During brain development, billions of axons must navigate over multiple spatial scales to reach specific neuronal targets, and so build the processing circuits that generate the intelligent behavior of animals. However, the limited information capacity of the zygotic genome puts a strong constraint on how, and which, axonal routes can be encoded. We propose and validate a mechanism of development that can provide an efficient encoding of this global wiring task. The key principle, confirmed through simulation, is that basic constraints on mitoses of neural stem cells-that mitotic daughters have similar gene expression to their parent and do not stray far from one another-induce a global hierarchical map of nested regions, each marked by the expression profile of its common progenitor population. Thus, a traversal of the lineal hierarchy generates a systematic sequence of expression profiles that traces a staged route, which growth cones can follow to their remote targets. We have analyzed gene expression data of developing and adult mouse brains published by the Allen Institute for Brain Science, and found them consistent with our simulations: gene expression indeed partitions the brain into a global spatial hierarchy of nested contiguous regions that is stable at least from embryonic day 11.5 to postnatal day 56. We use this experimental data to demonstrate that our axonal guidance algorithm is able to robustly extend arbors over long distances to specific targets, and that these connections result in a qualitatively plausible connectome. We conclude that, paradoxically, cell division may be the key to uniting the neurons of the brain.

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.

Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a wide range of parameters, this asymmetry brings interesting and computationally useful dynamical properties. When driven by input, the network explores potential solutions through highly unstable 'expansion' dynamics. This expansion is steered and constrained by negative divergence of the dynamics, which ensures that the dimensionality of the solution space continues to reduce until an acceptable solution manifold is reached. Then the system contracts stably on this manifold towards its final solution trajectory. The unstable positive feedback and cross inhibition that underlie expansion and divergence are common motifs in molecular and neuronal networks. Therefore we propose that very simple organizational constraints that combine these motifs can lead to spontaneous computation and so to the spontaneous modification of entropy that is characteristic of living systems.

The prenatal development of neural circuits must provide sufficient configuration to support at least a set of core postnatal behaviors. Although knowledge of various genetic and cellular aspects of development is accumulating rapidly, there is less systematic understanding of how these various processes play together in order to construct such functional networks. Here we make some steps toward such understanding by demonstrating through detailed simulations how a competitive co-operative ('winner-take-all', WTA) network architecture can arise by development from a single precursor cell. This precursor is granted a simplified gene regulatory network that directs cell mitosis, differentiation, migration, neurite outgrowth and synaptogenesis. Once initial axonal connection patterns are established, their synaptic weights undergo homeostatic unsupervised learning that is shaped by wave-like input patterns. We demonstrate how this autonomous genetically directed developmental sequence can give rise to self-calibrated WTA networks, and compare our simulation results with biological data.

Temporal spike codes play a crucial role in neural information processing. In particular, there is strong experimental evidence that interspike intervals (ISIs) are used for stimulus representation in neural systems. However, very few algorithmic principles exploit the benefits of such temporal codes for probabilistic inference of stimuli or decisions. Here, we describe and rigorously prove the functional properties of a spike-based processor that uses ISI distributions to perform probabilistic inference. The abstract processor architecture serves as a building block for more concrete, neural implementations of the belief-propagation (BP) algorithm in arbitrary graphical models (e.g., Bayesian networks and factor graphs). The distributed nature of graphical models matches well with the architectural and functional constraints imposed by biology. In our model, ISI distributions represent the BP messages exchanged between factor nodes, leading to the interpretation of a single spike as a random sample that follows such a distribution. We verify the abstract processor model by numerical simulation in full graphs, and demonstrate that it can be applied even in the presence of analog variables. As a particular example, we also show results of a concrete, neural implementation of the processor, although in principle our approach is more flexible and allows different neurobiological interpretations. Furthermore, electrophysiological data from area LIP during behavioral experiments are assessed in light of ISI coding, leading to concrete testable, quantitative predictions and a more accurate description of these data compared to hitherto existing models.

Current models of embryological development focus on intracellular processes such as gene expression and protein networks, rather than on the complex relationship between subcellular processes and the collective cellular organization these processes support. We have explored this collective behavior in the context of neocortical development, by modeling the expansion of a small number of progenitor cells into a laminated cortex with layer and cell type specific projections. The developmental process is steered by a formal language analogous to genomic instructions, and takes place in a physically realistic three-dimensional environment. A common genome inserted into individual cells control their individual behaviors, and thereby gives rise to collective developmental sequences in a biologically plausible manner. The simulation begins with a single progenitor cell containing the artificial genome. This progenitor then gives rise through a lineage of offspring to distinct populations of neuronal precursors that migrate to form the cortical laminae. The precursors differentiate by extending dendrites and axons, which reproduce the experimentally determined branching patterns of a number of different neuronal cell types observed in the cat visual cortex. This result is the first comprehensive demonstration of the principles of self-construction whereby the cortical architecture develops. In addition, our model makes several testable predictions concerning cell migration and branching mechanisms.

The brain combines and integrates multiple cues to take coherent, context-dependent action using distributed, event-based computational primitives. Computational models that use these principles in software simulations of recurrently coupled spiking neural networks have been demonstrated in the past, but their implementation in hybrid analog/digital Very Large Scale Integration (VLSI) spiking neural networks remains challenging. Here, we demonstrate a distributed spiking neural network architecture comprising multiple neuromorphic VLSI chips able to reproduce these types of cue combination and integration operations. This is achieved by encoding cues as population activities of input nodes in a network of recurrently coupled VLSI Integrate-and-Fire (I&F) neurons. The value of the cue is place-encoded, while its uncertainty is represented by the width of the population activity profile. Relationships among different cues are specified through bidirectional connectivity matrices, shared between the individual input node populations and an intermediate node population. The resulting network dynamics bidirectionally relate not only the values of three variables according to a specified relation, but also their uncertainties. When cues on two populations are specified, the standard deviation of the activity in the unspecified population varies approximately linearly with the widths of the two input cues, and has less than 6% error in position compared to the value specified by the inputs. The results suggest a mechanism for recurrently relating cues such that missing information can both be recovered and assigned a level of certainty.

The ongoing motor output of the brain depends on its remarkable ability to rapidly transform and fuse a variety of sensory streams in real-time. The brain processes these data using networks of neurons that communicate by asynchronous spikes, a technology that is dramatically different from conventional electronic systems. We report here a step towards constructing electronic systems with analogous performance to the brain. Our VLSI spiking neural network combines in real-time three distinct sources of input data; each is place-encoded on an individual neuronal population that expresses soft Winner-Take-All dynamics. These arrays are combined according to a user-specified function that is embedded in the reciprocal connections between the soft Winner-Take-All populations and an intermediate shared population. The overall network is able to perform function approximation (missing data can be inferred from the available streams) and cue integration (when all input streams are present they enhance one another synergistically). The network performs these tasks with about 80% and 90% reliability, respectively. Our results suggest that with further technical improvement, it may be possible to implement more complex probabilistic models such as Bayesian networks in neuromorphic electronic systems.

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory and inhibitory neurons are able to interact easily because their axons and dendrites are colocalized in the same small volume. However, quantitative neuroanatomical studies of the dimensions of axonal and dendritic trees of neurons in the neocortex show that this colocalization assumption is not valid. In this letter, we describe a simple modification to the WTA circuit design that permits the effects of distributed inhibitory neurons to be coupled through synchronization, and so allows a single WTA to be distributed widely in cortical space, well beyond the arborization of any single inhibitory neuron and even across different cortical areas. We prove by nonlinear contraction analysis and demonstrate by simulation that distributed WTA subsystems combined by such inhibitory synchrony are inherently stable. We show analytically that synchronization is substantially faster than winner selection. This circuit mechanism allows networks of independent WTAs to fully or partially compete with other.

An increasing number of research groups are developing custom hybrid analog/digital very large scale integration (VLSI) chips and systems that implement hundreds to thousands of spiking neurons with biophysically realistic dynamics, with the intention of emulating brainlike real-world behavior in hardware and robotic systems rather than simply simulating their performance on general-purpose digital computers. Although the electronic engineering aspects of these emulation systems is proceeding well, progress toward the actual emulation of brainlike tasks is restricted by the lack of suitable high-level configuration methods of the kind that have already been developed over many decades for simulations on general-purpose computers. The key difficulty is that the dynamics of the CMOS electronic analogs are determined by transistor biases that do not map simply to the parameter types and values used in typical abstract mathematical models of neurons and their networks. Here we provide a general method for resolving this difficulty. We describe a parameter mapping technique that permits an automatic configuration of VLSI neural networks so that their electronic emulation conforms to a higher-level neuronal simulation. We show that the neurons configured by our method exhibit spike timing statistics and temporal dynamics that are the same as those observed in the software simulated neurons and, in particular, that the key parameters of recurrent VLSI neural networks (e.g., implementing soft winner-take-all) can be precisely tuned. The proposed method permits a seamless integration between software simulations with hardware emulations and intertranslatability between the parameters of abstract neuronal models and their emulation counterparts. Most important, our method offers a route toward a high-level task configuration language for neuromorphic VLSI systems.

The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.

In this paper, we present a language for designing instruction codes leading to the formation of axonal and dendritic branching patterns. Our approach is based on the expression of membrane receptors, which induce specific actions such as elongation, retraction and bifurcation in response to the presence of signaling molecules. We show in simulation how we can use this instruction language to specify the intrinsic properties of neurons, so that their different elongating branches interact with the local environment, and form a desired global morphology.

This demonstration will show a distributed VLSI neuromorphic system implementing the soft Winner-Take-All (WTA) operation using spiking neurons. It also shows how recurrently connected instances of them can have persistent activity states, which can used for state-dependent computation. The live demonstration of this network will show that the position of a localized stimulus can be tracked and remembered along a trajectory initially encoded in the system. The visitors will experience the real-time, fast state-dependent processing of the sensory input occurring in the network.

An increasing number of research groups develop dedicated hybrid analog/digital very large scale integration (VLSI) devices implementing hundreds of spiking neurons with bio-physically realistic dynamics. However, despite the significant progress in their design, there is still little insight in translating circuitry of neural assemblies into desired (non-trivial) function. In this work, we propose to use neural circuits implementing the soft Winner-Take-All (WTA) function. By showing that recurrently connected instances of them can have persistent activity states, which can be used as a form of working memory, we argue that such circuits can perform state-dependent computation. We demonstrate such a network in a distributed neuromorphic system consisting of two multi-neuron chips implementing soft WTA, stimulated by an event-based vision sensor. The resulting network is able to track and remember the position of a localized stimulus along a trajectory previously encoded in the system.

We introduce a framework for decision making in which the learning of decision making is reduced to its simplest and biologically most plausible form: Hebbian learning on a linear neuron. We cast our Bayesian-Hebb learning rule as reinforcement learning in which certain decisions are rewarded and prove that each synaptic weight will on average converge exponentially fast to the log-odd of receiving a reward when its pre- and postsynaptic neurons are active. In our simple architecture, a particular action is selected from the set of candidate actions by a winner-take-all operation. The global reward assigned to this action then modulates the update of each synapse. Apart from this global reward signal, our reward-modulated Bayesian Hebb rule is a pure Hebb update that depends only on the coactivation of the pre- and postsynaptic neurons, not on the weighted sum of all presynaptic inputs to the postsynaptic neuron as in the perceptron learning rule or the Rescorla-Wagner rule. This simple approach to action-selection learning requires that information about sensory inputs be presented to the Bayesian decision stage in a suitably preprocessed form resulting from other adaptive processes (acting on a larger timescale) that detect salient dependencies among input features. Hence our proposed framework for fast learning of decisions also provides interesting new hypotheses regarding neural nodes and computational goals of cortical areas that provide input to the final decision stage.

Balancing a normal pencil on its tip requires rapid feedback control with latencies on the order of milliseconds. This demonstration shows how a pair of spike-based silicon retina dynamic vision sensors (DVS) is used to provide fast visual feedback for controlling an actuated table to balance an ordinary pencil. Two DVSs view the pencil from right angles. Movements of the pencil cause spike address-events (AEs) to be emitted from the DVSs. These AEs are transmitted to a PC over USB interfaces and are processed procedurally in real time. The PC updates its estimate of the pencil's location and angle in 3d space upon each incoming AE, applying a novel tracking method based on spike-driven fitting to a model of the vertical shape of the pencil. A PD-controller adjusts X-Y-position and velocity of the table to maintain the pencil balanced upright. The controller also minimizes the deviation of the pencil's base from the center of the table. The actuated table is built using ordinary high-speed hobby servos which have been modified to obtain feedback from linear position encoders via a microcontroller. Our system can balance any small, thin object such as a pencil, pen, chop-stick, or rod for many minutes. Balancing is only possible when incoming AEs are processed as they arrive from the sensors, typically at intervals below millisecond ranges. Controlling at normal image sensor sample rates (e.g. 60 Hz) results in too long latencies for a stable control loop.

Balancing a normal pencil on its tip requires rapid feedback control with latencies on the order of milliseconds. This demonstration shows how a pair of spike-based silicon retina dynamic vision sensors (DVS) is used to provide fast visual feedback for controlling an actuated table to balance an ordinary pencil. Two DVSs view the pencil from right angles. Movements of the pencil cause spike address-events (AEs) to be emitted from the DVSs. These AEs are transmitted to a PC over USB interfaces and are processed procedurally in real time. The PC updates its estimate of the pencil's location and angle in 3d space upon each incoming AE, applying a novel tracking method based on spike-driven fitting to a model of the vertical shape of the pencil. A PD-controller adjusts X-Y-position and velocity of the table to maintain the pencil balanced upright. The controller also minimizes the deviation of the pencil's base from the center of the table. The actuated table is built using ordinary high-speed hobby servos which have been modified to obtain feedback from linear position encoders via a microcontroller. Our system can balance any small, thin object such as a pencil, pen, chop-stick, or rod for many minutes. Balancing is only possible when incoming AEs are processed as they arrive from the sensors, typically at intervals below millisecond ranges. Controlling at normal image sensor sample rates (e.g. 60 Hz) results in too long latencies for a stable control loop.

The winner-take-all (WTA) computation in networks of recurrently connected neurons is an important decision element of many models of cortical processing. However, analytical studies of the WTA performance in recurrent networks have generally addressed rate-based models. Very few have addressed networks of spiking neurons, which are relevant for understanding the biological networks themselves and also for the development of neuromorphic electronic neurons that commmunicate by action potential like address-events. Here, we make steps in that direction by using a simplified Markov model of the spiking network to examine analytically the ability of a spike-based WTA network to discriminate the statistics of inputs ranging from stationary regular to nonstationary Poisson events. Our work extends previous theoretical results showing that a WTA recurrent network receiving regular spike inputs can select the correct winner within one interspike interval. We show first for the case of spike rate inputs that input discrimination and the effects of self-excitation and inhibition on this discrimination are consistent with results obtained from the standard rate-based WTA models. We also extend this discrimination analysis of spiking WTAs to nonstationary inputs with time-varying spike rates resembling statistics of real-world sensory stimuli. We conclude that spiking WTAs are consistent with their continuous counterparts for steady-state inputs, but they also exhibit high discrimination performance with nonstationary inputs.

Although conditional branching between possible behavioral states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem, we demonstrate by theoretical analysis and simulation how networks of richly interconnected neurons, such as those observed in the superficial layers of the neocortex, can embed reliable, robust finite state machines. We show how a multistable neuronal network containing a number of states can be created very simply by coupling two recurrent networks whose synaptic weights have been configured for soft winner-take-all (sWTA) performance. These two sWTAs have simple, homogeneous, locally recurrent connectivity except for a small fraction of recurrent cross-connections between them, which are used to embed the required states. This coupling between the maps allows the network to continue to express the current state even after the input that elicited that state is withdrawn. In addition, a small number of transition neurons implement the necessary input-driven transitions between the embedded states. We provide simple rules to systematically design and construct neuronal state machines of this kind. The significance of our finding is that it offers a method whereby the cortex could construct networks supporting a broad range of sophisticated processing by applying only small specializations to the same generic neuronal circuit.

From a theoretical point of view, statistical inference is an attractive model of brain operation. However, it is unclear how to implement these inferential processes in neuronal networks. We offer a solution to this problem by showing in detailed simulations how the belief propagation algorithm on a factor graph can be embedded in a network of spiking neurons. We use pools of spiking neurons as the function nodes of the factor graph. Each pool gathers "messages" in the form of population activities from its input nodes and combines them through its network dynamics. Each of the various output messages to be transmitted over the edges of the graph is computed by a group of readout neurons that feed in their respective destination pools. We use this approach to implement two examples of factor graphs. The first example, drawn from coding theory, models the transmission of signals through an unreliable channel and demonstrates the principles and generality of our network approach. The second, more applied example is of a psychophysical mechanism in which visual cues are used to resolve hypotheses about the interpretation of an object's shape and illumination. These two examples, and also a statistical analysis, demonstrate good agreement between the performance of our networks and the direct numerical evaluation of belief propagation.

This paper describes CAVIAR, a massively parallel hardware implementation of a spike-based sensing-processing-learning-actuating system inspired by the physiology of the nervous system. CAVIAR uses the asychronous address-event representation (AER) communication framework and was developed in the context of a European Union funded project. It has four custom mixed-signal AER chips, five custom digital AER interface components, 45k neurons (spiking cells), up to 5M synapses, performs 12G synaptic operations per second, and achieves millisecond object recognition and tracking latencies.

Event-driven spike-based processing systems offer new possibilities for real-time vision. Signals are encoded asynchronously in time thus preserving the time information of the occurrence of an event. The paper examines this form of coding using experimental data from a multi-layered multi-chip system which consists of an artificial retina, a convolution filter bank and a winner-take-all network which detect the position of a moving object. The spike outputs of the convolution stage can be described by an inhomogeneous Poisson distribution of Gaussian profile, although the underlying building blocks are completely deterministic and exhibit only a small amount of variation. The authors discuss a method for measuring the accuracy of the asynchronous spiking representation in both time and value, thereby quantifying the performance of the winner-take-all network in determining the position of a ball rotating in front of the system.

A non–linear dynamic system is called contracting if initial conditions are for- gotten exponentially fast, so that all trajectories converge to a single trajectory. We use contraction theory to derive an upper bound for the strength of recurrent connections that guarantees contraction for complex neural networks. Specifi- cally, we apply this theory to a special class of recurrent networks, often called Cooperative Competitive Networks (CCNs), which are an abstract representation of the cooperative-competitive connectivity observed in cortex. This specific type of network is believed to play a major role in shaping cortical responses and se- lecting the relevant signal among distractors and noise. In this paper, we analyze contraction of combined CCNs of linear threshold units and verify the results of our analysis in a hybrid analog/digital VLSI CCN comprising spiking neurons and dynamic synapses.

As man-made systems become more complex and autonomous, there is a growing need for novel engineering methods that offer self-construction, adaptation to the environment, and self-repair. In a step towards developing such methods, we demonstrate how a simple model multicellular organism can assemble itself by replication from a single cell and finally express a fundamental behavior: foraging. Previous studies have employed evolutionary approaches to this problem. Instead, we aim at explicit design of self-constructing and -repairing systems by hierarchical specification of elementary intracellular mechanisms via a kind of genetic code. The interplay between individual cells and the gradually increasing self-created complexity of the local structure that surrounds them causes the serial unfolding of the final functional organism. The developed structure continuously feeds back to the development process, and so the system is also capable of self-repair.

The growing interest in pulse-mode processing by neural networks is encouraging the development of hardware implementations of massively parallel, distributed networks of integrate-and-fire (I&F) neurons. We have developed a reconfigurable multi-chip neuronal system for modeling feature selectivity and applied it to oriented visual stimuli. Our system comprises a temporally differentiating imager and a VLSI competitive network of neurons which use an asynchronous address event representation (AER) for communication. Here we describe the overall system, and present experimental data demonstrating the effect of recurrent connectivity on the pulse-based orientation selectivity

Cooperative competitive networks are believed to play a central role in cortical processing and have been shown to exhibit a wide set of useful computational properties. We propose a VLSI implementation of a spiking cooperative competitive network and show how it can perform context dependent computation both in the mean firing rate domain and in spike timing correlation space. In the mean rate case the network amplifies the activity of neurons belonging to the selected stimulus and suppresses the activity of neurons receiving weaker stimuli. In the event correlation case, the recurrent network amplifies with a higher gain the correlation between neurons which receive highly correlated inputs while leaving the mean firing rate unaltered. We describe the network architecture and present experimental data demonstrating its context dependent computation capabilities.

The neurons of the neocortex communicate by asynchronous events called action potentials (or 'spikes'). However, for simplicity of simulation, most models of processing by cortical neural networks have assumed that the activations of their neurons can be approximated by event rates rather than taking account of individual spikes. The obstacle to exploring the more detailed spike processing of these networks has been reduced considerably in recent years by the development of hybrid analog-digital Very-Large Scale Integrated (hVLSI) neural networks composed of spiking neurons that are able to operate in real-time. In this paper we describe such a hVLSI neural network that performs an interesting task of selective attentional processing that was previously described for a simulated 'pointer-map' rate model by Hahnloser and colleagues. We found that most of the computational features of their rate model can be reproduced in the spiking implementation; but, that spike-based processing requires a modification of the original network architecture in order to memorize a previously attended target.

Circuits composed of threshold gates (McCulloch-Pitts neurons, or perceptrons) are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts. However, when such threshold circuits are designed to perform a specific computational task, they usually differ in one important respect from computations in the brain: they require very high activity. On average every second threshold gate fires (sets a 1 as output) during a computation. By contrast, the activity of neurons in the brain is much sparser, with only about 1% of neurons firing. This mismatch between threshold and neuronal circuits is due to the particular complexity measures (circuit size and circuit depth) that have been minimized in previous threshold circuit constructions. In this letter, we investigate a new complexity measure for threshold circuits, energy complexity, whose minimization yields computations with sparse activity. We prove that all computations by threshold circuits of polynomial size with entropy O(log n) can be restructured so that their energy complexity is reduced to a level near the entropy of circuit states. This entropy of circuit states is a novel circuit complexity measure, which is of interest not only in the context of threshold circuits but for circuit complexity in general. As an example of how this measure can be applied, we show that any polynomial size threshold circuit with entropy O(log n) can be simulated by a polynomial size threshold circuit of depth 3. Our results demonstrate that the structure of circuits that result from a minimization of their energy complexity is quite different from the structure that results from a minimization of previously considered complexity measures, and potentially closer to the structure of neural circuits in the nervous system. In particular, different pathways are activated in these circuits for different classes of inputs. This letter shows that such circuits with sparse activity have a surprisingly large computational power.

We present a mixed-mode analog/digital VLSI device comprising an array of leaky integrate-and-fire (I&F) neurons, adaptive synapses with spike-timing dependent plasticity, and an asynchronous event based communication infrastructure that allows the user to (re)configure networks of spiking neurons with arbitrary topologies. The asynchronous communication protocol used by the silicon neurons to transmit spikes (events) off-chip and the silicon synapses to receive spikes from the outside is based on the "address-event representation" (AER). We describe the analog circuits designed to implement the silicon neurons and synapses and present experimental data showing the neuron's response properties and the synapses characteristics, in response to AER input spike trains. Our results indicate that these circuits can be used in massively parallel VLSI networks of I&F neurons to simulate real-time complex spike-based learning algorithms.

We present a neuromorphic pattern generator for controlling the walking gaits of four-legged robots which is inspired by central pattern generators found in the nervous system and which is implemented as a very large scale integrated (VLSI) chip. The chip contains oscillator circuits that mimic the output of motor neurons in a strongly simplified way. We show that four coupled oscillators can produce rhythmic patterns with phase relationships that are appropriate to generate all four-legged animal walking gaits. These phase relationships together with frequency and duty cycle of the oscillators determine the walking behavior of a robot driven by the chip, and they depend on a small set of stationary bias voltages. We give analytic expressions for these dependencies. This chip reduces the complex, dynamic inter-leg control problem associated with walking gait generation to the problem of setting a few stationary parameters. It provides a compact and low power solution for walking gait control in robots.

A 5-layer neuromorphic vision processor whose components communicate spike events asychronously using the address-event- representation (AER) is demonstrated. The system includes a retina chip, two convolution chips, a 2D winner-take-all chip, a delay line chip, a learning classifier chip, and a set of PCBs for computer interfacing and address space remappings. The components use a mixture of analog and digital computation and will learn to classify trajectories of a moving object. A complete experimental setup and measurements results are shown.

A key question in the design of intelligent environments is how a space can influence the actions of its users, and how such behavior can be learned. We present the results of experiments conducted as part of the Ada project, an interactive entertainment exhibit deployed at the Swiss national exhibition Expo.02. We used a learning model called distributed adaptive control (DAC) that is based on the animal learning paradigms of classical and operant conditioning. DAC has been developed using mobile robots in foraging tasks. Here, it was applied to the learning of effective cues for guiding visitors in a given direction. Our results show that, by using this learning mechanism, Ada was able to influence the behavior of visitors by learning to deploy particular types of cues. Many visitors could be induced to move toward a region of the space that they normally avoided visiting-an effect that can be seen as a spatial classification of visitors into interactive and noninteractive categories. In our analysis, we also introduce a measure of human activity that combines different types of data to capture key aspects of human behavior in interactive spaces.

Modern approaches to the architecture of living and working environments emphasize the dynamic reconfiguration of space and function to meet the needs, comfort, and preferences of its inhabitants. Although it is possible for a human operator to specify a configuration explicitly, the size, sophistication, and dynamic requirements of modern buildings demands that they have autonomous intelligence that could satisfy the needs of its inhabitants without human intervention. We describe a multiagent framework for such intelligent building control that is deployed in a commercial building equipped with sensors and effectors. Multiple agents control subparts of the environment using fuzzy rules that link sensors and effectors. The agents communicate with one another by asynchronous, interest-based messaging. They implement a novel unsupervised online real-time learning algorithm that constructs a fuzzy rule-base, derived from very sparse data in a nonstationary environment. We have developed methods for evaluating the performance of systems of this kind. Our results demonstrate that the framework and the learning algorithm significantly improve the performance of the building.

Spatio-temporal processing of spike trains by neuronal networks depends on a variety of mechanisms distributed across synapses, dendrites, and somata. In natural systems, the spike trains and the processing mechanisms cohere though their common physical instantiation. This coherence is lost when the natural system is encoded for simulation on a general purpose computer. By contrast, analog VLSI circuits are, like neurons, inherently related by their real-time physics, and so, could provide a useful substrate for exploring neuronlike event-based processing. Here, we describe a hybrid analog-digital VLSI chip comprising a set of integrate-and-fire neurons and short-term dynamical synapses that can be configured into simple network architectures with some properties of neocortical neuronal circuits. We show that, despite considerable fabrication variance in the properties of individual neurons, the chip offers a viable substrate for exploring real-time spike-based processing in networks of neurons.

Ada is an entertainment exhibit that is able to interact with many people simultaneously, using a language of light and sound. "She " received 553,700 visitors over 5 months during the Swiss Expo.02 in 2002. In this paper we present the broad motivations, design and technologies behind Ada, and a first overview of the outcomes of the exhibit.

Despite immense progress in neuroscience, we remain restricted in our ability to construct autonomous behaving robots that match the competence of even simple animals. The barriers to the realisation of this goal include: the lack of knowledge of system integration issues, engineering limitations and organisational constraints common to many research laboratories. In this paper we describe our approach to addressing these issues by constructing an artificial organism within the framework of the Ada project - a large-scale public exhibit for the Swiss Expo.02 national exhibition.

There is strong anatomical and physiological evidence that neurons with large receptive fields located in higher visual areas are recurrently connected to neurons with smaller receptive fields in lower areas. We have previously described a minimal neuronal network architecture in which top-down attentional signals to large receptive field neurons can bias and selectively read out the bottom-up sensory information to small receptive field neurons (Hahnloser, Douglas, Mahowald, & Hepp, 1999). Here we study an enhanced model, where the role of attention is to recruit specific inter-areal feedback loops (e.g., drive neurons above firing threshold). We first illustrate the operation of recruitment on a simple example of visual stimulus selection. In the subsequent analysis, we find that attentional recruitment operates by dynamical modulation of signal amplification and response multistability. In particular, we find that attentional stimulus selection necessitates increased recruitment when the stimulus to be selected is of small contrast and of small distance away from distractor stimuli. The selectability of a low-contrast stimulus is dependent on the gain of attentional effects; for example, low-contrast stimuli can be selected only when attention enhances neural responses. However, the dependence of attentional selection on stimulus-distractor distance is not contingent on whether attention enhances or suppresses responses. The computational implications of attentional recruitment are that cortical circuits can behave as winner-take-all mechanisms of variable strength and can achieve close to optimal signal discrimination in the presence of external noise.

We describe a programmable multi-chip VLSI neuronal system that can be used for exploring spike-based information processing models. The system consists of a silicon retina, a PIC microcontroller, and a transceiver chip whose integrate-and-fire neurons are connected in a soft winner-take-all architecture. The circuit on this multi-neuron chip ap- proximates a cortical microcircuit. The neurons can be configured for different computational properties by the virtual connections of a se- lected set of pixels on the silicon retina. The virtual wiring between the different chips is effected by an event-driven communication pro- tocol that uses asynchronous digital pulses, similar to spikes in a neu- ronal system. We used the multi-chip spike-based system to synthe- size orientation-tuned neurons using both a feedforward model and a feedback model. The performance of our analog hardware spiking model matched the experimental observations and digital simulations of continuous-valued neurons. The multi-chip VLSI system has advantages over computer neuronal models in that it is real-time, and the computa- tional time does not scale with the size of the neuronal network.

We have developed an analog very-large-scale integrated (aVLSI) electronic circuit that emulates a compartmental model of a neuronal dendrite. The horizontal conductances of the compartmental model are implemented as a switched capacitor network. The transmembrane conductances are implemented as transconductance amplifiers. The electrotonic properties of our silicon cable are qualitatively similar to those of the ideal passive cable that is commonly used to model mathematically the electrotonic behavior of neurons. In particular the propagation of excitatory postsynaptic potentials is realistic, and we are easily able to emulate such classical synaptic integration models as direction selectivity. We are also able to emulate the backpropagation into the dendrite of single somatic spikes and bursts of spikes. Thus, this silicon dendrite is suitable for incorporation in detailed silicon neurons operating in real-time; in particular for the emulation of forward- and backpropagating electrical activities found in real neurons.

To control the walking gaits of a four-legged robot we present a novel neuromorphic VLSI chip that coordinates the relative phasing of the robot's legs similar to how spinal Central Pattern Generators are believed to control vertebrate locomotion [3]. The chip controls the leg move(cid:173) ments by driving motors with time varying voltages which are the out(cid:173) puts of a small network of coupled oscillators. The characteristics of the chip's output voltages depend on a set of input parameters. The rela(cid:173) tionship between input parameters and output voltages can be computed analytically for an idealized system. In practice, however, this ideal re(cid:173) lationship is only approximately true due to transistor mismatch and off(cid:173) sets. Fine tuning of the chip's input parameters is done automatically by the robotic system, using an unsupervised Support Vector (SV) learning algorithm introduced recently [7]. The learning requires only that the description of the desired output is given. The machine learns from (un(cid:173) labeled) examples how to set the parameters to the chip in order to obtain a desired motor behavior.

We use neural networks with pointer map architectures to provide simple attentional processing in a robotic task. A pointer map comprises a map of neurons that encode a stimulus. Besides global feedback inhibition, the map receives feedback excitation via a small group of pointer neurons that encode the location of a salient stimulus on the map as a vectorial representation. The pointer neurons are able to apply selective processing to a particular region of the network. The robot uses these properties to manoeuver in relation to an attended object. We implemented a controller composed of two pointer maps, and a motor map. The first pointer map reports the direction of a salient obstacle in a one-dimensional map of distance derived from infrared sensors. The second pointer map reports the direction to potential obstacles in a two-dimensional edge-enhanced image derived from a forward looking CCD-camera. These outputs are applied to a motor map, where they bias the motor control signals issued to the robots wheels, according to navigational intentions.

Constant current injection with superimposed periodic inhibition gives rise to phase locking as well as chaotic activity in rat neocortical neurons. Here we compare the behavior of a leaky integrate-and-fire neural model with that of a biophysically realistic model of the rat neuron to determine which membrane properties influence the response to such stimuli. We find that only the biophysical model with voltage-sensitive conductances can produce chaotic behavior.

It is generally assumed that nerve cells optimize their performance to reflect the statistics of their input. Electronic circuit analogs of neurons require similar methods of self-optimization for stable and autonomous operation. We here describe and demonstrate a biologically plausible adaptive algorithm that enables a neuron to adapt the current threshold and the slope (or gain) of its current-frequency relationship to match the man (or dc offset) and variance (or dynamic range or contrast) of the time-varying somatic input current. The adaptation algorithm estimates the somatic current signal from the spike train by way of the intracellular somatic calcium concentration, thereby continuously adjusting the neurons' firing dynamics. This principle is shown to work in an analog VLSI-designed silicon neuron.

Almost all models of orientation and direction selectivity in visual cortex are based on feedforward connection schemes, where genicu(cid:173) late input provides all excitation to both pyramidal and inhibitory neurons. The latter neurons then suppress the response of the for(cid:173) mer for non-optimal stimuli. However, anatomical studies show that up to 90 % of the excitatory synaptic input onto any corti(cid:173) cal cell is provided by other cortical cells. The massive excitatory feedback nature of cortical circuits is embedded in the canonical microcircuit of Douglas &. Martin (1991). We here investigate ana(cid:173) lytically and through biologically realistic simulations the function(cid:173) ing of a detailed model of this circuitry, operating in a hysteretic mode. In the model, weak geniculate input is dramatically ampli(cid:173) fied by intracortical excitation, while inhibition has a dual role: (i) to prevent the early geniculate-induced excitation in the null di(cid:173) rection and (ii) to restrain excitation and ensure that the neurons fire only when the stimulus is in their receptive-field. Among the 4 Humbert Suarez, Christo! Koch, Rodney Douglas insights gained are the possibility that hysteresis underlies visual cortical function, paralleling proposals for short-term memory, and strong limitations on linearity tests that use gratings. Properties of visual cortical neurons are compared in detail to this model and to a classical model of direction selectivity that does not include excitatory corti co-cortical connections. The model explain a num(cid:173) ber of puzzling features of direction-selective simple cells, includ(cid:173) ing the small somatic input conductance changes that have been measured experimentally during stimulation in the null direction. The model also allows us to understand why the velocity-response curve of area 17 neurons is different from that of their LG N affer(cid:173) ents, and the origin of expansive and compressive nonlinearities in the contrast-response curve of striate cortical neurons.

We have used the morphology derived from single horseradish peroxidase-labeled neurons, known membrane conductance properties and microanatomy to construct a model neocortical network that exhibits synchronized bursting. The network was composed of interconnected pyramidal (excitatory) neurons with different intrinsic burst frequencies, and smooth (inhibitory) neurons that provided global feedback inhibition to all of the pyramids. When the network was activated by geniculocortical afferents the burst discharges of the pyramids quickly became synchronized with zero average phase-shift. The synchronization was strongly dependent on global feedback inhibition, which acted to group the coactivated bursts generated by intracortical reexcitation. Our results suggest that the synchronized bursting observed between cortical neurons responding to coherent visual stimuli is a simple consequence of the principles of intracortical connectivity.

We examine the effect of inhibition on the axon initial segment (AIS) by the chandelier (“axoaxonic”) cells, using a simplified compartmental model of actual pyramidal neurons from cat visual cortex. We show that within generally accepted ranges, inhibition at the AIS cannot completely prevent action potential discharge: only small amounts of excitatory synaptic current can be inhibited. Moderate amounts of excitatory current always result in action potential discharge, despite AIS inhibition. Inhibition of the somadendrite by basket cells enhances the effect of AIS inhibition and vice versa. Thus the axoaxonic cells may act synergistically with basket cells: the AIS inhibition increases the threshold for action potential discharge, the basket cells then control the suprathreshold discharge.

We have used microanatomy derived from single neurons, and in vivo intracellular recordings to develop a simplified circuit of the visual cortex. The circuit explains the intracellular responses to pulse stimulation in terms of the interactions between three basic populations of neurons, and reveals the following features of cortical processing that are important to computational theories of neocortex. First, inhibition and excitation are not separable events. Activation of the cortex inevitably sets in motion a sequence of excitation and inhibition in every neuron. Second, the thalamic input does not provide the major excitation arriving at any neuron. Instead the intracortical excitatory connections provide most of the excitation. Third, the time evolution of excitation and inhibition is far longer than the synaptic delays of the circuits involved. This means that cortical processing cannot rely on precise timing between individual synaptic inputs.