Poisson balanced spiking networks

Structure, dynamics, coding and optimal biophysical parameters of efficient excitatory-inhibitory spiking networks

The principle of efficient coding posits that sensory cortical networks are designed to encode maximal sensory information with minimal metabolic cost. Despite the major influence of efficient coding in neuro-science, it has remained unclear whether fundamental empirical properties of neural network activity can be explained solely based on this normative principle. Here, we rigorously derive the structural, coding, biophysical and dynamical properties of excitatory-inhibitory recurrent networks of spiking neurons that emerge directly from imposing that the network minimizes an instantaneous loss function and a time-averaged performance measure enacting efficient coding. The optimal network has biologically-plausible biophysical features, including realistic integrate-and-fire spiking dynamics, spike-triggered adaptation, and a non-stimulus-specific excitatory external input regulating metabolic cost. The efficient network has excitatory-inhibitory recurrent connectivity between neurons with similar stimulus tuning implementing feature-specific competition, similar to that recently found in visual cortex. Networks with unstructured connectivity cannot reach comparable levels of coding efficiency. The optimal biophysical parameters include 4 to 1 ratio of excitatory vs inhibitory neurons and 3 to 1 ratio of mean inhibitory-to-inhibitory vs. excitatory-to-inhibitory connectivity that closely match those of cortical sensory networks. The efficient network has biologically-plausible spiking dynamics, with a tight instantaneous E-I balance that makes them capable to achieve efficient coding of external stimuli varying over multiple time scales. Together, these results explain how efficient coding may be implemented in cortical networks and suggests that key properties of biological neural networks may be accounted for by efficient coding.

Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

Establishing brain states in neuroimaging data

The definition of a brain state remains elusive, with varying interpretations across different sub-fields of neuroscience-from the level of wakefulness in anaesthesia, to activity of individual neurons, voltage in EEG, and blood flow in fMRI. This lack of consensus presents a significant challenge to the development of accurate models of neural dynamics. However, at the foundation of dynamical systems theory lies a definition of what constitutes the 'state' of a system-i.e., a specification of the system's future. Here, we propose to adopt this definition to establish brain states in neuroimaging timeseries by applying Dynamic Causal Modelling (DCM) to low-dimensional embedding of resting and task condition fMRI data. We find that ~90% of subjects in resting conditions are better described by first-order models, whereas ~55% of subjects in task conditions are better described by second-order models. Our work calls into question the status quo of using first-order equations almost exclusively within computational neuroscience and provides a new way of establishing brain states, as well as their associated phase space representations, in neuroimaging datasets.

Biophysical parameters control signal transfer in spiking network

Introduction

Information transmission and representation in both natural and artificial networks is dependent on connectivity between units. Biological neurons, in addition, modulate synaptic dynamics and post-synaptic membrane properties, but how these relate to information transmission in a population of neurons is still poorly understood. A recent study investigated local learning rules and showed how a spiking neural network can learn to represent continuous signals. Our study builds on their model to explore how basic membrane properties and synaptic delays affect information transfer.

Methods

The system consisted of three input and output units and a hidden layer of 300 excitatory and 75 inhibitory leaky integrate-and-fire (LIF) or adaptive integrate-and-fire (AdEx) units. After optimizing the connectivity to accurately replicate the input patterns in the output units, we transformed the model to more biologically accurate units and included synaptic delay and concurrent action potential generation in distinct neurons. We examined three different parameter regimes which comprised either identical physiological values for both excitatory and inhibitory units (Comrade), more biologically accurate values (Bacon), or the Comrade regime whose output units were optimized for low reconstruction error (HiFi). We evaluated information transmission and classification accuracy of the network with four distinct metrics: coherence, Granger causality, transfer entropy, and reconstruction error.

Results

Biophysical parameters showed a major impact on information transfer metrics. The classification was surprisingly robust, surviving very low firing and information rates, whereas information transmission overall and particularly low reconstruction error were more dependent on higher firing rates in LIF units. In AdEx units, the firing rates were lower and less information was transferred, but interestingly the highest information transmission rates were no longer overlapping with the highest firing rates.

Discussion

Our findings can be reflected on the predictive coding theory of the cerebral cortex and may suggest information transfer qualities as a phenomenological quality of biological cells.

Where is the error? Hierarchical predictive coding through dendritic error computation

Top-down feedback in cortex is critical for guiding sensory processing, which has prominently been formalized in the theory of hierarchical predictive coding (hPC). However, experimental evidence for error units, which are central to the theory, is inconclusive and it remains unclear how hPC can be implemented with spiking neurons. To address this, we connect hPC to existing work on efficient coding in balanced networks with lateral inhibition and predictive computation at apical dendrites. Together, this work points to an efficient implementation of hPC with spiking neurons, where prediction errors are computed not in separate units, but locally in dendritic compartments. We then discuss the correspondence of this model to experimentally observed connectivity patterns, plasticity, and dynamics in cortex.

Optimal noise level for coding with tightly balanced networks of spiking neurons in the presence of transmission delays

Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population of N weakly-coupled neurons to achieve errors that scale as [Formula: see text]. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scale superclassically as 1/N by combining the principles of predictive coding and fast and tight inhibitory-excitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actually improve coding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by deriving analytical expressions for coding error as a function of spike propagation delay and noise levels in predictive coding tight-balance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as power-laws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits.

The geometry of robustness in spiking neural networks

Neural systems are remarkably robust against various perturbations, a phenomenon that still requires a clear explanation. Here, we graphically illustrate how neural networks can become robust. We study spiking networks that generate low-dimensional representations, and we show that the neurons’ subthreshold voltages are confined to a convex region in a lower-dimensional voltage subspace, which we call a 'bounding box'. Any changes in network parameters (such as number of neurons, dimensionality of inputs, firing thresholds, synaptic weights, or transmission delays) can all be understood as deformations of this bounding box. Using these insights, we show that functionality is preserved as long as perturbations do not destroy the integrity of the bounding box. We suggest that the principles underlying robustness in these networks — low-dimensional representations, heterogeneity of tuning, and precise negative feedback — may be key to understanding the robustness of neural systems at the circuit level.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.