Pattern separability in a random neural net with inhibitory connections

Some interesting properties on pattern separation have been shown through researches by neural models of cerebellar cortex. It seems to us that those results are a part of the properties of pattern separation. A two layer random nerve net with inhibitory connections is given as a model of the cerebellar cortex. The model is composed of threshold elements there. A more general theory of pattern separation than those studied earlier is given, and the pattern separability of the model is considered. It is revealed that the standard deviation of threshold values of threshold elements has a great effect on the pattern separability and the control of the firing rate. The present study is also intended to investigate the pattern separability in such a case that the firing rate of input patterns are not equal, and a pattern includes the other pattern. It is assumed there that the standard deviation is small. Some properties of the degree of pattern separation are cleaned up.     

A Dendritic Mechanism for Decoding Traveling Waves: Principles and Applications to Motor Cortex

Traveling waves of neuronal oscillations have been observed in many cortical regions, including the motor and sensory cortex. Such waves are often modulated in a task-dependent fashion although their precise functional role remains a matter of debate. Here we conjecture that the cortex can utilize the direction and wavelength of traveling waves to encode information. We present a novel neural mechanism by which such information may be decoded by the spatial arrangement of receptors within the dendritic receptor field. In particular, we show how the density distributions of excitatory and inhibitory receptors can combine to act as a spatial filter of wave patterns. The proposed dendritic mechanism ensures that the neuron selectively responds to specific wave patterns, thus constituting a neural basis of pattern decoding. We validate this proposal in the descending motor system, where we model the large receptor fields of the pyramidal tract neurons — the principle outputs of the motor cortex — decoding motor commands encoded in the direction of traveling wave patterns in motor cortex. We use an existing model of field oscillations in motor cortex to investigate how the topology of the pyramidal cell receptor field acts to tune the cells responses to specific oscillatory wave patterns, even when those patterns are highly degraded. The model replicates key findings of the descending motor system during simple motor tasks, including variable interspike intervals and weak corticospinal coherence. By additionally showing how the nature of the wave patterns can be controlled by modulating the topology of local intra-cortical connections, we hence propose a novel integrated neuronal model of encoding and decoding motor commands.     

Learning shapes spontaneous activity itinerating over memorized states

Learning is a process that helps create neural dynamical systems so that an appropriate output pattern is generated for a given input. Often, such a memory is considered to be included in one of the attractors in neural dynamical systems, depending on the initial neural state specified by an input. Neither neural activities observed in the absence of inputs nor changes caused in the neural activity when an input is provided were studied extensively in the past. However, recent experimental studies have reported existence of structured spontaneous neural activity and its changes when an input is provided. With this background, we propose that memory recall occurs when the spontaneous neural activity changes to an appropriate output activity upon the application of an input, and this phenomenon is known as bifurcation in the dynamical systems theory. We introduce a reinforcement-learning-based layered neural network model with two synaptic time scales; in this network, I/O relations are successively memorized when the difference between the time scales is appropriate. After the learning process is complete, the neural dynamics are shaped so that it changes appropriately with each input. As the number of memorized patterns is increased, the generated spontaneous neural activity after learning shows itineration over the previously learned output patterns. This theoretical finding also shows remarkable agreement with recent experimental reports, where spontaneous neural activity in the visual cortex without stimuli itinerate over evoked patterns by previously applied signals. Our results suggest that itinerant spontaneous activity can be a natural outcome of successive learning of several patterns, and it facilitates bifurcation of the network when an input is provided.     

The Possible Role of Spike Patterns in Cortical Information Processing

When the same visual stimulus is presented across many trials, neurons in the visual cortex receive stimulus-related synaptic inputs that are reproducible across trials (S) and inputs that are not (N). The variability of spike trains recorded in the visual cortex and their apparent lack of spike-to-spike correlations beyond that implied by firing rate fluctuations, has been taken as evidence for a low S/N ratio. A recent re-analysis of in vivo cortical data revealed evidence for spike-to-spike correlations in the form of spike patterns. We examine neural dynamics at a higher S/N in order to determine what possible role spike patterns could play in cortical information processing. In vivo-like spike patterns were obtained in model simulations. Superpositions of multiple sinusoidal driving currents were especially effective in producing stable long-lasting patterns. By applying current pulses that were either short and strong or long and weak, neurons could be made to switch from one pattern to another. Cortical neurons with similar stimulus preferences are located near each other, have similar biophysical properties and receive a large number of common synaptic inputs. Hence, recordings of a single neuron across multiple trials are usually interpreted as the response of an ensemble of these neurons during one trial. In the presence of distinct spike patterns across trials there is ambiguity in what would be the corresponding ensemble, it could consist of the same spike pattern for each neuron or a set of patterns across neurons. We found that the spiking response of a neuron receiving these ensemble inputs was determined by the spike-pattern composition, which, in turn, could be modulated dynamically as a means for cortical information processing.     

Visual modelling

The first purpose of this paper is to present a neural net model of the visual cortex of higher vertebrates based on the electrophysiological properties of the ganglion cells. This model takes Hebb's law [1] as the physiological learning rule for synaptic modification. The model consists of 85 × 85 neurons forming a layer similar to the cortex. The neurones are massively connected via weights that are typically adapted. We simulate several input patterns and show that the model reproduces the pattern recognition, contours pictures and moving perception.     

Feedback enhances feedforward figure-ground segmentation by changing firing mode

In the visual cortex, feedback projections are conjectured to be crucial in figure-ground segregation. However, the precise function of feedback herein is unclear. Here we tested a hypothetical model of reentrant feedback. We used a previous developed 2-layered feedforward spiking network that is able to segregate figure from ground and included feedback connections. Our computer model data show that without feedback, neurons respond with regular low-frequency (～9 Hz) bursting to a figure-ground stimulus. After including feedback the firing pattern changed into a regular (tonic) spiking pattern. In this state, we found an extra enhancement of figure responses and a further suppression of background responses resulting in a stronger figure-ground signal. Such push-pull effect was confirmed by comparing the figure-ground responses with the responses to a homogenous texture. We propose that feedback controls figure-ground segregation by influencing the neural firing patterns of feedforward projecting neurons.     

A template matching model for pattern recognition: Self-organization of templates and template matching by a disinhibitory neural network

A template matching model for pattern recognition is proposed. By following a previouslyproposed algorithm for synaptic modification (Hirai, 1980), the template of a stimulus pattern is selforganized as a spatial distribution pattern of matured synapses on the cells receiving modifiable synapses. Template matching is performed by the disinhibitory neural network cascaded beyond the neural layer composed of the cells receiving the modifiable synapses. The performance of the model has been simulated on a digital computer. After repetitive presentations of a stimulus pattern, a cell receiving the modifiable synapses comes to have the template of that pattern. And the cell in the latter layer of the disinhibitory bitory neural network that receives the disinhibitory input from that cell becomes electively sensitive to that pattern. Learning patterns are not restricted by previously learned ones. They can be subset or superset patterns of the ones previously learned. If an unknown pattern is presented to the model, no cell beyond the disinhibitory neural network will respond. However, if previously learned patterns are embedded in that pattern, the cells which have the templates of those patterns respond and are assumed to transmit the information to higher center. The computer simulation also shows that the model can organize a clean template under a noisy environment.     

Further consideration on pattern separability in a random neural net with inhibitory connections

A two-layer random neural net with inhibitory connections composing of threshold elements has been regarded as a model of the cerebellar cortex. Many properties of pattern separation with the model have been disclosed through consideration on the degree of pattern separation. However, we have not shown yet that the degree of pattern separation is given by some different functions which are decided by the relation between the firing rates of input patterns. The present study is intended to reveal that the functions of the degree of pattern separation are synthesized with some different partial functions, and they are differently given on the relation between the firing rates of input patterns. Simultaneously, it is proved that the number of the functions also depend on the number of connections between two layers in the model. We also disclose the properties of the degree of pattern separation, and give some suggestions on the sizes of the firing rates of mossy fibers and granule cells under the knowledge about them.     

A neural mechanism of hierarchical discrimination of odors in the olfactory cortex based on spatiotemporal encoding of odor information

We propose a neural mechanism for discrimination of different complex odors in the olfactory cortex based on the dynamical encoding scheme. Both constituent molecules of the odor and their mixing ratios are encoded simultaneously into a spatiotemporal activity pattern (limit cycle attractor) in the olfactory bulb [Hoshino O, Kashimori Y, Kambara T (1998) Biol Cybern 79:109–120]. We present a functional model of the olfactory cortex consisting of some dynamical mapping modules. Each dynamical map is represented by itinerancy among the limit cycle attractors. When a temporal sequence of spatial activity patterns corresponding to a complex odor is injected from the bulb to the network of the olfactory cortex, the neural activity state of each mapping module is fixed to a relevant spatial pattern injected. Recognition of an odor is accomplished by a combination of firing patterns fixed in all the mapping modules. The stronger the response strength of the component, the earlier the component is recognized. The hierarchical discrimination of an odor is made by recognizing the components in order of decreasing response strengths. Received: 28 November 1998 / Accepted in revised form: 17 December 1999     

A model for feature linking via collective oscillations in the primary visual cortex

A neural network model for explaining experimentally observed neuronal responses in cat primary visual cortex is proposed. In our model, the basic functional unit is an orientation column which is represented by a large homogeneous population of neurons modeled as integrate-and-fire type excitable elements. The orientation column exhibits spontaneous collective oscillations in activity in response to suitable visual stimuli. Such oscillations are caused by mutual synchronization among the neurons within the column. Numerical simulation for various stimulus patterns shows that as a result of activity correlations between different columns, the amplitude and the phase of the oscillation in each column depend strongly on the global feature of the stimulus pattern. These results satisfactorily account for experimental observations.     

Pattern recall in networks of chaotic neurons

This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns.     

Pattern separability and the effect of the number of connections in a random neural net with inhibitory connections

It has been claimed that pattern separation in cerebellar cortex plays an important role in controlling movements and balance for vertebrates. A number of the neural models for cerebellar cortex have been proposed and their pattern separability has been analyzed. These results, however, only explain a part of pattern separability in random neural nets. The present paper is intended to study an extended theory of pattern separability in a new model with inhibitory connections. In addition to this, the effect of the number of connections on pattern separability is cleared up. It is also shown that the signal from the inhibitory connections has crucial importance for pattern separability.1977–1978 Exchange Visitor, on leave from the Department of Information Processing Engineering, Technical College, Yamaguchi University, Yamaguchi University     

A neural network model of the cerebellar cortex performing dynamic associations

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber — Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.     

Model of Familiarity Discrimination in the Perirhinal Cortex

Much evidence indicates that recognition memory involves two separable processes, recollection and familiarity discrimination, with familiarity discrimination being dependent on the perirhinal cortex of the temporal lobe. Here, we describe a new neural network model designed to mimic the response patterns of perirhinal neurons that signal information concerning the novelty or familiarity of stimuli. The model achieves very fast and accurate familiarity discrimination while employing biologically plausible parameters and Hebbian learning rules. The fact that the activity patterns of the model's simulated neurons are closely similar to those of neurons recorded from the primate perirhinal cortex indicates that this brain region could discriminate familiarity using principles akin to those of the model. If so, the capacity of the model establishes that the perirhinal cortex alone may discriminate the familiarity of many more stimuli than current neural network models indicate could be recalled (recollected) by all the remaining areas of the cerebral cortex. This efficiency and speed of detecting novelty provides an evolutionary advantage, thereby providing a reason for the existence of a familiarity discrimination network in addition to networks used for recollection.     

A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging

A neural field model is presented that captures the essential non-linear characteristics of activity dynamics across several millimeters of visual cortex in response to local flashed and moving stimuli. We account for physiological data obtained by voltage-sensitive dye (VSD) imaging which reports mesoscopic population activity at high spatio-temporal resolution. Stimulation included a single flashed square, a single flashed bar, the line-motion paradigm – for which psychophysical studies showed that flashing a square briefly before a bar produces sensation of illusory motion within the bar – and moving squares controls. We consider a two-layer neural field (NF) model describing an excitatory and an inhibitory layer of neurons as a coupled system of non-linear integro-differential equations. Under the assumption that the aggregated activity of both layers is reflected by VSD imaging, our phenomenological model quantitatively accounts for the observed spatio-temporal activity patterns. Moreover, the model generalizes to novel similar stimuli as it matches activity evoked by moving squares of different speeds. Our results indicate that feedback from higher brain areas is not required to produce motion patterns in the case of the illusory line-motion paradigm. Physiological interpretation of the model suggests that a considerable fraction of the VSD signal may be due to inhibitory activity, supporting the notion that balanced intra-layer cortical interactions between inhibitory and excitatory populations play a major role in shaping dynamic stimulus representations in the early visual cortex.     

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.     

Adaptive pattern classification and universal recoding: II. Feedback,expectation, olfaction,illusions

Part I of this paper describes a model for the parallel development and adult coding of neural feature detectors. It shows how any set of arbitrary spatial patterns can be recoded, or transformed, into any other spatial patterns (universal recoding), if there are sufficiently many cells in the network's cortex. This code is, however, unstable through time if arbitrarily many patterns can perturb a fixed number of cortical cells. This paper shows how to stabilize the code in the general case using feedback between cellular sites. A biochemically defined critical period is not necessary to stabilize the code, nor is it sufficient to ensure useful coding properties.We ask how short term memory can be reset in response to temporal sequences of spatial patterns. This leads to a context-dependent code in which no feature detector need uniquely characterize an input pattern; yet unique classification by the pattern of activity across feature detectors is possible. This property uses learned expectation mechanisms whereby unexpected patterns are temporarily suppressed and/or activate nonspecific arousal. The simplest case describes reciprocal interactions via trainable synaptic pathways (long term memory traces) between two recurrent on-center off-surround networks undergoing mass action (shunting) interactions. This unit can establish an adaptive resonance, or reverberation, between two regions if their coded patterns match, and can suppress the reverberation if their patterns do not match. This concept yields a model of olfactory coding within the olfactory bulb and prepyriform cortex. The resonance idea also includes the establishment of reverberation between conditioned reinforcers and generators of contingent negative variation if presently avialable sensory cues are compatible with the network's drive requirements at that time; and a search and lock mechanism whereby the disparity between two patterns can be minimized and the minimal disparity images locked into position. Stabilizing the code uses attentional mechanisms, in particular nonspecific arousal as a tuning and search device. We suggest that arousal is gated by a chemical transmitter system—for example, norepinephrine—whose relative states of accumulation at antagonistic pairs of on-cells and off-cells through time can shift the spatial pattern of STM activity across a field of feature detectors. For example, a sudden arousal increment in response to an un-expected pattern can reverse, or rebound, these relative activities, thereby suppressing incorrectly classified populations. The rebound mechanism has formal properties analogous to negative afterimages and spatial frequency adaptation.Supported in part by the Advanced Research Projects Agency under ONR Contract No. N00014-76-C-0185     

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns—rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.     

The functional geometry of local and horizontal connections in a model of V1.

A mathematical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous activity patterns that can arise in cortex.