Controlling activity fluctuations in large, sparsely connected random networks

Controlling activity in recurrent neural network models of brain regions is essential both to enable effective learning and to reproduce the low activities that exist in some cortical regions such as hippocampal region CA3. Previous studies of sparse, random, recurrent networks constructed with McCulloch-Pitts neurons used probabilistic arguments to set the parameters that control activity. Here, we extend this work by adding an additional, biologically appropriate, parameter to control the magnitude and stability of activity oscillations. The new constant can be considered to be the rest conductance in a shunting model or the threshold when subtractive inhibition is used. This new parameter is critical for large networks run at low activity levels. Importantly, extreme activity fluctuations that act to turn large networks totally on or totally off can now be avoided. We also show how the size of external input activity interacts with this parameter to affect network activity. Then the model based on fixed weights is extended to estimate activities in networks with distributed weights. Because the theory provides accurate control of activity fluctuations, the approach can be used to design a predictable amount of pseudorandomness into deterministic networks. Such nonminimal fluctuations improve learning in simulations trained on the transitive inference problem.     

Discrete recurrent neural networks for grammatical inference

Describes a novel neural architecture for learning deterministic context-free grammars, or equivalently, deterministic pushdown automata. The unique feature of the proposed network is that it forms stable state representations during learning-previous work has shown that conventional analog recurrent networks can be inherently unstable in that they cannot retain their state memory for long input strings. The authors have previously introduced the discrete recurrent network architecture for learning finite-state automata. Here they extend this model to include a discrete external stack with discrete symbols. A composite error function is described to handle the different situations encountered in learning. The pseudo-gradient learning method (introduced in previous work) is in turn extended for the minimization of these error functions. Empirical trials validating the effectiveness of the pseudo-gradient learning method are presented, for networks both with and without an external stack. Experimental results show that the new networks are successful in learning some simple pushdown automata, though overfitting and non-convergent learning can also occur. Once learned, the internal representation of the network is provably stable; i.e., it classifies unseen strings of arbitrary length with 100% accuracy.     

Dynamical synapses enhance neural information processing: gracefulness, accuracy, and mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity: short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning and may serve as substrates for neural systems manipulating temporal information on relevant timescales. This study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors: the network that is initially being stimulated to an active state decays to a silent state very slowly on the timescale of STD rather than on that of neuralsignaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.     

Effective neuronal learning with ineffective Hebbian learning rules

In this article we revisit the classical neuroscience paradigm of Hebbian learning. We find that it is difficult to achieve effective associative memory storage by Hebbian synaptic learning, since it requires network-level information at the synaptic level or sparse coding level. Effective learning can yet be achieved even with nonsparse patterns by a neuronal process that maintains a zero sum of the incoming synaptic efficacies. This weight correction improves the memory capacity of associative networks from an essentially bounded one to a memory capacity that scales linearly with network size. It also enables the effective storage of patterns with multiple levels of activity within a single network. Such neuronal weight correction can be successfully carried out by activity-dependent homeostasis of the neuron's synaptic efficacies, which was recently observed in cortical tissue. Thus, our findings suggest that associative learning by Hebbian synaptic learning should be accompanied by continuous remodeling of neuronally driven regulatory processes in the brain.     

Good teaching inputs do not correspond to desired responses in ecological neural networks

In this paper we analyze how supervised learning occurs in ecological neural networks, i.e. networks that interact with an autonomous external environment and, therefore, at least partially determine with their behavior their own input. Using an evolutionary method for selecting good teaching inputs we surprisingly find that to obtain a desired outputX it is better to use a teaching input different fromX. To explain this fact we claim that teaching inputs in ecological networks have two different effects: (a) to reduce the discrepancy between the actual output of the network and the teaching input, (b) to modify the network's behavior and, as a consequence, the network's learning experiences. Evolved teaching inputs appear to represent a compromise between these two needs. We finally show that evolved teaching inputs that are allowed to change during the learning process function differently at different stages of learning, first giving more weight to (b) and, later on, to (a).     

Correlations and population dynamics in cortical networks

The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.     

A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule, including passive forgetting and different timescales, for neuronal activity and learning dynamics. Previous numerical work has reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on neural network evolution. Furthermore, we show that sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest.     

Self-organizing continuous attractor networks and path integration: one-dimensional models of head direction cells

Some neurons encode information about the orientation or position of an animal, and can maintain their response properties in the absence of visual input. Examples include head direction cells in rats and primates, place cells in rats and spatial view cells in primates. 'Continuous attractor' neural networks model these continuous physical spaces by using recurrent collateral connections between the neurons which reflect the distance between the neurons in the state space (e.g. head direction space) of the animal. These networks maintain a localized packet of neuronal activity representing the current state of the animal. We show how the synaptic connections in a one-dimensional continuous attractor network (of for example head direction cells) could be self-organized by associative learning. We also show how the activity packet could be moved from one location to another by idiothetic (self-motion) inputs, for example vestibular or proprioceptive, and how the synaptic connections could self-organize to implement this. The models described use 'trace' associative synaptic learning rules that utilize a form of temporal average of recent cell activity to associate the firing of rotation cells with the recent change in the representation of the head direction in the continuous attractor. We also show how a nonlinear neuronal activation function that could be implemented by NMDA receptors could contribute to the stability of the activity packet that represents the current state of the animal.     

When response variability increases neural network robustness to synaptic noise

Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as detrimental noise that reduces the computational accuracy of neural circuits. Here we investigate the possibility that such response variability might in fact be beneficial, because it may partially compensate for a decrease in accuracy due to stochastic changes in the synaptic strengths of a network. We study the interplay between two kinds of noise, response (or neuronal) noise and synaptic noise, by analyzing their joint influence on the accuracy of neural networks trained to perform various tasks. We find an interesting, generic interaction: when fluctuations in the synaptic connections are proportional to their strengths (multiplicative noise), a certain amount of response noise in the input neurons can significantly improve network performance, compared to the same network without response noise. Performance is enhanced because response noise and multiplicative synaptic noise are in some ways equivalent. So if the algorithm used to find the optimal synaptic weights can take into account the variability of the model neurons, it can also take into account the variability of the synapses. Thus, the connection patterns generated with response noise are typically more resistant to synaptic degradation than those obtained without response noise. As a consequence of this interplay, if multiplicative synaptic noise is present, it is better to have response noise in the network than not to have it. These results are demonstrated analytically for the most basic network consisting of two input neurons and one output neuron performing a simple classification task, but computer simulations show that the phenomenon persists in a wide range of architectures, including recurrent (attractor) networks and sensorimotor networks that perform coordinate transformations. The results suggest that response variability could play an important dynamic role in networks that continuously learn.     

Learning beyond finite memory in recurrent networks of spiking neurons

We investigate possibilities of inducing temporal structures without fading memory in recurrent networks of spiking neurons strictly operating in the pulse-coding regime. We extend the existing gradient-based algorithm for training feedforward spiking neuron networks, SpikeProp (Bohte, Kok, & La Poutré, 2002), to recurrent network topologies, so that temporal dependencies in the input stream are taken into account. It is shown that temporal structures with unbounded input memory specified by simple Moore machines (MM) can be induced by recurrent spiking neuron networks (RSNN). The networks are able to discover pulse-coded representations of abstract information processing states coding potentially unbounded histories of processed inputs. We show that it is often possible to extract from trained RSNN the target MM by grouping together similar spike trains appearing in the recurrent layer. Even when the target MM was not perfectly induced in a RSNN, the extraction procedure was able to reveal weaknesses of the induced mechanism and the extent to which the target machine had been learned.     

前馈型神经元网络中的放电频率传递分析

本文建立了一个基于Hodgkin-Huxley神经元的前馈神经元网络模型,研究了平均放电频率在前馈神经元网络中的传递情况。研究结果显示,适当的层间连接概率与输人噪声强度能够提髙前馈神经元网络的同步效率,进而增强网络稳定传递放电频率的性能。此外,通过引入并调节突触时滞,发现适当的时滞对神经元耦合系统的完全同步和前馈神经元网络内信息传输有明显的促进作用。     

Noise tolerance of attractor and feedforward memory models

In short-term memory networks, transient stimuli are represented by patterns of neural activity that persist long after stimulus offset. Here, we compare the performance of two prominent classes of memory networks, feedback-based attractor networks and feedforward networks, in conveying information about the amplitude of a briefly presented stimulus in the presence of gaussian noise. Using Fisher information as a metric of memory performance, we find that the optimal form of network architecture depends strongly on assumptions about the forms of nonlinearities in the network. For purely linear networks, we find that feedforward networks outperform attractor networks because noise is continually removed from feedforward networks when signals exit the network; as a result, feedforward networks can amplify signals they receive faster than noise accumulates over time. By contrast, attractor networks must operate in a signal-attenuating regime to avoid the buildup of noise. However, if the amplification of signals is limited by a finite dynamic range of neuronal responses or if noise is reset at the time of signal arrival, as suggested by recent experiments, we find that attractor networks can outperform feedforward ones. Under a simple model in which neurons have a finite dynamic range, we find that the optimal attractor networks are forgetful if there is no mechanism for noise reduction with signal arrival but nonforgetful (perfect integrators) in the presence of a strong reset mechanism. Furthermore, we find that the maximal Fisher information for the feedforward and attractor networks exhibits power law decay as a function of time and scales linearly with the number of neurons. These results highlight prominent factors that lead to trade-offs in the memory performance of networks with different architectures and constraints, and suggest conditions under which attractor or feedforward networks may be best suited to storing information about previous stimuli.     

Random neural networks with synchronized interactions

Large-scale distributed systems, such as natural neuronal and artificial systems, have many local interconnections, but they often also have the ability to propagate information very fast over relatively large distances. Mechanisms that enable such behavior include very long physical signaling paths and possibly saccades of synchronous behavior that may propagate across a network. This letter studies the modeling of such behaviors in neuronal networks and develops a related learning algorithm. This is done in the context of the random neural network (RNN), a probabilistic model with a well-developed mathematical theory, which was inspired by the apparently stochastic spiking behavior of certain natural neuronal systems. Thus, we develop an extension of the RNN to the case when synchronous interactions can occur, leading to synchronous firing by large ensembles of cells. We also present an O(N3) gradient descent learning algorithm for an N-cell recurrent network having both conventional excitatory-inhibitory interactions and synchronous interactions. Finally, the model and its learning algorithm are applied to a resource allocation problem that is NP-hard and requires fast approximate decisions.     

Intrinsic adaptation in autonomous recurrent neural networks

A massively recurrent neural network responds on one side to input stimuli and is autonomously active, on the other side, in the absence of sensory inputs. Stimuli and information processing depend crucially on the quality of the autonomous-state dynamics of the ongoing neural activity. This default neural activity may be dynamically structured in time and space, showing regular, synchronized, bursting, or chaotic activity patterns. We study the influence of nonsynaptic plasticity on the default dynamical state of recurrent neural networks. The nonsynaptic adaption considered acts on intrinsic neural parameters, such as the threshold and the gain, and is driven by the optimization of the information entropy. We observe, in the presence of the intrinsic adaptation processes, three distinct and globally attracting dynamical regimes: a regular synchronized, an overall chaotic, and an intermittent bursting regime. The intermittent bursting regime is characterized by intervals of regular flows, which are quite insensitive to external stimuli, interceded by chaotic bursts that respond sensitively to input signals. We discuss these findings in the context of self-organized information processing and critical brain dynamics.     

Network capacity analysis for latent attractor computation

Attractor networks have been one of the most successful paradigms in neural computation, and have been used as models of computation in the nervous system. Recently, we proposed a paradigm called 'latent attractors' where attractors embedded in a recurrent network via Hebbian learning are used to channel network response to external input rather than becoming manifest themselves. This allows the network to generate context-sensitive internal codes in complex situations. Latent attractors are particularly helpful in explaining computations within the hippocampus--a brain region of fundamental significance for memory and spatial learning. Latent attractor networks are a special case of associative memory networks. The model studied here consists of a two-layer recurrent network with attractors stored in the recurrent connections using a clipped Hebbian learning rule. The firing in both layers is competitive--K winners take all firing. The number of neurons allowed to fire, K, is smaller than the size of the active set of the stored attractors. The performance of latent attractor networks depends on the number of such attractors that a network can sustain. In this paper, we use signal-to-noise methods developed for standard associative memory networks to do a theoretical and computational analysis of the capacity and dynamics of latent attractor networks. This is an important first step in making latent attractors a viable tool in the repertoire of neural computation. The method developed here leads to numerical estimates of capacity limits and dynamics of latent attractor networks. The technique represents a general approach to analyse standard associative memory networks with competitive firing. The theoretical analysis is based on estimates of the dendritic sum distributions using Gaussian approximation. Because of the competitive firing property, the capacity results are estimated only numerically by iteratively computing the probability of erroneous firings. The analysis contains two cases: the simple case analysis which accounts for the correlations between weights due to shared patterns and the detailed case analysis which includes also the temporal correlations between the network's present and previous state. The latter case predicts better the dynamics of the network state for non-zero initial spurious firing. The theoretical analysis also shows the influence of the main parameters of the model on the storage capacity.     

The number of synaptic inputs and the synchrony of large, sparse neuronal networks

The prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons. We study synchronization in models of large networks of spiking neurons with random sparse connectivity. Synchrony occurs only when the average number of synapses, M, that a cell receives is larger than a critical value, Mc. Below Mc, the system is in an asynchronous state. In the limit of weak coupling, assuming identical neurons, we reduce the model to a system of phase oscillators that are coupled via an effective interaction, gamma. In this framework, we develop an approximate theory for sparse networks of identical neurons to estimate Mc analytically from the Fourier coefficients of gamma. Our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it. We apply this theory to compute Mc for a model of inhibitory networks of integrate-and-fire (I&F) neurons as a function of the intrinsic neuronal properties (e.g., the refractory period Tr), the synaptic time constants, and the strength of the external stimulus, Iext. The number Mc is found to be nonmonotonous with the strength of Iext. For Tr = 0, we estimate the minimum value of Mc over all the parameters of the model to be 363.8. Above Mc, the neurons tend to fire in smeared one-cluster states at high firing rates and smeared two-or-more-cluster states at low firing rates. Refractoriness decreases Mc at intermediate and high firing rates. These results are compared to numerical simulations. We show numerically that systems with different sizes, N, behave in the same way provided the connectivity, M, is such that 1/Meff = 1/M - 1/N remains constant when N varies. This allows extrapolating the large N behavior of a network from numerical simulations of networks of relatively small sizes (N = 800 in our case). We find that our theory predicts with remarkable accuracy the value of Mc and the patterns of synchrony above Mc, provided the synaptic coupling is not too large. We also study the strong coupling regime of inhibitory sparse networks. All of our simulations demonstrate that increasing the coupling strength reduces the level of synchrony of the neuronal activity. Above a critical coupling strength, the network activity is asynchronous. We point out a fundamental limitation for the mechanisms of synchrony relying on inhibition alone, if heterogeneities in the intrinsic properties of the neurons and spatial fluctuations in the external input are also taken into account.     

A TSK-type recurrent fuzzy network for dynamic systems processingby neural network and genetic algorithms

In this paper, a TSK-type recurrent fuzzy network (TRFN) structure is proposed. The proposal calls for the design of TRFN by either neural network or genetic algorithms depending on the learning environment. A recurrent fuzzy network is described which develops from a series of recurrent fuzzy if-then rules with TSK-type consequent parts. The recurrent property comes from feeding the internal variables, derived from fuzzy firing strengths, back to both the network input and output layers. In this configuration, each internal variable is responsible for memorizing the temporal history of its corresponding fuzzy rule. The internal variable is also combined with external input variables in each rule's consequence, which shows an increase in network learning ability. TRFN design under different learning environments is next advanced. For problems where supervised training data is directly available, TRFN with supervised learning (TRFN-S) is proposed, and a neural network (NN) learning approach is adopted for TRFN-S design. An online learning algorithm with concurrent structure and parameter learning is proposed. With flexibility of partition in the precondition part, and outcome of TSK-type, the TRFN-S displays both small network size and high learning accuracy. For problems where gradient information for NN learning is costly to obtain or unavailable, like reinforcement learning, TRFN with Genetic learning (TRFN-G) is put forward. The precondition parts of TRFN-G are also partitioned in a flexible way, and all free parameters are designed concurrently by genetic algorithm. Owing to the well-designed network structure of TRFN, TRFN-G, like TRFN-S, is characterized by high learning accuracy. To demonstrate the superior properties of TRFN, TRFN-S is applied to dynamic system identification and TRFN-G to dynamic system control. By comparing the results to other types of recurrent networks and design configurations, the efficiency of TRFN is verified     

A fuzzy ensemble of parallel polynomial neural networks with information granules formed by fuzzy clustering

In this paper, we introduce a new category of fuzzy models called a fuzzy ensemble of parallel polynomial neural network (FEP²N²), which consist of a series of polynomial neural networks weighted by activation levels of information granules formed with the use of fuzzy clustering. The two underlying design mechanisms of the proposed networks rely on information granules resulting from the use of fuzzy C-means clustering (FCM) and take advantage of polynomial neural networks (PNNs).The resulting model comes in the form of parallel polynomial neural networks. In the design procedure, in order to estimate the optimal values of the coefficients of polynomial neural networks we use a weighted least square estimation algorithm. We incorporate various types of structures as the consequent part of the fuzzy model when using the learning algorithm. Among the diverse structures being available, we consider polynomial neural networks, which exhibit highly nonlinear characteristics when being viewed as local learning models.We use FCM to form information granules and to overcome the high dimensionality problem. We adopt PNNs to find the optimal local models, which can describe the relationship between the input variables and output variable within some local region of the input space.We show that the generalization capabilities as well as the approximation abilities of the proposed model are improved as a result of using polynomial neural networks. The performance of the network is quantified through experimentation in which we use a number of benchmarks already exploited within the realm of fuzzy or neurofuzzy modeling.     

Learning long-term dependencies in NARX recurrent neural networks

It has previously been shown that gradient-descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long-term dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. We show that the long-term dependencies problem is lessened for a class of architectures called nonlinear autoregressive models with exogenous (NARX) recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning can be more effective in NARX networks than in recurrent neural network architectures that have "hidden states" on problems including grammatical inference and nonlinear system identification. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are consistent with this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventional recurrent neural networks. We show that although NARX networks do not circumvent the problem of long-term dependencies, they can greatly improve performance on long-term dependency problems. We also describe in detail some of the assumptions regarding what it means to latch information robustly and suggest possible ways to loosen these assumptions.     

Emergence of memory-driven command neurons in evolved artificial agents

Using evolutionary simulations, we develop autonomous agents controlled by artificial neural networks (ANNs). In simple lifelike tasks of foraging and navigation, high performance levels are attained by agents equipped with fully recurrent ANN controllers. In a set of experiments sharing the same behavioral task but differing in the sensory input available to the agents, we find a common structure of a command neuron switching the dynamics of the network between radically different behavioral modes. When sensory position information is available, the command neuron reflects a map of the environment, acting as a location-dependent cell sensitive to the location and orientation of the agent. When such information is unavailable, the command neuron's activity is based on a spontaneously evolving short-term memory mechanism, which underlies its apparent place-sensitive activity. A two-parameter stochastic model for this memory mechanism is proposed. We show that the parameter values emerging from the evolutionary simulations are near optimal; evolution takes advantage of seemingly harmful features of the environment to maximize the agent's foraging efficiency. The accessibility of evolved ANNs for a detailed inspection, together with the resemblance of some of the results to known findings from neurobiology, places evolved ANNs as an excellent candidate model for the study of structure and function relationship in complex nervous systems.