An Hypothesis for a Novel Learning Mechanism in the Cerebellar Cortex

The cerebellar cortical circuitry may support a distinct second form of associative learning, complementary to the well-known synaptic plasticity (long term depression, LTD) that has been previously shown. As the granule cell axons ascend to the molecular layer, they make multiple synapses on the overlying Purkinje cells (PC). This ascending branch (AB) input, which has been ignored in models of cerebellar learning, is likely to be functionally distinct from the parallel fiber (PF) synaptic input. We predict that AB-PF correlations lead to Hebbian-type learning at the PF-PC synapse, including long term potentiation (LTP), and allowing the cortical circuit to combine AB-PF LTP for feedforward state prediction with climbing fiber LTD for feedback error correction. The new learning mechanism could therefore add computational capacity to cerebellar models and may explain more of the experimental data.     

A VLSI recurrent network of integrate-and-fire neurons connected by plastic synapses with long-term memory.

Electronic neuromorphic devices with on-chip, on-line learning should be able to modify quickly the synaptic couplings to acquire information about new patterns to be stored (synaptic plasticity) and, at the same time, preserve this information on very long time scales (synaptic stability). Here, we illustrate the electronic implementation of a simple solution to this stability-plasticity problem, recently proposed and studied in various contexts. It is based on the observation that reducing the analog depth of the synapses to the extreme (bistable synapses) does not necessarily disrupt the performance of the device as an associative memory, provided that 1) the number of neurons is large enough; 2) the transitions between stable synaptic states are stochastic; and 3) learning is slow. The drastic reduction of the analog depth of the synaptic variable also makes this solution appealing from the point of view of electronic implementation and offers a simple methodological alternative to the technological solution based on floating gates. We describe the full custom analog very large-scale integration (VLSI) realization of a small network of integrate-and-fire neurons connected by bistable deterministic plastic synapses which can implement the idea of stochastic learning. In the absence of stimuli, the memory is preserved indefinitely. During the stimulation the synapse undergoes quick temporary changes through the activities of the pre- and postsynaptic neurons; those changes stochastically result in a long-term modification of the synaptic efficacy. The intentionally disordered pattern of connectivity allows the system to generate a randomness suited to drive the stochastic selection mechanism. We check by a suitable stimulation protocol that the stochastic synaptic plasticity produces the expected pattern of potentiation and depression in the electronic network.     

Associate learning and correcting in a memristive neural network

This paper further studies the ability of the associate learning and self-correcting in a memristive artificial neural network (ANN). Different from the existing models, the present ANN contains the multiply-threshold neurons, the discrete charge-controlled memristors, and a new learning law named the max-input-feedback (MIF). We shall demonstrate the processes of the associative learning and associative correcting via a modified Pavlov experiment where more conditioning factors are considered. We also make some comparisons of MIF with spike-timing-dependent plasticity and back-propagation and show that MIF learning law is suitable to fast learning.     

突触长时程可塑性的动力模型

突触长时程可塑性使突触效能加强(长时程增强,LTP)或突触效能减弱(长时程压抑,LTD)是神经系统中潜在的学习和记忆。兴奋神经元突触的LTP和LTD是由突触前和突触后活动的精确定时所诱导。突触长时程可塑性传递改变涉及许多复杂的过程;例如,突触可塑性的两种形式由不同时程的Ca2+进入突触细胞诱导。我们给出了突触可塑性的LTP和LTD合成的过程、动力学模型及突触增强变化的预测模型,当用预测尖峰的不同频率训练和Poisson分布训练时,将产生不同的突触前和突触后的平均电压。     

Spike-timing-dependent plasticity: the relationship to rate-based learning for models with weight dynamics determined by a stable fixed point

Experimental evidence indicates that synaptic modification depends on the timing relationship between the presynaptic inputs and the output spikes that they generate. In this letter, results are presented for models of spike-timing-dependent plasticity (STDP) whose weight dynamics is determined by a stable fixed point. Four classes of STDP are identified on the basis of the time extent of their input-output interactions. The effect on the potentiation of synapses with different rates of input is investigated to elucidate the relationship of STDP with classical studies of long-term potentiation and depression and rate-based Hebbian learning. The selective potentiation of higher-rate synaptic inputs is found only for models where the time extent of the input-output interactions is input restricted (i.e., restricted to time domains delimited by adjacent synaptic inputs) and that have a time-asymmetric learning window with a longer time constant for depression than for potentiation. The analysis provides an account of learning dynamics determined by an input-selective stable fixed point. The effect of suppressive interspike interactions on STDP is also analyzed and shown to modify the synaptic dynamics.     

Self-regulation mechanism of temporally asymmetric Hebbian plasticity

Recent biological experimental findings have shown that synaptic plasticity depends on the relative timing of the pre- and postsynaptic spikes. This determines whether long-term potentiation (LTP) or long-term depression (LTD) is induced. This synaptic plasticity has been called temporally asymmetric Hebbian plasticity (TAH). Many authors have numerically demonstrated that neural networks are capable of storing spatiotemporal patterns. However, the mathematical mechanism of the storage of spatiotemporal patterns is still unknown, and the effect of LTD is particularly unknown. In this article, we employ a simple neural network model and show that interference between LTP and LTD disappears in a sparse coding scheme. On the other hand, the covariance learning rule is known to be indispensable for the storage of sparse patterns. We also show that TAH has the same qualitative effect as the covariance rule when spatiotemporal patterns are embedded in the network.     

A fast convergent rate preserving discontinuous Galerkin framework for rate-independent plasticity problems

In this paper a finite element framework based on the incomplete interior penalty Galerkin formulation, a non-symmetric discontinuous Galerkin method, is consistently formulated for modeling plasticity problems with small deformation. Because of its pure displacement-based framework, this proposed discontinuous Galerkin method is possibly able to completely preserve numerical integration algorithms efficiently developed in the traditional continuous Galerkin framework. Besides stresses on element interior quadrature points, stresses on element surface quadrature points are also required to return on yielding surfaces in this discontinuous Galerkin framework, which is able to provide more accurate material yielding profiles than the continuous Galerkin framework. The performance of the proposed discontinuous Galerkin framework has been evaluated in detail for J₂ and pressure-dependent plasticities using perfect plasticity, plasticity with hardening, and associative and non-associative material models. Quadratic convergent rates compatible to the tradition continuous Galerkin method for modeling plasticity problems have been achieved within a large penalty range in a nodal-based discontinuous Galerkin implementation.     

The modulation of learning state in a biological associative memory: an in vitro,in vivo,and in computo study of object recognition in mammalian olfactory cortex

During learning of overlapping input patterns in an associative memory, recall of previously stored patterns can interfere with the learning of new patterns. Most associative memory models avoid this difficulty by ignoring the effect of previously modified connections during learning, by clamping network activity to the patterns to be learned. Through the interaction of experimental and modeling techniques, we now have evidence to suggest that a somewhat analogous approach may have been taken by biology within the olfactory cerebral cortex. Specifically we have recently discovered that the naturally occurring neuromodulator acetylcholine produces a variety of effects on cortical cells and circuits which, when taken together, can prevent memory interference in a biologically realistic memory model. Further, it has been demonstrated that these biological mechanisms can actually improve the memory storage performance of previously published abstract neural network associative memory models.     

Short-term potentiation effect on pattern recall in sparsely coded neural network

It has been shown in studies of biological synaptic plasticity that synaptic efficacy can change in a very short time window, compared to the time scale associated with typical neural events. This time scale is small enough to possibly have an effect on pattern recall processes in neural networks. We study properties of a neural network which uses a cyclic Hebb rule. Then we add the short term potentiation of synapses in the recall phase. We show that this approach preserves the ability of the network to recognize the patterns stored by the network and that the network does not respond to other patterns at the same time. We show that this approach dramatically increases the capacity of the network at the cost of a longer pattern recall process. We discuss that the network possesses two types of recall. The fast recall does not need synaptic plasticity to recognize a pattern, while the slower recall utilizes synaptic plasticity. This is something that we all experience in our daily lives: some memories can be recalled promptly whereas recollection of other memories requires much more time.     

A novel application of artificial neural networks to structural analysis

In this work we use the continuous Hopfield network and the continuous bidirectional associative memory system (BAM) in order to develop two novel methods for structural analysis. The development of these techniques is based on the analogous relationship that results from comparing the energy functions of the above two models with that of the structural displacement method (i.e. the socalled stiffness matrix method) and it takes advantage of the fact that classical numerical methods do not have the characteristics of parallel computation that artificial neural networks have. Several examples related to structural deformation are used to illustrate the superiority of the BAM-based neural networks over other traditional numerical methods and the Hopfield model, especially for the case of large dimensional stiffness matrices.     

The restricted influence of sparseness of coding on the capacity of familiarity discrimination networks

Much evidence indicates that the perirhinal cortex is involved in the familiarity discrimination aspect of recognition memory. It has been previously shown under selective conditions that neural networks performing familiarity discrimination can achieve very high storage capacity, being able to deal with many times more stimuli than associative memory networks can in associative recall. The capacity of associative memories for recall has been shown to be highly dependent on the sparseness of coding. However, previous work on the networks of Bogacz et al, Norman and O'Reilly and Sohal and Hasselmo that model familiarity discrimination in the perirhinal cortex has not investigated the effects of the sparseness of encoding on capacity. This paper explores how sparseness of coding influences the capacity of each of these published models and establishes that sparse coding influences the capacity of the different models in different ways. The capacity of the Bogacz et al model can be made independent of the sparseness of coding. Capacity increases as coding becomes sparser for a simplified version of the neocortical part of the Norman and O'Reilly model, whereas capacity decreases as coding becomes sparser for a simplified version of the Sohal and Hasselmo model. Thus in general, and in contrast to associative memory networks, sparse encoding results in little or no advantage for the capacity of familiarity discrimination networks. Hence it may be less important for coding to be sparse in the perirhinal cortex than it is in the hippocampus. Additionally, it is established that the capacities of the networks are strongly dependent on the precise form of the learning rules (synaptic plasticity) used in the network. This finding indicates that the precise characteristics of synaptic plastic changes in the real brain are likely to have major influences on storage capacity.     

Stable competitive dynamics emerge from multispike interactions in a stochastic model of spike-timing-dependent plasticity

In earlier work we presented a stochastic model of spike-timing-dependent plasticity (STDP) in which STDP emerges only at the level of temporal or spatial synaptic ensembles. We derived the two-spike interaction function from this model and showed that it exhibits an STDP-like form. Here, we extend this work by examining the general n-spike interaction functions that may be derived from the model. A comparison between the two-spike interaction function and the higher-order interaction functions reveals profound differences. In particular, we show that the two-spike interaction function cannot support stable, competitive synaptic plasticity, such as that seen during neuronal development, without including modifications designed specifically to stabilize its behavior. In contrast, we show that all the higher-order interaction functions exhibit a fixed-point structure consistent with the presence of competitive synaptic dynamics. This difference originates in the unification of our proposed "switch" mechanism for synaptic plasticity, coupling synaptic depression and synaptic potentiation processes together. While three or more spikes are required to probe this coupling, two spikes can never do so. We conclude that this coupling is critical to the presence of competitive dynamics and that multispike interactions are therefore vital to understanding synaptic competition.     

Reducing the variability of neural responses: a computational theory of spike-timing-dependent plasticity

Experimental studies have observed synaptic potentiation when a presynaptic neuron fires shortly before a postsynaptic neuron and synaptic depression when the presynaptic neuron fires shortly after. The dependence of synaptic modulation on the precise timing of the two action potentials is known as spike-timing dependent plasticity (STDP). We derive STDP from a simple computational principle: synapses adapt so as to minimize the postsynaptic neuron's response variability to a given presynaptic input, causing the neuron's output to become more reliable in the face of noise. Using an objective function that minimizes response variability and the biophysically realistic spike-response model of Gerstner (2001), we simulate neurophysiological experiments and obtain the characteristic STDP curve along with other phenomena, including the reduction in synaptic plasticity as synaptic efficacy increases. We compare our account to other efforts to derive STDP from computational principles and argue that our account provides the most comprehensive coverage of the phenomena. Thus, reliability of neural response in the face of noise may be a key goal of unsupervised cortical adaptation.     

Spike-timing-dependent plasticity and relevant mutual information maximization

Synaptic plasticity was recently shown to depend on the relative timing of the pre- and postsynaptic spikes. This article analytically derives a spike-dependent learning rule based on the principle of information maximization for a single neuron with spiking inputs. This rule is then transformed into a biologically feasible rule, which is compared to the experimentally observed plasticity. This comparison reveals that the biological rule increases information to a near-optimal level and provides insights into the structure of biological plasticity. It shows that the time dependency of synaptic potentiation should be determined by the synaptic transfer function and membrane leak. Potentiation consists of weight-dependent and weight-independent components whose weights are of the same order of magnitude. It further suggests that synaptic depression should be triggered by rare and relevant inputs but at the same time serves to unlearn the baseline statistics of the network's inputs. The optimal depression curve is uniformly extended in time, but biological constraints that cause the cell to forget past events may lead to a different shape, which is not specified by our current model. The structure of the optimal rule thus suggests a computational account for several temporal characteristics of the biological spike-timing-dependent rules.     

Computational study of experience-dependent plasticity in adult rat cortical barrel-column

We model experience-dependent plasticity in the adult rat S1 cortical representation of the whiskers (the barrel cortex) which has been produced by trimming all whiskers on one side of the snout except two. This manipulation alters the pattern of afferent sensory activity while avoiding any direct nerve damage. Our simplified model circuitry represents multiple cortical layers and inhibitory neurons within each layer of a barrel-column. Utilizing a computational model we show that the evolution of the response bias in the barrel-column towards spared whiskers is consistent with synaptic modifications that follow the rules of the Bienenstock, Cooper and Munro (BCM) theory. The BCM theory postulates that a neuron possesses a dynamic synaptic modification threshold, thetaM, which dictates whether the neuron's activity at any given instant will lead to strengthening or weakening of the synapses impinging on it. However, the major prediction of our model is the explanation of the delay in response potentiation in the layer-IV neurons through a masking effect produced by the thresholded monotonically increasing inhibition expressed by either the logarithmic function, h(x) = mu log(1 + x), or by the power function, h(x) = mu x(0.8-0.9), where mu is a constant. Furthermore, simulated removal of the supragranular layers (layers II/III) reduces plasticity of neurons in the remaining layers (IV-VI) and points to the role of noise in synaptic plasticity.     

Short-Term Plasticity in a Computational Model of the Tail-Withdrawal Circuit in Aplysia

The tail-withdrawal circuit of Aplysia provides a useful model system for investigating synaptic dynamics. Sensory neurons within the circuit manifest several forms of synaptic plasticity. Here, we developed a model of the circuit and investigated the ways in which depression (DEP) and potentiation (POT) contributed to information processing. DEP limited the amount of motor neuron activity that could be elicited by the monosynaptic pathway alone. POT within the monosynaptic pathway did not compensate for DEP. There was, however, a synergistic interaction between POT and the polysynaptic pathway. This synergism extended the dynamic range of the network, and the interplay between DEP and POT made the circuit responded preferentially to long-duration, low-frequency inputs.     

PSECMAC: a novel self-organizing multiresolution associative memory architecture.

The cerebellum constitutes a vital part of the human brain system that possesses the capability to model highly nonlinear physical dynamics. The cerebellar model articulation controller (CMAC) associative memory network is a computational model inspired by the neurophysiological properties of the cerebellum, and it has been widely used for control, optimization, and various pattern recognition tasks. However, the CMAC network's highly regularized computing structure often leads to the following: 1) a suboptimal modeling accuracy, 2) poor memory utilization, and 3) the generalization-accuracy dilemma. Previous attempts to address these shortcomings have limited success and the proposed solutions often introduce a high operational complexity to the CMAC network. This paper presents a novel neurophysiologically inspired associative memory architecture named pseudo-self-evolving CMAC (PSECMAC) that nonuniformly allocates its computing cells to overcome the architectural deficiencies encountered by the CMAC network. The nonuniform memory allocation scheme employed by the proposed PSECMAC network is inspired by the cerebellar experience-driven synaptic plasticity phenomenon observed in the cerebellum, where significantly higher densities of synaptic connections are located in the frequently accessed regions. In the PSECMAC network, this biological synaptic plasticity phenomenon is emulated by employing a data-driven adaptive memory quantization scheme that defines its computing structure. A neighborhood-based activation process is subsequently implemented to facilitate the learning and computation of the PSECMAC structure. The training stability of the PSECMAC network is theoretically assured by the proof of its learning convergence, which will be presented in this paper. The performance of the proposed network is subsequently benchmarked against the CMAC network and several representative CMAC variants on three real-life applications, namely, pricing of currency futures option, banking failure classification, and modeling of the glucose-insulin dynamics of the human glucose metabolic process. The experimental results have strongly demonstrated the effectiveness of the PSECMAC network in addressing the architectural deficiencies of the CMAC network by achieving significant improvements in the memory utilization, output accuracy as well as the generalization capability of the network.     

Spike-driven synaptic dynamics generating working memory states

The collective behavior of a network, modeling a cortical module of spiking neurons connected by plastic synapses is studied. A detailed spike-driven synaptic dynamics is simulated in a large network of spiking neurons, implementing the full double dynamics of neurons and synapses. The repeated presentation of a set of external stimuli is shown to structure the network to the point of sustaining working memory (selective delay activity). When the synaptic dynamics is analyzed as a function of pre- and postsynaptic spike rates in functionally defined populations, it reveals a novel variation of the Hebbian plasticity paradigm: in any functional set of synapses between pairs of neurons (e.g., stimulated-stimulated, stimulated-delay, stimulated-spontaneous), there is a finite probability of potentiation as well as of depression. This leads to a saturation of potentiation or depression at the level of the ratio of the two probabilities. When one of the two probabilities is very high relative to the other, the familiar Hebbian mechanism is recovered. But where correlated working memory is formed, it prevents overlearning. Constraints relevant to the stability of the acquired synaptic structure and the regimes of global activity allowing for structuring are expressed in terms of the parameters describing the single-synapse dynamics. The synaptic dynamics is discussed in the light of experiments observing precise spike timing effects and related issues of biological plausibility.     

A viscoelastic-viscoplastic constitutive equation and its finite element implementation

A viscoelastic-viscoplastic constitutive model for isotropic materials undergoing isothermal infinitesimal deformation is proposed. The model is based on the assumption that the total strain rate is decomposable into a viscoelastic and a viscoplastic portion. Consequently, the model consists of a linear viscoelastic model in series with a modified plasticity model. This modified plasticity model adopts the classical Drucker-Prager yield surface with isotropic hardening and the associative flow rule of the invicid theory of plasticity. However, hardening is assumed to be a function of both the viscoplastic strain as well as the total strain rate. In this manner, the proposed model acquires the advantage of having both the initial and the subsequent yield surfaces to be a function of the strain rate, a property which has its experimental supportive evidence for viscoplastic materials such as polymers and some metals at highly elevated temperatures.A finite-element algorithm is developed to implement the constitutive equation derived in Part I. This algorithm adopts a combination of the tangent stiffness matrix and the initial load approach. The method of treating the transitional region between viscoelastic and viscoelastic-viscoplastic behavior is given. The details of implementation is described. Convergence of the computation scheme is discussed.Two examples are calculated numerically to demonstrate the strain rate and the pressure effects on the mechanical behavior of some viscoelastic-viscoplastic material. Results show that essential features in the stress-strain diagram obtained experimentally are exhibited by the model.     

How the shape of pre- and postsynaptic signals can influence STDP: a biophysical model

Spike-timing-dependent plasticity (STDP) is described by long-term potentiation (LTP), when a presynaptic event precedes a postsynaptic event, and by long-term depression (LTD), when the temporal order is reversed. In this article, we present a biophysical model of STDP based on a differential Hebbian learning rule (ISO learning). This rule correlates presynaptically the NMDA channel conductance with the derivative of the membrane potential at the synapse as the postsynaptic signal. The model is able to reproduce the generic STDP weight change characteristic. We find that (1) The actual shape of the weight change curve strongly depends on the NMDA channel characteristics and on the shape of the membrane potential at the synapse. (2) The typical antisymmetrical STDP curve (LTD and LTP) can become similar to a standard Hebbian characteristic (LTP only) without having to change the learning rule. This occurs if the membrane depolarization has a shallow onset and is long lasting. (3) It is known that the membrane potential varies along the dendrite as a result of the active or passive backpropagation of somatic spikes or because of local dendritic processes. As a consequence, our model predicts that learning properties will be different at different locations on the dendritic tree. In conclusion, such site-specific synaptic plasticity would provide a neuron with powerful learning capabilities.