Search

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. [ABSTRACT FROM AUTHOR]

All of our perceptual experiences arise from the activity of neural populations. Here we study the formation of such percepts under the assumption that they emerge from a linear readout, i.e., a weighted sum of the neurons’ firing rates. We show that this assumption constrains the trial-to-trial covariance structure of neural activities and animal behavior. The predicted covariance structure depends on the readout parameters, and in particular on the temporal integration window w and typical number of neurons K used in the formation of the percept. Using these predictions, we show how to infer the readout parameters from joint measurements of a subject’s behavior and neural activities. We consider three such scenarios: (1) recordings from the complete neural population, (2) recordings of neuronal sub-ensembles whose size exceeds K, and (3) recordings of neuronal sub-ensembles that are smaller than K. Using theoretical arguments and artificially generated data, we show that the first two scenarios allow us to recover the typical spatial and temporal scales of the readout. In the third scenario, we show that the readout parameters can only be recovered by making additional assumptions about the structure of the full population activity. Our work provides the first thorough interpretation of (feed-forward) percept formation from a population of sensory neurons. We discuss applications to experimental recordings in classic sensory decision-making tasks, which will hopefully provide new insights into the nature of perceptual integration. [ABSTRACT FROM AUTHOR]

Many neural systems can store short-term information in persistently firing neurons. Such persistent activity is believed to be maintained by recurrent feedback among neurons. This hypothesis has been fleshed out in detail for the oculomotor integrator (OI) for which the so-called "line attractor" network model can explain a large set of observations. Here we show that there is a plethora of such models, distinguished by the relative strength of recurrent excitation and inhibition. In each model, the firing rates of the neurons relax toward the persistent activity states. The dynamics of relaxation can be quite different, however, and depend on the levels of recurrent excitation and inhibition. To identify the correct model, we directly measure these relaxation dynamics by performing optogenetic perturbations in the OI of zebrafish expressing halorhodopsin or channelrhodopsin. We show that instantaneous, inhibitory stimulations of the OI lead to persistent, centripetal eye position changes ipsilateral to the stimulation. Excitatory stimulations similarly cause centripetal eye position changes, yet only contralateral to the stimulation. These results show that the dynamics of the OI are organized around a central attractor state-the null position of the eyes-which stabilizes the system against random perturbations. Our results pose new constraints on the circuit connectivity of the system and provide new insights into the mechanisms underlying persistent activity. [ABSTRACT FROM AUTHOR]

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated. [ABSTRACT FROM AUTHOR]

The brain has an impressive ability to withstand neural damage. Diseases that kill neurons can go unnoticed for years, and incomplete brain lesions or silencing of neurons often fail to produce any behavioral effect. How does the brain compensate for such damage, and what are the limits of this compensation? We propose that neural circuits immediately com pensate for neuron loss, thereby preserving their function as much as possible. We show that this compensation can explain changes in tuning curves induced by neuron silencing across a variety of systems, including the primary visual cortex. We find that compensatory mechanisms can be implemented through the dynamics of networks with a tight balance of excitation and inhibition, without requiring synaptic plasticity. The limits of this compen satory mechanism are reached when excitation and inhibition become unbalanced, thereby demarcating a recovery boundary, where signal representation fails and where diseases may become symptomatic. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Summary Dopamine neurons encode the difference between actual and predicted reward, or reward prediction error (RPE). Although many models have been proposed to account for this computation, it has been difficult to test these models experimentally. Here we established an awake electrophysiological recording system, combined with rabies virus and optogenetic cell-type identification, to characterize the firing patterns of monosynaptic inputs to dopamine neurons while mice performed classical conditioning tasks. We found that each variable required to compute RPE, including actual and predicted reward, was distributed in input neurons in multiple brain areas. Further, many input neurons across brain areas signaled combinations of these variables. These results demonstrate that even simple arithmetic computations such as RPE are not localized in specific brain areas but, rather, distributed across multiple nodes in a brain-wide network. Our systematic method to examine both activity and connectivity revealed unexpected redundancy for a simple computation in the brain. [ABSTRACT FROM AUTHOR]