Event-driven simulations of a plastic, spiking neural network

A Brain-Inspired Theory of Mind Spiking Neural Network for Reducing Safety Risks of Other Agents

Artificial Intelligence (AI) systems are increasingly applied to complex tasks that involve interaction with multiple agents. Such interaction-based systems can lead to safety risks. Due to limited perception and prior knowledge, agents acting in the real world may unconsciously hold false beliefs and strategies about their environment, leading to safety risks in their future decisions. For humans, we can usually rely on the high-level theory of mind (ToM) capability to perceive the mental states of others, identify risk-inducing errors, and offer our timely help to keep others away from dangerous situations. Inspired by the biological information processing mechanism of ToM, we propose a brain-inspired theory of mind spiking neural network (ToM-SNN) model to enable agents to perceive such risk-inducing errors inside others' mental states and make decisions to help others when necessary. The ToM-SNN model incorporates the multiple brain areas coordination mechanisms and biologically realistic spiking neural networks (SNNs) trained with Reward-modulated Spike-Timing-Dependent Plasticity (R-STDP). To verify the effectiveness of the ToM-SNN model, we conducted various experiments in the gridworld environments with random agents' starting positions and random blocking walls. Experimental results demonstrate that the agent with the ToM-SNN model selects rescue behavior to help others avoid safety risks based on self-experience and prior knowledge. To the best of our knowledge, this study provides a new perspective to explore how agents help others avoid potential risks based on bio-inspired ToM mechanisms and may contribute more inspiration toward better research on safety risks.

Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity

We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^N$$\end{document}2N various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε is the ratio of the time scales of the phase variables and synaptic weights, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ defines the sharpness of the plasticity boundary function. The limit \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \rightarrow 0$$\end{document}μ→0 corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^N$$\end{document}2N various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.

Collective firing patterns of neuronal networks with short-term synaptic plasticity

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Neural electrical activity and neural network growth

The development of central and peripheral neural system depends in part on the emergence of the correct functional connectivity in its input and output pathways. Now it is generally accepted that molecular factors guide neurons to establish a primary scaffold that undergoes activity-dependent refinement for building a fully functional circuit. However, a number of experimental results obtained recently shows that the neuronal electrical activity plays an important role in the establishing of initial interneuronal connections. Nevertheless, these processes are rather difficult to study experimentally, due to the absence of theoretical description and quantitative parameters for estimation of the neuronal activity influence on growth in neural networks. In this work we propose a general framework for a theoretical description of the activity-dependent neural network growth. The theoretical description incorporates a closed-loop growth model in which the neural activity can affect neurite outgrowth, which in turn can affect neural activity. We carried out the detailed quantitative analysis of spatiotemporal activity patterns and studied the relationship between individual cells and the network as a whole to explore the relationship between developing connectivity and activity patterns. The model, developed in this work will allow us to develop new experimental techniques for studying and quantifying the influence of the neuronal activity on growth processes in neural networks and may lead to a novel techniques for constructing large-scale neural networks by self-organization.

Equation-free analysis of spike-timing-dependent plasticity

Spike-timing-dependent plasticity is the process by which the strengths of connections between neurons are modified as a result of the precise timing of the action potentials fired by the neurons. We consider a model consisting of one integrate-and-fire neuron receiving excitatory inputs from a large number-here, 1000-of Poisson neurons whose synapses are plastic. When correlations are introduced between the firing times of these input neurons, the distribution of synaptic strengths shows interesting, and apparently low-dimensional, dynamical behaviour. This behaviour is analysed in two different parameter regimes using equation-free techniques, which bypass the explicit derivation of the relevant low-dimensional dynamical system. We demonstrate both coarse projective integration (which speeds up the time integration of a dynamical system) and the use of recently developed data mining techniques to identify the appropriate low-dimensional description of the complex dynamical systems in our model.

Sisyphus effect in pulse-coupled excitatory neural networks with spike-timing-dependent plasticity

The collective dynamics of excitatory pulse-coupled neural networks with spike-timing-dependent plasticity (STDP) is studied. Depending on the model parameters stationary states characterized by high or low synchronization can be observed. In particular, at the transition between these two regimes, persistent irregular low frequency oscillations between strongly and weakly synchronized states are observable, which can be identified as infraslow oscillations with frequencies ≃0.02-0.03 Hz. Their emergence can be explained in terms of the Sisyphus effect, a mechanism caused by a continuous feedback between the evolution of the coherent population activity and of the average synaptic weight. Due to this effect, the synaptic weights have oscillating equilibrium values, which prevents the neuronal population from relaxing into a stationary macroscopic state.

Emergence of slow collective oscillations in neural networks with spike-timing dependent plasticity

The collective dynamics of excitatory pulse coupled neurons with spike-timing dependent plasticity is studied. The introduction of spike-timing dependent plasticity induces persistent irregular oscillations between strongly and weakly synchronized states, reminiscent of brain activity during slow-wave sleep. We explain the oscillations by a mechanism, the Sisyphus Effect, caused by a continuous feedback between the synaptic adjustments and the coherence in the neural firing. Due to this effect, the synaptic weights have oscillating equilibrium values, and this prevents the system from relaxing into a stationary macroscopic state.