Izhikevich神经元网络的同步与联想记忆

联想记忆是人脑的一项重要功能。以Izhikevich神经元模型为节点,构建神经网络,神经元之间采用全连结的方式;以神经元群体的时空编码（spatio-temporal coding）理论研究所构建神经网络的联想记忆功能。在加入高斯白噪声的情况下,调节网络中神经元之间的连接强度的大小,当连接强度和噪声强度达到一个阈值时网络中部分神经元同步放电,实现了存储模式的联想记忆与恢复。仿真结果表明,神经元之间的连接强度在联想记忆的过程中发挥了重要的作用,噪声可以促使神经元间的同步放电,有助于神经网络实现存储模式的联想记忆与恢复。     

Synchronization of neural activity is a promising mechanism of memory information processing in networks of columns

Synchronization of the oscillatory discharge of cortical neurons could be a part of the mechanism that is involved in cortical information processing. On the assumption that the basic functional unit is the column composed of local excitatory and inhibitory cells and generating oscillatory neural activity, a network model that attains associative memory function is proposed. The synchronization of oscillation in the model is studied analytically using a sublattice analysis. In particular, the retrieval of a single memory pattern can be studied in the system, which can be derived from the original network model of interacting columns and is formally equivalent to a system of an isolated column. The network model simulated numerically shows a remarkable performance in which retrieval is achieved simultaneously for more than one memory pattern. The manifestations of this simultaneous retrieval in the network dynamics are successive transitions of the network state from a synchronized oscillation for a memory pattern to that for another memory pattern.     

Spiking neural network model for memorizing sequences with forward and backward recall

We present an oscillatory network of conductance based spiking neurons of Hodgkin–Huxley type as a model of memory storage and retrieval of sequences of events (or objects). The model is inspired by psychological and neurobiological evidence on sequential memories. The building block of the model is an oscillatory module which contains excitatory and inhibitory neurons with all-to-all connections. The connection architecture comprises two layers. A lower layer represents consecutive events during their storage and recall. This layer is composed of oscillatory modules. Plastic excitatory connections between the modules are implemented using an STDP type learning rule for sequential storage. Excitatory neurons in the upper layer project star-like modifiable connections toward the excitatory lower layer neurons. These neurons in the upper layer are used to tag sequences of events represented in the lower layer. Computer simulations demonstrate good performance of the model including difficult cases when different sequences contain overlapping events. We show that the model with STDP type or anti-STDP type learning rules can be applied for the simulation of forward and backward replay of neural spikes respectively.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

A neuron model with learning capability and its relation to mechanisms of association

A neuron model with the ability of learning has been examined by means of mathematical and statistical methods. By use of the established anatomical concepts the main features of the model can be described as follows.The synapses are randomly distributed on the dendrites in a way that can be described by poisson processes. The afferent connections to the synapses are also random.The input signals are divided into excitatory, inhibitory and unspecified signals. The latter, whose detailed action is not specified, may involve excitatory as well as inhibitory action on the cell. Signals are described in terms of impulse frequencies.Learning takes place through facilitation of excitatory synapses. The condition for facilitation is the occurrence of simultaneous presynaptic and postsynaptic activity. The synaptical changes occurring during repeated learning are superimposed. Inhibitory synapses are capable of influencing learning by blocking the dendritic transmission.It is shown that, under certain conditions, a collection of model cells is able to work as an associative memory. This means that a pattern of output signals that once occurred through the combined action of the excitatory, the inhibitory, and the unspecified signals may later be recalled by applying just the two former signal patterns. It is shown that excitatory and inhibitory signals are similar in their ability to evoke associations.However there is also a difference between excitation and inhibition due to the fact that the pattern of inhibitory signals is subject to a non-linear transformation. This implies that great similarity is required between the inhibitory pattern once present during learning and the inhibitory pattern that is fed in later in order to obtain an associative recall. This phenomenon is called pattern separation and is supposed to be of importance when discriminating between patterns.     

Biophysical mechanism of the interaction between default mode network and working memory network

Default mode network (DMN) is a functional brain network with a unique neural activity pattern that shows high activity in resting states but low activity in task states. This unique pattern has been proved to relate with higher cognitions such as learning, memory and decision-making. But neural mechanisms of interactions between the default network and the task-related network are still poorly understood. In this paper, a theoretical model of coupling the DMN and working memory network (WMN) is proposed. The WMN and DMN both consist of excitatory and inhibitory neurons connected by AMPA, NMDA, GABA synapses, and are coupled with each other only by excitatory synapses. This model is implemented to demonstrate dynamical processes in a working memory task containing encoding, maintenance and retrieval phases. Simulated results have shown that: (1) AMPA channels could produce significant synchronous oscillations in population neurons, which is beneficial to change oscillation patterns in the WMN and DMN. (2) Different NMDA conductance between the networks could generate multiple neural activity modes in the whole network, which may be an important mechanism to switch states of the networks between three different phases of working memory. (3) The number of sequentially memorized stimuli was related to the energy consumption determined by the network''s internal parameters, and the DMN contributed to a more stable working memory process. (4) Finally, this model demonstrated that, in three phases of working memory, different memory phases corresponded to different functional connections between the DMN and WMN. Coupling strengths that measured these functional connections differed in terms of phase synchronization. Phase synchronization characteristics of the contained energy were consistent with the observations of negative and positive correlations between the WMN and DMN reported in referenced fMRI experiments. The results suggested that the coupled interaction between the WMN and DMN played important roles in working memory.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11571-021-09674-1.     

Conductance-based refractory density model of primary visual cortex

A layered continual population model of primary visual cortex has been constructed, which reproduces a set of experimental data, including postsynaptic responses of single neurons on extracellular electric stimulation and spatially distributed activity patterns in response to visual stimulation. In the model, synaptically interacting excitatory and inhibitory neuronal populations are described by a conductance-based refractory density approach. Populations of two-compartment excitatory and inhibitory neurons in cortical layers 2/3 and 4 are distributed in the 2-d cortical space and connected by AMPA, NMDA and GABA type synapses. The external connections are pinwheel-like, according to the orientation of a stimulus. Intracortical connections are isotropic local and patchy between neurons with similar orientations. The model proposes better temporal resolution and more detailed elaboration than conventional mean-field models. In comparison to large network simulations, it excludes a posteriori statistical data manipulation and provides better computational efficiency and minimal parametrization.     

A cognitive and associative memory

By introducing a physiological constraint in the auto-correlation matrix memory, the system is found to acquire an ability in cognition i.e. the ability to identify and input pattern by its proximity to any one of the stored memories. The physiological constraint here is that the attribute of a given synapse (i.e. excitatory or inhibitory) is uniquely determined by the neuron it belongs. Thus the synaptic coupling is generally not symmetric. Analytical and numerical analyses revealed that the present model retrieves a memory if an input pattern is close to the pattern of the stored memories; if not, it gives a clear response by going into a special mode where almost all neurons are in the same state in each time step. This uniform mode may be stationary or periodic, depending on whether or not the number of the excitatory neurons exceeds the number of inhibitory neurons.     

Control of computational dynamics of coupled integrate-and-fire neurons

 Generation and control of different dynamical modes of computational processes in a net of interconnected integrate-and-fire neurons are demonstrated. A net architecture resembling a generic cortical structure is formed from pairs of excitatory and inhibitory units with excitatory connections between and inhibitory connections within pairs. Integrate-and-fire model neurons derived from detailed conductance-based models of neocortical pyramidal cells and fast-spiking interneurons are employed for the excitatory and inhibitory units, respectively. Firing-rate adaptation is incorporated into the excitatory units based on the regulation of the slow afterhyperpolarization phase of action potentials by intracellular calcium ions. Saturation of synaptic conductances is implemented for the interconnections between units. It is shown that neuronal adaptation of the excitatory units can generate richer net dynamics than relaxation to fixed-point attractors in a pattern space. At strong adaptivity, i.e. when the neuronal excitability is strongly influenced by the preceding activity, complex dynamics of either aperiodic or limit-cycle character are generated in both the pattern space and the phase space of all dynamical variables. This regime corresponds to an exploratory mode of the system, in which the pattern space can be searched. At weak adaptivity, the dynamics are governed by fixed-point attractors in the pattern space, and this corresponds to a mode for retrieval of a particular pattern. In the brain, neuronal adaptivity can be regulated by various neuromodulators. The results are in accordance with those recently obtained by means of more abstract models formulated in terms of mean firing rates. The increased realism makes the present model reveal more detailed mechanisms and strengthens the relevance of the conclusions to biological systems. The simplicity and realism of the coupled integrate-and-fire neurons make the present model useful for studies of systems in which the temporal aspects of neural coding are important. Received: 8 December 1995 / Accepted in revised form: 23 January 1997     

Functional model of biological neural networks

A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.     

Neuronal Mechanisms Encoding Global-to-Fine Information in Inferior-Temporal Cortex

Sugase et al. found that global information is represented at the initial transient firing of a single face-responsive neuron in inferior-temporal (IT) cortex, and that finer information is represented at the subsequent sustained firing. A feed-forward model and an attractor network are conceivable models to reproduce this dynamics. The attractor network, specifically an associative memory model, is employed to elucidate the neuronal mechanisms producing the dynamics. The results obtained by computer simulations show that a state of neuronal population initially approaches to a mean state of similar memory patterns, and that it finally converges to a memory pattern. This dynamics qualitatively coincides with that of face-responsive neurons. The dynamics of a single neuron in the model also coincides with that of a single face-responsive neuron. Furthermore, we propose two physiological experiments and predict the results from our model. Both predicted results are not explainable by the feed-forward model. Therefore, if the results obtained by actual physiological experiments coincide with our predicted results, the attractor network might be the neuronal mechanisms producing the dynamics of face-responsive neurons.     

Stochastic automaton models for interaction of excitatory and inhibitory impulse sequences in neurons

The mechanisms by which excitatory and inhibitory input impulse sequences interact in changing the spike probability in neurons are examined in the two mathematical neuron models; one is a real-time neuron model which is close to physiological reality, and the other a stochastic automaton model for the temporal pattern discrimination proposed in the previous paper (Tsukada et al., 1976), which is developed in this paper as neuron models for interaction of excitatory and inhibitory input impulse sequences. The interval distributions of the output spike train from these models tend to be multimodal and are compared with those used for experimental data, reported by Bishop et al. (1964) for geniculate neuron activity and Poisson process deleting model analyzed by Ten Hoopen et al. (1966). Special attention, moreover, should be paid to how different forms of inhibitory input are transformed into the output interval distributions through these neuron models. These results exhibit a clear correlation between inhibitory input form and output interval distribution. More detailed information on this mechanism is obtained from the computations of recurrence-time under the stationary condition to go from active state to itself for the first time, each of which is influenced by the inhibitory input forms. In addition to these facts, some resultant characteristics on interval histogram and serial correlation are discussed in relation to physiological data from the literature.     

NMDA receptors are not required for pattern completion during associative memory recall

Pattern completion, the ability to retrieve complete memories initiated by subsets of external cues, has been a major focus of many computation models. A previously study reports that such pattern completion requires NMDA receptors in the hippocampus. However, such a claim was derived from a non-inducible gene knockout experiment in which the NMDA receptors were absent throughout all stages of memory processes as well as animal's adult life. This raises the critical question regarding whether the previously described results were truly resulting from the requirement of the NMDA receptors in retrieval. Here, we have examined the role of the NMDA receptors in pattern completion via inducible knockout of NMDA receptors limited to the memory retrieval stage. By using two independent mouse lines, we found that inducible knockout mice, lacking NMDA receptor in either forebrain or hippocampus CA1 region at the time of memory retrieval, exhibited normal recall of associative spatial reference memory regardless of whether retrievals took place under full-cue or partial-cue conditions. Moreover, systemic antagonism of NMDA receptor during retention tests also had no effect on full-cue or partial-cue recall of spatial water maze memories. Thus, both genetic and pharmacological experiments collectively demonstrate that pattern completion during spatial associative memory recall does not require the NMDA receptor in the hippocampus or forebrain.     

Effects of phase on homeostatic spike rates

Recent experimental results by Talathi et al. (Neurosci Lett 455:145–149, 2009) showed a divergence in the spike rates of two types of population spike events, representing the putative activity of the excitatory and inhibitory neurons in the CA1 area of an animal model for temporal lobe epilepsy. The divergence in the spike rate was accompanied by a shift in the phase of oscillations between these spike rates leading to a spontaneous epileptic seizure. In this study, we propose a model of homeostatic synaptic plasticity which assumes that the target spike rate of populations of excitatory and inhibitory neurons in the brain is a function of the phase difference between the excitatory and inhibitory spike rates. With this model of homeostatic synaptic plasticity, we are able to simulate the spike rate dynamics seen experimentally by Talathi et al. in a large network of interacting excitatory and inhibitory neurons using two different spiking neuron models. A drift analysis of the spike rates resulting from the homeostatic synaptic plasticity update rule allowed us to determine the type of synapse that may be primarily involved in the spike rate imbalance in the experimental observation by Talathi et al. We find excitatory neurons, particularly those in which the excitatory neuron is presynaptic, have the most influence in producing the diverging spike rates and causing the spike rates to be anti-phase. Our analysis suggests that the excitatory neuronal population, more specifically the excitatory to excitatory synaptic connections, could be implicated in a methodology designed to control epileptic seizures.     

Memory model based on the plasticity of inhibiting neurons

A stochastic memory model based on the net of excitatory and inhibitory neurons is considered. Its learning ability is due to a decrease of the reactivity of inhibitory elements. Information capacity of such neuron net was estimated in relation to its structure parameters. It has been shown that in the definite range of their change the information capacity of the net under consideration significantly exceeds that of the neuron net with the memory based on the plasticity of excitatory elements.     

主动联想记忆神经网络模型

在信息编码能提高联想记忆的存贮能力和脑内存在主动活动机制的启发下,提出一个主动联想记忆模型。模型包括两个神经网络,其一为输入和输出网络,另一个为在学习时期能自主产生兴奋模式的主动网络。两个网络的神经元之间有突触联系。由于自主产生的兴奋模式与输入无关,并可能接近于相互正交,因此,本模型有较高的存贮能力。初步分析和计算机仿真证明：本模型确有比通常联想记忆模型高的存贮能力,特别是在输入模式间有高度相关情况下、最后,对提出的模型与双向自联想记忆和光学全息存贮机制的关系作了讨论。     

Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators

Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit.     

Anisotropic connectivity and cooperative phenomena as a basis for orientation sensitivity in the visual cortex

A computer simulation model of the neural circuitry underlying orientation sensitivity in cortical neurons is examined. The model consists of a network of 3000 neurons divided into two functionally distinct cell types: excitatory (E-cells) and inhibitory (I-cells). We demonstrate that both orientation sensitivity and shape selectivity can be accounted for by making the following assumptions: 1) thalamic afferents to a sheet of cortical neurons are retionotopically organized; 2) thalamic afferents come from a single neuron, or at most a few neurons, in the lateral geniculate nucleus; 3) cortical activity is cooperative, i.e. largely dependent on intracortical connections, some of which have anisotropies along directions parallel to the pial surface. Anisotropies are specified only by the distribution of cells which are postsynaptic to a particular neuron, without specifying the axonal or dendritic contributions. In this paper, orientation sensitivity arises through cooperative interactions among neurons having anisotropic excitatory, and isotropic inhibitory connections.     

Memories in context

Context-dependent associative memories are models that allow the retrieval of different vectorial responses given a same vectorial stimulus, depending on the context presented to the memory. The contextualization is obtained by doing the Kronecker product between two vectorial entries to the associative memory: the key stimulus and the context. These memories are able to display a wide variety of behaviors that range from all the basic operations of the logical calculus (including fuzzy logics) to the selective extraction of features from complex vectorial patterns. In the present contribution, we show that a context-dependent memory matrix stores a large amount of possible virtual associative memories, that awaken in the presence of a context. We show how the vectorial context allows a memory matrix to be representable in terms of its singular-value decomposition. We describe a neural interpretation of the model in which the Kronecker product is performed on the same neurons that sustain the memory. We explored, with numerical experiments, the reliability of chains of contextualized associations. In some cases, random disconnection produces the emergence of oscillatory behaviors of the system. Our results show that associative chains retain their performances for relatively large dimensions. Finally, we analyze the properties of some modules of context-dependent autoassociative memories inserted in recursive nets: the perceptual autoorganization in the presence of ambiguous inputs (e.g. the disambiguation of the Necker’s cube figure), the construction of intersection filters, and the feature extraction capabilities.