Adaptive modeling and inference of higher-order coordination in neuronal assemblies: A dynamic greedy estimation approach.

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Non-Asymptotic Guarantees for Reliable Identification of Granger Causality via the LASSO.

Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data duration to be useful and are not immune to confounding effects. In this work, we address this disconnect by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish fundamental limits for reliable identification of Granger causal influences using the proposed LASSO-based statistic. We further characterize the false positive error probability and test power of a simple thresholding rule for identifying Granger causal effects and provide two methods to set the threshold in a data-driven fashion. We present simulation studies and application to real data to compare the performance of our proposed method to ordinary least squares and existing LASSO-based methods in detecting Granger causal influences, which corroborate our theoretical results.

NLGC: Network localized Granger causality with application to MEG directional functional connectivity analysis.

Identifying the directed connectivity that underlie networked activity between different cortical areas is critical for understanding the neural mechanisms behind sensory processing. Granger causality (GC) is widely used for this purpose in functional magnetic resonance imaging analysis, but there the temporal resolution is low, making it difficult to capture the millisecond-scale interactions underlying sensory processing. Magnetoencephalography (MEG) has millisecond resolution, but only provides low-dimensional sensor-level linear mixtures of neural sources, which makes GC inference challenging. Conventional methods proceed in two stages: First, cortical sources are estimated from MEG using a source localization technique, followed by GC inference among the estimated sources. However, the spatiotemporal biases in estimating sources propagate into the subsequent GC analysis stage, may result in both false alarms and missing true GC links. Here, we introduce the Network Localized Granger Causality (NLGC) inference paradigm, which models the source dynamics as latent sparse multivariate autoregressive processes and estimates their parameters directly from the MEG measurements, integrated with source localization, and employs the resulting parameter estimates to produce a precise statistical characterization of the detected GC links. We offer several theoretical and algorithmic innovations within NLGC and further examine its utility via comprehensive simulations and application to MEG data from an auditory task involving tone processing from both younger and older participants. Our simulation studies reveal that NLGC is markedly robust with respect to model mismatch, network size, and low signal-to-noise ratio, whereas the conventional two-stage methods result in high false alarms and mis-detections. We also demonstrate the advantages of NLGC in revealing the cortical network-level characterization of neural activity during tone processing and resting state by delineating task- and age-related connectivity changes.

Dynamic estimation of auditory temporal response functions via state-space models with Gaussian mixture process noise.

Estimating the latent dynamics underlying biological processes is a central problem in computational biology. State-space models with Gaussian statistics are widely used for estimation of such latent dynamics and have been successfully utilized in the analysis of biological data. Gaussian statistics, however, fail to capture several key features of the dynamics of biological processes (e.g., brain dynamics) such as abrupt state changes and exogenous processes that affect the states in a structured fashion. Although Gaussian mixture process noise models have been considered as an alternative to capture such effects, data-driven inference of their parameters is not well-established in the literature. The objective of this paper is to develop efficient algorithms for inferring the parameters of a general class of Gaussian mixture process noise models from noisy and limited observations, and to utilize them in extracting the neural dynamics that underlie auditory processing from magnetoencephalography (MEG) data in a cocktail party setting. We develop an algorithm based on Expectation-Maximization to estimate the process noise parameters from state-space observations. We apply our algorithm to simulated and experimentally-recorded MEG data from auditory experiments in the cocktail party paradigm to estimate the underlying dynamic Temporal Response Functions (TRFs). Our simulation results show that the richer representation of the process noise as a Gaussian mixture significantly improves state estimation and capturing the heterogeneity of the TRF dynamics. Application to MEG data reveals improvements over existing TRF estimation techniques, and provides a reliable alternative to current approaches for probing neural dynamics in a cocktail party scenario, as well as attention decoding in emerging applications such as smart hearing aids. Our proposed methodology provides a framework for efficient inference of Gaussian mixture process noise models, with application to a wide range of biological data with underlying heterogeneous and latent dynamics.

Extracting neuronal functional network dynamics via adaptive Granger causality analysis.

Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca2+ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.

Neuro-current response functions: A unified approach to MEG source analysis under the continuous stimuli paradigm.

Characterizing the neural dynamics underlying sensory processing is one of the central areas of investigation in systems and cognitive neuroscience. Neuroimaging techniques such as magnetoencephalography (MEG) and Electroencephalography (EEG) have provided significant insights into the neural processing of continuous stimuli, such as speech, thanks to their high temporal resolution. Existing work in the context of auditory processing suggests that certain features of speech, such as the acoustic envelope, can be used as reliable linear predictors of the neural response manifested in M/EEG. The corresponding linear filters are referred to as temporal response functions (TRFs). While the functional roles of specific components of the TRF are well-studied and linked to behavioral attributes such as attention, the cortical origins of the underlying neural processes are not as well understood. In this work, we address this issue by estimating a linear filter representation of cortical sources directly from neuroimaging data in the context of continuous speech processing. To this end, we introduce Neuro-Current Response Functions (NCRFs), a set of linear filters, spatially distributed throughout the cortex, that predict the cortical currents giving rise to the observed ongoing MEG (or EEG) data in response to continuous speech. NCRF estimation is cast within a Bayesian framework, which allows unification of the TRF and source estimation problems, and also facilitates the incorporation of prior information on the structural properties of the NCRFs. To generalize this analysis to M/EEG recordings which lack individual structural magnetic resonance (MR) scans, NCRFs are extended to free-orientation dipoles and a novel regularizing scheme is put forward to lessen reliance on fine-tuned coordinate co-registration. We present a fast estimation algorithm, which we refer to as the Champ-Lasso algorithm, by leveraging recent advances in optimization, and demonstrate its utility through application to simulated and experimentally recorded MEG data under auditory experiments. Our simulation studies reveal significant improvements over existing methods that typically operate in a two-stage fashion, in terms of spatial resolution, response function reconstruction, and recovering dipole orientations. The analysis of experimentally-recorded MEG data without MR scans corroborates existing findings, but also delineates the distinct cortical distribution of the underlying neural processes at high spatiotemporal resolution. In summary, we provide a principled modeling and estimation paradigm for MEG source analysis tailored to extracting the cortical origin of electrophysiological responses to continuous stimuli.

Sparsity enables estimation of both subcortical and cortical activity from MEG and EEG.

Subcortical structures play a critical role in brain function. However, options for assessing electrophysiological activity in these structures are limited. Electromagnetic fields generated by neuronal activity in subcortical structures can be recorded noninvasively, using magnetoencephalography (MEG) and electroencephalography (EEG). However, these subcortical signals are much weaker than those generated by cortical activity. In addition, we show here that it is difficult to resolve subcortical sources because distributed cortical activity can explain the MEG and EEG patterns generated by deep sources. We then demonstrate that if the cortical activity is spatially sparse, both cortical and subcortical sources can be resolved with M/EEG. Building on this insight, we develop a hierarchical sparse inverse solution for M/EEG. We assess the performance of this algorithm on realistic simulations and auditory evoked response data, and show that thalamic and brainstem sources can be correctly estimated in the presence of cortical activity. Our work provides alternative perspectives and tools for characterizing electrophysiological activity in subcortical structures in the human brain.

Robust spectrotemporal decomposition by iteratively reweighted least squares.

Classical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series. This universally accepted approach fails to exploit the temporal continuity in the data and is not well-suited for signals with highly structured time-frequency representations. For a time series whose time-varying mean is the superposition of a small number of oscillatory components, we formulate nonparametric batch spectral analysis as a Bayesian estimation problem. We introduce prior distributions on the time-frequency plane that yield maximum a posteriori (MAP) spectral estimates that are continuous in time yet sparse in frequency. Our spectral decomposition procedure, termed spectrotemporal pursuit, can be efficiently computed using an iteratively reweighted least-squares algorithm and scales well with typical data lengths. We show that spectrotemporal pursuit works by applying to the time series a set of data-derived filters. Using a link between Gaussian mixture models, l1 minimization, and the expectation-maximization algorithm, we prove that spectrotemporal pursuit converges to the global MAP estimate. We illustrate our technique on simulated and real human EEG data as well as on human neural spiking activity recorded during loss of consciousness induced by the anesthetic propofol. For the EEG data, our technique yields significantly denoised spectral estimates that have significantly higher time and frequency resolution than multitaper spectral estimates. For the neural spiking data, we obtain a new spectral representation of neuronal firing rates. Spectrotemporal pursuit offers a robust spectral decomposition framework that is a principled alternative to existing methods for decomposing time series into a small number of smooth oscillatory components.

Robust decoding of selective auditory attention from MEG in a competing-speaker environment via state-space modeling.

The underlying mechanism of how the human brain solves the cocktail party problem is largely unknown. Recent neuroimaging studies, however, suggest salient temporal correlations between the auditory neural response and the attended auditory object. Using magnetoencephalography (MEG) recordings of the neural responses of human subjects, we propose a decoding approach for tracking the attentional state while subjects are selectively listening to one of the two speech streams embedded in a competing-speaker environment. We develop a biophysically-inspired state-space model to account for the modulation of the neural response with respect to the attentional state of the listener. The constructed decoder is based on a maximum a posteriori (MAP) estimate of the state parameters via the Expectation Maximization (EM) algorithm. Using only the envelope of the two speech streams as covariates, the proposed decoder enables us to track the attentional state of the listener with a temporal resolution of the order of seconds, together with statistical confidence intervals. We evaluate the performance of the proposed model using numerical simulations and experimentally measured evoked MEG responses from the human brain. Our analysis reveals considerable performance gains provided by the state-space model in terms of temporal resolution, computational complexity and decoding accuracy.

A transition in brain state during propofol-induced unconsciousness.

Rhythmic oscillations shape cortical dynamics during active behavior, sleep, and general anesthesia. Cross-frequency phase-amplitude coupling is a prominent feature of cortical oscillations, but its role in organizing conscious and unconscious brain states is poorly understood. Using high-density EEG and intracranial electrocorticography during gradual induction of propofol general anesthesia in humans, we discovered a rapid drug-induced transition between distinct states with opposite phase-amplitude coupling and different cortical source distributions. One state occurs during unconsciousness and may be similar to sleep slow oscillations. A second state occurs at the loss or recovery of consciousness and resembles an enhanced slow cortical potential. These results provide objective electrophysiological landmarks of distinct unconscious brain states, and could be used to help improve EEG-based monitoring for general anesthesia.

A Subspace Pursuit-based Iterative Greedy Hierarchical solution to the neuromagnetic inverse problem.

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness.

Convergence and Stability of a Class of Iteratively Re-weighted Least Squares Algorithms for Sparse Signal Recovery in the Presence of Noise.

In this paper, we study the theoretical properties of a class of iteratively re-weighted least squares (IRLS) algorithms for sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between this class of algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribution. The IRLS algorithms we consider are parametrized by 0 < ν ≤ 1 and ε > 0. The EM formalism, as well as the connection to GSMs, allow us to establish that the IRLS(ν, ε) algorithms minimize ε-smooth versions of the ℓ ν 'norms'. We leverage EM theory to show that, for each 0 < ν ≤ 1, the limit points of the sequence of IRLS(ν, ε) iterates are stationary point of the ε-smooth ℓ ν 'norm' minimization problem on the constraint set. Finally, we employ techniques from Compressive sampling (CS) theory to show that the class of IRLS(ν, ε) algorithms is stable for each 0 < ν ≤ 1, if the limit point of the iterates coincides the global minimizer. For the case ν = 1, we show that the algorithm converges exponentially fast to a neighborhood of the stationary point, and outline its generalization to super-exponential convergence for ν < 1. We demonstrate our claims via simulation experiments. The simplicity of IRLS, along with the theoretical guarantees provided in this contribution, make a compelling case for its adoption as a standard tool for sparse signal recovery.

Adaptive modeling and inference of higher-order coordination in neuronal assemblies: a dynamic greedy estimation approach.

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Behavioural relevance of redundant and synergistic stimulus information between functionally connected neurons in mouse auditory cortex.

Measures of functional connectivity have played a central role in advancing our understanding of how information is transmitted and processed within the brain. Traditionally, these studies have focused on identifying redundant functional connectivity, which involves determining when activity is similar across different sites or neurons. However, recent research has highlighted the importance of also identifying synergistic connectivity-that is, connectivity that gives rise to information not contained in either site or neuron alone. Here, we measured redundant and synergistic functional connectivity between neurons in the mouse primary auditory cortex during a sound discrimination task. Specifically, we measured directed functional connectivity between neurons simultaneously recorded with calcium imaging. We used Granger Causality as a functional connectivity measure. We then used Partial Information Decomposition to quantify the amount of redundant and synergistic information about the presented sound that is carried by functionally connected or functionally unconnected pairs of neurons. We found that functionally connected pairs present proportionally more redundant information and proportionally less synergistic information about sound than unconnected pairs, suggesting that their functional connectivity is primarily redundant. Further, synergy and redundancy coexisted both when mice made correct or incorrect perceptual discriminations. However, redundancy was much higher (both in absolute terms and in proportion to the total information available in neuron pairs) in correct behavioural choices compared to incorrect ones, whereas synergy was higher in absolute terms but lower in relative terms in correct than in incorrect behavioural choices. Moreover, the proportion of redundancy reliably predicted perceptual discriminations, with the proportion of synergy adding no extra predictive power. These results suggest a crucial contribution of redundancy to correct perceptual discriminations, possibly due to the advantage it offers for information propagation, and also suggest a role of synergy in enhancing information level during correct discriminations.

Altered directional functional connectivity underlies post-stroke cognitive recovery.

Cortical ischaemic strokes result in cognitive deficits depending on the area of the affected brain. However, we have demonstrated that difficulties with attention and processing speed can occur even with small subcortical infarcts. Symptoms appear independent of lesion location, suggesting they arise from generalized disruption of cognitive networks. Longitudinal studies evaluating directional measures of functional connectivity in this population are lacking. We evaluated six patients with minor stroke exhibiting cognitive impairment 6-8 weeks post-infarct and four age-similar controls. Resting-state magnetoencephalography data were collected. Clinical and imaging evaluations of both groups were repeated 6- and 12 months later. Network Localized Granger Causality was used to determine differences in directional connectivity between groups and across visits, which were correlated with clinical performance. Directional connectivity patterns remained stable across visits for controls. After the stroke, inter-hemispheric connectivity between the frontoparietal cortex and the non-frontoparietal cortex significantly increased between visits 1 and 2, corresponding to uniform improvement in reaction times and cognitive scores. Initially, the majority of functional links originated from non-frontal areas contralateral to the lesion, connecting to ipsilesional brain regions. By visit 2, inter-hemispheric connections, directed from the ipsilesional to the contralesional cortex significantly increased. At visit 3, patients demonstrating continued favourable cognitive recovery showed less reliance on these inter-hemispheric connections. These changes were not observed in those without continued improvement. Our findings provide supporting evidence that the neural basis of early post-stroke cognitive dysfunction occurs at the network level, and continued recovery correlates with the evolution of inter-hemispheric connectivity.

Time-dependent homeostatic mechanisms underlie brain-derived neurotrophic factor action on neural circuitry.

Plasticity and homeostatic mechanisms allow neural networks to maintain proper function while responding to physiological challenges. Despite previous work investigating morphological and synaptic effects of brain-derived neurotrophic factor (BDNF), the most prevalent growth factor in the central nervous system, how exposure to BDNF manifests at the network level remains unknown. Here we report that BDNF treatment affects rodent hippocampal network dynamics during development and recovery from glutamate-induced excitotoxicity in culture. Importantly, these effects are not obvious when traditional activity metrics are used, so we delve more deeply into network organization, functional analyses, and in silico simulations. We demonstrate that BDNF partially restores homeostasis by promoting recovery of weak and medium connections after injury. Imaging and computational analyses suggest these effects are caused by changes to inhibitory neurons and connections. From our in silico simulations, we find that BDNF remodels the network by indirectly strengthening weak excitatory synapses after injury. Ultimately, our findings may explain the difficulties encountered in preclinical and clinical trials with BDNF and also offer information for future trials to consider.

Sequential transmission of task-relevant information in cortical neuronal networks.

Cortical processing of task-relevant information enables recognition of behaviorally meaningful sensory events. It is unclear how task-related information is represented within cortical networks by the activity of individual neurons and their functional interactions. Here, we use two-photon imaging to record neuronal activity from the primary auditory cortex of mice during a pure-tone discrimination task. We find that a subset of neurons transiently encode sensory information used to inform behavioral choice. Using Granger causality analysis, we show that these neurons form functional networks in which information transmits sequentially. Network structures differ for target versus non-target tones, encode behavioral choice, and differ between correct versus incorrect behavioral choices. Correct behavioral choices are associated with shorter communication timescales, larger functional correlations, and greater information redundancy. In summary, specialized neurons in primary auditory cortex integrate task-related information and form functional networks whose structures encode both sensory input and behavioral choice.

Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity.

Neuronal activity correlations are key to understanding how populations of neurons collectively encode information. While two-photon calcium imaging has created a unique opportunity to record the activity of large populations of neurons, existing methods for inferring correlations from these data face several challenges. First, the observations of spiking activity produced by two-photon imaging are temporally blurred and noisy. Secondly, even if the spiking data were perfectly recovered via deconvolution, inferring network-level features from binary spiking data is a challenging task due to the non-linear relation of neuronal spiking to endogenous and exogenous inputs. In this work, we propose a methodology to explicitly model and directly estimate signal and noise correlations from two-photon fluorescence observations, without requiring intermediate spike deconvolution. We provide theoretical guarantees on the performance of the proposed estimator and demonstrate its utility through applications to simulated and experimentally recorded data from the mouse auditory cortex.

Real-Time Tracking of Magnetoencephalographic Neuromarkers during a Dynamic Attention-Switching Task.

In the last few years, a large number of experiments have been focused on exploring the possibility of using non-invasive techniques, such as electroencephalography (EEG) and magnetoencephalography (MEG), to identify auditory-related neuromarkers which are modulated by attention. Results from several studies where participants listen to a story narrated by one speaker, while trying to ignore a different story narrated by a competing speaker, suggest the feasibility of extracting neuromarkers that demonstrate enhanced phase locking to the attended speech stream. These promising findings have the potential to be used in clinical applications, such as EEG-driven hearing aids. One major challenge in achieving this goal is the need to devise an algorithm capable of tracking these neuromarkers in real-time when individuals are given the freedom to repeatedly switch attention among speakers at will. Here we present an algorithm pipeline that is designed to efficiently recognize changes of neural speech tracking during a dynamic-attention switching task and to use them as an input for a near real-time state-space model that translates these neuromarkers into attentional state estimates with a minimal delay. This algorithm pipeline was tested with MEG data collected from participants who had the freedom to change the focus of their attention between two speakers at will. Results suggest the feasibility of using our algorithm pipeline to track changes of attention in near-real time in a dynamic auditory scene.

Parallel Processing of Sound Dynamics across Mouse Auditory Cortex via Spatially Patterned Thalamic Inputs and Distinct Areal Intracortical Circuits.

Natural sounds have rich spectrotemporal dynamics. Spectral information is spatially represented in the auditory cortex (ACX) via large-scale maps. However, the representation of temporal information, e.g., sound offset, is unclear. We perform multiscale imaging of neuronal and thalamic activity evoked by sound onset and offset in awake mouse ACX. ACX areas differed in onset responses (On-Rs) and offset responses (Off-Rs). Most excitatory L2/3 neurons show either On-Rs or Off-Rs, and ACX areas are characterized by differing fractions of On and Off-R neurons. Somatostatin and parvalbumin interneurons show distinct temporal dynamics, potentially amplifying Off-Rs. Functional network analysis shows that ACX areas contain distinct parallel onset and offset networks. Thalamic (MGB) terminals show either On-Rs or Off-Rs, indicating a thalamic origin of On and Off-R pathways. Thus, ACX areas spatially represent temporal features, and this representation is created by spatial convergence and co-activation of distinct MGB inputs and is refined by specific intracortical connectivity.