Stored Patterns Research Articles

高知県高知市におけるコンビニエンスストアの立地展開の特異性

本稿は，高知県高知市におけるコンビニエンスストア（コンビニ）の立地要因を地理的条件から明らかにした．高知市におけるコンビニの立地は，他都市とは異なった展開を示した．高知市では，出店初期の1980年代に，主要道路沿い以外の地域への出店が多く，1990年代には，主要道路沿いへの出店が増加した．しかし，2000年代以降，他の地方都市と同様に，高知市においても，都心内部への集中出店や商圏環境の多様化がみられるようになった．外部条件の変化のうち，高速道路網の整備が，大手チェーンの参入および地元チェーンの出店戦略の変更を促進する要因として示唆された．特に，高知市では，地元チェーンがエリアフランチャイズ契約を通じて，県外資本のチェーンを運営している．したがって，契約条件の変更が，コンビニの立地パターンを劇的に変化させる要因の一つとなったことが明らかとなった．

High-Capacity Quantum Associative Memories

We review our models of quantum associative memories that represent the "quantization" of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely {\it eliminate crosstalk and spurious memories}. The number of control qubits plays the role of an inverse fictitious temperature, the accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models solve thus the capacity shortage problem of classical associative memories, providing a {\it polynomial improvement} in capacity. The price to pay is the probabilistic nature of information retrieval.

Multistability in Large Scale Models of Brain Activity.

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.

Structural plasticity and associative memory in balanced neural networks with spike-time dependent inhibitory plasticity

In recent work, Vogels and collaborators demonstrated the ability of spike-time dependent inhibitory plasticity to stabilise recurrent spiking neural networks by balancing out the excitatory input received by neurons in the network with the required amount of inhibition [1]. Further, as an application of this unsupervised balance, they showed that such a network can operate as a non-attractor associative memory, by being able to store patterns that become indistinguishable from the background activity of the network, but that can be recalled successfully by external stimuli. In other research, also related to homoeostasis in neuronal networks, Butz and colleagues investigated the rewiring of deafferentated neurons driven by homoeostatic structural plasticity [2,3]. Their work, based on biological observations of restructuring in the visual cortex [4,5], suggests that neurons endeavour to maintain an appropriate level of electrical activity by adjusting the number of synaptic contacts they make. In order to remedy the loss in electrical activity experienced by neurons as a result of deafferentation, they implemented a growth rule that enabled the neurons to increase the number of lateral connections. In our research, we measure the memory capacity of balanced spiking neural networks possessing capabilities of both fast synaptic and slow structural plasticity by calculating a signal to noise ratio [6]. The memory capacity of a network of neurons is dependent on various parameters such as the magnitude of the recall stimulus, the size of the pattern relative to the size of the network, the learning rule that dictates inhibitory plasticity, and so on. In this work, as an initial step, we investigate the memory capacity of a non lesioned network containing spike-time dependent plastic inhibitory synapses similar to the network used by Vogels and collaborators. Random, possibly overlapping patterns are iteratively stored in the network as Hebbian assemblies. In order to measure their signal to noise ratio, the stored patterns are recalled by the activation of a randomly selected subset of their neurons. In general, during the recall of the stored patterns, we observe a gradual decrease in the signal to noise ratio as more and more patterns are stored in the network. This signifies an inverse relation between the mean signal to noise ratio and the total number of such patterns that were stored in the network. We are currently investigating the performance of our balanced networks during and after focal lesions and homoeostatic rewiring.

A biologically based neural network model for decision making

We present a neural network model, describing an adaptive decision making process (DM), under varying internal and external contexts [1]. The model includes the three most crucial structures in both emotional and rational aspects of DM: amygdala, orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) [2-4]. Neural activities in these structures represent emotional attitude, expectancy value, and rules towards the options (Figure ​(Figure1).1). The DM is modeled at a level of mesoscopic neurodynamics, using biologically inspired neural networks [5]. Rational and emotional associations are encoded with cell assembly oscillations in all three structures, determining the value of an option, V(opt), as a product of the number of activated cells and the mean frequency and amplitude of their oscillations (Figure ​(Figure2).2). A decision is based on the competition among stored patterns, using cosine similarity of the frequency vectors f→. The option with highest value will win the competition in each system: Figure 1 Interactions of the main neural structures in the decision making process: Amygdala, orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC). Inputs from sensory modalities and from rational and emotional feedback. Figure 2 Activity of a cell assembly representing one of possible options. Red and green traces show the activity of the inhibitory neurons and the blue one the activity of all excitatory neurons. V(opt)|sopt|.⟨fopt ,Aopt ⟩=|sopt|.⟨fopt ,Aopt ⟩,∀opt=1,...,n The emotional system is goal directed on the predicted value of the options. Emotional memory of various options are formed and stored in the amygdala. A prediction signal is generated in OFC and an emotional response is measured as a level of satisfaction. LPFC is a pivotal structure in the rational analysis and is based on habitual DM. Declarative and procedural memories, as the main components of this system are activated by external stimuli. The bidirectional interactions between maintained rules in procedural memory, rational attitudes towards different options, and stored factual information in declarative memory, lead to the selection of an option as a rational decision. The integration of emotional and rational activities results in a final decision. When an action is executed as a result of a decision its experienced value is compared with the expected one, and stored in memory. Depending on the sign and the magnitude of the prediction error (expected value - real value), the stored emotional and rational attitude might be updated. The experience of our decisions/choices are learnt and may influence future decisions. For any particular input signal, the final decision could shift, depending on internal and external context. Large delayed rewards have a lower value, compared to small immediate rewards. This fact can be included with the help of a hyperbolic discounting function, which models the exponential reduction of rewards in terms of time.

Role of topology in the spontaneous cortical activity

Spontaneous cortical activity can show very complex collective emerging features, with, in some cases, the alternation of of network quiescence and of generalized spiking and neuronal depolarization [1]. Results on in vitro and in vivo up states has suggested that this spontaneous activity occurs in a highly structured way, with repeating spatiotemporal patterns of cellular activity [1,2]. Because of their stereotyped spatio-temporal dynamics, it has been conjectured that network up states are circuit attractors that could implement memory states [1]. The precise mechanisms by which these up states transitions occur is still unclear, but it seems to rely on network mechanisms [1]. Previous papers [3,4] have studied a leaky IF model whose connectivity was designed in such a manner as to favor the spontaneous emergence of collective oscillatory spatio-temporal patterns of spikes. In this model the alternation of up and down states does not depend on a kind of neuron bistability, nor on synaptic depression, but is rather a network effect. The model consists in N leaky IF units, with Poissonian noise. Structured connections Jij was fixed with a [3,4] inspired to spike time dependent plasticity (STDP). After the learning and pruning procedure [3], about 12% of the N(N-1) connections survive as positive connections, and about 27% as negative connections. There's a balance condition, such that the sum of connections entering on a single neuron ΣjJij is of order 1/√N, and therefore vanishes in the thermodynamic limit. In order to check if the transition region with bimodal distribution of the firing rate survive even after changes in the topology of the network, in this work we reshuffle a fraction of the connections. For each chosen connection we change the presynaptic neuron, choosing as the new presynaptic neuron a random neuron of the network. After reshuffling a fraction f of connections, not only the number of excitatory and inhibitory connections is the same as before, but also the strengths of the connections are the same, and only the topology (number of loops, mean path length, clustering coefficient, etc.) is changed. We observe that reshuffling the connections changes the features of the dynamics dramatically. Before reshuffling, i.e. with f = 0 and connections dictated by the learning rule of [3], the system has a transition from a regime of Poissonian noise activity to a regime of spontaneous persistent collective replay, and at the transition point the network dynamics shows an intermittent reactivation of the stored patterns, with alternation of up and down state, and bimodal distribution of spiking rate (fig. ​(fig.1A).1A). Reshuffling a small fraction of connections, leaving all the other parameters unchanged, we observe that the transition region with bimodal distribution disappears, and the dynamics is Poissonian with unimodal rate distribution for all the parameters investigated. These results shows the role of topology in dictating the emerging collective dynamics of neural circuits. Figure 1 Distribution of the spiking rates for the model with (A) no reshuffling f = 0, (B) reshuffling a fraction f = 0.1 of connections, and (C) all connections reshuffled f = 1. All other parameters are the same (N = 3000 neurons, H0/Θ = 0.221, noise ...

Effective approach for actually uncorrelated angular vibration pattern design of a ring laser angle sensor

For small ring laser angle sensors that have several tens of centimeters of laser cavity perimeter, the laser cavities must be vibrated using uncorrelated white angular vibration in order to overcome the dead band. However, due to the high Q-factor structure of the angular vibrator, the realized frequencies and amplitudes of the angular vibrations do not change simultaneously corresponding to the input electrical signals. Therefore, uncorrelated white angular vibrations must be designed considering the actual responses of the angular vibrators. Thus, the actually realized angular vibration patterns corresponding to several types of electrical sequence signals were generated and stored. Next, using the modeling of a ring laser angle sensor and applying the stored actual angular vibration patterns, the simulation outputs of a ring laser angle sensor were generated and analyzed using the Allan variance. The results demonstrated that the imperfection of the angular vibration produced a rate random walk as well as a bias fluctuation. Based on these results and as a method for the realizing an uncorrelated angular vibration pattern design that considers the response of the angular vibrator, a simulation method for the design using experimentally stored angular vibration patterns is proposed. Also, in order to obtain a suitable pattern amplitude, the minimum flicker rate errors were investigated through variations in the pattern amplitude of the stored actual angular vibration patterns. These results were confirmed experimentally.

Twin Neurons for Efficient Real-World Data Distribution in Networks of Neural Cliques: Applications in Power Management in Electronic Circuits.

Associative memories are data structures that allow retrieval of previously stored messages given part of their content. They, thus, behave similarly to the human brain's memory that is capable, for instance, of retrieving the end of a song, given its beginning. Among different families of associative memories, sparse ones are known to provide the best efficiency (ratio of the number of bits stored to that of the bits used). Recently, a new family of sparse associative memories achieving almost optimal efficiency has been proposed. Their structure, relying on binary connections and neurons, induces a direct mapping between input messages and stored patterns. Nevertheless, it is well known that nonuniformity of the stored messages can lead to a dramatic decrease in performance. In this paper, we show the impact of nonuniformity on the performance of this recent model, and we exploit the structure of the model to improve its performance in practical applications, where data are not necessarily uniform. In order to approach the performance of networks with uniformly distributed messages presented in theoretical studies, twin neurons are introduced. To assess the adapted model, twin neurons are used with the real-world data to optimize power consumption of electronic circuits in practical test cases.

A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks.

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network scenario, whose prototype is the Hopfield model. The model simplicity and the locality of the synaptic update rules come at the cost of a poor storage capacity, compared with the capacity achieved with perceptron learning algorithms. Here, by transforming the perceptron learning rule, we present an online learning rule for a recurrent neural network that achieves near-maximal storage capacity without an explicit supervisory error signal, relying only upon locally accessible information. The fully-connected network consists of excitatory binary neurons with plastic recurrent connections and non-plastic inhibitory feedback stabilizing the network dynamics; the memory patterns to be memorized are presented online as strong afferent currents, producing a bimodal distribution for the neuron synaptic inputs. Synapses corresponding to active inputs are modified as a function of the value of the local fields with respect to three thresholds. Above the highest threshold, and below the lowest threshold, no plasticity occurs. In between these two thresholds, potentiation/depression occurs when the local field is above/below an intermediate threshold. We simulated and analyzed a network of binary neurons implementing this rule and measured its storage capacity for different sizes of the basins of attraction. The storage capacity obtained through numerical simulations is shown to be close to the value predicted by analytical calculations. We also measured the dependence of capacity on the strength of external inputs. Finally, we quantified the statistics of the resulting synaptic connectivity matrix, and found that both the fraction of zero weight synapses and the degree of symmetry of the weight matrix increase with the number of stored patterns.

Modification of hemiplegic compensatory gait pattern by symmetry-based motion controller of HAL.

As one of several characteristics of hemiplegic patients after stroke, compensatory gait caused by affected limb is often seen. The purpose of this research is to apply a symmetry-based controller of a wearable type lower limb robot, Hybrid Assistive Limb (HAL) to hemiplegic patients with compensatory gait, and to investigate improvement of gait symmetry. The controller is designed respectively for swing phase and support phase according to characteristics of hemiplegic gait pattern. The controller during swing phase stores the motion of the unaffected limb and then provides motion support on the affected limb during the subsequent swing using the stored pattern to realize symmetric gait based on spontaneous limb swing. Moreover, the controller during support phase provides motion to extend hip and knee joints to support wearer's body. Clinical tests were conducted in order to assess the modification of gait symmetry. Our case study involved participation of one chronic stroke patient who performs abnormally-compensatory gait for both of the affected and unaffected limbs. As a result, the patient's gait symmetry was improved by providing motion support during the swing phase on the affected side and motion constraint during the support phase on the unaffected side. The study showed promising basis for the effectiveness of the controller for the future clinical study.

Oscillatory Neural Networks Based on TMO Nano-Oscillators and Multi-Level RRAM Cells

In massively parallel computational tasks, such as pattern recognition, conventional computing architectures have insufficient power efficiency for energy constrained environments. This has made alternative architectures, such as neuromorphic computing, increasingly attractive. Oscillatory neural networks (ONNs) are one promising architecture, but efficient hardware implementations have been limited by shortcomings in CMOS technology, specifically in the efficient implementation of oscillators and synaptic weights. The authors have recently demonstrated that metal-oxide based resistive switching (RRAM) structures can be engineered to create low-power, scalable, voltage-controlled oscillators that utilize inherent meta-stability in the device. This work proposes an RRAM-based ONN that couples oscillatory “neurons” through weighted “synapses” using oscillator phase as the state-variable. This paper demonstrates a robust architecture using only a few logic gates per neuron to implement phase initialization and locking of these oscillators, and demonstrate their capability to identify stored patterns from noisy inputs. Using measured characteristics of RRAMs as oscillators and programmable resistors, compact models are derived and used to simulate both an 8-neuron and 20-neuron network.

Efficient transmission of subthreshold signals in complex networks of spiking neurons.

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.

Hierarchical neural networks perform both serial and parallel processing

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal-to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of different patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system.The price to pay for those remarkable capabilities lies in a network’s capacity smaller than the mean field counterpart, thus yielding a new budget principle: the wider the multitasking capabilities, the lower the network load and vice versa. This may have important implications in our understanding of biological complexity.

Towards Scalable Distributed Framework for Urban Congestion Traffic Patterns Warehousing

We put forward architecture of a framework for integration of data from moving objects related to urban transportation network. Most of this research refers to the GPS outdoor geolocation technology and uses distributed cloud infrastructure with big data NoSQL database. A network of intelligent mobile sensors, distributed on urban network, produces congestion traffic patterns. Congestion predictions are based on extended simulation model. This model provides traffic indicators calculations, which fuse with the GPS data for allowing estimation of traffic states across the whole network. The discovery process of congestion patterns uses semantic trajectories metamodel given in our previous works. The challenge of the proposed solution is to store patterns of traffic, which aims to ensure the surveillance and intelligent real-time control network to reduce congestion and avoid its consequences. The fusion of real-time data from GPS-enabled smartphones integrated with those provided by existing traffic systems improves traffic congestion knowledge, as well as generating new information for a soft operational control and providing intelligent added value for transportation systems deployment.

Metastable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network

In this paper, we introduce and investigate the statistical mechanics of hierarchical neural networks. First, we approach these systems à la Mattis, by thinking of the Dyson model as a single-pattern hierarchical neural network. We also discuss the stability of different retrievable states as predicted by the related self-consistencies obtained both from a mean-field bound and from a bound that bypasses the mean-field limitation. The latter is worked out by properly reabsorbing the magnetization fluctuations related to higher levels of the hierarchy into effective fields for the lower levels. Remarkably, mixing Amitʼs ansatz technique for selecting candidate-retrievable states with the interpolation procedure for solving for the free energy of these states, we prove that, due to gauge symmetry, the Dyson model accomplishes both serial and parallel processing. We extend this scenario to multiple stored patterns by implementing the Hebb prescription for learning within the couplings. This results in Hopfield-like networks constrained on a hierarchical topology, for which, by restricting to the low-storage regime where the number of patterns grows at its most logarithmical with the amount of neurons, we prove the existence of the thermodynamic limit for the free energy, and we give an explicit expression of its mean-field bound and of its related improved bound. We studied the resulting self-consistencies for the Mattis magnetizations, which act as order parameters, are studied and the stability of solutions is analyzed to get a picture of the overall retrieval capabilities of the system according to both mean-field and non-mean-field scenarios. Our main finding is that embedding the Hebbian rule on a hierarchical topology allows the network to accomplish both serial and parallel processing. By tuning the level of fast noise affecting it or triggering the decay of the interactions with the distance among neurons, the system may switch from sequential retrieval to multitasking features, and vice versa. However, since these multitasking capabilities are basically due to the vanishing ‘dialogue’ between spins at long distance, this effective penury of links strongly penalizes the networkʼs capacity, with results bounded by low storage.

IJARCCE - Computer and Communication Engineering

Data mining is a highly evolving and developing frontier in data and information systems and their applications. Its a concept of extracting data from large data set and converts into understandable format. Automated prospective analysis and knowledge driven decisions make data more proactive. Pattern matching used for control flow of patterns, checks similarity between already stored templates with input template. Patterns are procedure for converting input data. The existing system pay-as-you-go style matching technique has poor discriminative feature were this technique depend mainly on time. So it will affect 1: n matching for events and when matching events with heterogeneous data it may result in duplication of data. In proposed system, as Generic Pattern Matching technique implies to validate similarity between two events. Number of events internally stores and maintains all the characteristics of events. Patterns are compared with all stored patterns with in the data set. Pattern matching enhances several events to improve the performance and efficiency of events. This is independent of time so 1 : n issue can be sorted out. It will also retrieve exact result without any approximate value.

Long-term memory stabilized by noise-induced rehearsal.

Cortical networks can maintain memories for decades despite the short lifetime of synaptic strengths. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of ongoing spike-timing-dependent plasticity (STDP) on the stability of memory patterns stored in synapses of an attractor neural network. We show that certain classes of STDP rules can stabilize all stored memory patterns despite a short lifetime of synapses. In our model, unstructured neural noise, after passing through the recurrent network connections, carries the imprint of all memory patterns in temporal correlations. STDP, combined with these correlations, leads to reinforcement of all stored patterns, even those that are never explicitly visited. Our findings may provide the functional reason for irregular spiking displayed by cortical neurons and justify models of system memory consolidation. Therefore, we propose that irregular neural activity is the feature that helps cortical networks maintain stable connections.

Overcoming catastrophic interference in connectionist networks using Gram-Schmidt orthogonalization.

Connectionist models of memory storage have been studied for many years, and aim to provide insight into potential mechanisms of memory storage by the brain. A problem faced by these systems is that as the number of items to be stored increases across a finite set of neurons/synapses, the cumulative changes in synaptic weight eventually lead to a sudden and dramatic loss of the stored information (catastrophic interference, CI) as the previous changes in synaptic weight are effectively lost. This effect does not occur in the brain, where information loss is gradual. Various attempts have been made to overcome the effects of CI, but these generally use schemes that impose restrictions on the system or its inputs rather than allowing the system to intrinsically cope with increasing storage demands. We show here that catastrophic interference occurs as a result of interference among patterns that lead to catastrophic effects when the number of patterns stored exceeds a critical limit. However, when Gram-Schmidt orthogonalization is combined with the Hebb-Hopfield model, the model attains the ability to eliminate CI. This approach differs from previous orthogonalisation schemes used in connectionist networks which essentially reflect sparse coding of the input. Here CI is avoided in a network of a fixed size without setting limits on the rate or number of patterns encoded, and without separating encoding and retrieval, thus offering the advantage of allowing associations between incoming and stored patterns.PACS Nos.: 87.10.+e, 87.18.Bb, 87.18.Sn, 87.19.La

Sequence memory based on coherent spin-interaction neural networks.

Sequence information processing, for instance, the sequence memory, plays an important role on many functions of brain. In the workings of the human brain, the steady-state period is alterable. However, in the existing sequence memory models using heteroassociations, the steady-state period cannot be changed in the sequence recall. In this work, a novel neural network model for sequence memory with controllable steady-state period based on coherent spininteraction is proposed. In the proposed model, neurons fire collectively in a phase-coherent manner, which lets a neuron group respond differently to different patterns and also lets different neuron groups respond differently to one pattern. The simulation results demonstrating the performance of the sequence memory are presented. By introducing a new coherent spin-interaction sequence memory model, the steady-state period can be controlled by dimension parameters and the overlap between the input pattern and the stored patterns. The sequence storage capacity is enlarged by coherent spin interaction compared with the existing sequence memory models. Furthermore, the sequence storage capacity has an exponential relationship to the dimension of the neural network.

Noise facilitation in associative memories of exponential capacity.

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.