Neuromorphic engineering combines the architectural and computational principles of systems neuroscience with semiconductor electronics, with the aim of building efficient and compact devices that mimic the synaptic and neural machinery of the brain. The energy consumptions promised by neuromorphic engineering are extremely low, comparable to those of the nervous system. Until now, however, the neuromorphic approach has been restricted to relatively simple circuits and specialized functions, thereby obfuscating a direct comparison of their energy consumption to that used by conventional von Neumann digital machines solving real-world tasks. Here we show that a recent technology developed by IBM can be leveraged to realize neuromorphic circuits that operate as classifiers of complex real-world stimuli. Specifically, we provide a set of general prescriptions to enable the practical implementation of neural architectures that compete with state-of-the-art classifiers. We also show that the energy consumption of these architectures, realized on the IBM chip, is typically two or more orders of magnitude lower than that of conventional digital machines implementing classifiers with comparable performance. Moreover, the spike-based dynamics display a trade-off between integration time and accuracy, which naturally translates into algorithms that can be flexibly deployed for either fast and approximate classifications, or more accurate classifications at the mere expense of longer running times and higher energy costs. This work finally proves that the neuromorphic approach can be efficiently used in real-world applications and has significant advantages over conventional digital devices when energy consumption is considered.

The matching law constitutes a quantitative description of choice behavior that is often observed in foraging tasks. According to the matching law, organisms distribute their behavior across available response alternatives in the same proportion that reinforcers are distributed across those alternatives. Recently a few biophysically plausible neural network models have been proposed to explain the matching behavior observed in the experiments. Here we study systematically the learning dynamics of these networks while performing a matching task on the concurrent variable interval (VI) schedule. We found that the model neural network can operate in one of three qualitatively different regimes depending on the parameters that characterize the synaptic dynamics and the reward schedule: (1) a matching behavior regime, in which the probability of choosing an option is roughly proportional to the baiting fractional probability of that option; (2) a perseverative regime, in which the network tends to make always the same decision; and (3) a tristable regime, in which the network can either perseverate or choose the two targets randomly approximately with the same probability. Different parameters of the synaptic dynamics lead to different types of deviations from the matching law, some of which have been observed experimentally. We show that the performance of the network depends on the number of stable states of each synapse and that bistable synapses perform close to optimal when the proper learning rate is chosen. Because our model provides a link between synaptic dynamics and qualitatively different behaviors, this work provides us with insight into the effects of neuromodulators on adaptive behaviors and psychiatric disorders.

We present a model of spike-driven synaptic plasticity inspired by experimental observations and motivated by the desire to build an electronic hardware device that can learn to classify complex stimuli in a semisupervised fashion. During training, patterns of activity are sequentially imposed on the input neurons, and an additional instructor signal drives the output neurons toward the desired activity. The network is made of integrate-and-fire neurons with constant leak and a floor. The synapses are bistable, and they are modified by the arrival of presynaptic spikes. The sign of the change is determined by both the depolarization and the state of a variable that integrates the postsynaptic action potentials. Following the training phase, the instructor signal is removed, and the output neurons are driven purely by the activity of the input neurons weighted by the plastic synapses. In the absence of stimulation, the synapses preserve their internal state indefinitely. Memories are also very robust to the disruptive action of spontaneous activity. A network of 2000 input neurons is shown to be able to classify correctly a large number (thousands) of highly overlapping patterns (300 classes of preprocessed Latex characters, 30 patterns per class, and a subset of the NIST characters data set) and to generalize with performances that are better than or comparable to those of artificial neural networks. Finally we show that the synaptic dynamics is compatible with many of the experimental observations on the induction of long-term modifications (spike-timing-dependent plasticity and its dependence on both the postsynaptic depolarization and the frequency of pre- and postsynaptic neurons).

Learning in a neuronal network is often thought of as a linear superposition of synaptic modifications induced by individual stimuli. However, since biological synapses are naturally bounded, a linear superposition would cause fast forgetting of previously acquired memories. Here we show that this forgetting can be avoided by introducing additional constraints on the synaptic and neural dynamics. We consider Hebbian plasticity of excitatory synapses. A synapse is modified only if the postsynaptic response does not match the desired output. With this learning rule, the original memory performances with unbounded weights are regained, provided that (1) there is some global inhibition, (2) the learning rate is small, and (3) the neurons can discriminate small differences in the total synaptic input (e.g., by making the neuronal threshold small compared to the total postsynaptic input). We prove in the form of a generalized perceptron convergence theorem that under these constraints, a neuron learns to classify any linearly separable set of patterns, including a wide class of highly correlated random patterns. During the learning process, excitation becomes roughly balanced by inhibition, and the neuron classifies the patterns on the basis of small differences around this balance. The fact that synapses saturate has the additional benefit that nonlinearly separable patterns, such as similar patterns with contradicting outputs, eventually generate a subthreshold response, and therefore silence neurons that cannot provide any information.

Rate models are often used to study the behavior of large networks of spiking neurons. Here we propose a procedure to derive rate models that take into account the fluctuations of the input current and firing-rate adaptation, two ubiquitous features in the central nervous system that have been previously overlooked in constructing rate models. The procedure is general and applies to any model of firing unit. As examples, we apply it to the leaky integrate-and-fire (IF) neuron, the leaky IF neuron with reversal potentials, and to the quadratic IF neuron. Two mechanisms of adaptation are considered, one due to an after hyperpolarization current and the other to an adapting threshold for spike emission. The parameters of these simple models can be tuned to match experimental data obtained from neocortical pyramidal neurons. Finally, we show how the stationary model can be used to predict the time-varying activity of a large population of adapting neurons.

We present a new technique, based on a proposed event-based strategy (Mattia & Del Giudice, 2000), for efficiently simulating large networks of simple model neurons. The strategy was based on the fact that interactions among neurons occur by means of events that are well localized in time (the action potentials) and relatively rare. In the interval between two of these events, the state variables associated with a model neuron or a synapse evolved deterministically and in a predictable way. Here, we extend the event-driven simulation strategy to the case in which the dynamics of the state variables in the inter-event intervals are stochastic. This extension captures both the situation in which the simulated neurons are inherently noisy and the case in which they are embedded in a very large network and receive a huge number of random synaptic inputs. We show how to effectively include the impact of large background populations into neuronal dynamics by means of the numerical evaluation of the statistical properties of single-model neurons under random current injection. The new simulation strategy allows the study of networks of interacting neurons with an arbitrary number of external afferents and inherent stochastic dynamics.

We present a model for spike-driven dynamics of a plastic synapse, suited for a VLSI implementation. The synaptic device behaves as a capacitor on short timescales and preserves the memory of two stable states (efficacies) on long timescales. The transitions (LTP/LTD) are stochastic because both the number and the distribution of neural spikes in any finite (stimulation) interval fluctuate, even at fixed pre- and postsynaptic spike rates. The dynamics of the single synapse is studied analytically by extending the solution to a classic problem in queuing theory (Takàcs process). The model of the synapse is implemented in a VLSI and consists of only 18 transistors. It is also directly simulated. The simulations indicate that LTP/LTD probabilities versus rates are robust to fluctuations of the electronic parameters in a wide range of rates. The solutions for these probabilities are in very good agreement with both the simulations and measurements. Moreover, the probabilities are readily manipulable by variations of the chip's parameters, even in ranges where they are very small. The tests of the electronic device cover the range from spontaneous activity (3–4 Hz) to stimulus-driven rates (50 Hz). Low transition probabilities can be maintained in all ranges, even though the intrinsic time constants of the device are short (∼ 100 ms). Synaptic transitions are triggered by elevated presynaptic rates: for low presynaptic rates, there are essentially no transitions. The synaptic device can preserve its memory for years in the absence of stimulation. Stochasticity of learning is a result of the variability of interspike intervals; noise is a feature of the distributed dynamics of the network. The fact that the synapse is binary on long timescales solves the stability problem of synaptic efficacies in the absence of stimulation. Yet stochastic learning theory ensures that it does not affect the collective behavior of the network, if the transition probabilities are low and LTP is balanced against LTD.

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

We discuss paradigmatic properties of the activity of single cells comprising an attractor—a developed stable delay activity distribution. To demonstrate these properties and a methodology for measuring their values, we present a detailed account of the spike activity recorded from a single cell in the inferotemporal cortex of a monkey performing a delayed match-to-sample (DMS) task of visual images. In particular, we discuss and exemplify (1) the relation between spontaneous activity and activity immediately preceding the first stimulus in each trial during a series of DMS trials, (2) the effect on the visual response (i.e., activity during stimulation) of stimulus degradation (moving in the space of IT afferents), (3) the behavior of the delay activity (i.e., activity following visual stimulation) under stimulus degradation (attractor dynamics and the basin of attraction), and (4) the propagation of information between trials—the vehicle for the formation of (contextual) correlations by learning a fixed stimulus sequence (Miyashita, 1988). In the process of the discussion and demonstration, we expose effective tools for the identification and characterization of attractor dynamics. 1

We discuss the long term maintenance of acquired memory in synaptic connections of a perpetually learning electronic device. This is affected by ascribing each synapse a finite number of stable states in which it can maintain for indefinitely long periods. Learning uncorrelated stimuli is expressed as a stochastic process produced by the neural activities on the synapses. In several interesting cases the stochastic process can be analyzed in detail, leading to a clarification of the performance of the network, as an associative memory, during the process of uninterrupted learning. The stochastic nature of the process and the existence of an asymptotic distribution for the synaptic values in the network imply generically that the memory is a palimpsest but capacity is as low as log N for a network of N neurons. The only way we find for avoiding this tight constraint is to allow the parameters governing the learning process (the coding level of the stimuli; the transition probabilities for potentiation and depression and the number of stable synaptic levels) to depend on the number of neurons. It is shown that a network with synapses that have two stable states can dynamically learn with optimal storage efficiency, be a palimpsest, and maintain its (associative) memory for an indefinitely long time provided the coding level is low and depression is equilibrated against potentiation. We suggest that an option so easily implementable in material devices would not have been overlooked by biology. Finally we discuss the stochastic learning on synapses with variable number of stable synaptic states.