Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model

Evaluation of Spiking Neural Nets-Based Image Classification Using the Runtime Simulator RAVSim

Spiking Neural Networks (SNNs) help achieve brain-like efficiency and functionality by building neurons and synapses that mimic the human brain's transmission of electrical signals. However, optimal SNN implementation requires a precise balance of parametric values. To design such ubiquitous neural networks, a graphical tool for visualizing, analyzing, and explaining the internal behavior of spikes is crucial. Although some popular SNN simulators are available, these tools do not allow users to interact with the neural network during simulation. To this end, we have introduced the first runtime interactive simulator, called Runtime Analyzing and Visualization Simulator (RAVSim),a developed to analyze and dynamically visualize the behavior of SNNs, allowing end-users to interact, observe output concentration reactions, and make changes directly during the simulation. In this paper, we present RAVSim with the current implementation of runtime interaction using the LIF neural model with different connectivity schemes, an image classification model using SNNs, and a dataset creation feature. Our main objective is to primarily investigate binary classification using SNNs with RGB images. We created a feed-forward network using the LIF neural model for an image classification algorithm and evaluated it by using RAVSim. The algorithm classifies faces with and without masks, achieving an accuracy of 91.8% using 1000 neurons in a hidden layer, 0.0758 MSE, and an execution time of ∼10[Formula: see text]min on the CPU. The experimental results show that using RAVSim not only increases network design speed but also accelerates user learning capability.

A framework for macroscopic phase-resetting curves for generalised spiking neural networks

Brain rhythms emerge from synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferring the PRC and developing a systematic phase reduction theory for large-scale brain rhythms remains an outstanding challenge. Here we present a theoretical framework and methodology to compute the PRC of generic spiking networks with emergent collective oscillations. We adopt a renewal approach where neurons are described by the time since their last action potential, a description that can reproduce the dynamical feature of many cell types. For a sufficiently large number of neurons, the network dynamics are well captured by a continuity equation known as the refractory density equation. We develop an adjoint method for this equation giving a semi-analytical expression of the infinitesimal PRC. We confirm the validity of our framework for specific examples of neural networks. Our theoretical framework can link key biological properties at the individual neuron scale and the macroscopic oscillatory network properties. Beyond spiking networks, the approach is applicable to a broad class of systems that can be described by renewal processes.

The formation of oscillatory neuronal assemblies at the network level has been hypothesized to be fundamental to many cognitive and motor functions. One prominent tool to understand the dynamics of oscillatory activity response to stimuli, and hence the neural code for which it is a substrate, is a nonlinear measure called Phase-Resetting Curve (PRC). At the network scale, the PRC defines the measure of how a given synaptic input perturbs the timing of next upcoming volley of spike assemblies: either advancing or delaying this timing. As a further application, one can use PRCs to make unambiguous predictions about whether communicating networks of neurons will phase-lock as it is often observed across the cortical areas and what would be this stable phase-configuration: synchronous, asynchronous or with asymmetric phase-shifts. The latter configuration also implies a preferential flow of information form the leading network to the follower, thereby giving causal signatures of directed functional connectivity. Because of the key position of the PRC in studying synchrony, information flow and entrainment to external forcing, it is crucial to move toward a theory that allows to compute the PRCs of network-wide oscillations not only for a restricted class of models, as has been done in the past, but to network descriptions that are generalized and can reflect flexibly single cell properties. In this manuscript, we tackle this issue by showing how the PRC for network oscillations can be computed using the adjoint systems of partial differential equations that define the dynamics of the neural activity density.

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar.