A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.

Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.

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.

Spiking neurons, receiving temporally encoded inputs, can compute radial basis functions (RBFs) by storing the relevant information in their delays. In this paper we show how these delays can be learned using exclusively locally available information (basically the time difference between the pre- and postsynaptic spikes). Our approach gives rise to a biologically plausible algorithm for finding clusters in a high-dimensional input space with networks of spiking neurons, even if the environment is changing dynamically. Furthermore, we show that our learning mechanism makes it possible that such RBF neurons can perform some kind of feature extraction where they recognize that only certain input coordinates carry relevant information. Finally we demonstrate that this model allows the recognition of temporal sequences even if they are distorted in various ways.

A novel approach for unsupervised domain adaptation for neural networks is proposed. It relies on metricbased regularization of the learning process. The metric-based regularization aims at domain-invariant latent feature representations by means of maximizing the similarity between domain-specific activation distributions. The proposed metric results from modifying an integral probability metric such that it becomes less translation-sensitive on a polynomial function space. The metric has an intuitive interpretation in the dual space as the sum of differences of higher order central moments of the corresponding activation distributions. Under appropriate assumptions on the input distributions, error minimization is proven for the continuous case. As demonstrated by an analysis of standard benchmark experiments for sentiment analysis, object recognition and digit recognition, the outlined approach is robust regarding parameter changes and achieves higher classification accuracies than comparable approaches. 1

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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.

Abstract:This chapter surveys web resources regarding computer models and analysis tools for neural microcircuits. In particular it describes the features of a new website (www.lsm.tugraz.at) that facilitates the creation of computer models for cortical neural microcircuits of various sizes and levels of detail, as well as tools for evaluating the computational power of these models in a Matlabenvironment.