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Decorrelation of neural-network activity by inhibitory feedback
Tom Tetzlaff, Moritz Helias, Gaute T. Einevoll, Markus Diesmann
TL;DR
Shared presynaptic input can generate correlations that impair neural information encoding, yet recurrent networks often exhibit fewer correlations than shared input predicts. Using linear theory and leaky integrate-and-fire simulations, the paper shows that inhibitory feedback suppresses spike-train correlations and population-rate fluctuations in purely inhibitory and excitatory-inhibitory networks. The suppression reflects specific correlation structures, rather than merely correlations between excitatory and inhibitory neurons.
Problem
Shared presynaptic input should correlate finite neural networks, but observed recurrent-network correlations are smaller than expected, limiting information encoding and reliable decoding.
Method
The authors combine a linear network model with leaky integrate-and-fire simulations and compare intact recurrent feedback with perturbed feedback statistics.
Results
Inhibitory feedback suppresses spike-train correlations and population-rate fluctuations in purely inhibitory and excitatory-inhibitory networks.
Takeaways & Limitations
Shared-input correlations are canceled by negative spike-train correlations in purely inhibitory networks and by a specific EE, EI, II correlation structure in excitatory-inhibitory networks.
Takeaways & Limitations
The predicted excitatory-inhibitory correlation structure assumes identical internal dynamics and homogeneous connectivity for excitatory and inhibitory neurons.
Abstract
from arXiv · showhide
Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent theoretical and experimental studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. By means of a linear network model and simulations of networks of leaky integrate-and-fire neurons, we show that shared-input correlations are efficiently suppressed by inhibitory feedback. To elucidate the effect of feedback, we compare the responses of the intact recurrent network and systems where the statistics of the feedback channel is perturbed. The suppression of spike-train correlations and population-rate fluctuations by inhibitory feedback can be observed both in purely inhibitory and in excitatory-inhibitory networks. The effect is fully understood by a linear theory and becomes already apparent at the macroscopic level of the population averaged activity. At the microscopic level, shared-input correlations are suppressed by spike-train correlations: In purely inhibitory networks, they are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).
Author summary
Inhibitory feedback actively suppresses correlations in recurrent neural networks, including both excitatory-inhibitory and purely inhibitory networks. The authors derive this mechanism analytically for leaky integrate-and-fire networks.
- Inhibitory feedback actively suppresses spike-train correlations despite shared presynaptic input.
- The decorrelation mechanism applies to networks composed of excitatory and inhibitory neurons as well as purely inhibitory networks.
- For leaky integrate-and-fire neurons, the authors derive the correlation structure analytically.
1 Introduction
Correlations can limit information encoding and reliable decoding, yet neighboring cortical neurons often show weak correlations despite substantial shared input. The paper argues that recurrent inhibitory feedback suppresses these correlations and population-rate fluctuations through a mechanism that does not require balanced excitation and inhibition.
- Correlated spike trains limit the information encoded by spatio-temporal activity and impair reliable decoding in noise.
- Neighboring cortical neurons can remain weakly correlated despite sharing substantial presynaptic input.
- Prior work attributes part of shared-input suppression to nonlinear spike generation, but recurrent dynamics produce still smaller correlations.
- Negative feedback alone efficiently suppresses correlations, including in purely inhibitory networks, without requiring balanced excitation and inhibition.
- Simulations show that inhibitory feedback reduces low-frequency spike-train correlations and population-rate fluctuations relative to expectations from shared input.
2 Results
Recurrent inhibitory feedback suppresses low-frequency population-rate fluctuations and shared-input correlations in LIF networks, including purely inhibitory and mixed excitatory-inhibitory systems. Linear theory explains this suppression and shows that its frequency dependence and coupling structure persist across network-model variants.
- 2.1 Suppression of population-rate fluctuations in LIF networks: Finite recurrent networks share presynaptic inputs, yet feedback networks show substantially weaker response correlations and population-rate fluctuations than matched feedforward networks.The comparison preserves the external drive, and the feedforward replacement uses independent Poisson inputs matched to the intact network's mean firing rate.
- 2.1 Suppression of population-rate fluctuations in LIF networks: Differences in population-rate spectra are primarily caused by spike-train cross-correlations, because single-neuron power spectra and auto-correlations are nearly unchanged between feedback and feedforward conditions.Population activity therefore provides a macroscopic measure of pairwise spike-train correlations.
- 2.1 Suppression of population-rate fluctuations in LIF networks: Low-frequency fluctuation suppression occurs in both purely inhibitory and mixed excitatory-inhibitory LIF networks, for instantaneous and delayed low-pass synapses.With low-pass synapses, the suppression is somewhat more restricted to frequencies below 10 Hz but remains similarly pronounced.
- 2.2 Suppression of population-activity fluctuations by negative feedback: Negative feedback alone efficiently suppresses low-frequency fluctuations, without requiring balanced excitation and inhibition.For strong effective coupling, the zero-frequency power ratio decreases as w̄^-2, while high-frequency suppression vanishes as the response transfer function approaches zero.
- 2.2 Suppression of population-activity fluctuations by negative feedback: The zero-frequency suppression ratio is independent of external-input amplitude and spectrum, and is insensitive to the exact neuron, synapse, input, or delay model.This robustness follows because the low-frequency transfer function approaches unity, making the detailed response kernel irrelevant at zero frequency.
- 2.3 Population-activity fluctuations in excitatory-inhibitory networks: In mixed excitatory-inhibitory networks, increasing coupling can increase absolute population-rate fluctuations while still decreasing their ratio relative to the feedforward case.In inhibition-dominated regimes, the sum activity receives effectively negative self-feedback and behaves qualitatively like a purely inhibitory network.
3 Discussion
The discussion identifies inhibitory negative feedback as the mechanism that suppresses shared-input correlations, population-rate fluctuations, and low-frequency activity fluctuations in recurrent networks. It also clarifies the theory’s scope, experimentally testable predictions, and limitations.
- Mechanism: Negative feedback suppresses pairwise correlations and low-frequency population-activity fluctuations, allowing neurons to fire more independently than shared input would predict.Perturbing feedback statistics, such as replacing feedback with uncorrelated feedforward input, can amplify both response correlations and population-rate fluctuations.
- Mechanism: In mixed excitatory-inhibitory networks, suppression arises from a specific correlation structure among EE, EI, and II pairings rather than merely from E-I correlations.The proposed structure under simplifying assumptions is CEE > CEI > CII.
- Mechanism: In purely inhibitory networks, negative population-averaged spike-train correlations compensate for the positive contribution of shared input.The same decorrelation principle therefore does not require a balance of excitation and inhibition.
- Theory and predictions: The theory focuses on integrated, low-frequency correlations and distinguishes connected from unconnected neuron pairs to relate observed correlations to synaptic connectivity.The integrated covariance structure is presented as experimentally testable, although direct testing may require reanalysis of data or predictions for complete correlation functions.
- Theory and predictions: A linear theory captures recurrent-network correlations and is quantitatively accurate for asynchronous-irregular integrate-and-fire networks with realistic coupling and postsynaptic potentials up to about 1 mV.The approach uses an analytical equivalence between a reduced linear model and spiking integrate-and-fire neurons, exploiting closure of second-order fluctuation descriptions for linear dynamics.
- Limitations: The conclusions are constrained by linearization, perturbative response assumptions, Poisson presynaptic input, small synaptic amplitudes, homogeneous connectivity, and identical E-I internal dynamics.The model does not prevent high-frequency oscillation buildup associated with synfire explosion, and its correlation structure may not apply when firing rates or connectivity are heterogeneous.
4 Methods
The study combines LIF-network simulations with a linear reduction to analyze population-averaged correlations and inhibitory-feedback decorrelation. The linear theory uses Volterra response expansions, self-consistent covariance equations, and stability analysis, while the LIF response kernel is obtained through Fokker–Planck theory.
- Network models: The authors study sparsely connected purely inhibitory and excitatory-inhibitory LIF networks and compare simulations with predictions from a linear model.Network simulations were carried out with NEST, with model details and parameters specified separately.
- Linear reduction: Neural activity is approximated by a Volterra expansion up to linear order in the incoming spike trains.The approximation treats each neuron's response as a functional of the history of its afferent spike trains and retains only the linear term.
- Correlation theory: The linearized dynamics yields pairwise spike-train correlations through response kernels and auto- and cross-correlation functions.The correlation derivation is formulated for positive time lags and averages over stationary network realizations.
- Validity and stability: The linear theory is restricted to its stability domain, whereas nonlinear LIF dynamics prevents the explosive fluctuation growth predicted beyond instability.For the reported parameters, the instability boundary occurs near J = 2.8 mV.
- Population averaging: Population averaging replaces individual variances and covariances with averages over statistically equivalent neuron pairs and connectivity realizations.For excitatory-inhibitory networks, this procedure produces a four-dimensional linear system for subpopulation variances and unconnected-pair covariances.
- Feedback mechanism: The self-consistency equations require cancellation between shared-input and correlation-induced terms when effective coupling is large and correlations remain small.Because the shared prefactor Kw is typically much greater than one, the two order-ε contributions must have opposite signs.