Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.

In computational neuroscience, as well as in machine learning, neuromorphic devices promise an accelerated and scalable alternative to neural network simulations. Their neural connectivity and synaptic capacity depend on their specific design choices, but is always intrinsically limited. Here, we present a strategy to achieve structural plasticity that optimizes resource allocation under these constraints by constantly rewiring the pre- and postsynaptic partners while keeping the neuronal fan-in constant and the connectome sparse. In particular, we implemented this algorithm on the analog neuromorphic system BrainScaleS-2. It was executed on a custom embedded digital processor located on chip, accompanying the mixed-signal substrate of spiking neurons and synapse circuits. We evaluated our implementation in a simple supervised learning scenario, showing its ability to optimize the network topology with respect to the nature of its training data, as well as its overall computational efficiency.

We present first experimental results on the novel BrainScaleS-2 neuromorphic architecture based on an analog neuro-synaptic core and augmented by embedded microprocessors for complex plasticity and experiment control. The high acceleration factor of 1000 compared to biological dynamics enables the execution of computationally expensive tasks, by allowing the fast emulation of long-duration experiments or rapid iteration over many consecutive trials. The flexibility of our architecture is demonstrated in a suite of five distinct experiments, which emphasize different aspects of the BrainScaleS-2 system.

We demonstrate five experiments that are performed on the novel BrainScaleS-2 neuromorphic architecture based on an analog neuro-synaptic core and augmented by embedded microprocessors for complex plasticity and experiment control. The high acceleration factor of 1000 compared to biological dynamics enables the execution of computationally expensive tasks, by allowing the fast emulation of long-duration experiments or rapid iteration over many consecutive trials. The experiments were chosen to emphasize different aspects of the BrainScaleS-2 system, especially involving on-chip plasticity and closed-loop scenarios.

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functional Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

The extreme complexity of the brain has attracted the attention of neuroscientists and other researchers for a long time. More recently, the neuromorphic hardware has matured to provide a new powerful tool to study neuronal dynamics. Here, we study neuronal dynamics using different settings on a neuromorphic chip built with flexible parameters of neuron models. Our unique setting in the network of leaky integrate-and-fire (LIF) neurons is to introduce a weak noise environment. We observed three different types of collective neuronal activities, or phases, separated by sharp boundaries, or phase transitions. From this, we construct a rudimentary phase diagram of neuronal dynamics and demonstrate that a noise-induced chaotic phase (N-phase), which is dominated by neuronal avalanche activity (intermittent aperiodic neuron firing), emerges in the presence of noise and its width grows with the noise intensity. The dynamics can be manipulated in this N-phase. Our results and comparison with clinical data is consistent with the literature and our previous work showing that healthy brain must reside in the N-phase. We argue that the brain phase diagram with further refinement may be used for the diagnosis and treatment of mental disease and also suggest that the dynamics may be manipulated to serve as a means of new information processing (e.g., for optimization). Neuromorphic chips, similar to the one we used but with a variety of neuron models, may be used to further enhance the understanding of human brain function and accelerate the development of neuroscience research.

How spiking networks are able to perform probabilistic inference is an intriguing question, not only for understanding information processing in the brain, but also for transferring these computational principles to neuromorphic silicon circuits. A number of computationally powerful spiking network models have been proposed, but most of them have only been tested, under ideal conditions, in software simulations. Any implementation in an analog, physical system, be it in vivo or in silico, will generally lead to distorted dynamics due to the physical properties of the underlying substrate. In this paper, we discuss several such distortive effects that are difficult or impossible to remove by classical calibration routines or parameter training. We then argue that hierarchical networks of leaky integrate-and-fire neurons can offer the required robustness for physical implementation and demonstrate this with both software simulations and emulation on an accelerated analog neuromorphic device.

This paper presents an extension of the BrainScaleS accelerated analog neuromorphic hardware model. The scalable neuromorphic architecture is extended by the support for multi-compartment models and non-linear dendrites. These features are part of a 65 nm prototype Application Specific Integrated Circuit (ASIC). It allows to emulate different spike types observed in cortical pyramidal neurons: NMDA plateau potentials, calcium and sodium spikes. By replicating some of the structures of these cells, they can be configured to perform coincidence detection within a single neuron. Built-in plasticity mechanisms can modify not only the synaptic weights, but also the dendritic synaptic composition to efficiently train large multi-compartment neurons. Transistor-level simulations demonstrate the functionality of the analog implementation and illustrate analogies to biological measurements.

Emulating spiking neural networks on analog neuromorphic hardware offers several advantages over simulating them on conventional computers, particularly in terms of speed and energy consumption. However, this usually comes at the cost of reduced control over the dynamics of the emulated networks. In this paper, we demonstrate how iterative training of a hardware-emulated network can compensate for anomalies induced by the analog substrate. We first convert a deep neural network trained in software to a spiking network on the BrainScaleS wafer-scale neuromorphic system, thereby enabling an acceleration factor of 10000 compared to the biological time domain. This mapping is followed by the in-the-loop training, where in each training step, the network activity is first recorded in hardware and then used to compute the parameter updates in software via backpropagation. An essential finding is that the parameter updates do not have to be precise, but only need to approximately follow the correct gradient, which simplifies the computation of updates. Using this approach, after only several tens of iterations, the spiking network shows an accuracy close to the ideal software-emulated prototype. The presented techniques show that deep spiking networks emulated on analog neuromorphic devices can attain good computational performance despite the inherent variations of the analog substrate.

Despite being originally inspired by the central nervous system, artificial neural networks have diverged from their biological archetypes as they have been remodeled to fit, particular tasks. In this paper, we review several possibilites to reverse map these architectures to biologically more realistic spiking networks with the aim of emulating them on fast, low-power neuromorphic hardware. Since many of these devices employ analog components, which cannot, be perfectly controlled, finding ways to compensate for the resulting effects represents a key challenge. Here, we discuss three different, strategies to address this problem: the addition of auxiliary network components for stabilizing activity, the utilization of inherently robust, architectures and a training method for hardware-emulated networks that, functions without, perfect, knowledge of the system's dynamics and parameters. For all three scenarios, we corroborate our theoretical considerations with experimental results on accelerated analog neuromorphic platforms.

Temporal coding is one approach to representing information in spiking neural networks. An example of its application is the location of sounds by barn owls that requires especially precise temporal coding. Dependent upon the azimuthal angle, the arrival times of sound signals are shifted between both ears. In order to determine these interaural time differences, the phase difference of the signals is measured. We implemented this biologically inspired network on a neuromorphic hardware system and demonstrate spike-timing dependent plasticity on an analog, highly accelerated hardware substrate. Our neuromorphic implementation enables the resolution of time differences of less than 50 ns. On-chip Hebbian learning mechanisms select inputs from a pool of neurons which code for the same sound frequency. Hence, noise caused by different synaptic delays across these inputs is reduced. Furthermore, learning compensates for variations on neuronal and synaptic parameters caused by device mismatch intrinsic to the neuromorphic substrate.

This demonstration is based on the wafer-scale neuromophic system presented in the previous papers by Schemmel et. al. (20120), Scholze et. al. (2011) and Millner et. al. (2010). The demonstration setup will allow the visitors to monitor and partially manipulate the neural events at every level. They will get an insight into the complex interplay between packet-based and realtime communication necessary to combine continuous-time mixed-signal neural networks with a packet-based transport network. Several network experiments implemented on the setup will be accessible for user interaction.

We will set up a fully functional system consisting of a custom design hardware framework (Figures 1 and 2) with the neural network chips described in the appended 4-page paper, Section II-A. The framework is connected digitally to a host PC, on which we will run a software that provides the simulator-like, flexible and non-expert usability of the neuromorphic device as described in the appended paper, Section II-B. We will also connect an oscilloscope via which arbitrarily selectable neuron membranes or other analog parameters can be recorded directly from the chips.

In this paper we describe our approach towards highly configurable neuromorphic hardware systems that serve as useful and flexible tools in modeling neuroscience. We utilize a mixed-signal VLSI model that implements a massively accelerated network of spiking neurons, and we describe a novel methodological framework that allows to exploit both the speed and the programmability of this device for the systematic and simulator-like exploration of cortical network architectures. We present a variety of experimental results that illustrate the functionality of our modeling platform, and we verify all hardware measurements with reference software simulations. Especially on the network level these comparison studies are unique in terms of the quantitative correspondence between the data. The presented hardware experiments include high-conductance states in hardware neurons and the application of synaptic depression and facilitation for self-adjusting network architectures.

Modeling neural tissue is an important tool to investigate biological neural networks. Until recently, most of this modeling has been done using numerical methods. In the European research project "FACETS" this computational approach is complemented by different kinds of neuromorphic systems. A special emphasis lies in the usability of these systems for neuroscience. To accomplish this goal an integrated software/hardware framework has been developed which is centered around a unified neural system description language, called PyNN, that allows the scientist to describe a model and execute it in a transparent fashion on either a neuromorphic hardware system or a numerical simulator. A very large analog neuromorphic hardware system developed within FACETS is able to use complex neural models as well as realistic network topologies, i.e. it can realize more than 10000 synapses per neuron, to allow the direct execution of models which previously could have been simulated numerically only.

We describe an accelerated hardware neuron being capable of emulating the adap-tive exponential integrate-and-fire neuron model. Firing patterns of the membrane stimulated by a step current are analyzed in transistor level simulation and in silicon on a prototype chip. The neuron is destined to be the hardware neuron of a highly integrated wafer-scale system reaching out for new computational paradigms and opening new experimentation possibilities. As the neuron is dedicated as a universal device for neuroscientific experiments, the focus lays on parameterizability and reproduction of the analytical model.

Under typical synaptical stimulation, cortical neurons exhibit a total membrane conductance which, compared to a situation without any input spikes, is significantly increased. This results in a shorter membrane time constant and thus in an increased capability of the neuron to detect coincidences in its synaptic input. For this study, a neuromorphic hardware device was utilized, which does not provide direct access to its membrane conductances. Motivated by the aim of finding biologically realistic configuration regimes for the chip operation, a purely spike-based method for the estimation of membrane conductances is presented, allowing to test the hardware membrane dynamics. A proof of principle is given by pure software simulations. Hardware results are presented which illustrate the functionality of the method and show the possibility to generate high-conductance states in the utilized VLSI neurons. In the final section, limits and useful implications of the proposed method are discussed.

This paper presents a network architecture to interconnect VLSI neural network chips to build a distributed ANN system. The architecture combines techniques from circuit switching and packet switching to provide two different service classes: isochronous connections and best-effort packet transfers. The isochronous connections are able to transport the axonal data of artificial neurons between VLSI ANN models that feature a speedup of multiples orders of magnitudes compared to biology. The connections use reserved bandwidth to provide loss-less transmissions as well as a low end-to-end delay with bounded jitter. Best-effort packet transfers use the remaining bandwidth for on-demand multi-purpose communication. The data forwarding is performed between synchronized instances of a dedicated switch architecture used at each network node. The switch is scalable in terms of port numbers and line speed. Its low complexity allows for an implementation within programmable logic or directly within a VLSI neural network chip. A reference implementation of the proposed network architecture is presented within an existing framework that hosts VLSI neural network chips operating at speedups of 104to 105. The network architecture is further not limited to VLSI neural networks, but it can in principle be used in all network environments that require isochronous connections as well as packet processing.

An analog VLSI hardware architecture for the distributed simulation of large-scale spiking neural networks has been developed. Several hundred integrated computing nodes, each hosting up to 512 neurons, will be interconnected and operated on un-cut silicon wafers. The electro-technical aspects and the details of the hardware implementation are covered in a separate contribution to this conference. This paper focuses on the usability of the system by demonstrating that biologically relevant network models can in fact be mapped to this system. Different network configurations are established on the hardware by programmable switch matrices, repeaters, and address decoders. Systematic routing algorithms are presented to map a given network model to the hardware system. Routing is simulated for several network examples, proving the systempsilas practical applicability. Furthermore, the routing simulations are used to fix values for yet open hardware parameters.

This paper introduces a novel design of an artificial neural network tailored for wafer-scale integration. The presented VLSI implementation includes continuous-time analog neurons with up to 16 k inputs. A novel interconnection and routing scheme allows the mapping of a multitude of network models derived from biology on the VLSI neural network while maintaining a high resource usage. A single 20 cm wafer contains about 60 million synapses. The implemented neurons are highly accelerated compared to biological real time. The power consumption of the dense interconnection network providing the necessary communication bandwidth is a critical aspect of the system integration. A novel asynchronous low-voltage signaling scheme is presented that makes the wafer-scale approach feasible by limiting the total power consumption while simultaneously providing a flexible, programmable network topology.

When studying the different aspects of synaptic plasticity, the timescales involved range from milliseconds to hours, thus covering at least seven orders of magnitude. To make this temporal dynamic range accessible to the experimentalist, we have developed a highly accelerated analog VLSI model of leaky integrate and fire neurons. It incorporates fast and slow synaptic facilitation and depression mechanisms in its conductance based synapses. By using a 180 nm process 105synapses fit on a 25 mm2die. A single chip can model the temporal evolution of the synaptic weights in networks of up to 384 neurons with an acceleration factor of 105while recording the neural action potentials with a temporal resolution better than 30μs biological time. This reduces the time needed for a 10 minute experiment to merely 6 ms, paving the way for complex parameter searches to reproduce biological findings. Due to a digital communication structure larger networks can be built from multiple chips while retaining an acceleration factor of a least 104.

We propose a Markov process model for spike-frequency adapting neural ensembles that synthesizes existing mean-adaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unified and tractable framework that goes beyond renewal and mean-adaptation theories by accounting for correlations between subsequent interspike intervals. A method for efficiently generating inhomogeneous realizations of the proposed Markov process is given, numerical methods for solving the population equation are presented, and an expression for the first-order interspike interval correlation is derived. Further, we show that the full five-dimensional master equation for a conductance-based integrate-and-fire neuron with spike-frequency adaptation and a relative refractory mechanism driven by Poisson spike trains can be reduced to a two-dimensional generalization of the proposed Markov process by an adiabatic elimination of fast variables. For static and dynamic stimulation, negative serial interspike interval correlations and transient population responses, respectively, of Monte Carlo simulations of the full five-dimensional system can be accurately described by the proposed two-dimensional Markov process.

Convolutional neural networks are known to be powerful image classifiers. In this work, a method is proposed for training convolutional networks for implementation on an existing mixed digital-analog VLSI hardware architecture. The binary threshold neurons provided by this architecture cannot be trained using gradient-based methods. The convolutional layers are trained with a clustering method, locally in each layer. The output layer is trained using the Perceptron learning rule. Competitive results are obtained on hand-written digits (MNIST) and traffic signs. The analog hardware enables high integration and low power consumption, but inherent error sources affect the computation accuracy. Networks trained as suggested are highly robust against random changes of synaptic weights occuring on the hardware substrate, and work well even with only three distinct weight values (-1, 0, +1), reducing computational complexity to mere counting.

This paper describes an area-efficient mixed-signal implementation of synapse-based long term plasticity realized in a VLSI model of a spiking neural network. The artificial synapses are based on an implementation of spike time dependent plasticity (STDP). In the biological specimen, STDP is a mechanism acting locally in each synapse. The presented electronic implementation succeeds in maintaining this high level of parallelism and simultaneously achieves a synapse density of more than 9k synapses per mm2in a 180 nm technology. This allows the construction of neural micro-circuits close to the biological specimen while maintaining a speed several orders of magnitude faster than biological real time. The large acceleration factor enhances the possibilities to investigate key aspects of plasticity, e.g. by performing extensive parameter searches.

This work presents an incremental training approach that allows for the use of simple evolutionary algorithms to efficiently train the weights of fast mixed-signal hardware neural networks. The training strategy is tested on a set of common classification benchmark problems (E.coli, yeast, thyroid and wine) and the results are comparable to those of other investigations. They demonstrate that the used hardware neural network architecture can successfully be trained to solve real-world problems. It is also shown that the presented training strategy is suited for use in conjunction with a specialized coprocessor that speeds up evolutionary algorithms by performing the genetic operations within a configurable logic. With the ability to integrate the coprocessor into the training strategy, an important prerequisite is fulfilled to exploit the speed of the neural hardware during training.

This work presents a new VLSI model for biological neural systems, a unified research tool for neuro- as well as computer science. It allows construction of neural microcircuits close to the biological specimen while maintaining a speed several orders faster than real time. The synapse model includes an implementation of spike time dependent plasticity (STDP). Therefore, the VLSI system allows the investigation of key aspects of plasticity without a speed penalty. Additionally, this system is a research tool for new concepts of information processing like liquid or any-time computing. The analog, continuous-time operation of the neuron is implemented in a contemporary deep-submicron process technology. Thereby it realizes a powerful computing system that is not based on the Turing paradigm.

Computation without stable states is a computing paradigm dif- ferent from Turing's and has been demonstrated for various types of simulated neural networks. This publication transfers this to a hardware implemented neural network. Results of a software im- plementation are reproduced showing that the performance peaks when the network exhibits dynamics at the edge of chaos. The liquid computing approach seems well suited for operating analog computing devices such as the used VLSI neural network.

This paper presents experimental results obtained during the training of an analog hardware neural network for the prediction of cellular localization sites of proteins in yeast and E.coli. The synaptic weights of the network are optimized by an evolutionary chip-in-the-loop algorithm. The results provide a first demonstration of the applicability of the presented neural network architecture to real-world problems that require the ability to generalize and to handle quasi-continuous multi-bit inputs.