Distribution Of Synaptic Weights Research Articles

Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity.

Structural inhomogeneities in synaptic efficacies have a strong impact on population response dynamics of cortical networks and are believed to play an important role in their functioning. However, little is known about how such inhomogeneities could evolve by means of synaptic plasticity. Here we present an adaptive model of a balanced neuronal network that combines two different types of plasticity, STDP and synaptic scaling. The plasticity rules yield both long-tailed distributions of synaptic weights and firing rates. Simultaneously, a highly connected subnetwork of driver neurons with strong synapses emerges. Coincident spiking activity of several driver cells can evoke population bursts and driver cells have similar dynamical properties as leader neurons found experimentally. Our model allows us to observe the delicate interplay between structural and dynamical properties of the emergent inhomogeneities. It is simple, robust to parameter changes and able to explain a multitude of different experimental findings in one basic network.

Role of the site of synaptic competition and the balance of learning forces for Hebbian encoding of probabilistic Markov sequences.

The majority of distinct sensory and motor events occur as temporally ordered sequences with rich probabilistic structure. Sequences can be characterized by the probability of transitioning from the current state to upcoming states (forward probability), as well as the probability of having transitioned to the current state from previous states (backward probability). Despite the prevalence of probabilistic sequencing of both sensory and motor events, the Hebbian mechanisms that mold synapses to reflect the statistics of experienced probabilistic sequences are not well understood. Here, we show through analytic calculations and numerical simulations that Hebbian plasticity (correlation, covariance, and STDP) with pre-synaptic competition can develop synaptic weights equal to the conditional forward transition probabilities present in the input sequence. In contrast, post-synaptic competition can develop synaptic weights proportional to the conditional backward probabilities of the same input sequence. We demonstrate that to stably reflect the conditional probability of a neuron's inputs and outputs, local Hebbian plasticity requires balance between competitive learning forces that promote synaptic differentiation and homogenizing learning forces that promote synaptic stabilization. The balance between these forces dictates a prior over the distribution of learned synaptic weights, strongly influencing both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. Together, these results demonstrate a simple correspondence between the biophysical organization of neurons, the site of synaptic competition, and the temporal flow of information encoded in synaptic weights by Hebbian plasticity while highlighting the utility of balancing learning forces to accurately encode probability distributions, and prior expectations over such probability distributions.

Stress and Cocaine Trigger Divergent and Cell Type–Specific Regulation of Synaptic Transmission at Single Spines in Nucleus Accumbens

BackgroundRepeated exposure to cocaine or social stress leads to lasting structural and functional synaptic alterations in medium spiny neurons (MSNs) of nucleus accumbens (NAc). Although cocaine-induced and stress-induced structural changes in dendritic spines have been well documented, few studies have investigated functional consequences of cocaine and stress at the level of single spines. MethodsWe exposed mice to chronic cocaine or chronic social defeat stress and used two-photon laser scanning microscopy with glutamate photo-uncaging and whole-cell recording to examine synaptic strength at individual spines on two distinct types of NAc MSNs in acute slices after 24 hours of cocaine withdrawal and after chronic social defeat stress. ResultsIn animals treated with cocaine, average synaptic strength was reduced specifically at large mushroom spines of MSNs expressing dopamine receptor type 1 (D1-MSNs). In contrast, cocaine promoted a rightward shift in the distribution of synaptic weights toward larger synaptic responses in MSNs expressing dopamine receptor type 2 (D2-MSNs). After chronic social defeat stress, resilient animals displayed an upregulation of synaptic strength at large mushroom spines of D1-MSNs and a concomitant downregulation in D2-MSNs. Although susceptible mice did not exhibit a significant overall change in synaptic strength on D1-MSNs or D2-MSNs, we observed a slight leftward shift in cumulative distribution of large synaptic responses in both cell types. ConclusionsThis study provides the first functional cell type–specific and spine type–specific comparison of synaptic strength at a single spine level between cocaine-induced and stress-induced neuroadaptations and demonstrates that psychoactive drugs and stress trigger divergent changes in synaptic function in NAc.

A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model.

We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks.Electronic Supplementary MaterialThe online version of this article (doi:10.1186/s13408-015-0020-y) contains supplementary material 1.

Enhanced polychronization in a spiking network with metaplasticity.

Computational models of metaplasticity have usually focused on the modeling of single synapses (Shouval et al., 2002). In this paper we study the effect of metaplasticity on network behavior. Our guiding assumption is that the primary purpose of metaplasticity is to regulate synaptic plasticity, by increasing it when input is low and decreasing it when input is high. For our experiments we adopt a model of metaplasticity that demonstrably has this effect for a single synapse; our primary interest is in how metaplasticity thus defined affects network-level phenomena. We focus on a network-level phenomenon called polychronicity, that has a potential role in representation and memory. A network with polychronicity has the ability to produce non-synchronous but precisely timed sequences of neural firing events that can arise from strongly connected groups of neurons called polychronous neural groups (Izhikevich et al., 2004). Polychronous groups (PNGs) develop readily when spiking networks are exposed to repeated spatio-temporal stimuli under the influence of spike-timing-dependent plasticity (STDP), but are sensitive to changes in synaptic weight distribution. We use a technique we have recently developed called Response Fingerprinting to show that PNGs formed in the presence of metaplasticity are significantly larger than those with no metaplasticity. A potential mechanism for this enhancement is proposed that links an inherent property of integrator type neurons called spike latency to an increase in the tolerance of PNG neurons to jitter in their inputs.

A neural network model of reliably optimized spike transmission.

We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.

Criticality in cortical ensembles is supported by complex functional networks

Complex network topologies represent the necessary substrate to support complex brain function. It is widely recognized that the topological features of cortical networks are tightly linked to aspects of brain function by supporting which electrophysiological patterns can and cannot occur. In this work, we investigated the interplay between network topology and spontaneous dynamics within the framework of neuronal avalanches and self-organized criticality (SOC) [1]. The main goal of this study is to sustain the hypothesis that the emergence of critical states, which in their turn would optimize functional properties in the cortex, is supported by specific complex network topologies. Experimental evidences showed that dissociated cortical assemblies coupled to Micro-Electrode Arrays (MEAs) can exhibit scale-free distributions of neuronal avalanches [2], a hallmark of SOC, thus demonstrating that they preserve self-organization properties featured by in vivo-formed cell assemblies [3]. However, the determinants of the emergence of different dynamical states (critical, subcritical or supercritical) remain unclear. Here, we adopted a reverse-engineering approach, by making use of an in silico neuronal network model reproducing the spiking and bursting activity of biological networks to explore the relationship between connectivity and dynamics. In our computational network model, connectivity is known a priori and thus it is possible to establish interdependencies between the avalanche distributions and the actual connectivity. Network topologies were designed following the canonical architectures of scale-free, random, and small-world graphs [4]. We simulated the spontaneous activity, by sweeping the most common parameters used to characterize these graphs, such as clustering coefficient, connection density, synaptic weight distributions, etc. [5]. From the simulations, we found that: (i) random networks only showed super-critical dynamics in a physiologically relevant domain of activity parameters (e.g. firing rate); (ii) scale-free and small-world architectures may account for the variability observed in the experimental data and the transition from subcriticality to criticality is ruled by the degree of “small-worldness”; (iii) excitation and inhibition should be appropriately balanced to allow for criticality [6].

Computational Implications of Lognormally Distributed Synaptic Weights

The connectivity structure of neural networks has significant implications for neural information processing, and much experimental effort has been made to clarify the structure of neural networks in the brain, i.e., both graph structure and weight structure of synaptic connections. A traditional view of neural information processing suggests that neurons compute in a highly parallel and distributed manner, in which the cooperation of many weak synaptic inputs is necessary to activate a single neuron. Recent experiments, however, have shown that not all synapses are weak in cortical circuits, but some synapses are extremely strong (several tens of times larger than the average weight). In fact, the weights of excitatory synapses between cortical excitatory neurons often obey a lognormal distribution with a long tail of strong synapses. Here, we review some of our important and recent works on computation with sparsely distributed synaptic weights and discuss the possible implications of this synaptic principle for neural computation by spiking neurons. We demonstrate that internal noise emerges from long-tailed distributions of synaptic weights to produce stochastic resonance effect in the reverberating synaptic pathways constituted by strong synapses. We show a spike-timing-dependent plasticity rule and other mechanisms that produce such weight distributions. A possible hardware realization of lognormally connected networks is also shown.

Shaping Synaptic Learning by the Duration of Postsynaptic Action Potential in a New STDP Model

Single spikes and their timing matter in changing synaptic efficacy, which is known as spike-timing-dependent plasticity (STDP). Most previous studies treated spikes as all-or-none events, and considered their duration and magnitude as negligible. Here we explore the effects of action potential (AP) duration on synaptic plasticity in a simplified model neuron using computer simulations. We propose a novel STDP model that depresses synapses using an AP duration dependent LTD window and induces potentiation of synaptic strength when presynaptic spikes arrive before and during a postsynaptic AP (dSTDP). We demonstrate that AP duration is another key factor for insensitizing the postsynaptic neural firing and for controlling the shape of synaptic weight distribution. Extended AP durations produce a wide unimodal weight distribution that resembles the ones reported experimentally and make the postsynaptic neuron tranquil when disturbed by poisson noise spike trains, while equivalently sensitive to the synchronized. Our results suggest that the impact of AP duration, modeled here as an AP-dependent STDP window, on synaptic plasticity can be dramatic and should motivate future STDP studies.

The Influence of Synaptic Weight Distribution on Neuronal Population Dynamics

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.

Heterosynaptic Plasticity Prevents Runaway Synaptic Dynamics

Spike timing-dependent plasticity (STDP) and other conventional Hebbian-type plasticity rules are prone to produce runaway dynamics of synaptic weights. Once potentiated, a synapse would have higher probability to lead to spikes and thus to be further potentiated, but once depressed, a synapse would tend to be further depressed. The runaway synaptic dynamics can be prevented by precisely balancing STDP rules for potentiation and depression; however, experimental evidence shows a great variety of potentiation and depression windows and magnitudes. Here we show that modifications of synapses to layer 2/3 pyramidal neurons from rat visual and auditory cortices in slices can be induced by intracellular tetanization: bursts of postsynaptic spikes without presynaptic stimulation. Induction of these heterosynaptic changes depended on the rise of intracellular calcium, and their direction and magnitude correlated with initial state of release mechanisms. We suggest that this type of plasticity serves as a mechanism that stabilizes the distribution of synaptic weights and prevents their runaway dynamics. To test this hypothesis, we develop a cortical neuron model implementing both homosynaptic (STDP) and heterosynaptic plasticity with properties matching the experimental data. We find that heterosynaptic plasticity effectively prevented runaway dynamics for the tested range of STDP and input parameters. Synaptic weights, although shifted from the original, remained normally distributed and nonsaturated. Our study presents a biophysically constrained model of how the interaction of different forms of plasticity--Hebbian and heterosynaptic--may prevent runaway synaptic dynamics and keep synaptic weights unsaturated and thus capable of further plastic changes and formation of new memories.

Preconfigured, Skewed Distribution of Firing Rates in the Hippocampus and Entorhinal Cortex

Despite the importance of the discharge frequency in neuronal communication, little is known about the firing-rate patterns of cortical populations. Using large-scale recordings from multiple layers of the entorhinal-hippocampal loop, we found that the firing rates of principal neurons showed a lognormal-like distribution in all brain states. Mean and peak rates within place fields of hippocampal neurons were also strongly skewed. Importantly, firing rates of the same neurons showed reliable correlations in different brain states and testing situations, as well as across familiar and novel environments. The fraction of neurons that participated in population oscillations displayed a lognormal pattern. Such skewed firing rates of individual neurons may be due to a skewed distribution of synaptic weights, which is supported by our observation of a lognormal distribution of the efficacy of spike transfer from principal neurons to interneurons. The persistent skewed distribution of firing rates implies that a preconfigured, highly active minority dominates information transmission in cortical networks.

Dynamics and lifetime of persistent activity states in random networks of spiking neurons with strong synapses

The selective persistent activation of populations of neurons in the prefrontal cortex during active memory tasks is one of the best-studied neural correlates of a higher cognitive function, the so-called working memory. Yet, the respective roles of network and neuron properties in this activity are not fully understood. Spiking neuron network models often rely on a selective excitatory connectivity and generate spike trains that are more regular than what is experimentally observed, thus necessitating additional assumptions, such as intrinsic cellular bistability or additional external noisy input. Recently, it was shown that very simple random networks of excitatory and inhibitory spiking neurons can generate persistent asynchronous-irregular activity only by admitting a certain fraction of comparably strong synaptic weights [1,2]. A large number of experiments showed that synaptic weight distributions are indeed commonly characterized by a large fraction of weak weights and a heavy tail of quite strong weights [e.g. 2,3]. Here, we demonstrate how including such strong synaptic couplings leads to the occurrence of a firing-rate attractor at moderate rates with highly irregular individual spike trains. Based on the firing-rate transfer of the network, we show that the firing-rate dynamics becomes bistable if the synapses are sufficiently strong: in addition to the quiescent state, a second stable fixed point at moderate firing rates emerges by a saddle-node bifurcation. However, the population firing-rate is characterized by pronounced inherent fluctuations that perpetually perturb this fixed point. It is the trade-off between the size of the population fluctuations and the size of the basin of attraction that thus determines the onset and lifetime of persistent activity states. Moreover, individual neuronal activity turns out to be very irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong coupling strength in the network combined with the finite memory time constant of the neurons. Thus, such irregular neuron dynamics can be a pure network phenomenon, and do not require intracellular bistability or additional high-variability noise as previously suggested.

On the influence of inhibitory STDP on balanced state random networks

The distribution of synaptic efficacies in neural networks takes fundamental influence on their dynamics and the modification of synaptic strengths forms the foundation of learning and memory. A prominent plasticity rule that has been observed in vitro is spike-timing-dependent plasticity (STDP). While first studied in glutamatergic synapses, recently also STDP of GABAergic synapses came into the focus of experimental and theoretical research [1]. We study random balanced state networks of leaky integrate-and-fire neurons in the asynchronous irregular (AI) regime [2] that is believed to be a good theoretical fit to the activity of cortical networks in vivo. We consider driven networks that receive Poisson input as well as networks in a self-sustained state of activity. In order to assess the influence of excitatory and inhibitory STDP on the network dynamics, we introduce these two plasticity rules independently, observing network dynamics and weight distributions after a transient phase. Note that both additive and multiplicative STDP rules yield the same network dynamics as described below. When introducing excitatory STDP alone, parameters involving the maximal weight have to be fine-tuned in order to keep the network activity stably in the AI regime [3]. For almost all parameter values the network activity becomes unstable, leaving the AI regime and settling in a pathological, highly synchronized state with saturated firing rates of most cells, see Figure ​Figure1A.1A. We also observed that even without STDP, few strong excitatory connections can substantially destabilize network dynamics yielding pathological states. Interestingly, this destabilization does not happen when in addition to excitatory STDP we also introduce STDP for inhibitory synapses projecting onto excitatory cells. The latter setup results in a network that stably rests in the AI regime, see Figure ​Figure1A.1A. Both STDP rules yield near-Gaussian distributions of synaptic weights, see Figure ​Figure1B.1B. Inhibitory STDP even manages to stabilize a network that was brought to a pathological state by excitatory STDP, see Figure ​Figure1A.1A. This clearly shows that inhibitory STDP has a stabilizing effect on network dynamics and we expect that especially in combination with synaptic scaling and in the context of clustered networks [4] other non-trivial dynamical effects will become visible. Figure 1 A. Raster plot of 30 randomly sampled cells showing network activity. Red line: activation of excitatory STDP, green line: activation of inhibitory STDP. B. Weight distributions of plastic synapses converging onto 100 randomly sampled excitatory neurons. ...

The interplay between STDP rules and anticipated synchronization in the organization of neuronal networks

Neuronal networks are able to synchronize in phase-locking regimes. Depending on the structural connectivity it is possible to determine the sign of the phase difference between oscillatory nodes. Specially in unidirectionally coupled motifs the relative phase difference is usually positive. However it has been shown that in the presence of dynamical inhibitory loops, unidirectionally coupled neuron models may present both positive or negative phase difference [1]. The unusual regime in which the phase difference is negative is called anticipated synchronization (AS) [2]. It means that two neurons or two neuronal populations coupled in a master-slave configuration can oscillate in such a way that the slave leads the master. These results are important in light of the growing experimental evidence that the synaptic strength between neurons can undergo spike-timing-dependent plasticity (STDP) [3]. In the delayed synchronization regime the master (pre-synaptic) neuron fires a spike before the slave (post-synaptic) neuron, which under STDP rules would facilitate long term potentiation (LTP), whereas in the AS regime the slave neuron fires a spike before the master neuron, contributing to long term depression (LTD) [4]. Since it has been shown previously that a simple 3-neuron motif can undergo a continuous transition from positive to negative values of relative phase via changes in synaptic conductances [1], the interplay between these regimes and STDP mechanisms is likely to play a very significant role in the organization of the system dynamics. Considering that in certain situations the relative potentiation in strong synapses is less intense than in weak synapses, but the depression do not show this dependence [5], we compare the effects of additive, multiplicative and hybrid rules in our motifs. Together with AS regimes in neuronal populations, STDP rules give synaptic weight distributions that are comparable to experiments in cortex [6,7].

Integration of Sensory Quanta in Cuneate Nucleus Neurons In Vivo

Discriminative touch relies on afferent information carried to the central nervous system by action potentials (spikes) in ensembles of primary afferents bundled in peripheral nerves. These sensory quanta are first processed by the cuneate nucleus before the afferent information is transmitted to brain networks serving specific perceptual and sensorimotor functions. Here we report data on the integration of primary afferent synaptic inputs obtained with in vivo whole cell patch clamp recordings from the neurons of this nucleus. We find that the synaptic integration in individual cuneate neurons is dominated by 4–8 primary afferent inputs with large synaptic weights. In a simulation we show that the arrangement with a low number of primary afferent inputs can maximize transfer over the cuneate nucleus of information encoded in the spatiotemporal patterns of spikes generated when a human fingertip contact objects. Hence, the observed distributions of synaptic weights support high fidelity transfer of signals from ensembles of tactile afferents. Various anatomical estimates suggest that a cuneate neuron may receive hundreds of primary afferents rather than 4–8. Therefore, we discuss the possibility that adaptation of synaptic weight distribution, possibly involving silent synapses, may function to maximize information transfer in somatosensory pathways.

Associative memory model with long-tail-distributed Hebbian synaptic connections

The postsynaptic potentials of pyramidal neurons have a non-Gaussian amplitude distribution with a heavy tail in both hippocampus and neocortex. Such distributions of synaptic weights were recently shown to generate spontaneous internal noise optimal for spike propagation in recurrent cortical circuits. However, whether this internal noise generation by heavy-tailed weight distributions is possible for and beneficial to other computational functions remains unknown. To clarify this point, we construct an associative memory (AM) network model of spiking neurons that stores multiple memory patterns in a connection matrix with a lognormal weight distribution. In AM networks, non-retrieved memory patterns generate a cross-talk noise that severely disturbs memory recall. We demonstrate that neurons encoding a retrieved memory pattern and those encoding non-retrieved memory patterns have different subthreshold membrane-potential distributions in our model. Consequently, the probability of responding to inputs at strong synapses increases for the encoding neurons, whereas it decreases for the non-encoding neurons. Our results imply that heavy-tailed distributions of connection weights can generate noise useful for AM recall.

Soft-bound Synaptic Plasticity Increases Storage Capacity

Accurate models of synaptic plasticity are essential to understand the adaptive properties of the nervous system and for realistic models of learning and memory. Experiments have shown that synaptic plasticity depends not only on pre- and post-synaptic activity patterns, but also on the strength of the connection itself. Namely, weaker synapses are more easily strengthened than already strong ones. This so called soft-bound plasticity automatically constrains the synaptic strengths. It is known that this has important consequences for the dynamics of plasticity and the synaptic weight distribution, but its impact on information storage is unknown. In this modeling study we introduce an information theoretic framework to analyse memory storage in an online learning setting. We show that soft-bound plasticity increases a variety of performance criteria by about 18% over hard-bound plasticity, and likely maximizes the storage capacity of synapses.

Effects of synaptic connectivity on liquid state machine performance

The Liquid State Machine (LSM) is a biologically plausible computational neural network model for real-time computing on time-varying inputs, whose structure and function were inspired by the properties of neocortical columns in the central nervous system of mammals. The LSM uses spiking neurons connected by dynamic synapses to project inputs into a high dimensional feature space, allowing classification of inputs by linear separation, similar to the approach used in support vector machines (SVMs). The performance of a LSM neural network model on pattern recognition tasks mainly depends on its parameter settings. Two parameters are of particular interest: the distribution of synaptic strengths and synaptic connectivity. To design an efficient liquid filter that performs desired kernel functions, these parameters need to be optimized. We have studied performance as a function of these parameters for several models of synaptic connectivity. The results show that in order to achieve good performance, large synaptic weights are required to compensate for a small number of synapses in the liquid filter, and vice versa. In addition, a larger variance of the synaptic weights results in better performance for LSM benchmark problems. We also propose a genetic algorithm-based approach to evolve the liquid filter from a minimum structure with no connections, to an optimized kernel with a minimal number of synapses and high classification accuracy. This approach facilitates the design of an optimal LSM with reduced computational complexity. Results obtained using this genetic programming approach show that the synaptic weight distribution after evolution is similar in shape to that found in cortical circuitry.

Storage of Correlated Patterns in Standard and Bistable Purkinje Cell Models

The cerebellum has long been considered to undergo supervised learning, with climbing fibers acting as a ‘teaching’ or ‘error’ signal. Purkinje cells (PCs), the sole output of the cerebellar cortex, have been considered as analogs of perceptrons storing input/output associations. In support of this hypothesis, a recent study found that the distribution of synaptic weights of a perceptron at maximal capacity is in striking agreement with experimental data in adult rats. However, the calculation was performed using random uncorrelated inputs and outputs. This is a clearly unrealistic assumption since sensory inputs and motor outputs carry a substantial degree of temporal correlations. In this paper, we consider a binary output neuron with a large number of inputs, which is required to store associations between temporally correlated sequences of binary inputs and outputs, modelled as Markov chains. Storage capacity is found to increase with both input and output correlations, and diverges in the limit where both go to unity. We also investigate the capacity of a bistable output unit, since PCs have been shown to be bistable in some experimental conditions. Bistability is shown to enhance storage capacity whenever the output correlation is stronger than the input correlation. Distribution of synaptic weights at maximal capacity is shown to be independent on correlations, and is also unaffected by the presence of bistability.