intensity (23 ± 1%; n = 6) or after processing with the hearing aid (22 ± 1%; n = 6).

To gain a better understanding of the differential impact of the background noise with and without hearing loss, we used MCCA to jointly align the signal dynamics for all animals with normal hearing and hearing loss so that we could make direct comparisons. We first analyzed the results for speech in quiet. When compared at best intensity (Figure 8a), there was good alignment between the dynamics for animals with normal hearing and hearing loss. The correlation for pairs of animals after projection onto the first CC, which accounted for 88 ± 2% and 71 ± 7% of the variance in animals with normal hearing (n = 6) and hearing loss (n = 6), respectively, was 0.94 ± 0.01 (n = 36). The correlation after projection onto the second CC, which accounted for the remaining variance, was lower (0.44 ± 0.03; n = 36).

Figure 8

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With the hearing aid (Figure 8b), the alignment between the dynamics for animals with normal hearing and hearing loss was even better. The correlation after projection onto the first CC remained high (0.94 ± 0.01; n = 36) and the correlation after projection onto the second CC rose substantially (0.73 ± 0.01; n = 36). These results are consistent with the analysis for speech in quiet above that suggested that only minimal distortions in the signal dynamics for animals with hearing loss remain after frequency-weighted amplification is provided (Figure 6).

For speech in noise, the alignment was generally worse overall. When compared at best intensity (Figure 8c), the correlations after projection onto the CCs were 79 ± 1%, 74 ± 3%, and 18 ± 3%, respectively (n = 36). But even for the first two CCs for which the alignment was relatively good, the percent of the variance accounted for by each was substantially different for normal hearing animals and those with hearing loss. The first CC, which provided a clean reflection of each consonant, accounted for 56 ± 1% of the variance for normal hearing animals (n = 6), but only 38 ± 7% of the variance for animals with hearing loss (n = 6). Conversely, the second CC, which was dominated by the background noise, accounted for 41 ± 6% of the variance for animals with hearing loss (n = 6), but only 28 ± 1% of the variance for animals with normal hearing. Thus, while the neural subspaces encoding the speech and the background noise seem to be similar for all animals, the balance of variance between these subspaces is tilted much more toward background noise in animals with hearing loss.

Given the nature of the hearing loss (larger elevation in intensity thresholds at high frequencies; Figure 2—figure supplement 1) and the spectral properties of speech babble (higher power at low frequencies; Figure 7b), the hypersensitivity of animals with hearing loss to the background noise is somewhat expected. However, the problem was, if anything, exacerbated by the selective amplification of high frequencies provided by the hearing aid (Figure 8d). The CC that was dominated by the background noise (now the first CC, since it produced the highest correlation) accounted for 46 ± 6% of the variance for animals with hearing loss (n = 6), but only 31 ± 1% of the variance for animals with normal hearing, while the CC that provided a clean reflection of each consonant (now the second CC) accounted for 56 ± 1% of the variance for normal hearing animals (n = 6), but only 33 ± 6% of the variance for animals with hearing loss (n = 6). Thus, it appears that hearing loss allows the signal dynamics to be captured by background noise at the expense of foreground speech in a way that cannot be corrected by simple frequency-dependent amplification.

To characterize the distortions in spectral processing that underlie this effect, we examined how the processing of one narrowband sound is impacted by the presence of another. We used narrowband noise modulated by a 20 Hz sinusoidal envelope as the target sound and narrowband noise modulated by a pink noise envelope as the masker (Figure 8e). We varied the center frequency of the target and masker separately and the intensity of the target and masker together (to maintain a constant target-to-masker ratio). We presented the target sounds to the DNN for each animal with and without the masker sounds and measured the differences between the signal dynamics across the two conditions by computing their correlation.

For animals with normal hearing, the correlation between the target only and target plus masker dynamics ranged from 0.25 to 0.75, with the masker having the largest impact when its center frequency was similar to that of the target (Figure 8f). When compared at the same high intensity (70 dB SPL), the correlation for animals with hearing loss was typically lower than normal when the masker center frequency was low, especially when the target center frequency was high (Figure 8g). This regime (high-frequency target, low-frequency masker) is comparable to the speech-in-noise scenario analyzed above (many consonants contain substantial high-frequency content, while speech babble is dominated by low frequencies, see Figure 7b), and the increased impact of the masker with hearing loss is consistent with observed hypersensitivity to background noise at the expense of foreground speech. For high-frequency maskers, the correlation for animals with hearing loss was often higher than normal, especially for low-frequency targets. This is unsurprising given the sloping nature of the hearing loss, but this regime (low-frequency target, high-frequency masker) is uncommon in real-world speech.

When the correlation for animals with normal hearing and hearing loss was compared either at the best intensity (Figure 8h) or after frequency-weighted amplification with the hearing aid (Figure 8i), the pattern of results was similar. In the regime that is most comparable to consonants in speech babble (low-frequency masker, high-frequency target), the correlation for animals with hearing loss was lower than normal. Thus, hearing loss appears to create deficits in spectral processing that manifest as highly nonlinear distortions in cross-frequency interactions that are particularly problematic for real-world speech in noise and cannot be corrected by simply compensating for lost sensitivity.

The effects of hearing loss beyond increased detection thresholds are often ignored in clinical assessment and treatment. But these suprathreshold effects are, in fact, the main problem for many people in real-world settings, such as busy workplaces or social gatherings, where sound intensities are high and amplification via a hearing aid provides little benefit. The clinical neglect of suprathreshold effects is not due to a lack of awareness, but rather to a lack of effective treatments. And the lack of effective treatments stems from a lack of understanding of how the many physiological changes that accompany hearing loss contribute to complex perceptual deficits.

Many specific suprathreshold impairments with plausible links to speech-in-noise perception have been identified, such as decreased frequency selectivity, dynamic range, or temporal resolution (Moore, 2007). But the extent to which each of these specific impairments contributes to real-world hearing problems has been difficult to determine. Our results suggest that changes in spectral processing, particularly in the interactions between different frequencies, are the primary problem. While impaired spectral processing was evident for simple tones as a clustering of dynamical trajectories within the signal manifold, this impairment does not appear to be a major problem for the neural coding of speech per se as suitable amplification corrected many of the distortions caused by hearing loss for speech in quiet. For speech in noise, however, there was a hypersensitivity to background noise with hearing loss that amplification (simple or frequency-weighted) did little to alleviate, and this was consistent with observed interactions between narrowband sounds, which revealed an increased disruption of high-frequency targets by low-frequency maskers both with and without amplification.

These results are consistent with a recent study that found that hearing loss caused the IC activity patterns elicited by different phonemes to become less distinct, and that a hearing aid failed to correct this problem for speech in noise (Armstrong et al., 2022). They are also consistent with a body of work demonstrating that listeners with hearing loss struggle to combine temporal envelope cues across frequency channels (Healy and Bacon, 2002; Healy and Carson, 2010; Souza and Boike, 2006; Grant et al., 2007). When speech is reduced to a single amplitude-modulated band, speech recognition performance is similar for all listeners, independent of their hearing status, suggesting that temporal processing of the speech envelope per se is unaffected by hearing loss. But as additional amplitude-modulated bands are added, performance increases more for normal hearing listeners than for those with hearing loss, suggesting that the latter group are less able to make use of complementary temporal information across multiple frequency channels. This difference is most pronounced when comparing the ability to make use of temporal modulations in high-frequency channels (4–6 kHz) in the presence of temporal modulations in lower frequency channels (1–2 kHz) (Grant et al., 2007), and it does not appear to be a simple consequence of broadened frequency tuning but rather a specific deficit in cross-frequency interactions (Healy and Carson, 2010).

Understanding exactly what is going wrong with spectral processing after hearing loss at a mechanistic level remains a challenge. The effects of hearing loss on spectral processing in the cochlea have been well described in terms of the observed changes in the frequency tuning curves of individual AN fibers. After hearing loss, the tuning curve ‘tip’ (corresponding to the characteristic frequency [CF] to which the fiber is most sensitive) becomes less sensitive and may shift toward lower frequencies while the ‘tail’ (corresponding to frequencies below CF) may become more sensitive (Young, 2012). It is difficult to know the degree to which these changes distort the basic tonotopic map in the cochlea (i.e., the relationship between CF and cochlear position) because few studies have identified the cochlear position from which recorded fibers originate. The limited data that exist suggest that the effect of hearing loss on CF tonotopy is modest (Liberman and Kiang, 1984), but the effect on the tonotopic map of best frequency (BF; the frequency that elicits the strongest response from a fiber at higher intensities) can be much larger (Henry et al., 2016), and can be accompanied by more complex changes in spectral processing such as decreased synchrony capture (Young, 2012).

One recent study has provided insight into how the complex spectral distortions in the cochlea impact the neural coding of speech in noise in the AN (Parida and Heinz, 2022). In animals with mild-to-moderate sensorineural hearing loss, fibers with high CFs responded excessively to low-frequency sounds and it was this effect (rather than changes in frequency selectivity per se or temporal processing) that appeared to be most responsible for the disrupted neural coding of speech in noise. These results are consistent with our observations of hypersensitivity to background noise and increased disruption of high-frequency targets by low-frequency maskers in the IC. The distortion of spectral processing that we observe as clustering of network dynamics for simple tones in the IC, however, does not appear to be present in the AN. It is difficult to be certain since no directly comparable analysis has been performed on experimental AN responses, but our analysis of simulated AN responses suggests that hearing loss has more complex effects on the signal dynamics in the AN than simply causing clustering (Figure 4—figure supplement 1). This transformation from complex distortions in signal dynamics for tones in the AN to the simple clustering observed in the IC could arise from normal central processing of distorted peripheral inputs, but it is also possible that plastic changes in central processing that follow hearing loss facilitate a shift into a new dynamical regime.

Distorted spectral processing has also recently been observed in the auditory cortex after mild-to-moderate sloping sensorineural hearing loss (McGill et al., 2022). Animals displayed behavioral hypersensitivity for detection of tones at the edge frequencies around which the hearing loss increased from mild to moderate as well as an overrepresentation of these frequencies in the cortical tonotopic map of BF. The mechanisms underlying these phenomena are not entirely clear. Some cortical neurons tuned to these edge frequencies exhibited increased neural gain and synchrony, and direct stimulation of thalamocortical afferents demonstrated that hearing loss caused an increase in gain within the local cortical circuit. But the frequency tuning of the stimulated afferents was unknown and, thus, it is difficult to separate the effects that were cortical in origin from those that were inherited from lower levels. It is possible that the altered neural representation of spectral features that we observed in the IC results in changes in the coactivation patterns across the cortical network, prompting the plastic reorganization in the cortex. Future research should be focused on developing a coherent model of how peripheral and central changes combine to create auditory processing deficits, perhaps through coordinated experiments across many brain areas in a single species.

The complex suprathreshold effects of hearing loss that are evident in the distorted neural signal dynamics observed in this study present a difficult challenge for hearing aid designers. Current hearing aids compensate for changes in the threshold and dynamic range of auditory processing using a framework built around a bank of bandpass filters with automatic gain control. The signal processing that can be performed by such a framework is highly constrained, and it is difficult to imagine how it could be used to compensate for problems such as hypersensitivity to background noise that involve highly nonlinear interactions across frequency bands. It is possible that with a better understanding of exactly how different frequencies are interacting, new signal processing frameworks can be designed to offset the more complex effects of hearing loss. But engineering such a framework that is flexible enough to provide benefit in a wide range of real-world settings will require conceptual advances that may not be forthcoming in the near term.

One alternative approach to improving the perception of speech in noise that is already showing promise is speech enhancement, that is, the suppression of background noise. Hearing aids have offered noise suppression for many years, but the simple filters based on low-order statistics that are used by current devices often provide little real-world benefit (Brons et al., 2014; Cox et al., 2014). Recent research on speech enhancement via DNNs has demonstrated the potential to yield dramatic improvements in performance (Wang, 2017; Luo and Mesgarani, 2019). This ‘deep denoising’ may prove effective in situations with a single talker where it is obvious which sound is of interest. But in others, for example, with multiple talkers, a sound that is of primary interest one minute may become a distraction the next. It may be possible to implement cognitive control to direct enhancement toward the sound of interest but there are many significant technical challenges that must be overcome before this approach can be widely applied (Geirnaert et al., 2021).

A more flexible alternative is to identify optimal processing algorithms for hearing aids empirically by providing DNNs with the data they need to learn how best to transform sounds in order to elicit normal neural activity from an impaired auditory system (Lesica, 2018; Drakopoulos and Verhulst, 2022). By taking advantage of the nonlinear capacity of DNNs with minimal assumptions, it should be possible to identify novel general-purpose algorithms that go well beyond the hand-designed processing in current devices. Such algorithms would be especially valuable in important contexts such as listening to music – a major problem for hearing aid users (Madsen and Moore, 2014) – in which denoising cannot help. There are, of course, limits to the degree of hearing restoration that any hearing aid can provide in cases of severe hearing loss. But the vast majority of people with hearing loss have only mild-to-moderate cochlear damage (Wilson et al., 2017), and there should be sufficient functionality remaining within the auditory system for a hearing aid to leverage when attempting elicit the necessary patterns of neural activity.

Building computational models of sensory processing has been a long-standing goal in systems neuroscience. Current models of the sensory periphery can be highly accurate. For example, there are numerous models of the cochlea that faithfully capture the transformation of incoming sound into basilar membrane motion and AN activity (Saremi et al., 2016; Verhulst et al., 2018). Models of sensory processing in the brain, however, have generally been much less accurate, with even the best models missing out on a significant fraction of the explainable variance in subcortical and cortical neural activity (Williamson et al., 2016; Rahman et al., 2020; McFarland et al., 2013; Vintch et al., 2015).

Until recently, efforts to model central sensory processing were constrained by the difficulties of fitting high-capacity models with limited experimental data. But deep learning has provided a new approach to fitting models that are well matched to sensory processing, and new methods for large-scale electrophysiology can provide the required big data. Initial efforts to use DNNs to model the sensory periphery have shown that they can be as accurate as hand-designed biophysical models. In one recent study, a DNN trained to replicate an established model of the cochlea provided accurate and generalizable predictions of the model’s response to speech and tones (Baby et al., 2021). In another study, a DNN trained on retinal ganglion cell activity predicted nearly all of the explainable variance in responses to natural images (Maheswaranathan et al., 2019).

DNN models of sensory processing in the brain have also been shown to outperform traditional models. DNN models of V1 responses to natural images explained 50 and 80% of the explainable variance in single-unit spike counts and calcium activity, respectively (Cadena et al., 2019; Walker et al., 2019), while DNN models of V4 explained 90% of the explainable variance in multi-unit spike counts (Bashivan et al., 2019). DNN models of A1 responses to speech and other natural sounds perform similarly well, explaining much of the explainable variance in high-gamma activity, fMRI voxel responses, or time-varying spike rates (Keshishian et al., 2020; Kell et al., 2018; Pennington and David, 2022).

Our results improve on these initial successes in several important ways. Firstly, our models simulate neural activity with full temporal resolution, that is, spike times with millisecond precision. While lower temporal resolution may be sufficient to describe sensory processing in some contexts, precise spike timing carries critical information about speech (Garcia-Lazaro et al., 2013). Secondly, the activity produced by our models is nearly indistinguishable from that recorded experimentally, capturing more than 95% of the explainable variance in many cases. This is especially remarkable considering the full temporal resolution (with lower resolution, variance at fine time scales, which is typically the most difficult to capture, is simply ignored). Finally, our use of a low-dimensional bottleneck allows us to achieve this performance within a framework that also provides a compact and interpretable description of the latent dynamics that underlie the full network activity patterns.

With these advances, it should now be possible to use computational models of the brain for exploratory basic research, with benefits that are both scientific (studies are no longer data limited) and ethical (animal experiments can be limited to confirmatory studies), as well as for technology development (such as improved hearing aids, as described above). With further effort, it may be possible to build models that are not only black-box simulators but also mirror the underlying structure of biological systems (Jazayeri and Ostojic, 2021; Chung and Abbott, 2021). Such models would provide powerful platforms for testing mechanistic hypotheses and developing new ways to address complex network-level dysfunctions that remain difficult to treat (such as tinnitus).

Experiments were performed on 12 young-adult gerbils of both sexes that were born and raised in standard laboratory conditions. Six of the animals were exposed to noise when they were 16–18 weeks old. (These six were chosen from among many that were noise exposed based on the pattern of hearing loss that they exhibited: sloping mild-to-moderate in both ears.) The number of animals used was not predetermined. Because of the investigative nature of the study, the key outcome measures were not known in advance and, thus, a pre-study power analysis based on anticipated effect sizes was not possible. The duration of the data collection from each animal was predetermined based on the results of preliminary experiments in which the amount of neural activity required for manifold analysis and deep learning to yield stable results was assessed. Assignment to the control and hearing loss groups was random on a per-animal basis (i.e., animals from the same litter were often assigned to different groups). Investigators were not blinded during data collection or analysis (since the difference between animals with normal hearing and hearing loss is immediately apparent upon the observation of sound-evoked neural activity), but all analyses were fully automated and objective. ABR recordings and large-scale IC recordings were made from all animals when they were 20–24 weeks old. All experimental protocols were approved by the UK Home Office (PPL P56840C21).

Mild-to-moderate sensorineural hearing loss was induced by exposing anesthetized gerbils to high-pass filtered noise with a 3 dB/octave roll-off below 2 kHz at 118 dB SPL for 3 hr (Armstrong et al., 2022; Suberman et al., 2011). For anesthesia, an initial injection of 0.2 ml per 100 g body weight was given with fentanyl (0.05 mg per ml), medetomidine (1 mg per ml), and midazolam (5 mg per ml) in a ratio of 4:1:10. A supplemental injection of approximately 1/3 of the initial dose was given after 90 min. Internal temperature was monitored and maintained at 38.7°C.

Animals were placed in a sound-attenuated chamber and anesthetized for surgery with an initial injection of 1 ml per 100 g body weight of ketamine (100 mg per ml), xylazine (20 mg per ml), and saline in a ratio of 5:1:19. The same solution was infused continuously during recording at a rate of approximately 2.2 μl per min. Internal temperature was monitored and maintained at 38.7°C. A small metal rod was mounted on the skull and used to secure the head of the animal in a stereotaxic device. The pinnae were removed and speakers (Etymotic ER-2) coupled to tubes were inserted into both ear canals along with microphones (Etymotic ER-10B+) for calibration. The frequency response of these speakers measured at the entrance of the ear canal was flat (±5 dB) between 0.2 and 8 kHz. Two craniotomies were made along with incisions in the dura mater, and a 256-channel multi-electrode array was inserted into the central nucleus of the IC in each hemisphere (Armstrong et al., 2022). The arrays were custom-designed to maximize coverage of the portion of the gerbil IC that is sensitive to the frequencies that are present in speech.

Before beginning the IC recordings, ABRs were measured. Subdermal needles were used as electrodes with the active electrodes placed behind the ear over the bulla (one on each side), the reference placed over the nose, and the ground placed in a rear leg. Recordings were bandpass-filtered between 300 and 3000 Hz. The parallel ABR method (Polonenko and Maddox, 2019) was used, with randomly timed tones at multiple frequencies presented simultaneously and independently to each ear. The tone frequencies were 500, 1000, 2000, 4000, and 8000 Hz. Each tone was five cycles long and multiplied by a Blackman window of the same duration. Tones were presented at a rate of 40 per s per frequency with alternating polarity for 100 s at each intensity. The activity recorded in the 30 ms following each tone was extracted and thresholds for each frequency were defined as the lowest intensity at which the root mean square (RMS) of the median response across presentations was more than twice the RMS of the median activity recorded in the absence of sound.

MUA was measured from recordings on each channel of the electrode array as follows: (1) a bandpass filter was applied with cutoff frequencies of 700 and 5000 Hz; (2) the standard deviation of the background noise in the bandpass-filtered signal was estimated as the median absolute deviation/0.6745 (this estimate is more robust to outlier values, e.g., neural spikes, than direct calculation); (3) times at which the bandpass-filtered signal made a positive crossing of a threshold of 3.5 standard deviations were identified and grouped into bins with a width of 1.3 ms. Only units with a signal correlation (across repeated trials of the speech in the test set) of 0.2 or higher were used for manifold learning and DNN training (420 ± 24 [mean ± SD] units from each animal out of 512 total channels).

For each animal, the MUA was represented as an $MxT$ matrix, where $M$ is the number of units and $T$ is the number of time bins. Separate matrices ${\mathit{R}}_{train}$ , ${\mathit{R}}_{test1}$ , and ${\mathit{R}}_{test2}$ were formed for the training set and each repetition of the test set (see ‘Speech’ above).

We applied PCA to ${\mathit{R}}_{train}$ (after subtracting the mean from each row) to obtain the PCs, ranked in order of the amount of neural variance they explain. We projected the activity in ${\mathit{R}}_{test1}$ onto a chosen number of PCs to obtain the latent dynamics within the manifold spanned by those PCs, yielding a new $DxT$ matrix ${\mathit{X}}_{test1}=\mathit{Z}{\mathit{R}}_{test1}$ , where $\mathit{Z}$ is the $DxM$ matrix containing the first $D$ PCs. We reconstructed the activity in ${\mathit{R}}_{test1}$ from the latent dynamics as ${\displaystyle {\hat{\mathit{R}}}_{test1}={\mathit{Z}}^{\mathit{T}}{\mathit{X}}_{test1}}$ (plus the originally subtracted means) and measured the total variance explained as the ratio of the covariance between ${\mathit{R}}_{test1}$ and ${\displaystyle {\hat{\mathit{R}}}_{test1}}$ and the square root of the product of their variances. We reconstructed the activity in ${\mathit{R}}_{test2}$ from the same latent dynamics as ${\displaystyle {\hat{\mathit{R}}}_{test2}={\mathit{Z}}^{\mathit{T}}{\mathit{X}}_{test1}}$ (plus the means of the rows of ${\mathit{R}}_{test2}$) and measured the signal variance explained as the ratio of the covariance between ${\mathit{R}}_{test2}$ and ${\displaystyle {\hat{\mathit{R}}}_{test2}}$ and the square root of the product of their variances. We defined the dimensionality of the signal manifold for each animal based on the number PCs required to explain 95% of the signal variance.

We measured the similarity between the signal dynamics for different animals as the variance explained after linear regression of one set of dynamics ${\mathit{X}}_{test1}$ onto another ${\mathit{Y}}_{test1}={\mathit{X}}_{test1}\beta +\epsilon$, where $\beta$ is a matrix of regression coefficients and $\epsilon$ is a vector of error terms.

DNNs were used to transform sound input into neural activity across four stages: (1) a SincNet layer (Ravanelli and Bengio, 2018) with 48 bandpass filters of length 32 samples, each with two learnable parameters (center frequency, bandwidth), followed by symmetric log activations $Y=\text{sgn}\left(x\right)\mathrm{l}\mathrm{o}\mathrm{g}(\left|x\right|+1)$; (2) a stack of five 1-D convolutional layers, each with 128 filters of length 32 samples and stride 2, followed by PReLU activations; (3) a 1-D bottleneck convolutional layer with a specified number of filters of length 32 and stride 1, followed by PReLU activations; and (4) a linear readout layer followed by exponential activations. The only hyperparameter that was varied was the number of filters in the bottleneck layer. For comparison with a linear–nonlinear (LN) model, we used a network with the same stages 1 and 4 and a single convolutional layer between them with 128 filters of length 256 samples and stride 1, followed by PReLU activations.

Models were trained to transform 24,414.0625 kHz sound input frames of length 8192 samples into 762.9395 Hz neural activity frames of length 192 samples (corresponding to temporal decimation by a factor of 5 via the strided convolutions in the encoder block plus a final cropping layer that removed 32 samples at the start and end of each frame to eliminate convolutional edge effects). Sound inputs were scaled such that an RMS of 1 corresponded to a level of 94 dB SPL. Training was performed in MATLAB on a local PC with GPUs (2x NVIDIA RTX 3080) with a batch size of 64 for 10 epochs and took about 8 hr for a typical model. The Adam optimizer was used with a learning rate of 0.0001. The optimization was framed as Poisson regression with loss function ${\displaystyle \sum _{M,T}\left(\hat{\mathit{R}}-\mathit{R}\mathrm{l}\mathrm{o}\mathrm{g}\left(\hat{\mathit{R}}\right)\right)}$ , where $\mathit{R}$ is the recorded neural activity, ${\displaystyle \hat{\mathit{R}}}$ is the network output, $M$ is the number of units, and $T$ is the number of time bins.

For each animal, data were split into training and test sets (see ‘Speech’ above). The training set was used to learn the optimal values of the DNN parameters. The final performance of the optimized network was measured on the test set by calculating the percent of the explainable variance in the recorded responses that was explained by the network outputs based on the ratio of the covariance between ${\mathit{R}}_{test1}$ and ${\displaystyle \hat{\mathit{R}}}$ and the covariance between ${\mathit{R}}_{test1}$ and ${\mathit{R}}_{test2}$ , where ${\displaystyle \hat{\mathit{R}}}$ is the network output and ${\mathit{R}}_{test1}$ and ${\mathit{R}}_{test2}$ are the recorded responses to the two presentations of the test speech.

For each animal, the activations in the bottleneck layer for all sounds from a given class (e.g., all pure tones or all consonants in noise) were extracted to form the $D_{b}xT$ signal dynamics matrix $\mathit{X}$, where $D_b$ is the number of bottleneck channels and $T$ is the number of time bins. For visualization, we applied PCA to the dynamics in $\mathit{X}$ and projected them onto a chosen number of PCs.

A 10-channel wide-dynamic range compression hearing aid was simulated using a program provided by Prof. Johsua Alexander (Purdue University) (Alexander and Masterson, 2015). The crossover frequencies between channels were 200, 500, 1000, 1750, 2750, 4000, 5500, 7000, and 8500 Hz. The intensity thresholds below which amplification was linear for each channel were 45, 43, 40, 38, 35, 33, 28, 30, 36, and 44 dB SPL. The attack and release times (the time constants of the changes in gain following an increase or decrease in the intensity of the incoming sound, respectively) for all channels were 5 and 40 ms, respectively. The gain and compression ratio for each channel were fit individually for each ear of each gerbil using the Cam2B.v2 software provided by Prof. Brian Moore (Cambridge University) (Moore et al., 2010). The gain before compression typically ranged from 10 dB at low frequencies to 30 dB at high frequencies. The compression ratios typically ranged from 1 to 2.5, that is, the increase in sound intensity required to elicit a 1 dB increase in the hearing output ranged from 1 dB to 2.5 dB when compression was engaged.

For each animal, the signal dynamics matrix $\mathit{X}$ was reshaped to yield $\tilde{\mathit{X}}$ , an $Sx\left(D_{b}x{T}_S\right)$ matrix, where $S$ is the number of sounds from a given class and $T_S$ is the number of times bins associated with an individual sound. An $SxS$ representational dissimilarity matrix (RDM) was formed, with each entry equal to one minus the correlation between a pair of rows in $\tilde{\mathit{X}}$ . To compute overall representational similarity, the upper triangular values (excluding the diagonal) from two $\tilde{\mathit{X}}$ matrices were reshaped into vectors and the correlation between them was computed. For speech, dynamics were averaged across all instances of each consonant before RDMs were computed.

To align two sets of signal dynamics, $\mathit{U}=\mathit{X}\mathit{A}$ and $\mathit{V}=\mathit{Y}\mathit{B}$ were computed using QR factorization and singular value decomposition (MATLAB cannoncorr), where $\mathit{X}$ and $\mathit{Y}$ are the matrices containing the original dynamics, $\mathit{A}$ and $\mathit{B}$ are the matrices containing the canonical components, and $\mathit{U}$ and $\mathit{V}$ are the aligned dynamics. Overall similarity after alignment was computed as ${\displaystyle \sum _{d=1}^{D_b}\rho \left(U_d,V_d\right)\ast \left(\rho {\left({\hat{X}}_d,\mathit{X}\right)}^2+\rho {\left({\hat{Y}}_d,\mathit{Y}\right)}^2\right)/2}$, with the second term in the product acting as the ‘weight for the correlation associated with each pair of CCs’ that is referred to in the ‘Results.’ $U_d$ and $V_d$ are the projections of $\mathit{X}$ and $\mathit{Y}$ onto the $d^{th}$ pair of canonical components, ${\displaystyle {\hat{X}}_d=X\ast \left(a_d\ast {\left(a_d^T{a}_d\right)}^{-1}\ast a_d\right)}$ and ${\displaystyle {\hat{Y}}_d=Y\ast \left(b_d\ast {\left(b_d^T{b}_d\right)}^{-1}\ast b_d\right)}$ are the reconstructions of $\mathit{X}$ and $\mathit{Y}$ from the $d^{th}$ pair of canonical components and $\rho$ denotes point-by-point correlation. To jointly align more than two sets of dynamics, multiway CCA was used (de Cheveigné et al., 2019) (MATLAB NoiseTools nt_mcca).

For each animal, the signal dynamics matrix $\mathit{X}$ was reshaped such that each row contained the dynamics for one consonant instance. A support vector machine was trained (MATLAB fitcecoc) to identify consonants from signal dynamics with a max-wins voting strategy based on all possible combinations of binary classifiers and tenfold cross-validation.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. For the purpose of Open Access, the authors have applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission.

The authors thank A de Cheveigné, S Ostojic, JÁ Gallego, and F Bruford for their advice. This work was supported by a Wellcome Trust Senior Research Fellowship (200942/Z/16/Z) and a grant from the UK Engineering and Physical Sciences Research Council (EP/W004275/1). The funding sources were not involved in study design, data collection and interpretation, or the decision to submit the work for publication.

All experimental protocols were approved by the UK Home Office (PPL P56840C21). Every effort was made to minimize suffering.

© 2023, Sabesan et al.

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