Search

Purpose. Causal relationship recognition is a fundamental operation in neural networks aimed at learning behavior, action planning, and inferring external world dynamics. This operation is particularly crucial for reinforcement learning (RL). In the context of spiking neural networks (SNNs), events are represented as spikes emitted by network neurons or input nodes. Detecting causal relationships within these events is essential for effective RL implementation. Methods. This research paper presents a novel approach to realize causal relationship recognition using a simple spiking binary neuron. The proposed method leverages specially designed synaptic plasticity rules, which are both straightforward and efficient. Notably, our approach accounts for the temporal aspects of detected causal links and accommodates the representation of spiking signals as single spikes or tight spike sequences (bursts), as observed in biological brains. Furthermore, this study places a strong emphasis on the hardware-friendliness of the proposed models, ensuring their efficient implementation on modern and future neuroprocessors. Results. Being compared with precise machine learning techniques, such as decision tree algorithms and convolutional neural networks, our neuron demonstrates satisfactory accuracy despite its simplicity. Conclusion. We introduce a multi-neuron structure capable of operating in more complex environments with enhanced accuracy, making it a promising candidate for the advancement of RL applications in SNNs.

Neuromorphic computing, commonly understood as a computing approach built upon neurons, synapses, and their dynamics, as opposed to Boolean gates, is gaining large mindshare due to its direct application in solving current and future computing technological problems, such as smart sensing, smart devices, self-hosted and self-contained devices, artificial intelligence (AI) applications, etc. In a largely software-defined implementation of neuromorphic computing, it is possible to throw enormous computational power or optimize models and networks depending on the specific nature of the computational tasks. However, a hardware-based approach needs the identification of well-suited neuronal and synaptic models to obtain high functional and energy efficiency, which is a prime concern in size, weight, and power (SWaP) constrained environments. In this work, we perform a study on the characteristics of hardware neuron models (namely, inference errors, generalizability and robustness, practical implementability, and memory capacity) that have been proposed and demonstrated using a plethora of emerging nano-materials technology-based physical devices, to quantify the performance of such neurons on certain classes of problems that are of great importance in real-time signal processing like tasks in the context of reservoir computing. We find that the answer on which neuron to use for what applications depends on the particulars of the application requirements and constraints themselves, i.e., we need not only a hammer but all sorts of tools in our tool chest for high efficiency and quality neuromorphic computing.

The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances in the spiking activity raises the question how these models relate to each other. In particular it is hard to distinguish between generic properties of covariances and peculiarities due to the abstracted model. Here we present a unified view on pairwise covariances in recurrent networks in the irregular regime. We consider the binary neuron model, the leaky integrate-and-fire model, and the Hawkes process. We show that linear approximation maps each of these models to either of two classes of linear rate models, including the Ornstein-Uhlenbeck process as a special case. The distinction between both classes is the location of additive noise in the rate dynamics, which is located on the output side for spiking models and on the input side for the binary model. Both classes allow closed form solutions for the covariance. For output noise it separates into an echo term and a term due to correlated input. The unified framework enables us to transfer results between models. For example, we generalize the binary model and the Hawkes process to the situation with synaptic conduction delays and simplify derivations for established results. Our approach is applicable to general network structures and suitable for the calculation of population averages. The derived averages are exact for fixed out-degree network architectures and approximate for fixed in-degree. We demonstrate how taking into account fluctuations in the linearization procedure increases the accuracy of the effective theory and we explain the class dependent differences between covariances in the time and the frequency domain. Finally we show that the oscillatory instability emerging in networks of integrate-and-fire models with delayed inhibitory feedback is a model-invariant feature: the same structure of poles in the complex frequency plane determines the population power spectra.

The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances in the spiking activity raises the question how these models relate to each other. In particular it is hard to distinguish between generic properties of covariances and peculiarities due to the abstracted model. Here we present a unified view on pairwise covariances in recurrent networks in the irregular regime. We consider the binary neuron model, the leaky integrate-and-fire (LIF) model, and the Hawkes process. We show that linear approximation maps each of these models to either of two classes of linear rate models (LRM), including the Ornstein-Uhlenbeck process (OUP) as a special case. The distinction between both classes is the location of additive noise in the rate dynamics, which is located on the output side for spiking models and on the input side for the binary model. Both classes allow closed form solutions for the covariance. For output noise it separates into an echo term and a term due to correlated input. The unified framework enables us to transfer results between models. For example, we generalize the binary model and the Hawkes process to the situation with synaptic conduction delays and simplify derivations for established results. Our approach is applicable to general network structures and suitable for the calculation of population averages. The derived averages are exact for fixed out-degree network architectures and approximate for fixed in-degree. We demonstrate how taking into account fluctuations in the linearization procedure increases the accuracy of the effective theory and we explain the class dependent differences between covariances in the time and the frequency domain. Finally we show that the oscillatory instability emerging in networks of LIF models with delayed inhibitory feedback is a model-invariant feature: the same structure of poles in the complex frequency plane determines the population power spectra. [ABSTRACT FROM AUTHOR]

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the mean field approach for populations of spiking neurons. We introduce the general idea in networks of binary neurons, starting from the most basic results and then generalizing to more relevant situations. This allows to derive the mean field equations in a simplified setting. We then derive the mean field equations for populations of integrate-and-fire neurons. An effort is made to derive the main equations of the theory using only elementary methods from calculus and probability theory. The chapter ends with a discussion of the assumptions of the theory and some of the consequences of violating those assumptions. This discussion includes an introduction to balanced and metastable networks and a brief catalogue of successful applications of the mean field approach to the study of neural circuits., (© 2022. The Author(s).)