Noise-invariant representations of sound emerge along the canonical cortical hierarchy

This is an uncorrected proof. Figures Abstract Neurons in the auditory system must represent behaviorally relevant sounds in the presence of background noise (BN) to support noise-invariant perception and behavior. Although the primary auditory cortex (ACtx) has been implicated in constructing noise-invariant representations, it remains unclear which excitatory subpopulations within ACtx carry out this transformation from noise-dependent to noise-invariant coding. To address this, we presented pure tones with and without continuous BN to head-fixed mice and used two-photon calcium imaging to record sound-evoked activity from three major excitatory subpopulations in ACtx: layer (L)2/3 intratelencephalic (IT) neurons, L5 IT neurons, and L5 extratelencephalic (ET) neurons. L2/3 IT neurons exhibited strong noise dependence at the level of single-neuron responses, pairwise interactions, and population representations. In contrast, deep-layer pathways showed greater noise invariance, with L5 IT neurons preserving stable representations most consistently and L5 ET neurons exhibiting more limited invariance at the population level. These findings reveal a functional division of labor in ACtx, in which superficial neurons remain noise-dependent and deep-layer broadcast pathways, particularly L5 IT, preferentially carry noise-invariant representations, suggesting that excitatory subpopulations contribute differentially to the construction and propagation of noise-invariant codes. Citation: Suarez Omedas T, Williamson RS (2026) Noise-invariant representations of sound emerge along the canonical cortical hierarchy. PLoS Biol 24(7): e3003915. https://doi.org/10.1371/journal.pbio.3003915 Academic Editor: Manuel S. Malmierca, Universidad de Salamanca, SPAIN Received: December 19, 2025; Accepted: July 8, 2026; Published: July 20, 2026 Copyright: © 2026 Suarez Omedas, Williamson. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: The data generated in this study have been deposited in an open-access Zenodo repository and can be accessed here: https://doi.org/10.5281/zenodo.21111739. Custom scripts used to analyze the data have been deposited to the same Zenodo repository, as well as in a GitHub repository, which can be found here: https://github.com/WilliamsonLab-Pitt/BackgroundNoise-Characterization. Funding: This work was supported by NIH/NIDCD (https://www.nidcd.nih.gov/) grants R21DC018327 and R01DC020459, and the Klingenstein-Simons Fellowship in Neuroscience (https://klingenstein.org/esther-a-joseph-klingenstein-fund/neuroscience/) to RSW. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Abbreviations: ACtx, auditory cortex; BF, best frequency; BN, background noise; ET, extratelencephalic; FAR, false alarm rate; FRAs, frequency response areas; HR, hit rate; IC, inferior colliculus; IMI, information modulation index; IT, intratelencephalic; No-BN, without BN; PCA, principal component analysis; PCs, principal components; PV, parvalbumin; ReLU, rectified linear unit; RMA, reduced major axis; ROIs, regions of interest; SOM, somatostatin; SNR, signal-to-noise ratio; TV, total variation. Introduction The auditory system continuously faces the task of accurately representing sound features, even if they are embedded in background noise (BN). Robust, or ideally invariant, coding of acoustic attributes such as frequency and intensity enables animals to detect threats and allows humans to understand speech in complex acoustic scenes (e.g., the cocktail-party setting). The construction of such a noise-invariant neural code, one that represents acoustic characteristics regardless of BN, poses a central challenge for auditory processing. As BN increases and the signal-to-noise ratio (SNR) worsens, the acoustic waveform at the ear is distorted, cochlear responses are reshaped, and these changes propagate through the ascending auditory pathway [1–9]. Despite extensive work on BN effects across numerous auditory brain regions [2,10–14], the precise locus and circuit mechanisms by which noise‑invariant representations first emerge remain unresolved. Sounds reaching the ear are decomposed by the cochlea into frequency components that are relayed along the ascending auditory pathway [15,16]. When sounds are embedded in BN, their spectrotemporal structure becomes distorted, producing measurable changes in neural representations in the auditory periphery [10,11], midbrain [12,17–19], and cortex [2,13,14]. BN can modify both single-neuron and population responses of neurons in the ascending auditory pathway, shifting firing rates and reshaping population activity patterns [10–12,17], degrading spatial cues [10], suppressing sound-evoked activity [2,20], and modulating baseline firing [1]. Across the pathway, representations generally become more noise‑invariant as signals ascend toward auditory cortex (ACtx) [1,9]; responses in primary ACtx are closer to noise‑invariant than in the periphery yet remain measurably affected by BN [4,21], whereas nonprimary fields often exhibit stronger invariance [4,9,22]. These observations identify ACtx as a critical locus where invariance to BN is refined, motivating the question of how cortical circuits support this transformation. ACtx is a hub for sound processing and the brain-wide broadcast of auditory information, roles that are particularly important in complex acoustic environments where sounds are embedded in BN [7]. Inactivation of ACtx significantly impairs pure tone detection in BN, and disrupting somatostatin‑ or parvalbumin‑positive interneurons produces similar behavioral deficits [6,23], underscoring a role for ACtx in supporting noise-invariant perception. Building on these findings, recent work suggests that ACtx transforms noise-dependent inputs into noise-invariant representations through adjustments of excitatory-inhibitory balance [2,5,6] and cholinergic neuromodulation [3]. Nevertheless, the computations that implement noise invariance remain unclear, in part because prior studies have not considered the functional diversity of excitatory subpopulations within the cortical microcircuit. Within ACtx, excitatory neurons are stratified across layers and projection classes [24–29]. Two major subpopulations, intratelencephalic (IT) and extratelencephalic (ET) neurons, differ in their anatomical, genetic, and functional properties [30–32]. In ACtx, layer (L)2/3 IT neurons form dense intracortical networks and are positioned to perform local computations on incoming sensory input [27]. In contrast, L5 IT and ET neurons constitute broadcast pathways: L5 IT neurons project widely within the telencephalon [29,31,33–36], whereas L5 ET neurons target subcortical structures such as the inferior colliculus (IC) and thalamus [28,29,32]. These subpopulations make distinct contributions to cortical function, including learning perceptually relevant information [25], amplifying sensory signals after injury [35], and regulating thalamic transmission [28]. Given these divergent roles and projection patterns, we tested whether L2/3 neurons are more susceptible to BN, and whether L5 IT and L5 ET neurons preferentially transmit noise‑invariant signals to downstream targets. We examined noise invariance at three analytical levels of sensory representation (single-neuron, pairwise, and population) in three major ACtx excitatory subpopulations: L2/3, L5 IT, and L5 ET. Using in vivo two-photon calcium imaging in mice, we recorded responses to pure tones presented with and without BN. L2/3 neurons exhibited pronounced noise dependence at all three levels of sensory representation, while both L5 IT and L5 ET populations exhibited robust, noise-invariant coding. Thus, while superficial neurons alter their representations in the presence of noise, deep-layer output pathways maintain stable representations, indicating that noise invariance is preferentially expressed within the cortical output stages of ACtx. Results To assess noise invariance in sound representations across excitatory subpopulations of ACtx, we performed in vivo two-photon calcium imaging to record activity from three targeted groups: L2/3 (n = 961 neurons; N = 7 mice), L5 IT (n = 2,576; N = 6) and L5 ET (n = 566; N = 4) (Fig 1A). GCaMP8s expression was selectively driven in each subpopulation using genetic and viral strategies (see Materials and methods). Head-fixed mice were imaged through a cranial window over right ACtx, while pure tones were delivered monaurally to the left ear (Fig 1B). Tones spanned 4–45 kHz in half-octave steps and 20–70 dB SPL in 10 dB SPL steps (8 frequencies × 6 intensities = 48 unique conditions), each repeated 20 times. Each mouse completed two sessions: one without BN (No-BN) and one with continuous BN at 50 db SPL (Fig 1C, 1D). Fluorescence calcium traces were extracted and deconvolved using standard approaches [37,38]. All deconvolved responses were z-scored relative to the pre-stimulus baseline for each session (Fig 1E). (A) Schematic illustrating excitatory subpopulations in auditory cortex (ACtx). (B) Two-photon imaging setup for recordings in awake, head-fixed mice. (Created in BioRender. Suarez Omedas, T. (2026) (https://BioRender.com/b9y9ncp) is licensed under CC BY 4.0). (C) Schematic of acoustic stimulation in the absence (No-BN) and presence (BN) of continuous background noise. (D) Example fields of view (FoVs) from each recorded subpopulation. Imaging depths were 206 m (L2/3), 415 m (L5 IT), and 494 m (L5 ET). (E) Example sound-evoked calcium responses and corresponding z-scored deconvolved spikes at the best frequency for one representative neuron from each FoV shown in D. BN attenuates single-neuron responses in L2/3 We first asked whether single‑neuron responses in each excitatory subpopulation are noise‑invariant. To do so, we analyzed two complementary aspects of single‑neuron activity: (i) mean stimulus‑locked responses, summarized by frequency and intensity tuning curves, and (ii) trial‑to‑trial response distributions, which capture variability not reflected in the mean. Tuning analyses assessed additive and multiplicative changes between No‑BN and BN conditions, whereas distributional analyses quantified stimulus information and its modulation by BN. For each sound-responsive neuron (see Materials and methods), we computed frequency response areas (FRAs) by averaging sound-evoked activity across all trials for each frequency–intensity combination (Fig 2A). From these FRAs, we derived frequency and intensity tuning curves for the No-BN and BN conditions by marginalizing over the complementary stimulus dimension. To compare frequency tuning across noise conditions, we aligned each neuron’s tuning curve to its best frequency (BF) and averaged the resultant BF-centered curves for each subpopulation. BF-centered frequency tuning curves showed a significant reduction in L2/3, but no change in L5 IT or ET (Fig 2B top row, two-way ANOVA, main effect for BN, L2/3: p = 0.0135; L5 IT: p = 0.9014; L5 ET: p = 0.8156). This reduction was accompanied by a significant interaction between frequency and BN in L2/3, concentrated at BF (interaction between frequency and BN: ; Tukey–Kramer post hoc test for BF: ). Average intensity tuning curves likewise decreased in L2/3 but not in L5 IT or ET (Fig 2B bottom row, two-way ANOVA, main effect for BN, L2/3: , L5 IT: p = 0.8450, L5 ET: p = 0.8609). These trends in average tuning curves were also observed in curves constructed from calcium dF/F rather than deconvolved spikes (S1A Fig). To ensure that these changes in tuning curves were not driven by neurons’ No-BN responses being too close to their physiological floor or ceiling, we split the responsive neurons for each subpopulation into low- and high-responding groups according to whether their firing at BF was below or above the subpopulation median. The general trend of suppressed tuning curves in L2/3 and noise-invariant tuning curves in L5 IT and L5 ET was preserved in both low- and high-responding groups (S2A, S2B Fig). Together, these results indicate that, on average, L2/3 neurons’ tuning curves are suppressed in the presence of BN, while L5 IT and L5 ET curves remain unchanged. (A) Example frequency response area (FRA) from an L2/3 neuron in the absence (No-BN, left) and presence (BN, right) of background noise. Both panels use the same color scale, with lighter colors indicating larger responses. (B) Average best-frequency-centered frequency tuning curves (top row) and average intensity tuning curves (bottom row) for each subpopulation. (C) Schematic illustrating linear transformations between tuning curves across BN conditions (left) and reduced major axis (RMA) regression used to quantify these changes (right). Dotted line indicates the unity line. (D) Example frequency tuning curves for a single neuron recorded in No-BN and BN (left) and corresponding RMA regression (right). Estimated slope and intercept coefficients are shown above the plot. (E) Same as D, but for intensity tuning curves. (F) Distributions of RMA slope coefficients (left) and intercept coefficients (right) that differed significantly from 1 and 0, respectively, for frequency (magenta) and intensity (cyan) tuning curves. Number of neurons with significant regressions for L2/3, L5 IT and L5 ET respectively: n = 272, 204, 88 frequency slopes, n = 222, 140, 65 intensity slopes, n = 161,113,49 frequency intercepts, n = 107,82,43 intensity intercepts. Percentage of neurons with at least one significant coefficient (of the four frequency and intensity slope and intercept coefficients) for L2/3, L5 IT and L5 ET respectively: 87.7%, 89.0%, and 83.4%. (G) Proportions of significant RMA coefficients classified as additive, subtractive, multiplicative, or divisive for each subpopulation. Same n as in F. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. Alongside stability in tuning curves, we calculated the reliability of each responsive neuron’s responses by quantifying the variability of sound-evoked activity to repetitions of the same sound [26]. We found that L2/3 neurons showed a small reduction in single-cell reliability in BN, while L5 IT and L5 ET neurons did not show a significant change (S1B Fig). Although averaged tuning curves showed that L2/3 responses were altered differently from those in L5 IT and L5 ET, these averages do not capture how individual neurons adjusted their tuning curves in BN. To quantify neuron-by-neuron changes that underlie the population-level trends, we performed reduced major axis (RMA) regression between each responsive neuron’s No-BN and BN tuning curves (Fig 2C) [35,39]. This approach estimates how much a tuning curve shifts (additive/subtractive) and/or scales (multiplicative/divisive) in BN (Fig 2C). Each neuron produced four coefficients: a slope and intercept for its frequency tuning curve, and a slope and intercept for its intensity tuning curve (Fig 2D, 2E). Slope values greater than one indicated multiplicative scaling, whereas values less than one indicated divisive scaling. Similarly, intercept coefficients greater than zero indicated additive shifts, whereas values less than zero indicated subtractive shifts. Each coefficient was tested for significance (see Materials and methods), and only significant coefficients were analyzed. The distribution of slope coefficients differed across subpopulations (Fig 2F left, Kruskal–Wallis test, main effect for frequency slope: ; main effect for intensity slope: ). L2/3 neurons showed lower slope values than both L5 IT and ET populations for frequency and intensity tuning (Dunn–Šidák post hoc test for frequency and intensity curves, respectively, L2/3-L5 IT: and , L2/3-L5 ET: p = 0.0114 and p = 0.0021, L5 IT-L5 ET: p = 0.8289 and p = 0.9683), indicating that BN produced a stronger divisive scaling of responses in L2/3 than in either deep-layer subpopulation. Intercept coefficients for frequency tuning curves also differed across subpopulations (Fig 2F right, Kruskal–Wallis test, main effect for frequency intercept: p = 0.0020), with L2/3 neurons showing lower intercepts than L5 IT and L5 ET neurons (Dunn–Šidák post hoc test, L2/3-L5 IT p = 0.0304, L2/3-L5 ET: p = 0.0058, L5 IT-L5 ET: p = 0.6027). However, no measurable differences in intensity tuning curve intercepts were recorded (Fig 2F, right, Kruskal–Wallis test, main effect for intensity intercept: p = 0.6599). To assess overall trends in tuning curve modulation across subpopulations, we computed, for each subpopulation, the proportion of neurons showing suppressive versus enhancing changes. Deviations above or below 50% indicate whether a subpopulation tends to increase or decrease its responses in BN. If the effect were not subpopulation-specific, these proportions would be similar across subpopulations. We found that the proportions of multiplicative versus divisive coefficients differed between subpopulations for both frequency and intensity slopes (Fig 2G left, separate chi-squared tests for frequency and intensity slopes, respectively; and , S1, S2 Tables), as well as for additive versus subtractive frequency intercepts (Fig 2G right, chi-squared test for frequency intercepts: p = 0.0026, S1 Table). In L2/3 neurons, the proportions of frequency and intensity slopes were strongly biased toward divisive changes (binomial test for frequency and intensity slopes: and ). In contrast, L5 IT and L5 ET neurons showed proportions closer to 50%, with the only significant biases favoring enhancement of tuning curves via multiplicative or additive changes, specifically in the intensity slopes of L5 IT neurons (binomial test: p = 0.0342) and in the frequency intercepts of L5 ET neurons (binomial test: p = 0.0094). Together, these results indicate that, although individual neurons in all subpopulations can either enhance or suppress their tuning, L2/3 neurons tended to exhibit predominantly divisive changes, whereas L5 IT and ET neurons maintain more balanced, and in some cases mildly enhancing, tuning shifts. While tuning curves and single-cell reliability characterize the magnitude and consistency of single-neuron responses, they do not quantify how much stimulus-specific information each neuron’s response distribution carries. To quantify this, we applied an information-theoretic framework to measure how much of the variability in each neuron’s responses was explained by the auditory stimulus (Fig 3A). For each responsive neuron, we computed the distribution of its sound-evoked responses across trials and then quantified how much auditory information it encoded by computing the mutual information between responses and stimuli I(resp;stim) [40–43]. Mutual information approaches zero when a neuron’s activity is independent of sound frequency and intensity, and increases as responses become more stimulus-driven. Across all three subpopulations, single neurons showed a consistent reduction in stimulus-response mutual information in the presence of BN (Fig 3C, Wilcoxon rank sum test, L2/3: , L5 IT: , L5 ET: ). To enable a direct comparison of the effect of BN on information across subpopulations, we calculated an information modulation index (IMI) ranging from −1 to –1, which indicates whether a neuron conveyed more information about the stimuli in No-BN or BN (Fig 3A). IMIs near 1 reflect greater encoding in BN, whereas IMIs near −1 indicate a loss of stimulus information in BN (Fig 3B). All subpopulations contained neurons with positive and negative IMIs, revealing diverse BN-induced changes in single-neuron encoding (Fig 3D, Kruskal-Wallis test, main effect for subpopulation: ). On average, L2/3 neurons exhibited more negative IMIs than L5 IT and ET populations (Fig 3E; Dunn–Šidák post hoc test; L2/3-L5 IT ; L2/3-L5 ET p = 0.0011), whereas the two L5 subpopulations did not differ from each other (Dunn-Šidák post hoc test, L5 IT-L5 ET p = 0.1425). These findings indicate that L2/3 neurons reduce stimulus-related information in BN, whereas L5 IT and ET neurons maintain more noise-invariant response distributions. Together, these results show that BN induces stronger response suppression and reduced information encoding in L2/3, while L5 IT and ET neurons preserve balanced tuning and noise-invariant representations. (A) Schematic illustrating mutual information between neural responses and the auditory stimulus, I(resp;stim), in relation to the entropy of each variable. (B) Mathematical formulation of mutual information between neural activity and stimulus identity, along with the definition of the information modulation index (IMI). (C) Distribution of mutual information values of responsive neurons for each subpopulation in No-BN and BN. (D) Cumulative distributions of IMI values for each excitatory subpopulation (L2/3: n = 423, L5 IT: n = 290, L5 ET: n = 163). (E) Mean IMI values corresponding to the distributions in D. Same n as in D. Error bars denote mean s.e.m. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. BN reduces shared neural variability across spatial scales in IT but not ET neural responses While single-neuron analyses reveal how individual responses change with BN, they do not capture how activity is coordinated within the densely interconnected cortical circuit. To determine whether BN alters coordinated activity between neurons, we quantified pairwise functional connectivity using two complementary measures: noise correlations and signal correlations. If BN alters local circuit interactions, its effects should be reflected in the spatial organization of pairwise noise and signal correlations. Noise correlations quantify the shared trial-to-trial variability between two neurons after removing stimulus-driven activity, providing an estimate of their functional coupling [44–51]. To test whether BN modulates this coupling, we examined how noise correlations between sound-responsive neurons varied as a function of intersomatic distance (see Materials and methods), distinguishing whether BN preferentially affects local subnetworks or acts broadly across ACtx. Consistent with previous studies [50,52], the strongest noise correlations were observed at short intersomatic distances (Fig 4C, two-way ANOVA, main effect for intersomatic distance, L2/3: , L5 IT: , L5 ET: ). BN reduced noise correlations in L2/3 and L5 IT neurons, but not in L5 ET neurons (Fig 4C, two-way ANOVA, main effect for BN, L2/3: p = 0.0089, L5 IT: p = 0.0022, L5 ET: p = 0.1302). In all subpopulations, this BN-induced reduction did not depend strongly on intersomatic distance, as indicated by nonsignificant interactions (Fig 4C, two-way ANOVA, interaction between BN and intersomatic distance, L2/3: p = 0.9398, L5 IT: p = 0.9768, L5 ET: p = 0.4861). (A) Mean-subtracted trial-by-trial responses for an example pair of simultaneously recorded neurons (left) and the corresponding noise correlation matrix for all neuron pairs within an example field of view (FoV; right). (B) Same as A, but showing signal correlations computed from tuning curves for the same example neurons. (C) Mean noise correlations plotted as a function of intersomatic distance under No-BN and BN conditions (L2/3: n = 9,266, L5 IT: n = 3,720, L5 ET: n = 2,258 neuron pairs). (D) BN-induced change in noise correlations at short (≤200 m) and long (>200 m) intersomatic distances. (E) Same as C, but for signal correlations (same n as in C). (F) Same as D, but for signal correlations (same n as in D). Shaded regions denote mean s.e.m. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. However, because the BN-induced reduction in noise correlations was asymmetric across distance, with larger effects at short distances and smaller effects at long distances (Fig 4C, right), we assessed whether BN differentially affected noise correlations across spatial scales by comparing BN-induced changes at short () and long distances (). L5 ET neurons showed a stronger BN-induced reduction in noise correlations at short distances (Fig 4D, Wilcoxon rank sum test, L5 ET: p = 0.0285), whereas L2/3 and L5 IT neurons showed similar reductions at short and long distances (Fig 4D, Wilcoxon rank sum test, L2/3: p = 0.9239, L5 IT: p = 0.8463). These results indicate that BN broadly reduces shared variability across spatial scales in L2/3 and L5 IT populations, but acts more locally within L5 ET networks. Because the BN used in this study was generated using a random seed, the instantaneous frequency content at the time of stimulus presentation could vary between repetitions of the same stimulus. If ACtx neurons encoded these fluctuations, noise correlations could be artificially reduced as a result. To test whether ACtx neurons encode random noise differently from frozen noise, we ran a control experiment in which we presented 400 bursts of a frozen noise waveform (identical on every trial) followed by 400 bursts of randomly generated white noise (a new waveform on every trial) while recording from L2/3 ACtx neurons (S3A Fig, n = 110). We computed noise correlations between all pairs of simultaneously recorded neurons (S3B Fig), and found that on average the noise correlations did not differ between frozen and random noise (S3C, S3D Fig). We note, however, that this control used discrete noise bursts rather than continuous BN, and therefore provides partial but not exhaustive evidence against trial-varying contamination of our noise correlation estimates. Next, we assessed pairwise functional connectivity through signal correlations among responsive neurons, defined as the correlation between the tuning curves of two neurons (Fig 4B). BN induced a decrease in signal correlations only in L2/3 neurons (Fig 4E left, two-way ANOVA, main effect for BN, L2/3: ), whereas L5 IT and L5 ET neurons showed no significant change between BN conditions (Fig 4E center and right, two-way ANOVA, main effect for BN, L5 IT: p = 0.3666, L5 ET: p = 0.3435). For all subpopulations, the effect of BN on signal correlations did not differ between short and long intersomatic distances (Fig 4F, Wilcoxon rank sum test, L2/3: p = 0.1262, L5 IT: p = 0.1289, L5 ET: p = 0.4635). Taken together with our prior analyses, these results indicate that BN not only reduces L2/3 response amplitudes, but also makes their tuning curves less similar to one another, whereas L5 IT and L5 ET neurons maintain stable tuning similarity across BN conditions. Population-level decoding of pure tones is noise-invariant in L5 IT Although single-neuron activity and pairwise correlations reveal how BN modulates inputs to individual neurons and pairs, neural representations ultimately arise from the collective output of entire populations [53–57]. We therefore asked two key questions regarding how BN influences population-level stimulus representations: 1) does BN reduce the ability of neural populations to detect the presence of a pure tone, and 2) does BN impair their ability to discriminate between different pure tone frequencies? To evaluate the noise invariance of population-level representations, we performed two decoding analyses to address both detection and discrimination of pure tones. We trained classifiers on trial-wise population activity (responsive and nonresponsive) to test whether each subpopulation could reliably detect the presence of a sound and identify its frequency across BN conditions. To capture potential nonlinear interactions among neurons and to maintain a consistent architecture across decoding analyses, we first trained artificial neural networks to classify whether a sound was present on each trial based solely on sound-evoked activity (see Materials and methods) (Fig 5A). Because classification performance depends on the number of neurons provided to the classifier, we trained all classifiers on randomly selected subsets of 40 neurons. This choice balanced the need for sufficient neurons to support reliable classification while avoiding oversampling in smaller FoVs, ensuring robust and comparable performance across FoVs. Each network consisted of an input layer of 40 units, two hidden layers of 16 units, and a single readout unit. Hidden layers used a ReLU activation function, and the readout was passed through a sigmoid nonlinearity, with outputs above 0.5 classified as sound-present. We cross-validated all decoding analyses by separating trials into independent training sets and measuring accuracy in the testing sets. We trained independent classifiers for each frequency to ensure that any reduction in classification performance under BN reflected diminished sound detection, rather than reductions arising from mismatches in frequency tuning between the trials used in the training and testing sets. For some example FoVs, detection performance in BN was markedly reduced (Fig 5B). Comparing average detection performance between No-BN and BN sessions revealed that L2/3 and L5 ET neurons exhibited reduced detection performance under BN, whereas L5 IT neurons showed noise-invariant detection of pure tones (Fig 5D, paired t test, L2/3: , L5 IT: p = 0.4586, L5 ET: p = 0.0073). (A) Schematic of the artificial neural network used for binary detection decoding. (B) Example neurometric decoding curves from a representative L2/3 FoV in BN (left) and No-BN (right). The classifier was trained on 40 simultaneously recorded neurons and evaluated at 8 kHz only. (C) Paired scatter plot of cross-validated detection performance (d’) for each frequency–intensity combination under No-BN and BN conditions. n denotes the number of binary classifiers. (D) Mean detection performance (d’) for each excitatory subpopulation, averaged across decoding runs shown in C. (E) Schematic of the artificial neural network used for multinomial discrimination decoding. (F) Example confusion matrices from a representative L2/3 FoV in BN (left) and No-BN (right). The classifier was trained on 40 simultaneously recorded neurons and evaluated at 70 dB SPL only. (G) Paired scatter plot of cross-validated discrimination accuracy for each stimulus intensity under No-BN and BN conditions. n denotes the number of multinomial classifiers. (H) Mean discrimination accuracy for each excitatory subpopulation, averaged across decoding runs shown in G. Error bars denote mean s.e.m. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. We noted that L5 IT classifiers’ detection performance was on average lower than that of L2/3 and L5 ET classifiers in No-BN. To ensure that the BN-induced reductions in decoding performance of L2/3 and L5 ET did not simply reflect a starting-point difference, we restricted each subpopulation’s classifiers to the d-prime range spanned by L5 IT (between −0.5 and 2.5 d-prime; S4A Fig). We found that within this matched range, both L2/3 and L5 ET classifiers continued to show a BN-induced reduction in decoding performance (S4B Fig), while L5 IT classifiers remained noise-invariant. This argues against a starting-point artifact and supports a genuine subpopulation-specific transformation. To answer whether ACtx neural subpopulations can reliably discriminate pure tone frequencies, we next trained neural networks to classify each trial into one of the eight possible frequencies (Fig 5E). To make discrimination decoding directly comparable to detection decoding and to allow for the same degree of nonlinear interaction in the hidden layers, we used an identical architecture except for the readout: the output layer contained eight units instead of one. Each output unit corresponded to a single frequency, and a softmax function was applied to normalize the outputs and select the decoded frequency on each trial (Fig 5F). In this multinomial task, decoding accuracy remained stable for L5 IT neurons but decreased significantly for L2/3 and L5 ET neurons (Fig 5H, paired t test, L2/3: , L5 IT: p = 0.1521, L5 ET: p = 0.0026). Thus, L5 IT neural populations preserve both detection and discrimination decoding performance across BN conditions, while both L2/3 and L5 ET neural populations show reduced decoding performance for both sound detection and frequency discrimination in BN. To assess whether these BN-induced decoding effects depend on tone intensity relative to the BN level (50 dB SPL), we separately analyzed classifiers trained on tones above and below 50 dB SPL (excluding tones at 50 dB SPL; S4C, S4D Fig). For tones above 50 dB SPL, both detection and discrimination accuracy decreased significantly under BN in L2/3, and discrimination accuracy decreased significantly under BN in L5 ET; L5 IT decoding remained noise-invariant in both metrics. For tones below 50 dB SPL, BN-induced reductions were smaller in magnitude but followed the same direction across all subpopulations. These results indicate that the subpopulation-specific patterns of noise invariance we report hold across SNR regimes, with the strongest BN-induced decoding decreases observed when tones are audible above the noise floor. L5 IT neurons maintain neural manifold geometry While population-level decoding provides an estimate of how well each subpopulation encodes the specific pure-tone features used here, it does not address how many additional features (for example, more frequencies or stimulus dimensions) the same population could, in principle, encode. To assess the impact of BN on the structure and capacity of neural representations, we examined the geometry of population activity across conditions. Manifold geometry analysis [58] provides a way to quantify the efficiency of a population code by estimating the capacity of a neural population to represent multiple perceptual features. Recent work has shown that neural population activity can be described in terms of neural manifolds and their effective dimensionality, which capture the dominant structure of population responses [58–60]. When sound-evoked responses are embedded in an n-dimensional space (one axis per neuron), activity trajectories typically lie on a lower-dimensional manifold rather than filling the entire space [53,61]. Within this framework, responses to different stimuli (e.g., pure tone frequencies) form distinct manifold objects in neural space, each consisting of the set of response patterns associated with a given stimulus. The geometry of these manifold objects, particularly their size and dimensionality, constrains how efficiently a population can represent multiple stimuli [58]. For example, in a simulated population of three neurons, responses to three different stimuli might form manifold objects that resemble a line, disk, or sphere (Fig 6A, top). Lower-dimensional objects (e.g., lines and disks embedded in three dimensions) can be packed more efficiently in neural space, which promotes separability between manifold objects and increases the number of objects that can be encoded simultaneously. In contrast, larger or higher-dimensional objects quickly constrain the population representational capacity by making manifold objects less linearly separable [58] (Fig 6A, bottom). Thus, smaller and lower-dimensional manifolds correspond to a more efficient neural code, while larger and higher-dimensional manifolds reflect poorer encoding. (A) Simulated examples of manifold objects encoded by three neurons, illustrating differences in manifold geometry. Insets show the manifold capacity (), radius (), and dimensionality () for the highlighted light pink manifold object in both examples. (B) Manifold geometry metrics for each excitatory subpopulation, with manifold objects constructed by pooling all intensities for each frequency (L2/3: n = 961, L5 IT: n = 2,576, L5 ET: n = 566 neurons). (C) Manifold geometry metrics as a function of stimulus intensity, with manifold objects constructed from individual frequency–intensity combinations. Same n as in B. (D) Example sound-evoked population activity from a L2/3 FoV projected onto the first two principal components (left), and total variation (TV) of the population activity across principal components for each BN condition (right). The dotted line indicates the number of principal components required to explain 60% of the variance for this FoV. (E) Same as D, shown for an example L5 IT FoV. (F) Difference in total variation between No-BN and BN conditions for each FoV, shown separately for each subpopulation (L2/3: n = 10, L5 IT: n = 11, L5 ET: n = 5 FoVs). Error bars denote mean s.e.m. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. Using this framework, we tested how BN affects manifold geometry across excitatory subpopulations. We quantified three established metrics of manifold structure: capacity (), radius () and dimensionality () which together reflect the efficiency of population-level encoding [58,59,62]. Effective encoding is characterized by high , low , and low , whereas reduced efficiency is marked by lower capacity and larger, higher dimensional manifolds (Fig 6A). In this simplified example, the neural manifold is composed of three neurons, which sets the maximum possible manifold dimensionality to 3. We first constructed manifold objects by pooling responses across all intensities for each frequency under No-BN and BN conditions, yielding eight objects per condition. Because manifold metrics depend on the dimensionality of the neural population, we analyzed randomly selected subsets of 40 simultaneously recorded neurons (responsive and nonresponsive) and resampled across subsets to approximate trends in the full population, which sets the maximum manifold dimensionality to 40. L2/3 and L5 ET neurons showed significant BN-dependent changes in all three metrics (Fig 6B, Wilcoxon signed rank test for , and , respectively, L2/3: , , , L5 ET: , , ). In contrast, L5 IT neurons showed no significant BN-related differences in manifold capacity, radius, or dimensionality (Fig 6B, Wilcoxon signed rank test for , and , L5 IT: p = 0.1148, p = 0.1488, p = 0.1363). To examine the effects of BN on manifold geometry at a finer stimulus scale, we repeated this analysis using one manifold per frequency–intensity combination, yielding 48 manifold objects per BN condition. This allowed us to assess how BN affected the geometry of representations for specific acoustic stimuli. L2/3 and L5 ET manifolds shifted toward less efficient geometry (Fig 6B, 6C, two way ANOVA, main effect of BN for , and , respectively, L2/3: , , , L5 ET: , , ). In contrast, L5 IT manifolds showed noise-invariant capacity and dimensionality, with BN selectively increasing manifold radius (two way ANOVA, main effect of BN for , and , respectively, L5 IT: p = 0.1097, p = 0.0329, p = 0.0546). These results demonstrate that the manifold geometry of L2/3 and L5 ET populations is particularly susceptible to BN, while L5 IT neurons preserve a more noise-invariant manifold structure. Although manifold geometry analysis characterizes the structure of individual manifold objects, it does not capture the global spread of all objects within the neural representational space. To assess whether BN alters this global dispersion of sound-evoked population activity, we first visualized the data using principal component analysis (PCA; see Materials and methods). In some FoVs, the first two principal components (PCs) revealed a clear contraction of the span of stimulus representations under BN (Fig 6D, left), while in others the overall spread appeared unchanged (Fig 6E, left). To quantify these differences, we identified for each FoV the minimum number of PCs that explained at least 60% of the variance in sound-evoked activity under both BN conditions (Fig 6D, 6E, right). We then projected the data into this reduced space and computed the manifold size as the total variation (TV) of the projected activity (see Materials and methods). TV provides a robust scalar measure of the effective radius of the point cloud in lower-dimensional projections of varying dimensionality, enabling comparisons across FoVs. This analysis revealed a significant reduction in manifold size for L2/3 populations under BN (Fig 6F, Wilcoxon signed rank test, L2/3: p = 0.0020), while the L5 IT and ET populations did not show a change in TV under BN (Wilcoxon signed rank test, L5 IT: p = 0.5771, L5 ET: p = 0.1250). Thus, the global representational space contracted in L2/3 under BN, while remaining effectively noise invariant in L5 IT and L5 ET populations. These two analyses, manifold geometry and manifold size, revealed an apparent discrepancy for L5 ET. In L2/3, BN both reduced the efficiency of manifold geometry and contracted overall manifold size, whereas L5 IT remained noise-invariant in both measures. In contrast, L5 ET neurons showed less efficient manifold geometry under BN, but preserved their global manifold size. Although this pattern is difficult to visualize directly, it implies that individual manifold objects became larger and more high-dimensional without increasing the overall spread of the full set of objects. This could occur if manifolds expand inward (toward the origin) or toward one another rather than outward, two possibilities that are not mutually exclusive. This scenario is consistent with the decoding results (Fig 5D and Fig 5H), where L5 ET detection and discrimination performance decline under BN, as would be expected if near-boundary trials are displaced toward neighboring frequencies or toward the origin in neural space. Overall, BN degrades the efficiency of population-level encoding within manifold objects in L5 ET, while the total neural subspace used for population-level representations remains unchanged. Discussion We imaged sound-evoked responses in defined excitatory subpopulations of the ACtx with in vivo two-photon microscopy. To distinguish how different circuit elements contribute to noise invariance, we compared an excitatory subpopulation primarily involved in local processing (L2/3) with two deep-layer subpopulations that broadcast information to distant targets (L5 IT and L5 ET). Although the neural representations of sounds differed across subpopulations at baseline, we asked whether each subpopulation’s encoding of pure tones was preserved or degraded when stimuli were embedded in BN. All three subpopulations adjusted their responses when tones were embedded in BN, but noise invariance was concentrated in the broadcast pathways. L2/3 neurons showed clear noise dependence, including suppressed single-neuron responses (Figs 2 and 3), decreased pairwise correlations (Fig 4), and reduced fidelity in population-level encoding of tone identity (Figs 5 and 6). Under identical experimental conditions, L5 IT neurons maintained stable single-neuron and population-level representations, with noise-related differences appearing only in pairwise correlations (Fig 4C). L5 ET neurons expressed a more limited form of noise invariance: their single-neuron and pairwise responses were largely stable across BN conditions, whereas their population decoding performance and manifold structure were not. Together, these results show that excitatory subpopulations in ACtx rely on different representational levels to preserve sensory information in noise and reveal a functional stratification of noise invariance across the cortical microcircuit. Significance of noise invariance for sound processing ACtx plays a critical role in extracting behaviorally relevant sound features [6,25,63–65], and the canonical cortical microcircuit carries and transforms sensory information within ACtx [31]. In this circuit, thalamocortical inputs primarily innervate L4, which relays information to L2/3, then to L5 and L6, where signals are broadcast widely throughout the brain [28,29,32,66]. L2/3 neurons are the first major cortical recipients of L4 input and provide dense, complex projections to L5 [27], a principal output layer with extensive long-range targets [32,67–72]. Along the ascending auditory pathway, sound representations become increasingly noise-invariant from the periphery to ACtx [1,9,17], and even more so in higher-order ACtx [22]. When considered together, the hierarchical organization from periphery to cortex and from L4 to L2/3 to L5 supports a model in which ACtx integrates noise-dependent inputs, refines them through subpopulation-specific computations, and broadcasts increasingly noise-invariant representations of sounds that can drive adaptive behavior [18,19,31,73,74]. Our findings characterize how noise invariance is expressed at the level of cortical representations within each subpopulation, rather than at the level of perception. Establishing a direct link between these representations and noise-invariant perception requires concurrent behavioral readouts (e.g., tone-in-noise detection) and ideally cell-type-specific perturbations during behavior, neither of which are part of the present study. Future investigations could pursue this by transiently inactivating excitatory subpopulations at the time of sound presentation and measuring whether the behavioral output remains noise invariant. Because L2/3 neurons respond strongly to low-intensity tones, the BN-induced suppression of these responses could be described not as a degraded representation of tone identity, but as an invariant representation of tone salience relative to the background. Notably, the divisive scaling we observe in L2/3 (Fig 2F, 2G) is the canonical signature of contrast gain normalization, in which a neuron’s response is divided by a measure of background drive [74], the operation required to compute a tone’s level relative to its acoustic context. These two framings describe the same data from different downstream perspectives: our analyses quantify whether tone-identity coding is preserved across BN conditions, but the same modulation could equally support a salience-relative-to-background readout. We therefore emphasize that our use of “invariance” refers specifically to the within-population preservation of tone-identity representations, rather than to a broader claim about which representation is most behaviorally relevant. Prior studies have examined sensory representations that remain invariant to factors other than BN. For example, work on level invariance shows that ACtx representations can remain stable despite changes in sound intensity [75,76], and nonprimary ACtx can form distractor-invariant representations of sounds when they are behaviorally relevant [77,78]. In the visual system, a rich body of work has investigated how neurons in the visual pathway support object recognition independently of changes in rotation, position, and other variables [79–83]. A common limitation of many of these studies is that they treat cortical excitatory neurons as a homogeneous population, overlooking the heterogeneity of subpopulations within a cortical column. In light of our findings, this gap raises the possibility that invariant coding in other sensory modalities may also arise from specialized computation by distinct excitatory subpopulations. Multiple studies have demonstrated that auditory cortex activity is modulated by global variables such as arousal [26,84,85] and overt movement [84–87], which could influence the degree of noise invariance observed across subpopulations in the present study. By presenting multiple repetitions of each unique stimulus under both No-BN and BN conditions, we aimed to average out trial-to-trial fluctuations that could be attributed to changes in internal state. Nevertheless, future work could directly examine the relationship between subpopulation-specific noise invariance and arousal state by recording pupil size, facial motion, and locomotion during sound presentation with and without BN. A further methodological consideration is that two-photon calcium imaging is poorly suited to measuring absolute spontaneous firing rates, because baseline GCaMP fluorescence varies across sessions for indicator-specific reasons unrelated to spontaneous spiking. Whether subpopulation-specific differences in spontaneous activity contribute to the noise invariance we report, and whether spontaneous activity itself is differentially modulated by BN across L2/3, L5 IT, and L5 ET, would be better assessed using electrophysiological recordings that are not subject to these indicator-specific confounds. In this study, we used pure tones as the signal and white noise as the masker. Pure tones give precise control of frequency and intensity to isolate mechanisms of noise invariance and are a common stimulus choice in work probing noise-invariant representations in the auditory system [2,3,6,10,88], but they sample only a small region of the space of natural sounds. Extending our findings to more complex stimuli will require careful stimulus design. For example, time-varying stimuli, such as amplitude-modulated tones, introduce fluctuations in SNR over time and would require ACtx neurons to express noise invariance both for spectral content and for temporal envelope tracking. Human studies suggest that envelope tracking can remain relatively preserved in BN [89], but the contribution of ACtx neurons to time-varying noise invariance is not yet known. Stimuli with richer spectral structure, such as frequency sweeps and natural vocalizations, would demand invariance across multiple spectral and temporal channels. Although ACtx neurons exhibit multiplexed responses to several sound features [41,78,90–92], future work should test whether individual neurons maintain a consistent degree of noise invariance across different regions of their receptive fields and whether population-level codes support multiplexed forms of noise invariance across features and timescales. Additionally, the complexity of the BN could affect the degree of noise invariance achieved by each subpopulation. The findings in this study may not generalize to BN that does not have a flat frequency spectrum, such as pink noise, or to narrowband noise that overlaps with the frequency of the acoustic stimulus. Differences in noise invariance between L5 subpopulations At the level of individual neurons, L5 IT and ET populations exhibited a similar degree of noise invariance in both tuning and response distributions (Fig 2B and 2G). However, differences become more pronounced in pairwise and population-level representations. Pairwise analyses showed that L5 IT neurons exhibited reduced noise correlations across all intersomatic distances, whereas L5 ET neurons showed reductions primarily locally (Fig 4C, 4D). Noise correlations can reflect shared inputs, functional coupling, and the information content of population responses [93–95]. The broad reduction in L5 IT (and L2/3) correlations suggests more global changes in correlated variability under BN, whereas the spatially restricted effects in L5 ET may reflect BN-dependent modulation of local subnetworks within this subpopulation. Population-level differences were even more striking. Decoding analyses showed that BN impaired both sound detection and frequency discrimination in L5 ET neurons, whereas L5 IT decoding performance remained stable (Fig 5D and 5H). Although L5 IT detection decoding was on average lower than that of L5 ET and L2/3 (Fig 5D), both of the latter subpopulations showed significant reductions in decoding performance when matched to the performance range of L5 IT (S4A, S4B Fig), suggesting that noise robustness in L5 IT is not simply a consequence of lower baseline performance. Consistent with this result, manifold geometry analyses revealed that BN disrupted the fine-scale structure of sound representations in L5 ET neurons, altering manifold capacity, radius, and dimensionality, while affecting only manifold radius in L5 IT neurons (Fig 6C). Notably, despite these changes in fine-scale geometry, the global structure of sound representations in both L5 IT and L5 ET populations remained noise invariant, as reflected by stable manifold size across BN conditions (Fig 6F). In L5 ET neurons, this dissociation between degraded fine-scale geometry and preserved global structure suggests that BN may cause individual manifold objects to expand toward one another or toward the origin, without changing the overall extent of the population-level representation. Together, these results indicate that L5 ET neurons preserve the global size of their neural manifold under BN, but exhibit degraded stimulus-specific geometry, whereas L5 IT neurons maintain both global and fine-scale structure. This divergence may reflect differences in the functional demands of their downstream targets. If L5 IT and L5 ET projection targets differ in computational requirements or modularity, the corresponding cortical output pathways may differentially shape population responses to preserve noise-invariant representations appropriate for their target circuits. These findings add to a growing body of evidence that L5 IT and L5 ET neurons are functionally distinct. Across cortical areas, these subpopulations differ in their projection targets as well as in multiple morphological and physiological properties [24,31,32,68,96,97]. Here, we show that although both L5 IT and L5 ET neurons participate in broadcast pathways and exhibit noise invariance at multiple representational levels, they differ in the extent to which specific pairwise and population-level metrics remain noise invariant. One possible explanation for this differential modulation by BN is that L5 IT and L5 ET neurons receive distinct long-range inputs [32,68]. Differences in top-down modulation could lead to subpopulation-specific effects of BN by selectively enhancing or suppressing neuronal responses, thereby shaping the degree of noise invariance expressed at the population level. An additional possibility is that these subpopulations differ in their local circuit organization, including recurrent connectivity within each group and their interactions with other neural populations, such as inhibitory interneurons [70,98,99]. Together, differences in long-range inputs, local recurrence, and inhibitory interactions may underlie the distinct patterns of noise invariance observed between L5 IT and L5 ET neurons. Future studies could directly test these ideas by transiently inactivating cortical regions that provide top-down input to L5 neurons, such as posterior parietal cortex or anterior cingulate cortex, and by using cell-type-specific optogenetic perturbations to assess whether local microcircuits are differentially engaged in the presence of BN. Potential mechanisms that lead to noise invariance Early work on noise invariance emphasized mechanisms in the auditory periphery and midbrain that reduce the overall gain of auditory nerve responses [11,17,19,100]. Although such mechanisms can improve sound coding in noisy environments, noise-dependent distortions of sound representations remain evident beyond the periphery, indicating that global gain adjustments alone are insufficient to account for noise-invariant coding. Instead, peripheral adaptations likely constitute the initial stage of a multistep computation that is progressively refined in downstream auditory structures. Cholinergic projections from the basal forebrain exhibit strong layer-, subpopulation-, and region-specific organization. Across cortical areas, basal forebrain inputs exert layer-specific effects [101,102], and within ACtx, cholinergic innervation differs between primary and nonprimary subdivisions [20,102]. At the cellular level, cholinergic signaling differentially modulates ACtx excitatory subpopulations, including L5 IT, L5 ET [69,103], and L6 neurons [104,105]. In parallel, sound representations become progressively more noise invariant across layers of the cortical microcircuit in primary ACtx and between primary and nonprimary auditory fields, mirroring differences in cholinergic innervation and functional responses across these populations. Recent work has implicated cholinergic input to ACtx as a potential mechanism supporting noise-invariant representations, in part through its effects on spontaneous firing rates and local synchrony [3]. Given that BN shapes feedforward sensory inputs to ACtx [1,9], it remains unclear whether cholinergic modulation influences the feedforward propagation of sound representations through the cortical hierarchy in a way that promotes noise invariance. Future studies could test this by transiently inhibiting cholinergic inputs to ACtx and examining whether excitatory subpopulations represent sounds with reduced noise invariance. Together, these observations raise the possibility that neuromodulatory influences contribute to subpopulation-specific differences in noise invariance across the auditory hierarchy and within the ACtx microcircuit. In addition to neuromodulatory influences, inhibitory circuits have been proposed as mechanisms contributing to the construction of noise-invariant representations in ACtx. Inhibitory neurons play well-established roles in sensory processing, including surround suppression [5,106,107], suppressive feedback [108,109], and temporal sharpening [110,111]. With respect to noise invariance, inactivation of parvalbumin (PV) or somatostatin (SOM) interneurons impairs behavioral performance in noisy conditions to a degree comparable to inactivation of ACtx itself [6]. This result indicates that PV and SOM activity is necessary for detecting sounds in BN, but also suggests that inhibitory neurons alone do not fully account for the cortical mechanisms underlying noise-invariant perception. Consistent with this interpretation, optogenetic activation of PV neurons suppresses ACtx tuning curves in a manner similar to BN; however, combining PV activation with BN produces even stronger suppression, indicating that PV activity alone is insufficient to explain the full modulation of tuning curves observed in noisy environments [2]. Notably, many of these studies have treated inhibitory neurons as a homogeneous population within ACtx. In contrast, both theoretical and experimental work suggest that feedforward inhibition may support contrast gain control within the canonical cortical microcircuit [74], potentially supporting noise invariance by selectively modulating the gain of individual neurons according to their receptive fields and bottom-up inputs. Under this framework, inhibitory neurons would themselves be differentially engaged by BN and would, in turn, selectively enhance or suppress excitatory neurons within the same layer, thereby stabilizing sound representations in noisy conditions. This distinction becomes particularly relevant given that inhibitory interneuron classes (parvalbumin-, somatostatin-, and VIP-positive) are differentially distributed across cortical layers and form distinct connectivity patterns with L2/3 versus L5 pyramidal neurons [98,99,112], which may give rise to layer-specific mechanisms of noise invariance. A key prediction of this mechanism is that noise invariance within inhibitory neurons should increase throughout the cortical microcircuit, from L2/3 to L5, a pattern that is consistent with our findings. Future experiments could directly test this hypothesis by identifying interneuron populations in L2/3 whose activity is selectively modulated by BN and determining whether their trial-by-trial influence on local excitatory neurons adjusts gain in a manner that promotes noise-invariant sound representations in either nearby L2/3 neurons or in L5 neurons in the same cortical column. Our results demonstrate that excitatory subpopulations in ACtx make distinct and complementary contributions to constructing noise-invariant representations. We speculate that a complete mechanism for noise invariance within ACtx must include components that differentially influence the three excitatory subpopulations examined here and can account for the mixed pattern of invariance across single-neuron, pairwise, and population levels. Such components may include finely tuned gain control by inhibitory interneurons, as well as neuromodulatory inputs that are selectively engaged in the presence of BN. Conclusions Disentangling sensory signals from BN is a fundamental process that enables animals to represent stimuli accurately and generate appropriate behavioral responses. We show that excitatory subpopulations in ACtx respond differentially to sounds in BN, depending on their laminar position and projection class within the cortical microcircuit. This subpopulation-specific organization supports the idea that deep-layer broadcast pathways preferentially carry noise-invariant representations, whereas superficial populations remain more noise-dependent. Our findings bridge the noise-dependent representations observed in earlier stages of the auditory pathway with the more noise-invariant representations reported in higher auditory areas. Together, they underscore the role of excitatory subpopulations in implementing the computations that give rise to noise-invariant coding. Materials and methods Ethics statement All procedures were approved by the University of Pittsburgh Animal Care and Use Committee (protocol #: 19065155) and followed the guidelines established by the National Institute of Health for the care and use of laboratory animals. Mice Data were collected from 17 mice (10–16 weeks old, both male and female). For L2/3 recordings, we used two C57BL/6 mice (#000664, Jackson Labs) and five Emx1-Cre mice (#005628, Jackson Labs). For L5 IT recordings, we used six Tlx3-Cre mice (B6.FVB(Cg)-Tg(Tlx3-Cre)PL56Gsat/Mmucd, MMRRC). For L5 ET mice, we used four C57BL/6 mice. All mice were housed on a 12 h light/dark cycle with ad libitum access to food and water. All imaging was conducted during the dark cycle. Surgical procedures Virus-mediated gene delivery. Mice were anesthetized with 4% isoflurane and positioned in a stereotaxic frame (model 1900, Kopf). Throughout the procedure, a surgical plane of anesthesia was maintained using a continuous infusion of isoflurane (2%) in oxygen. Mice lay atop a homeothermic blanket system (Fine Science Tools) that maintained core body temperature at ~36.5 °C. The scalp was shaved and sterilized with alternating applications of iodine and ethanol, followed by subcutaneous injection of lidocaine hydrochloride (5 mg/ml) for local analgesia. For ACtx injections, a ∼1 cm incision was made between the right eye and ear to expose the temporalis muscle, which was then retracted. Two burr holes (∼0.3 mm diameter each) were drilled along the right temporal ridge, spanning a region 1.5–2.5 mm rostral to the lambdoid suture. For IC injections, a midline incision was made to expose bregma and lambda. The skull was leveled such that the vertical difference between bregma and lambda was less than 100 m, and a single burr hole was drilled at 4.8 mm caudal and 0.9 mm lateral to bregma. Viral injections were performed using a motorized stereotaxic injector (Nanoject III, Drummond Scientific). For ACtx injections, 250 nl of either a nonconditional GCaMP8s virus (pGP-AAV-syn-jGCaMP8s-WPRE, Addgene, titer: 3.5 x 1012 vg/mL) or a Cre-dependent GCaMP8s virus (pGP-AAV-syn-FLEX-jGCaMP8s-WPRE, Addgene, titer: 6 x 1012 vg/mL) was delivered at a depth of ~450 m below the pial surface at each injection site. The nonconditional virus was injected into the two C57BL/6 mice in our L2/3 cohort, while the Cre-dependent virus was used in all Emx1-Cre and Tlx3-Cre mice. The nonconditional approach was used before we established the Emx1-Cre line in our lab and is consistent with our prior published work [24,26]. For IC injections, 250 nl of retrograde GCaMP8s virus (pGP-AAV-syn-jGCaMP8s-WPRE, Addgene, titer: 4 x 1012 vg/mL) was delivered at depths of 900 m and 400 m below the pial surface. Following injections, the surgical sites were closed, antibiotic ointment was applied, and postoperative analgesia was administered subcutaneously (carprofen, 5 mg/ml). Mice were provided with ad libitum access to a carprofen MediGel and were closely monitored for three days following surgery. Cranial window implantation. Mice were brought to a surgical plane of anesthesia using the same anesthesia and temperature-control procedures described above. The dorsal surface of the skull was exposed, and the periosteum was removed. The skull was cleaned with 70% ethanol and chemically etched before affixing a custom titanium head plate (eMachineShop). The head plate was secured to the skull with opaque dental cement (C&B Metabond) and allowed to fully cure. After head-plate attachment, the temporalis muscle was retracted to expose the temporal ridge. A circular outline (3 mm diameter) centered over the temporal ridge ~0.5 mm above the lambdoid suture was marked using a biopsy punch. The skull within and around this outline was thinned using a hand drill to create a flat surface. Once sufficiently thinned, the outlined bone was carefully removed with a scalpel to expose the underlying cortex. A cranial window was constructed by placing a stack of glass coverslips (two 3 mm diameter and one 4 mm diameter) over the exposed brain. The edges of the craniotomy were sealed with silicone elastomer (Kwik-Sil) to create an airtight seal, and the window was secured with opaque dental cement applied around the perimeter of the 4 mm coverslip. All remaining exposed skull was covered with dental cement, and the surrounding skin was affixed to the cement using Vetbond (3M) tissue adhesive. Mice recovered under the same postoperative analgesia and monitoring conditions used following viral injections. Acoustic stimulation Stimuli were generated with a 24-bit digital-to-analog converter (National Instruments model PXI-4461) using custom scripts written in MATLAB (MathWorks) and LabVIEW (National Instruments). Acoustic stimuli were delivered via a free-field speaker (PUI Audio) facing the left ear and calibrated using a free-field prepolarized microphone (377C01, PCB Piezotronics). Pure tones varied in frequency (4–45 kHz, 1/2 octave steps) and intensity (20–70 dB SPL, 10 dB SPL steps), yielding 48 unique frequency–intensity combinations. BN was continuous broadband white noise (0–50 kHz) presented at 50 dB SPL. For the frozen noise control (S3 Fig), we presented 50 ms white noise bursts under two conditions within the same session: a frozen condition (400 trials), in which a fixed seed produced an identical waveform on every trial, and a random condition (400 trials), in which a new seed produced a different waveform on each trial. Calcium imaging Light-reversed mice were awake and head-fixed for all recording sessions. Prior to imaging, mice were habituated to head-fixation and the recording chamber for several days. Neural activity in response to four pure tones (4, 8, 16, and 32 kHz) was captured by widefield fluorescence imaging (Bergamo, ThorLabs) and used to functionally confirm the location of the right primary ACtx. Two-photon calcium imaging was conducted using an InSightX3 (Spectra Physics) laser tuned to 940 nm and a water-immersion objective (Nikon 16x). All two-photon imaging (Bergamo, ThorLabs) was of the right ACtx. Mice were head-fixed upright with the microscope rotated to be parallel to the cranial window (~40–50° tilt). Images were collected at 30 Hz. The depth below pial surface used for recordings depended on neuron subtype (L2/3: 140–250 m, L5 IT: 350–500 m, L5 ET: 450–600 m). We imaged on average 1.7, 1.6, and 1.3 FoVs per mouse for L2/3, L5 IT, and L5 ET, respectively. Separate FoVs from the same mouse were imaged at least 50 m above or below previous imaging planes to ensure spatial independence. All two-photon calcium imaging was conducted within a dark, sound-attenuating chamber. Two imaging sessions were performed for each FoV: one No-BN and one BN. Each session consisted of 960 trials, comprising 20 repetitions of 50 ms pure tones presented in pseudo-random order. Each trial was 3 s long: 0.5 s of pre-stimulus baseline followed by the 50 ms pure tone, with the remaining ∼2.45 s allowing neural activity to return to baseline. Stimulation parameters were identical across sessions, with the sole difference being that continuous broadband white noise (0–50 kHz, 50 dB SPL) was delivered from a secondary speaker positioned directly below the primary stimulation speaker during BN sessions. Each session lasted ~48 min, corresponding to a total of ∼88,000 imaging frames per session. Data analysis Image processing. Two-photon imaging data were processed using the open-source software Suite2P [37]. Image stacks were motion-corrected by rigid registration, and regions of interest (ROIs) were automatically detected with neuropil subtraction. All ROIs were manually curated to ensure that they corresponded to individual neurons. Calcium fluorescence traces were deconvolved to estimate spike rates and then z-scored within each session by subtracting the baseline mean and dividing by the baseline standard deviation. This within-session normalization was necessary because baseline GCaMP fluorescence varies across sessions and across cells for indicator-specific reasons (expression level, intracellular dynamics, photobleaching) unrelated to underlying spontaneous spiking. As a consequence, our dataset is well suited to comparing evoked responses across BN conditions but cannot directly resolve subpopulation-specific differences in spontaneous firing rate, which would be better characterized using electrophysiological recordings. To align ROIs across paired No-BN and BN sessions from the same FoV, we used the ROICaT cell-matching algorithm (https://github.com/RichieHakim/ROICaThttps://github.com/RichieHakim/ROICaT), which registers Suite2P outputs from paired sessions and identifies ROIs with overlapping spatial footprints as matching neurons. On average, 63% of neurons were matched across sessions (L2/3: 55%, L5 IT: 70%, and L5 ET: 67%). For all analyses, the single-trial response for each neuron was calculated as the mean z-scored deconvolved spike rate within a 0.5 s window starting at stimulus onset. Responsiveness. Neuronal responsiveness was determined using an approach adapted from Kato and colleagues [113]. A neuron was considered responsive to a given stimulus if it met two criteria: (1) sound-evoked responses exceeded 0.5 z-scores above baseline in at least 50% of trials, and (2) the mean sound-evoked response across all trials exceeded 1 z-score. Responsiveness was assessed separately for each unique frequency–intensity combination using all available trials pooled across both No-BN and BN sessions. A neuron was classified as sound responsive if it met these criteria for at least one stimulus. Tuning curves. Each recorded neuron was tested with 20 trials of each unique stimulus, yielding a total of 960 trials per session (48 frequency–intensity combinations). Neural activity within a fixed response window (0.5 s following sound onset) was averaged across trials to construct a FRA for each neuron. FRAs were represented as matrices with eight rows corresponding to frequencies and six columns corresponding to intensities (Fig 2A). Frequency tuning curves were derived by averaging responses across all intensities for each frequency, and intensity tuning curves were derived by averaging responses across all frequencies for each intensity. To construct population-averaged frequency tuning curves, individual neuron tuning curves were centered on their BF and then averaged within each subpopulation. The BF of each neuron was identified as the frequency at which its intensity-averaged frequency tuning curve had its peak response. Intensity tuning curves were averaged across neurons without re-centering. RMA regression. To compare tuning curves of individual neurons across BN conditions, we used RMA regression [21,39]. Unlike ordinary least-squares regression, RMA accounts for measurement noise in both variables. For each neuron, RMA was applied separately to frequency and intensity tuning curves to estimate slope and intercept parameters. Only slope and intercept estimates that differed significantly from their null values (slope = 1, intercept = 0) were included in subsequent analyses. Statistical significance was assessed using one-sample t tests comparing the estimated coefficients to their respective null values, with standard errors derived from the residual variance of the fitted model [114]. Intercepts significantly greater than or less than zero were classified as additive or subtractive shifts, respectively, whereas slopes significantly greater than or less than one were classified as multiplicative or divisive scaling. Single-cell reliability. To quantify the reliability of sound-evoked activity, we measured the consistency of each neuron’s responses across repeated presentations of the same stimulus [26]. For each neuron, we computed the variance of the evoked response to each unique frequency-intensity combination, averaged these variances across all combinations, and normalized them by the total variance across all trials and stimuli. Lower values of this metric indicate more consistent responses across repeated presentations. This analysis was performed on all sound-responsive neurons. Mutual information. Before computing mutual information, we empirically estimated the marginal and joint probability distributions P(X), P(S), and P(X,S). Neural responses X were discretized by binning sound-evoked activity using a fixed bin width of 0.2 z-scored responses. Stimulus identity S was encoded as an integer index ranging from 1 to the total number of unique stimuli (48) and had a uniform distribution by experimental design. The joint distribution P(X,S) was obtained by histogramming sound-evoked responses separately for each stimulus and normalizing across all trials. Mutual information between the neural response and stimulus identity was computed as: This calculation yielded a single nonnegative scalar value quantifying how much information a neuron’s responses conveyed about stimulus identity. Mutual information was computed separately for the BN and No-BN conditions. Because the stimulus set represented only a limited sampling of the auditory space encoded by ACtx neurons, we applied a bias correction to each mutual information estimate. For each neuron, bias was estimated using the analytically derived approximation from Panzeri and colleagues [115]: where |R| denotes the number of response bins with nonzero probability in P(X), denotes the number of response bins with nonzero probability in the conditional distribution , and N is the total number of stimulus presentations. The estimated bias was subtracted from each mutual information value. To quantify how BN altered stimulus-related information on a neuron-by-neuron basis, we computed an IMI: Each neuron was thus assigned an IMI value ranging from −1 to +1. Positive IMI values indicate greater stimulus-related information in BN than in No-BN, values near zero indicate little difference between conditions, and negative values indicate greater information encoding in No-BN. Pairwise correlations. Noise correlations (spike-count correlations) were computed by subtracting, for each neuron, its mean response across trials for a given stimulus and then calculating the Pearson correlation coefficient between the resulting trial-by-trial residuals for each pair of simultaneously recorded neurons. Signal correlations (tuning correlations) were computed as the Pearson correlation between the corresponding entries of the FRAs of pairs of simultaneously recorded neurons. All correlation analyses were restricted to neurons classified as sound responsive. Detection and discrimination decoding. We evaluated stimulus-encoded information at the population level using two decoding approaches: discrimination and detection. For detection decoding, we constructed training datasets consisting of sound-on and sound-off trials. Sound-on trials were drawn from responses to tones presented at 60 and 70 dB SPL for a single frequency, whereas sound-off trials consisted of randomly sampled neural activity measured 2 s after sound onset, when no stimulus was present. We trained artificial neural network classifiers using MATLAB’s fitcnet function (Statistics and Machine Learning Toolbox). Each classifier consisted of an input layer of 40 units, two hidden layers of 16 units with rectified linear unit (ReLU) activation functions, and a single readout unit passed through a sigmoid activation function (range 0–1). Trials were classified as sound-present if the readout exceeded a threshold of 0.5. Classifiers were trained separately for each frequency to avoid confounds arising from frequency tuning differences between training and testing data. Detection performance was quantified using d’ (d-prime), which incorporates both hit rate (HR) and false alarm rate (FAR): For discrimination decoding, we trained a neural network with the same architecture used for detection decoding, except that the output layer consisted of eight units (one per frequency), with a softmax activation function rather than a sigmoid. Network performance was assessed using 10-fold cross-validation, and decoding accuracy was quantified as the mean classification accuracy across folds. To control for intensity-dependent effects, discrimination decoding was performed using trials from a single sound intensity at a time and repeated independently for each intensity. Manifold geometry. To characterize the population-level geometry of sound-evoked neural activity, we applied a mean-field-theoretic manifold geometry analysis [58]. This framework quantifies the classification capacity of a neural population by describing the geometric structure of population responses to different stimulus categories. For each frequency, we extracted population activity from a single FoV and represented each trial as a vector in , where each dimension corresponded to the activity of one neuron. To standardize dimensionality across FoVs and subpopulations, we analyzed randomly sampled subsets of n = 40 neurons and resampled with replacement to approximate the full recorded population. Trials corresponding to the same stimulus category formed a point cloud in neural space, which was treated as a single neural manifold. For each manifold, we extracted three geometric metrics: manifold radius (), effective dimensionality (), and classification capacity (). We performed this analysis in two complementary ways. First, we pooled trials across all intensities for each frequency, yielding one manifold per frequency (Fig 6B). Second, we constructed separate manifolds for each frequency-intensity combination, yielding a finer-grained analysis of population geometry (Fig 6C). Manifold geometry analysis quantifies how efficiently population responses to different stimuli can be separated in high-dimensional neural space. The manifold radius measures the spatial extent of trial-to-trial variability within a stimulus category, whereas the effective dimensionality reflects the number of dimensions required to capture this variability. Together, these metrics describe how compact and low-dimensional a stimulus representation is, properties that facilitate separability from other stimulus manifolds. For example, if responses to a given frequency become more consistent across trials, the corresponding point cloud contracts toward a single point, resulting in smaller values of and . The manifold capacity provides an integrated measure of coding efficiency by quantifying how many such manifolds can be linearly separated by the same neural population. In the mean-field framework, is inversely related to both and ; thus, reductions in capacity indicate increased manifold size, increased dimensionality, or both. For our purposes, serves as a compact summary metric linking population geometry to the efficiency of stimulus encoding. Manifold size. To quantify the global size of the neural manifold, we first projected population activity into a lower-dimensional subspace that captured a substantial fraction of the variance in neural responses. For each neuron, we computed the peri-stimulus time–averaged activity for each unique stimulus (48 total), pooling trials from both No-BN and BN sessions. The activity of all simultaneously recorded neurons was then aggregated into a matrix, where t denotes time points and n denotes the number of neurons. We reduced the dimensionality of this matrix using PCA, projecting the data into a subspace, where p was chosen as the minimum number of PCs required to explain at least 60% of the total variance. After projecting the neural activity into this reduced space, we quantified the overall size of the population representation by computing its TV, defined as where is the covariance matrix of the projected neural activity. TV provides a scalar measure of the overall spread of population responses in the reduced neural space and thus serves as an estimate of global manifold size. Statistical analysis All statistical analyses were performed in MATLAB (MathWorks). Data are reported as mean ± s.e.m. unless otherwise noted. When data did not meet assumptions of normality, nonparametric statistical tests were used. For multi-group comparisons, post hoc tests were performed using Tukey’s or Dunn’s procedures, as appropriate. Statistical significance in figures is denoted as * p < 0.05, ** p < 0.01, and *** p < 0.0001. Supporting information S1 Fig. Single-neuron normalization and reliability. (A) Same average tuning curves as in Fig 2B, using calcium responses in dF/F rather than z-scored deconvolved spikes. Two-way ANOVA, main effect for BN, frequency and intensity respectively, L2/3: , L5 IT: p = 0.5089,0.7766, L5 ET: p = 0.6088,0.8374. (B) Distributions of single-cell reliability in No-BN and BN for each subpopulation. Wilcoxon rank sum test, L2/3: p = 0.0030, L5 IT: p = 0.3521, L5 ET: p = 0.7459. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. https://doi.org/10.1371/journal.pbio.3003915.s001 (EPS) S2 Fig. Noise invariance is not modulated by floor or ceiling effects. (A) Best-frequency-centered frequency tuning curves of the bottom 50% responding neurons (left column) and top 50% responding neurons (right column) for each subpopulation. Numbers next to the subpopulations indicate percentile ranges of responsive neurons included in each plot. Two-way ANOVA, main effect for BN, low and high responders respectively, L2/3: , L5 IT: p = 0.4375,0.3843, L5 ET: p = 0.3376,0.8231. (B) Same as in A with average intensity tuning curves instead. Two-way ANOVA, main effect for BN, low and high responders respectively, L2/3: , L5 IT: p = 0.1779,0.2586, L5 ET: p = 0.2054,0.5186. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. https://doi.org/10.1371/journal.pbio.3003915.s002 (EPS) S3 Fig. Randomly generated noise does not affect noise correlations in ACtx. (A) Schematic illustrating trials with the same frozen noise burst (left column) and randomly generated noise burst per trial (right column). (B) Matrix of noise correlations in sound-evoked activity from frozen noise (left), random noise (center) and the difference between the two conditions (right). (C) Distributions of noise correlations under frozen and random noise. Paired t test, p = 0.1425. (D) Distribution of paired differences in noise correlations from C. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. https://doi.org/10.1371/journal.pbio.3003915.s003 (EPS) S4 Fig. Noise-invariant decoding is not scale-dependent. (A) Same decoding performance as in Fig 5C, but restricting the data included to −0.5 to 2.5 d-prime to match the range of decoding performance of L5 IT. (B) Same as Fig 5D, but using the restricted ranges from A. Paired t test, L2/3: , L5 IT: p = 0.2211, L5 ET: p = 0.0217. (C) Detection decoding in intensities under 50 dB SPL (20–40 dB SPL) and above 50 dB SPL (60–70 dB SPL). Two-way ANOVA, Tukey-Kramer post hoc test for under and over 50 dB SPL respectively, L2/3: p = 0.8475,0.0398, L5 IT: p = 0.9438,0.9811, L5 ET: p = 0.9999,0.1489. (D) Same as C for discrimination decoding. Two-way ANOVA, Tukey–Kramer post hoc test for under and over 50 dB SPL, respectively, L2/3: p = 0.0538,0.0338, L5 IT: p = 0.1456,0.6442, L5 ET: p = 0.5935,0.0397. The data underlying this Figure can be found in https://doi.org/10.5281/zenodo.21111739. https://doi.org/10.1371/journal.pbio.3003915.s004 (EPS) S1 Table. Per-FoV slope and bias modulation proportions for frequency tuning curves. https://doi.org/10.1371/journal.pbio.3003915.s005 (PDF) S2 Table. Per-FoV slope and bias modulation proportions for intensity tuning curves. https://doi.org/10.1371/journal.pbio.3003915.s006 (PDF) Acknowledgments We thank current and former members of the Williamson Lab for helpful feedback and discussions. References - 1. Rabinowitz NC, Willmore BDB, King AJ, Schnupp JWH. Constructing noise-invariant representations of sound in the auditory pathway. PLoS Biol. 2013;11(11):e1001710. pmid:24265596 - 2. Christensen RK, Lindén H, Nakamura M, Barkat TR. White noise background improves tone discrimination by suppressing cortical tuning curves. Cell Rep. 2019;29(7):2041-2053.e4. pmid:31722216 - 3. Christensen RK, Studer F, Barkat TR. Background white noise increases neuronal activity by reducing membrane fluctuations and slow-wave oscillations in auditory cortex. Prog Neurobiol. 2025;246:102720. pmid:39863149 - 4. Carruthers IM, Laplagne DA, Jaegle A, Briguglio JJ, Mwilambwe-Tshilobo L, Natan RG, et al. Emergence of invariant representation of vocalizations in the auditory cortex. J Neurophysiol. 2015;114(5):2726–40. pmid:26311178 - 5. Lakunina AA, Nardoci MB, Ahmadian Y, Jaramillo S. Somatostatin-expressing interneurons in the auditory cortex mediate sustained suppression by spectral surround. J Neurosci. 2020;40(18):3564–75. pmid:32220950 - 6. Lakunina AA, Menashe N, Jaramillo S. Contributions of distinct auditory cortical inhibitory neuron types to the detection of sounds in background noise. eNeuro. 2022;9(2). - 7. Souffi S, Nodal FR, Bajo VM, Edeline J-M. When and how does the auditory cortex influence subcortical auditory structures? New insights about the roles of descending cortical projections. Front Neurosci. 2021;15:690223. pmid:34413722 - 8. Souffi S, Lorenzi C, Huetz C, Edeline J. Robustness to noise in the auditory system: a distributed and predictable property. eNeuro. 2021;8(2). - 9. Schneider DM, Woolley SMN. Sparse and background-invariant coding of vocalizations in auditory scenes. Neuron. 2013;79(1):141–52. pmid:23849201 - 10. Reiss LAJ, Ramachandran R, May BJ. Effects of signal level and background noise on spectral representations in the auditory nerve of the domestic cat. J Assoc Res Otolaryngol. 2011;12(1):71–88. pmid:20824483 - 11. Sachs MB, Voigt HF, Young ED. Auditory nerve representation of vowels in background noise. J Neurophysiol. 1983;50(1):27–45. pmid:6875649 - 12. Mokri Y, Worland K, Ford M, Rajan R. Effect of background noise on neuronal coding of interaural level difference cues in rat inferior colliculus. Eur J Neurosci. 2015;42(1):1685–704. pmid:25865218 - 13. Liang F, Bai L, Tao HW, Zhang LI, Xiao Z. Thresholding of auditory cortical representation by background noise. Front Neural Circuits. 2014;8:133. pmid:25426029 - 14. Brugge JF, Reale RA, Hind JE. Spatial receptive fields of primary auditory cortical neurons in quiet and in the presence of continuous background noise. J Neurophysiol. 1998;80(5):2417–32. pmid:9819253 - 15. Ruggero MA, Narayan SS, Temchin AN, Recio A. Mechanical bases of frequency tuning and neural excitation at the base of the cochlea: comparison of basilar-membrane vibrations and auditory-nerve-fiber responses in chinchilla. Proc Natl Acad Sci U S A. 2000;97(22):11744–50. pmid:11050204 - 16. Davis RL, Liu Q. Complex primary afferents: what the distribution of electrophysiologically-relevant phenotypes within the spiral ganglion tells us about peripheral neural coding. Hear Res. 2011;276(1–2):34–43. pmid:21276843 - 17. Fritzinger JB, Carney LH. Mechanisms of tone-in-noise encoding in the inferior colliculus. J Neurosci. 2025;45(23):e1907242025. pmid:40335155 - 18. Agarwalla S, Farhadi A, Carney LH. Forward masking in the inferior colliculus: dynamics of discharge-rate recovery after narrowband noise maskers. J Acoust Soc Am. 2025;157(5):3680–93. pmid:40358229 - 19. Wang Y, Abrams KS, Carney LH, Henry KS. Midbrain-level neural correlates of behavioral tone-in-noise detection: dependence on energy and envelope cues. J Neurosci. 2021;41(34):7206–23. pmid:34266898 - 20. Bajo VM, Leach ND, Cordery PM, Nodal FR, King AJ. The cholinergic basal forebrain in the ferret and its inputs to the auditory cortex. Eur J Neurosci. 2014;40(6):2922–40. pmid:24945075 - 21. Mesgarani N, David SV, Fritz JB, Shamma SA. Mechanisms of noise robust representation of speech in primary auditory cortex. Proc Natl Acad Sci U S A. 2014;111(18):6792–7. pmid:24753585 - 22. Kell AJE, McDermott JH. Invariance to background noise as a signature of non-primary auditory cortex. Nat Commun. 2019;10(1):3958. pmid:31477711 - 23. Weible AP, Liu C, Niell CM, Wehr M. Auditory cortex is required for fear potentiation of gap detection. J Neurosci. 2014;34(46):15437–45. pmid:25392510 - 24. Schneider NA, Malina MI, Williamson RS. A cortical output channel for perceptual categorization. BioRxiv. 2025. - 25. Krall RF, Cassidy RM, Ghimire M, Chambers CN, Arnold MP, Brougher LI, et al. Primary auditory cortex is necessary for the acquisition and expression of categorical behavior. Curr Biol. 2025;35(17):4061-4074.e4. pmid:40795849 - 26. Kaufman KJ, Krall RF, Williamson RS. Pupil-linked arousal heterogeneously modulates cell-type-specific sensory processing. Sci Adv. 2026;12(14):eadz6495. pmid:41931609 - 27. Meng X, Winkowski DE, Kao JPY, Kanold PO. Sublaminar subdivision of mouse auditory cortex layer 2/3 based on functional translaminar connections. J Neurosci. 2017;37(42):10200–14. pmid:28931571 - 28. Llano DA, Sherman SM. Differences in intrinsic properties and local network connectivity of identified layer 5 and layer 6 adult mouse auditory corticothalamic neurons support a dual corticothalamic projection hypothesis. Cereb Cortex. 2009;19(12):2810–26. pmid:19351905 - 29. Williamson RS, Polley DB. Parallel pathways for sound processing and functional connectivity among layer 5 and 6 auditory corticofugal neurons. eLife. 2019;8. - 30. Tasic B, Yao Z, Graybuck LT, Smith KA, Nguyen TN, Bertagnolli D, et al. Shared and distinct transcriptomic cell types across neocortical areas. Nature. 2018;563(7729):72–8. pmid:30382198 - 31. Harris KD, Shepherd GMG. The neocortical circuit: themes and variations. Nat Neurosci. 2015;18(2):170–81. pmid:25622573 - 32. Kim EJ, Juavinett AL, Kyubwa EM, Jacobs MW, Callaway EM. Three types of cortical layer 5 neurons that differ in brain-wide connectivity and function. Neuron. 2015;88(6):1253–67. pmid:26671462 - 33. Winer JA. Decoding the auditory corticofugal systems. Hear Res. 2005;207(1–2):1–9. pmid:16091301 - 34. Harris KD, Mrsic-Flogel TD. Cortical connectivity and sensory coding. Nature. 2013;503(7474):51–8. pmid:24201278 - 35. Asokan MM, Williamson RS, Hancock KE, Polley DB. Sensory overamplification in layer 5 auditory corticofugal projection neurons following cochlear nerve synaptic damage. Nat Commun. 2018;9(1):2468. pmid:29941910 - 36. Chen X, Sun Y-C, Zhan H, Kebschull JM, Fischer S, Matho K, et al. High-throughput mapping of long-range neuronal projection using in situ sequencing. Cell. 2019;179(3):772-786.e19. pmid:31626774 - 37. Pachitariu M, Stringer C, Schröder S, Dipoppa M, Rossi LF, Carandini M, et al. Suite2p: beyond 10,000 neurons with standard two-photon microscopy. BioRxiv. 2016. - 38. Friedrich J, Zhou P, Paninski L. Fast online deconvolution of calcium imaging data. PLoS Comput Biol. 2017;13(3):e1005423. pmid:28291787 - 39. Phillips EA, Hasenstaub AR. Asymmetric effects of activating and inactivating cortical interneurons. eLife. 2016;5. - 40. Nelken I, Chechik G. Information theory in auditory research. Hear Res. 2007;229(1–2):94–105. pmid:17300891 - 41. Walker KMM, Bizley JK, King AJ, Schnupp JWH. Multiplexed and robust representations of sound features in auditory cortex. J Neurosci. 2011;31(41):14565–76. pmid:21994373 - 42. Zan P, Presacco A, Anderson S, Simon JZ. Mutual information analysis of neural representations of speech in noise in the aging midbrain. J Neurophysiol. 2019;122(6):2372–87. pmid:31596649 - 43. Nocon JC, Witter J, Gritton H, Han X, Houghton C, Sen K. A robust and compact population code for competing sounds in auditory cortex. J Neurophysiol. 2023;130(3):775–87. pmid:37646080 - 44. Cohen MR, Kohn A. Measuring and interpreting neuronal correlations. Nat Neurosci. 2011;14(7):811–9. pmid:21709677 - 45. Kohn A, Smith MA. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J Neurosci. 2005;25(14):3661–73. pmid:15814797 - 46. Zohary E, Shadlen MN, Newsome WT. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature. 1994;370(6485):140–3. pmid:8022482 - 47. Abbott LF, Dayan P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 1999;11(1):91–101. pmid:9950724 - 48. Smith MA, Kohn A. Spatial and temporal scales of neuronal correlation in primary visual cortex. J Neurosci. 2008;28(48):12591–603. pmid:19036953 - 49. Smith MA, Sommer MA. Spatial and temporal scales of neuronal correlation in visual area V4. J Neurosci. 2013;33(12):5422–32. pmid:23516307 - 50. Smith GB, Sederberg A, Elyada YM, Van Hooser SD, Kaschube M, Fitzpatrick D. The development of cortical circuits for motion discrimination. Nat Neurosci. 2015;18(2):252–61. pmid:25599224 - 51. Yu Y, Stirman JN, Dorsett CR, Smith S. Visual information is broadcast among cortical areas in discrete channels. 2024. - 52. Khoury CF, Fala NG, Runyan CA. The spatial scale of somatostatin subnetworks increases from sensory to association cortex. Cell Rep. 2022;40(10):111319. pmid:36070697 - 53. Semedo JD, Zandvakili A, Machens CK, Yu BM, Kohn A. Cortical areas interact through a communication subspace. Neuron. 2019;102(1):249-259.e4. pmid:30770252 - 54. Semedo JD, Jasper AI, Zandvakili A, Krishna A, Aschner A, Machens CK, et al. Feedforward and feedback interactions between visual cortical areas use different population activity patterns. Nat Commun. 2022;13(1):1099. pmid:35232956 - 55. Russo AA, Khajeh R, Bittner SR, Perkins SM, Cunningham JP, Abbott LF, et al. Neural trajectories in the supplementary motor area and motor cortex exhibit distinct geometries, compatible with different classes of computation. Neuron. 2020;107(4):745-758.e6. pmid:32516573 - 56. MacDowell CJ, Libby A, Jahn CI, Tafazoli S, Ardalan A, Buschman TJ. Multiplexed subspaces route neural activity across brain-wide networks. Nat Commun. 2025;16(1):3359. pmid:40204762 - 57. Srinath R, Ruff DA, Cohen MR. Attention improves information flow between neuronal populations without changing the communication subspace. Curr Biol. 2021;31(23):5299-5313.e4. pmid:34699782 - 58. Chung LDD, Sompolinsky H. Classification and geometry of general perceptual manifolds. Phys Rev X. 2018;8(3):031003. - 59. Paraouty N, Yao JD, Varnet L, Chou C-N, Chung S, Sanes DH. Sensory cortex plasticity supports auditory social learning. Nat Commun. 2023;14(1):5828. pmid:37730696 - 60. Avitan L, Stringer C. Not so spontaneous: multi-dimensional representations of behaviors and context in sensory areas. Neuron. 2022;110(19):3064–75. pmid:35863344 - 61. Stringer C, Pachitariu M, Steinmetz N, Carandini M, Harris KD. High-dimensional geometry of population responses in visual cortex. Nature. 2019;571(7765):361–5. pmid:31243367 - 62. Cohen U, Chung S, Lee DD, Sompolinsky H. Separability and geometry of object manifolds in deep neural networks. Nat Commun. 2020;11(1):746. pmid:32029727 - 63. Drieu C, Zhu Z, Wang Z, Fuller K, Wang A, Elnozahy S, et al. Rapid emergence of latent knowledge in the sensory cortex drives learning. Nature. 2025;641(8064):960–70. pmid:40108473 - 64. Blackwell JM, Taillefumier TO, Natan RG, Carruthers IM, Magnasco MO, Geffen MN. Stable encoding of sounds over a broad range of statistical parameters in the auditory cortex. Eur J Neurosci. 2016;43(6):751–64. pmid:26663571 - 65. Kuchibhotla K, Bathellier B. Neural encoding of sensory and behavioral complexity in the auditory cortex. Curr Opin Neurobiol. 2018;52:65–71. pmid:29709885 - 66. Steinfeld R, Tacão-Monteiro A, Renart A. Differential representation of sensory information and behavioral choice across layers of the mouse auditory cortex. Curr Biol. 2024;34(10):2200-2211.e6. pmid:38733991 - 67. Douglas RJ, Martin KAC. Neuronal circuits of the neocortex. Annu Rev Neurosci. 2004;27:419–51. pmid:15217339 - 68. Baker AL, O’Toole RJ, Gulledge AT. Preferential cholinergic excitation of corticopontine neurons. J Physiol. 2018;596(9):1659–79. pmid:29330867 - 69. Moberg S, Takahashi N. Neocortical layer 5 subclasses: from cellular properties to roles in behavior. Front Synaptic Neurosci. 2022;14:1006773. pmid:36387773 - 70. Onodera K, Kato HK. Translaminar recurrence from layer 5 suppresses superficial cortical layers. Nat Commun. 2022;13(1):2585. pmid:35546553 - 71. Frezel N, Platonova E, Voigt FF, Mateos JM, Kastli R, Ziegler U, et al. In-depth characterization of layer 5 output neurons of the primary somatosensory cortex innervating the mouse dorsal spinal cord. Cereb Cortex Commun. 2020;1(1):tgaa052. pmid:34296117 - 72. Tang L, Higley MJ. Layer 5 circuits in V1 differentially control visuomotor behavior. Neuron. 2020;105(2):346-354.e5. pmid:31757603 - 73. Bastos AM, Usrey WM, Adams RA, Mangun GR, Fries P, Friston KJ. Canonical microcircuits for predictive coding. Neuron. 2012;76(4):695–711. pmid:23177956 - 74. Willmore BDB, Cooke JE, King AJ. Hearing in noisy environments: noise invariance and contrast gain control. J Physiol. 2014;592(16):3371–81. pmid:24907308 - 75. Sadagopan S, Wang X. Level invariant representation of sounds by populations of neurons in primary auditory cortex. J Neurosci. 2008;28(13):3415–26. pmid:18367608 - 76. Sun W, Marongelli EN, Watkins PV, Barbour DL. Decoding sound level in the marmoset primary auditory cortex. J Neurophysiol. 2017;118(4):2024–33. pmid:28701545 - 77. Heller CR, Hamersky GR, David SV. Task-specific invariant representation in auditory cortex. eLife. 2024;12. - 78. Town SM, Wood KC, Bizley JK. Sound identity is represented robustly in auditory cortex during perceptual constancy. Nat Commun. 2018;9(1):4786. pmid:30429465 - 79. DiCarlo JJ, Cox DD. Untangling invariant object recognition. Trends Cogn Sci. 2007;11(8):333–41. pmid:17631409 - 80. Logothetis NK, Pauls J, Bülthoff HH, Poggio T. View-dependent object recognition by monkeys. Curr Biol. 1994;4(5):401–14. pmid:7922354 - 81. Riesenhuber M, Poggio T. Hierarchical models of object recognition in cortex. Nat Neurosci. 1999;2(11):1019–25. pmid:10526343 - 82. Mocz V, Vaziri-Pashkam M, Chun MM, Xu Y. Predicting identity-preserving object transformations across the human ventral visual stream. J Neurosci. 2021;41(35):7403–19. - 83. Benucci A. Motor-related signals support localization invariance for stable visual perception. PLoS Comput Biol. 2022;18(3):e1009928. pmid:35286305 - 84. McGinley MJ, Vinck M, Reimer J, Batista-Brito R, Zagha E, Cadwell CR, et al. Waking state: rapid variations modulate neural and behavioral responses. Neuron. 2015;87(6):1143–61. pmid:26402600 - 85. Reimer J, McGinley MJ, Liu Y, Rodenkirch C, Wang Q, McCormick DA, et al. Pupil fluctuations track rapid changes in adrenergic and cholinergic activity in cortex. Nat Commun. 2016;7:13289. pmid:27824036 - 86. Schneider DM, Nelson A, Mooney R. A synaptic and circuit basis for corollary discharge in the auditory cortex. Nature. 2014;513(7517):189–94. pmid:25162524 - 87. Schneider DM, Sundararajan J, Mooney R. A cortical filter that learns to suppress the acoustic consequences of movement. Nature. 2018;561(7723):391–5. pmid:30209396 - 88. Resnik J, Polley DB. Cochlear neural degeneration disrupts hearing in background noise by increasing auditory cortex internal noise. Neuron. 2021;109(6):984-996.e4. pmid:33561398 - 89. Souffi S, Varnet L, Zaidi M, Bathellier B, Huetz C, Edeline J-M. Reduction in sound discrimination in noise is related to envelope similarity and not to a decrease in envelope tracking abilities. J Physiol. 2023;601(1):123–49. pmid:36373184 - 90. Giroud J, Trébuchon A, Mercier M, Davis MH, Morillon B. The human auditory cortex concurrently tracks syllabic and phonemic timescales via acoustic spectral flux. Sci Adv. 2024;10(51):eado8915. pmid:39705351 - 91. Angeloni C, Geffen MN. Contextual modulation of sound processing in the auditory cortex. Curr Opin Neurobiol. 2018;49:8–15. pmid:29125987 - 92. Downer JD, Verhein JR, Rapone BC, O’Connor KN, Sutter ML. An emergent population code in primary auditory cortex supports selective attention to spectral and temporal sound features. J Neurosci. 2021;41(36):7561–77. pmid:34210783 - 93. Panzeri S, Moroni M, Safaai H, Harvey CD. The structures and functions of correlations in neural population codes. Nat Rev Neurosci. 2022;23(9):551–67. pmid:35732917 - 94. Kohn A, Coen-Cagli R, Kanitscheider I, Pouget A. Correlations and neuronal population information. Annu Rev Neurosci. 2016;39:237–56. pmid:27145916 - 95. Averbeck BB, Latham PE, Pouget A. Neural correlations, population coding and computation. Nat Rev Neurosci. 2006;7(5):358–66. pmid:16760916 - 96. Li N, Chen T-W, Guo ZV, Gerfen CR, Svoboda K. A motor cortex circuit for motor planning and movement. Nature. 2015;519(7541):51–6. pmid:25731172 - 97. Lur G, Vinck MA, Tang L, Cardin JA, Higley MJ. Projection-specific visual feature encoding by layer 5 cortical subnetworks. Cell Rep. 2016;14(11):2538–45. pmid:26972011 - 98. Naka A, Adesnik H. Inhibitory circuits in cortical layer 5. Front Neural Circuits. 2016;10:35. pmid:27199675 - 99. Sun YJ, Kim Y-J, Ibrahim LA, Tao HW, Zhang LI. Synaptic mechanisms underlying functional dichotomy between intrinsic-bursting and regular-spiking neurons in auditory cortical layer 5. J Neurosci. 2013;33(12):5326–39. pmid:23516297 - 100. Wagner W, Frey K, Heppelmann G, Plontke SK, Zenner H-P. Speech-in-noise intelligibility does not correlate with efferent olivocochlear reflex in humans with normal hearing. Acta Otolaryngol. 2008;128(1):53–60. pmid:17851961 - 101. Verhoog MB, Obermayer J, Kortleven CA, Wilbers R, Wester J, Baayen JC, et al. Layer-specific cholinergic control of human and mouse cortical synaptic plasticity. Nat Commun. 2016;7:12826. pmid:27604129 - 102. Chavez C, Zaborszky L. Basal forebrain cholinergic-auditory cortical network: primary versus nonprimary auditory cortical areas. Cereb Cortex. 2017;27(3):2335–47. pmid:27073229 - 103. Baker A, Kalmbach B, Morishima M, Kim J, Juavinett A, Li N, et al. Specialized subpopulations of deep-layer pyramidal neurons in the neocortex: bridging cellular properties to functional consequences. J Neurosci. 2018;38(24):5441–55. pmid:29798890 - 104. Clayton KK, Williamson RS, Hancock KE, Tasaka G-I, Mizrahi A, Hackett TA, et al. Auditory corticothalamic neurons are recruited by motor preparatory inputs. Curr Biol. 2021;31(2):310-321.e5. pmid:33157020 - 105. Vattino LG, Clayton KK, Hackett TA, Polley DB, Takesian AE. Layer 6 is a hub for cholinergic modulation in the mouse auditory cortex. Cereb Cortex. 2026;36(1):bhaf338. pmid:41569342 - 106. Adesnik H, Bruns W, Taniguchi H, Huang ZJ, Scanziani M. A neural circuit for spatial summation in visual cortex. Nature. 2012;490(7419):226–31. pmid:23060193 - 107. Ozeki H, Finn IM, Schaffer ES, Miller KD, Ferster D. Inhibitory stabilization of the cortical network underlies visual surround suppression. Neuron. 2009;62(4):578–92. pmid:19477158 - 108. Hishida R, Horie M, Tsukano H, Tohmi M, Yoshitake K, Meguro R, et al. Feedback inhibition derived from the posterior parietal cortex regulates the neural properties of the mouse visual cortex. Eur J Neurosci. 2019;50(6):2970–87. pmid:31012509 - 109. Nassi JJ, Lomber SG, Born RT. Corticocortical feedback contributes to surround suppression in V1 of the alert primate. J Neurosci. 2013;33(19):8504–17. pmid:23658187 - 110. Morabito A, Zerlaut Y, Dhanasobhon D, Berthaux E, Pinho CM, Tzilivaki A, et al. Distinct dendritic integration strategies control dynamics of inhibition in the neocortex. Neuron. 2025;113(18):2962-2978.e10. pmid:40592329 - 111. Cai D, Han R, Liu M, Xie F, You L, Zheng Y, et al. A critical role of inhibition in temporal processing maturation in the primary auditory cortex. Cereb Cortex. 2018;28(5):1610–24. pmid:28334383 - 112. Studer F, Barkat TR. Inhibition in the auditory cortex. Neurosci Biobehav Rev. 2022;132:61–75. pmid:34822879 - 113. Kato HK, Asinof SK, Isaacson JS. Network-level control of frequency tuning in auditory cortex. Neuron. 2017;95(2):412-423.e4. pmid:28689982 - 114. Allen MP. The t test for the simple regression coefficient. In: Understanding regression analysis. 1997. p. 66–70. - 115. Panzeri S, Senatore R, Montemurro MA, Petersen RS. Correcting for the sampling bias problem in spike train information measures. J Neurophysiol. 2007;98(3):1064–72. pmid:17615128