Fast learning without synaptic plasticity in spiking neural networks

Spiking neural networks are of high current interest, both from the perspective of modelling neural networks of the brain and for porting their fast learning capability and energy efficiency into neuromorphic hardware. But so far we have not been able to reproduce fast learning capabilities of the brain in spiking neural networks. Biological data suggest that a synergy of synaptic plasticity on a slow time scale with network dynamics on a faster time scale is responsible for fast learning capabilities of the brain. We show here that a suitable orchestration of this synergy between synaptic plasticity and network dynamics does in fact reproduce fast learning capabilities of generic recurrent networks of spiking neurons. This points to the important role of recurrent connections in spiking networks, since these are necessary for enabling salient network dynamics. We show more specifically that the proposed synergy enables synaptic weights to encode more general information such as priors and task structures, since moment-to-moment processing of new information can be delegated to the network dynamics.

Context association in pyramidal neurons through local synaptic plasticity in apical dendrites

The unique characteristics of neocortical pyramidal neurons are thought to be crucial for many aspects of information processing and learning in the brain. Experimental data suggests that their segregation into two distinct compartments, the basal dendrites close to the soma and the apical dendrites branching out from the thick apical dendritic tuft, plays an essential role in cortical organization. A recent hypothesis states that layer 5 pyramidal cells associate top-down contextual information arriving at their apical tuft with features of the sensory input that predominantly arrives at their basal dendrites. It has however remained unclear whether such context association could be established by synaptic plasticity processes. In this work, we formalize the objective of such context association learning through a mathematical loss function and derive a plasticity rule for apical synapses that optimizes this loss. The resulting plasticity rule utilizes information that is available either locally at the synapse, through branch-local NMDA spikes, or through global Ca2+events, both of which have been observed experimentally in layer 5 pyramidal cells. We show in computer simulations that the plasticity rule enables pyramidal cells to associate top-down contextual input patterns with high somatic activity. Furthermore, it enables networks of pyramidal neuron models to perform context-dependent tasks and enables continual learning by allocating new dendritic branches to novel contexts.

Memory-Dependent Computation and Learning in Spiking Neural Networks Through Hebbian Plasticity

Spiking neural networks (SNNs) are the basis for many energy-efficient neuromorphic hardware systems. While there has been substantial progress in SNN research, artificial SNNs still lack many capabilities of their biological counterparts. In biological neural systems, memory is a key component that enables the retention of information over a huge range of temporal scales, ranging from hundreds of milliseconds up to years. While Hebbian plasticity is believed to play a pivotal role in biological memory, it has so far been analyzed mostly in the context of pattern completion and unsupervised learning in artificial and SNNs. Here, we propose that Hebbian plasticity is fundamental for computations in biological and artificial spiking neural systems. We introduce a novel memory-augmented SNN architecture that is enriched by Hebbian synaptic plasticity. We show that Hebbian enrichment renders SNNs surprisingly versatile in terms of their computational as well as learning capabilities. It improves their abilities for out-of-distribution generalization, one-shot learning, cross-modal generative association, language processing, and reward-based learning. This suggests that powerful cognitive neuromorphic systems can be built based on this principle.

Restoring Vision in Adverse Weather Conditions With Patch-Based Denoising Diffusion Models

Image restoration under adverse weather conditions has been of significant interest for various computer vision applications. Recent successful methods rely on the current progress in deep neural network architectural designs (e.g., with vision transformers). Motivated by the recent progress achieved with state-of-the-art conditional generative models, we present a novel patch-based image restoration algorithm based on denoising diffusion probabilistic models. Our patch-based diffusion modeling approach enables size-agnostic image restoration by using a guided denoising process with smoothed noise estimates across overlapping patches during inference. We empirically evaluate our model on benchmark datasets for image desnowing, combined deraining and dehazing, and raindrop removal. We demonstrate our approach to achieve state-of-the-art performances on both weather-specific and multi-weather image restoration, and experimentally show strong generalization to real-world test images.

Classification of Whisker Deflections From Evoked Responses in the Somatosensory Barrel Cortex With Spiking Neural Networks

Spike-based neuromorphic hardware has great potential for low-energy brain-machine interfaces, leading to a novel paradigm for neuroprosthetics where spiking neurons in silicon read out and control activity of brain circuits. Neuromorphic processors can receive rich information about brain activity from both spikes and local field potentials (LFPs) recorded by implanted neural probes. However, it was unclear whether spiking neural networks (SNNs) implemented on such devices can effectively process that information. Here, we demonstrate that SNNs can be trained to classify whisker deflections of different amplitudes from evoked responses in a single barrel of the rat somatosensory cortex. We show that the classification performance is comparable or even superior to state-of-the-art machine learning approaches. We find that SNNs are rather insensitive to recorded signal type: both multi-unit spiking activity and LFPs yield similar results, where LFPs from cortical layers III and IV seem better suited than those of deep layers. In addition, no hand-crafted features need to be extracted from the data—multi-unit activity can directly be fed into these networks and a simple event-encoding of LFPs is sufficient for good performance. Furthermore, we find that the performance of SNNs is insensitive to the network state—their performance is similar during UP and DOWN states.

Cortical oscillations support sampling-based computations in spiking neural networks

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.

Dendritic Computing: Branching Deeper into Machine Learning

In this paper, we discuss the nonlinear computational power provided by dendrites in biological and artificial neurons. We start by briefly presenting biological evidence about the type of dendritic nonlinearities, respective plasticity rules and their effect on biological learning as assessed by computational models. Four major computational implications are identified as improved expressivity, more efficient use of resources, utilizing internal learning signals, and enabling continual learning. We then discuss examples of how dendritic computations have been used to solve real-world classification problems with performance reported on well known data sets used in machine learning. The works are categorized according to the three primary methods of plasticity used-structural plasticity, weight plasticity, or plasticity of synaptic delays. Finally, we show the recent trend of confluence between concepts of deep learning and dendritic computations and highlight some future research directions.

Spike frequency adaptation supports network computations on temporally dispersed information

For solving tasks such as recognizing a song, answering a question, or inverting a sequence of symbols, cortical microcircuits need to integrate and manipulate information that was dispersed over time during the preceding seconds. Creating biologically realistic models for the underlying computations, especially with spiking neurons and for behaviorally relevant integration time spans, is notoriously difficult. We examine the role of spike frequency adaptation in such computations and find that it has a surprisingly large impact. The inclusion of this well-known property of a substantial fraction of neurons in the neocortex - especially in higher areas of the human neocortex - moves the performance of spiking neural network models for computations on network inputs that are temporally dispersed from a fairly low level up to the performance level of the human brain.

STDP Forms Associations between Memory Traces in Networks of Spiking Neurons

Memory traces and associations between them are fundamental for cognitive brain function. Neuron recordings suggest that distributed assemblies of neurons in the brain serve as memory traces for spatial information, real-world items, and concepts. However, there is conflicting evidence regarding neural codes for associated memory traces. Some studies suggest the emergence of overlaps between assemblies during an association, while others suggest that the assemblies themselves remain largely unchanged and new assemblies emerge as neural codes for associated memory items. Here we study the emergence of neural codes for associated memory items in a generic computational model of recurrent networks of spiking neurons with a data-constrained rule for spike-timing-dependent plasticity. The model depends critically on 2 parameters, which control the excitability of neurons and the scale of initial synaptic weights. By modifying these 2 parameters, the model can reproduce both experimental data from the human brain on the fast formation of associations through emergent overlaps between assemblies, and rodent data where new neurons are recruited to encode the associated memories. Hence, our findings suggest that the brain can use both of these 2 neural codes for associations, and dynamically switch between them during consolidation.

Emergence of Stable Synaptic Clusters on Dendrites Through Synaptic Rewiring

The connectivity structure of neuronal networks in cortex is highly dynamic. This ongoing cortical rewiring is assumed to serve important functions for learning and memory. We analyze in this article a model for the self-organization of synaptic inputs onto dendritic branches of pyramidal cells. The model combines a generic stochastic rewiring principle with a simple synaptic plasticity rule that depends on local dendritic activity. In computer simulations, we find that this synaptic rewiring model leads to synaptic clustering, that is, temporally correlated inputs become locally clustered on dendritic branches. This empirical finding is backed up by a theoretical analysis which shows that rewiring in our model favors network configurations with synaptic clustering. We propose that synaptic clustering plays an important role in the organization of computation and memory in cortical circuits: we find that synaptic clustering through the proposed rewiring mechanism can serve as a mechanism to protect memories from subsequent modifications on a medium time scale. Rewiring of synaptic connections onto specific dendritic branches may thus counteract the general problem of catastrophic forgetting in neural networks.

The location of the axon initial segment affects the bandwidth of spike initiation dynamics

The dynamics and the sharp onset of action potential (AP) generation have recently been the subject of intense experimental and theoretical investigations. According to the resistive coupling theory, an electrotonic interplay between the site of AP initiation in the axon and the somato-dendritic load determines the AP waveform. This phenomenon not only alters the shape of APs recorded at the soma, but also determines the dynamics of excitability across a variety of time scales. Supporting this statement, here we generalize a previous numerical study and extend it to the quantification of the input-output gain of the neuronal dynamical response. We consider three classes of multicompartmental mathematical models, ranging from ball-and-stick simplified descriptions of neuronal excitability to 3D-reconstructed biophysical models of excitatory neurons of rodent and human cortical tissue. For each model, we demonstrate that increasing the distance between the axonal site of AP initiation and the soma markedly increases the bandwidth of neuronal response properties. We finally consider the Liquid State Machine paradigm, exploring the impact of altering the site of AP initiation at the level of a neuronal population, and demonstrate that an optimal distance exists to boost the computational performance of the network in a simple classification task.

The neurons in the brain encode information through electrical impulses. The performance of a cell in terms of its ability to process and transfer information downstream thus depends heavily on the machinery of initiation of these impulses. In this work, we consider both the cell morphology and the biophysical properties of impulse initiation as the primary parameters that influence information processing in single neurons, as well as in networks. We specifically analyze the location of nerve impulse initiation along the cell’s axon and the way the neuron transfers incoming information. By using single-cell models of various complexity as well as network models, we conclude that information processing is sensitive to the geometrical details of impulse initiation.

Embodied Synaptic Plasticity With Online Reinforcement Learning

The endeavor to understand the brain involves multiple collaborating research fields. Classically, synaptic plasticity rules derived by theoretical neuroscientists are evaluated in isolation on pattern classification tasks. This contrasts with the biological brain which purpose is to control a body in closed-loop. This paper contributes to bringing the fields of computational neuroscience and robotics closer together by integrating open-source software components from these two fields. The resulting framework allows to evaluate the validity of biologically-plausibe plasticity models in closed-loop robotics environments. We demonstrate this framework to evaluate Synaptic Plasticity with Online REinforcement learning (SPORE), a reward-learning rule based on synaptic sampling, on two visuomotor tasks: reaching and lane following. We show that SPORE is capable of learning to perform policies within the course of simulated hours for both tasks. Provisional parameter explorations indicate that the learning rate and the temperature driving the stochastic processes that govern synaptic learning dynamics need to be regulated for performance improvements to be retained. We conclude by discussing the recent deep reinforcement learning techniques which would be beneficial to increase the functionality of SPORE on visuomotor tasks.

Efficient Reward-Based Structural Plasticity on a SpiNNaker 2 Prototype

Advances in neuroscience uncover the mechanisms employed by the brain to efficiently solve complex learning tasks with very limited resources. However, the efficiency is often lost when one tries to port these findings to a silicon substrate, since brain-inspired algorithms often make extensive use of complex functions, such as random number generators, that are expensive to compute on standard general purpose hardware. The prototype chip of the second generation SpiNNaker system is designed to overcome this problem. Low-power advanced RISC machine (ARM) processors equipped with a random number generator and an exponential function accelerator enable the efficient execution of brain-inspired algorithms. We implement the recently introduced reward-based synaptic sampling model that employs structural plasticity to learn a function or task. The numerical simulation of the model requires to update the synapse variables in each time step including an explorative random term. To the best of our knowledge, this is the most complex synapse model implemented so far on the SpiNNaker system. By making efficient use of the hardware accelerators and numerical optimizations, the computation time of one plasticity update is reduced by a factor of 2. This, combined with fitting the model into to the local static random access memory (SRAM), leads to 62% energy reduction compared to the case without accelerators and the use of external dynamic random access memory (DRAM). The model implementation is integrated into the SpiNNaker software framework allowing for scalability onto larger systems. The hardware-software system presented in this paper paves the way for power-efficient mobile and biomedical applications with biologically plausible brain-inspired algorithms.

Memory-Efficient Deep Learning on a SpiNNaker 2 Prototype

The memory requirement of deep learning algorithms is considered incompatible with the memory restriction of energy-efficient hardware. A low memory footprint can be achieved by pruning obsolete connections or reducing the precision of connection strengths after the network has been trained. Yet, these techniques are not applicable to the case when neural networks have to be trained directly on hardware due to the hard memory constraints. Deep Rewiring (DEEP R) is a training algorithm which continuously rewires the network while preserving very sparse connectivity all along the training procedure. We apply DEEP R to a deep neural network implementation on a prototype chip of the 2nd generation SpiNNaker system. The local memory of a single core on this chip is limited to 64 KB and a deep network architecture is trained entirely within this constraint without the use of external memory. Throughout training, the proportion of active connections is limited to 1.3%. On the handwritten digits dataset MNIST, this extremely sparse network achieves 96.6% classification accuracy at convergence. Utilizing the multi-processor feature of the SpiNNaker system, we found very good scaling in terms of computation time, per-core memory consumption, and energy constraints. When compared to a X86 CPU implementation, neural network training on the SpiNNaker 2 prototype improves power and energy consumption by two orders of magnitude.

Feedback Inhibition Shapes Emergent Computational Properties of Cortical Microcircuit Motifs

Cortical microcircuits are very complex networks, but they are composed of a relatively small number of stereotypical motifs. Hence, one strategy for throwing light on the computational function of cortical microcircuits is to analyze emergent computational properties of these stereotypical microcircuit motifs. We are addressing here the question how spike timing-dependent plasticity shapes the computational properties of one motif that has frequently been studied experimentally: interconnected populations of pyramidal cells and parvalbumin-positive inhibitory cells in layer 2/3. Experimental studies suggest that these inhibitory neurons exert some form of divisive inhibition on the pyramidal cells. We show that this data-based form of feedback inhibition, which is softer than that of winner-take-all models that are commonly considered in theoretical analyses, contributes to the emergence of an important computational function through spike timing-dependent plasticity: The capability to disentangle superimposed firing patterns in upstream networks, and to represent their information content through a sparse assembly code.SIGNIFICANCE STATEMENT We analyze emergent computational properties of a ubiquitous cortical microcircuit motif: populations of pyramidal cells that are densely interconnected with inhibitory neurons. Simulations of this model predict that sparse assembly codes emerge in this microcircuit motif under spike timing-dependent plasticity. Furthermore, we show that different assemblies will represent different hidden sources of upstream firing activity. Hence, we propose that spike timing-dependent plasticity enables this microcircuit motif to perform a fundamental computational operation on neural activity patterns.

Unsupervised learning in probabilistic neural networks with multi-state metal-oxide memristive synapses

In an increasingly data-rich world the need for developing computing systems that cannot only process, but ideally also interpret big data is becoming continuously more pressing. Brain-inspired concepts have shown great promise towards addressing this need. Here we demonstrate unsupervised learning in a probabilistic neural network that utilizes metal-oxide memristive devices as multi-state synapses. Our approach can be exploited for processing unlabelled data and can adapt to time-varying clusters that underlie incoming data by supporting the capability of reversible unsupervised learning. The potential of this work is showcased through the demonstration of successful learning in the presence of corrupted input data and probabilistic neurons, thus paving the way towards robust big-data processors.

Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.

Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition

During the last decade, Bayesian probability theory has emerged as a framework in cognitive science and neuroscience for describing perception, reasoning and learning of mammals. However, our understanding of how probabilistic computations could be organized in the brain, and how the observed connectivity structure of cortical microcircuits supports these calculations, is rudimentary at best. In this study, we investigate statistical inference and self-organized learning in a spatially extended spiking network model, that accommodates both local competitive and large-scale associative aspects of neural information processing, under a unified Bayesian account. Specifically, we show how the spiking dynamics of a recurrent network with lateral excitation and local inhibition in response to distributed spiking input, can be understood as sampling from a variational posterior distribution of a well-defined implicit probabilistic model. This interpretation further permits a rigorous analytical treatment of experience-dependent plasticity on the network level. Using machine learning theory, we derive update rules for neuron and synapse parameters which equate with Hebbian synaptic and homeostatic intrinsic plasticity rules in a neural implementation. In computer simulations, we demonstrate that the interplay of these plasticity rules leads to the emergence of probabilistic local experts that form distributed assemblies of similarly tuned cells communicating through lateral excitatory connections. The resulting sparse distributed spike code of a well-adapted network carries compressed information on salient input features combined with prior experience on correlations among them. Our theory predicts that the emergence of such efficient representations benefits from network architectures in which the range of local inhibition matches the spatial extent of pyramidal cells that share common afferent input.

A compound memristive synapse model for statistical learning through STDP in spiking neural networks

Memristors have recently emerged as promising circuit elements to mimic the function of biological synapses in neuromorphic computing. The fabrication of reliable nanoscale memristive synapses, that feature continuous conductance changes based on the timing of pre- and postsynaptic spikes, has however turned out to be challenging. In this article, we propose an alternative approach, the compound memristive synapse, that circumvents this problem by the use of memristors with binary memristive states. A compound memristive synapse employs multiple bistable memristors in parallel to jointly form one synapse, thereby providing a spectrum of synaptic efficacies. We investigate the computational implications of synaptic plasticity in the compound synapse by integrating the recently observed phenomenon of stochastic filament formation into an abstract model of stochastic switching. Using this abstract model, we first show how standard pulsing schemes give rise to spike-timing dependent plasticity (STDP) with a stabilizing weight dependence in compound synapses. In a next step, we study unsupervised learning with compound synapses in networks of spiking neurons organized in a winner-take-all architecture. Our theoretical analysis reveals that compound-synapse STDP implements generalized Expectation-Maximization in the spiking network. Specifically, the emergent synapse configuration represents the most salient features of the input distribution in a Mixture-of-Gaussians generative model. Furthermore, the network's spike response to spiking input streams approximates a well-defined Bayesian posterior distribution. We show in computer simulations how such networks learn to represent high-dimensional distributions over images of handwritten digits with high fidelity even in presence of substantial device variations and under severe noise conditions. Therefore, the compound memristive synapse may provide a synaptic design principle for future neuromorphic architectures.

A comparison of manual neuronal reconstruction from biocytin histology or 2-photon imaging: morphometry and computer modeling

Accurate 3D reconstruction of neurons is vital for applications linking anatomy and physiology. Reconstructions are typically created using Neurolucida after biocytin histology (BH). An alternative inexpensive and fast method is to use freeware such as Neuromantic to reconstruct from fluorescence imaging (FI) stacks acquired using 2-photon laser-scanning microscopy during physiological recording. We compare these two methods with respect to morphometry, cell classification, and multicompartmental modeling in the NEURON simulation environment. Quantitative morphological analysis of the same cells reconstructed using both methods reveals that whilst biocytin reconstructions facilitate tracing of more distal collaterals, both methods are comparable in representing the overall morphology: automated clustering of reconstructions from both methods successfully separates neocortical basket cells from pyramidal cells but not BH from FI reconstructions. BH reconstructions suffer more from tissue shrinkage and compression artifacts than FI reconstructions do. FI reconstructions, on the other hand, consistently have larger process diameters. Consequently, significant differences in NEURON modeling of excitatory post-synaptic potential (EPSP) forward propagation are seen between the two methods, with FI reconstructions exhibiting smaller depolarizations. Simulated action potential backpropagation (bAP), however, is indistinguishable between reconstructions obtained with the two methods. In our hands, BH reconstructions are necessary for NEURON modeling and detailed morphological tracing, and thus remain state of the art, although they are more labor intensive, more expensive, and suffer from a higher failure rate due to the occasional poor outcome of histological processing. However, for a subset of anatomical applications such as cell type identification, FI reconstructions are superior, because of indistinguishable classification performance with greater ease of use, essentially 100% success rate, and lower cost.

Integration of nanoscale memristor synapses in neuromorphic computing architectures

Conventional neuro-computing architectures and artificial neural networks have often been developed with no or loose connections to neuroscience. As a consequence, they have largely ignored key features of biological neural processing systems, such as their extremely low-power consumption features or their ability to carry out robust and efficient computation using massively parallel arrays of limited precision, highly variable, and unreliable components. Recent developments in nano-technologies are making available extremely compact and low power, but also variable and unreliable solid-state devices that can potentially extend the offerings of availing CMOS technologies. In particular, memristors are regarded as a promising solution for modeling key features of biological synapses due to their nanoscale dimensions, their capacity to store multiple bits of information per element and the low energy required to write distinct states. In this paper, we first review the neuro- and neuromorphic computing approaches that can best exploit the properties of memristor and scale devices, and then propose a novel hybrid memristor-CMOS neuromorphic circuit which represents a radical departure from conventional neuro-computing approaches, as it uses memristors to directly emulate the biophysics and temporal dynamics of real synapses. We point out the differences between the use of memristors in conventional neuro-computing architectures and the hybrid memristor-CMOS circuit proposed, and argue how this circuit represents an ideal building block for implementing brain-inspired probabilistic computing paradigms that are robust to variability and fault tolerant by design.

Reinforcement learning on slow features of high-dimensional input streams

Humans and animals are able to learn complex behaviors based on a massive stream of sensory information from different modalities. Early animal studies have identified learning mechanisms that are based on reward and punishment such that animals tend to avoid actions that lead to punishment whereas rewarded actions are reinforced. However, most algorithms for reward-based learning are only applicable if the dimensionality of the state-space is sufficiently small or its structure is sufficiently simple. Therefore, the question arises how the problem of learning on high-dimensional data is solved in the brain. In this article, we propose a biologically plausible generic two-stage learning system that can directly be applied to raw high-dimensional input streams. The system is composed of a hierarchical slow feature analysis (SFA) network for preprocessing and a simple neural network on top that is trained based on rewards. We demonstrate by computer simulations that this generic architecture is able to learn quite demanding reinforcement learning tasks on high-dimensional visual input streams in a time that is comparable to the time needed when an explicit highly informative low-dimensional state-space representation is given instead of the high-dimensional visual input. The learning speed of the proposed architecture in a task similar to the Morris water maze task is comparable to that found in experimental studies with rats. This study thus supports the hypothesis that slowness learning is one important unsupervised learning principle utilized in the brain to form efficient state representations for behavioral learning.

Connectivity, Dynamics, and Memory in Reservoir Computing with Binary and Analog Neurons

Reservoir computing (RC) systems are powerful models for online computations on input sequences. They consist of a memoryless readout neuron that is trained on top of a randomly connected recurrent neural network. RC systems are commonly used in two flavors: with analog or binary (spiking) neurons in the recurrent circuits. Previous work indicated a fundamental difference in the behavior of these two implementations of the RC idea. The performance of an RC system built from binary neurons seems to depend strongly on the network connectivity structure. In networks of analog neurons, such clear dependency has not been observed. In this letter, we address this apparent dichotomy by investigating the influence of the network connectivity (parameterized by the neuron in-degree) on a family of network models that interpolates between analog and binary networks. Our analyses are based on a novel estimation of the Lyapunov exponent of the network dynamics with the help of branching process theory, rank measures that estimate the kernel quality and generalization capabilities of recurrent networks, and a novel mean field predictor for computational performance. These analyses reveal that the phase transition between ordered and chaotic network behavior of binary circuits qualitatively differs from the one in analog circuits, leading to differences in the integration of information over short and long timescales. This explains the decreased computational performance observed in binary circuits that are densely connected. The mean field predictor is also used to bound the memory function of recurrent circuits of binary neurons.

Spiking neurons can learn to solve information bottleneck problems and extract independent components

Independent component analysis (or blind source separation) is assumed to be an essential component of sensory processing in the brain and could provide a less redundant representation about the external world. Another powerful processing strategy is the optimization of internal representations according to the information bottleneck method. This method would allow extracting preferentially those components from high-dimensional sensory input streams that are related to other information sources, such as internal predictions or proprioceptive feedback. However, there exists a lack of models that could explain how spiking neurons could learn to execute either of these two processing strategies. We show in this article how stochastically spiking neurons with refractoriness could in principle learn in an unsupervised manner to carry out both information bottleneck optimization and the extraction of independent components. We derive suitable learning rules, which extend the well-known BCM rule, from abstract information optimization principles. These rules will simultaneously keep the firing rate of the neuron within a biologically realistic range.

Functional network reorganization in motor cortex can be explained by reward-modulated Hebbian learning

The control of neuroprosthetic devices from the activity of motor cortex neurons benefits from learning effects where the function of these neurons is adapted to the control task. It was recently shown that tuning properties of neurons in monkey motor cortex are adapted selectively in order to compensate for an erroneous interpretation of their activity. In particular, it was shown that the tuning curves of those neurons whose preferred directions had been misinterpreted changed more than those of other neurons. In this article, we show that the experimentally observed self-tuning properties of the system can be explained on the basis of a simple learning rule. This learning rule utilizes neuronal noise for exploration and performs Hebbian weight updates that are modulated by a global reward signal. In contrast to most previously proposed reward-modulated Hebbian learning rules, this rule does not require extraneous knowledge about what is noise and what is signal. The learning rule is able to optimize the performance of the model system within biologically realistic periods of time and under high noise levels. When the neuronal noise is fitted to experimental data, the model produces learning effects similar to those found in monkey experiments.

A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback

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

A major open problem in computational neuroscience is to explain how learning, i.e., behaviorally relevant modifications in the central nervous system, can be explained on the basis of experimental data on synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a rule for changes in the strength of an individual synapse that is supported by experimental data from a variety of species. However, it is not clear how this synaptic plasticity rule can produce meaningful modifications in networks of neurons. Only if one takes into account that consolidation of synaptic plasticity requires a third signal, such as changes in the concentration of a neuromodulator (that might, for example, be related to rewards or expected rewards), then meaningful changes in the structure of networks of neurons may occur. We provide in this article an analytical foundation for such reward-modulated versions of STDP that predicts when this type of synaptic plasticity can produce functionally relevant changes in networks of neurons. In particular we show that seemingly inexplicable experimental data on biofeedback, where a monkey learnt to increase the firing rate of an arbitrarily chosen neuron in the motor cortex, can be explained on the basis of this new learning theory.

On the classification capability of sign-constrained perceptrons

The perceptron (also referred to as McCulloch-Pitts neuron, or linear threshold gate) is commonly used as a simplified model for the discrimination and learning capability of a biological neuron. Criteria that tell us when a perceptron can implement (or learn to implement) all possible dichotomies over a given set of input patterns are well known, but only for the idealized case, where one assumes that the sign of a synaptic weight can be switched during learning. We present in this letter an analysis of the classification capability of the biologically more realistic model of a sign-constrained perceptron, where the signs of synaptic weights remain fixed during learning (which is the case for most types of biological synapses). In particular, the VC-dimension of sign-constrained perceptrons is determined, and a necessary and sufficient criterion is provided that tells us when all 2(m) dichotomies over a given set of m patterns can be learned by a sign-constrained perceptron. We also show that uniformity of L(1) norms of input patterns is a sufficient condition for full representation power in the case where all weights are required to be nonnegative. Finally, we exhibit cases where the sign constraint of a perceptron drastically reduces its classification capability. Our theoretical analysis is complemented by computer simulations, which demonstrate in particular that sparse input patterns improve the classification capability of sign-constrained perceptrons.

Correction of tailor's bunion with the Boesch technique: a retrospective study

BACKGROUND

The Boesch technique(1,2) is a minimally-invasive and time-saving subcutaneous subcapital metatarsal osteotomy. Since 1984, we have been using this osteotomy technique for patients with a symptomatic tailor's bunion in whom conservative treatment has failed. This distal osteotomy is stabilized by a combination of a Kirschner wire and a special dressing. The results of this technique in patients with symptomatic tailor's bunion were reviewed.

METHODS

Between March, 1998, and June, 2002, surgery was done in 77 feet of 65 patients with a mean age of 64.6 years. The mean followup was 56.6 (range 14 to 79) months. The 100-point American Orthopaedic foot and Ankle Society (AOFAS) Lesser Metatarsophalangeal-Interphalangeal Scale was used for scoring.

RESULTS

86.4% of 57 patients (66 feet) were free of pain at final followup. The mean 4-5 intermetatarsal angle was 12 degrees before and 8 degrees after surgery. The mean lateral deviation of the fifth metatarsal was 5.7 degrees before and 5.1 degrees after surgery. The mean fifth metatarsophalangeal angle was 17.8 degrees before and 6.2 degrees after surgery. The mean preoperative 100-point AOFAS score was 59.1 (range 23 to 88) and the postoperative score, 95.2 (range 73 to 100). The overall results were excellent in 87.9%, (58 feet) good in 6.1% (4 feet), and satisfactory in 6.1%; none was poor.

CONCLUSIONS

The advantages of the subcutaneous subcapital Boesch technique are that it is time saving, it causes less bone and soft-tissue trauma, and it is performed under local anesthesia without a tourniquet. It is an effective operative option for symptomatic tailor's bunion; excellent and good clinical and radiographic results were found in 86.4% (57 patients, 66 feet) of the patients.

Edge of chaos and prediction of computational performance for neural circuit models

We analyze in this article the significance of the edge of chaos for real-time computations in neural microcircuit models consisting of spiking neurons and dynamic synapses. We find that the edge of chaos predicts quite well those values of circuit parameters that yield maximal computational performance. But obviously it makes no prediction of their computational performance for other parameter values. Therefore, we propose a new method for predicting the computational performance of neural microcircuit models. The new measure estimates directly the kernel property and the generalization capability of a neural microcircuit. We validate the proposed measure by comparing its prediction with direct evaluations of the computational performance of various neural microcircuit models. The proposed method also allows us to quantify differences in the computational performance and generalization capability of neural circuits in different dynamic regimes (UP- and DOWN-states) that have been demonstrated through intracellular recordings in vivo.

What can a neuron learn with spike-timing-dependent plasticity?

Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.

Input prediction and autonomous movement analysis in recurrent circuits of spiking neurons

Temporal integration of information and prediction of future sensory inputs are assumed to be important computational tasks of generic cortical microcircuits. It has remained open how cortical microcircuits could possibly achieve this, especially since they consist--in contrast to most neural network models--of neurons and synapses with heterogeneous dynamic responses. It turns out, however, that the diversity of computational units increases the capability of microcircuit models for temporal integration. Furthermore the prediction of future input may be rather easy for such circuits since it suffices to train the readouts from such microcircuits. In this article we show that very simple readouts from a generic recurrently connected circuit of integrate-and-fire neurons with diverse dynamic synapses can be trained in an unsupervised manner to predict movements of different objects, that move within an unlimited number of combinations of speed, angle, and offset over a simulated sensory field. The autonomously trained microcircuit model is also able to compute the direction of motion, which is a computationally difficult problem ('aperture problem') since it requires disambiguation of local sensory readings through the context of other sensory readings at the current and preceding moments. Furthermore the same circuit can be trained simultaneously in a supervised manner to also report the shape and velocity of the moving object. Finally it is shown that the trained neural circuit supports novelty detection and the generation of 'imagined movements'. Altogether the results of this article suggest that it is not necessary to construct specific and biologically unrealistic neural circuit models for specific sensory processing tasks, since 'found' generic cortical microcircuit models in combination with very simple perceptron-like readouts can easily be trained to solve such computational tasks.

Indomethacin versus meloxicam for prevention of heterotopic ossification after total hip arthroplasty

BACKGROUND

Heterotopic ossification (HO) is a recognized postsurgical complication after total hip arthroplasty. Brooker et al. [6] established a grading system to define the degree of HO. The results of several studies have shown that non-steroidal anti-inflammatory drugs (NSAID) and radiation therapy reliably reduce the occurrence of severe HO. The exact cause and mechanism of bone formation are not known. The efficacy of indomethacin versus meloxicam for the prevention of heterotopic periarticular ossification and clinical NSAID side-effects after primary, cementless total hip arthroplasty was evaluated.

METHODS

Probands underwent cementless total hip replacements at the Orthopaedic Department, Hospital Wiener Neustadt, from January 1997 to January 1998, did not take NSAID up to 4 weeks preoperatively and had no NSAID contraindications. Patients were separated into two groups by different hospitalisation floors. All patients selected for this study suffered from primary or secondary coxarthrosis. Data were collected as a prospective, randomised, parallel group study. Patients were given 50 mg indomethacin 2 times daily ( n=58) vs 7.5 mg meloxicam ( n=58) in a 12-day treatment course.

RESULTS

A two-sided Cochran-Armitage trend test showed no statistically significant difference ( p<0.05) for one of the drugs regarding influence on ectopic bone formation according to the grading system of Brooker et al.

CONCLUSION

Our study demonstrates that there is no statistically significant trend that indomethacin or meloxicam protects a hip arthroplasty better from heterotopic bone formation. We prefer indomethacin therapy because it is almost half the price of meloxicam therapy, and we recommend indomethacin in a 12-day treatment course given 50 mg 2 times daily as an effective, inexpensive and easily administered HO prophylaxis.

Hallux valgus correction by the method of Bösch: a new technique with a seven-to-ten-year follow-up

Subcapital osteotomy of the first metatarsal is used as the treatment of choice for the correction of hallux valgus. The advantages are a short operation time, no soft tissue procedures, secure union, avoidance of metatarsal head (MTH) necrosis and a varus malalignment. An alternative temporary fixation of hallux valgus also having an arthrosis is performed with a specially developed angle plate (Synthes-Stratec, Austria) with the skin incision lengthened to 1-cm. Adequate displacement of the MTH over the sesamoid bones provides a permanent satisfying result even without an operation on the abductor or the adductor. This article reviews 98 feet of 64 patients who were examined in a follow-up study from the initial 114 cases that were operated. The mean follow-up time was 8 years and 9 months.