We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-andfire models, interacting with current-based or conductance-based synapses, using clock-driven or NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.

Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as a candidate for a learning rule that could explain how behaviorally relevant adaptive changes in complex networks of spiking neurons could be achieved in a self-organizing manner through local synaptic plasticity. However, the capabilities and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. Our model for this experiment relies on a combination of reward-modulated STDP with variable spontaneous firing activity. Hence it also provides a possible functional explanation for trial-to-trial variability, which is characteristic for cortical networks of neurons but has no analogue in currently existing artificial computing systems. In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics.

An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.

A recurrent spiking neural network is proposed that implements planning as probabilistic inference for finite and infinite horizon tasks. The architecture splits this problem into two parts: The stochastic transient firing of the network embodies the dynamics of the planning task. With appropriate injected input this dynamics is shaped to generate high-reward state trajectories. A general class of reward-modulated plasticity rules for these afferent synapses is presented. The updates optimize the likelihood of getting a reward through a variant of an Expectation Maximization algorithm and learning is guaranteed to convergence to a local maximum. We find that the network dynamics are qualitatively similar to transient firing patterns during planning and foraging in the hippocampus of awake behaving rats. The model extends classical attractor models and provides a testable prediction on identifying modulating contextual information. In a real robot arm reaching and obstacle avoidance task the ability to represent multiple task solutions is investigated. The neural planning method with its local update rules provides the basis for future neuromorphic hardware implementations with promising potentials like large data processing abilities and early initiation of strategies to avoid dangerous situations in robot co-worker scenarios.

The Parallel Circuit SIMulator (PCSIM) is a software package for simulation of neural circuits. It is primarily designed for distributed simulation of large scale networks of spiking point neurons. Although its computational core is written in C++, PCSIM's primary interface is implemented in the Python programming language, which is a powerful programming environment and allows the user to easily integrate the neural circuit simulator with data analysis and visualization tools to manage the full neural modeling life cycle. The main focus of this paper is to describe PCSIM's full integration into Python and the benefits thereof. In particular we will investigate how the automatically generated bidirectional interface and PCSIM's object-oriented modular framework enable the user to adopt a hybrid modeling approach: using and extending PCSIM's functionality either employing pure Python or C++ and thus combining the advantages of both worlds. Furthermore, we describe several supplementary PCSIM packages written in pure Python and tailored towards setting up and analyzing neural simulations.