How We Learn; How We Remember: Toward an Understanding of Brain and Neural Systems

The following sections are included:

• ACKNOWLEDGEMENTS

• CONTENTS

• GENERAL INTRODUCTION

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A model of long-term memory, motivated by the anatomy and physiology of the mamalian central nervous system is proposed. We suggest that what is of importance to the nervous system is the collective individual activities of large numbers of individual neurons and that just such a collection of activities constitutes the memory trace. We assume that the long-term memory is the sum of such individual traces. With a minimum of some of the functions of a biological memory and that many of its properties are reminiscent of the brain. Throughout the emphasis is on consistency with the known physiology.

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A brief account is given of some of the properties of a neural model which displays on a primitive level features which suggest some of the mental behavior associated with animal memory and learning. The model as well as the basic passive procedure by which the neural network modifies itself with experience is consistent with known neurophysiology as well as with what information might be available in the neuron network. One must, however, assume that there exists a means of communication (electrical or chemical) between the cell body and dendrite ends–communication in a direction opposite to the flow of electrical signals. This same modification procedure could also lead to the formation of cells of the type observed by Hubel & Wiesel in the cat's visual cortex. It is suggestive that a network modification procedure that could produce such early processing cells might also be responsible, in cortex, for ‘higher’ mental processes. The explicit mathematics employed here is that of linear transformations on a vector space. However, as only certain topological properties are used, it is possible to construct a more general non-linear theory.

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Passive modification of the strength of synaptic junctions that results in the construction of internal mappings with some of the properties of memory is shown to lead to the development of Hubel-Wiesel type feature detectors in visual cortex. With such synaptic modification a cortical cell can become committed to an arbitrary but repeated external pattern, and thus fire every time the pattern is presented even if that cell has no genetic pre-disposition to respond to the particular pattern. The additional assumption of lateral inhibition between cortical cells severely limits the number of cells which respond to one pattern as well as the number of patterns that are picked up by a cell. The introduction of a simple neural mapping from the visual field to the lateral geniculate leads to an interaction between patterns which, combined with our assumptions above, seems to lead to a progression of patterns from column to column of the type observed by Hubel and Wiesel in monkey.

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We assume that between lateral geniculate and visual cortical cells there exist labile synapses that modify themselves in a new fashion called threshold passive modification and in addition, non-labile synapses that contain permanent information. In the theory which results there is an increase in the specificity of response of a cortical cell when it is exposed to stimuli due to normal patterned visual experience. Non-patterned input, such as might be expected when an animal is dark-reared or raised with eyelids sutured, results in a loss of specificity, with details depending on whether noise to labile and non-labile junctions is correlated. Specificity can sometimes be regained, however, with a return of input due to patterned vision. We propose that this provides a possible explanation of experimental results obtained by Imbert and Buisseret (1975); Blakemore and Van Sluyters (1975); Buisseret and Imbert (1976); and Frégnac and Imbert (1977, 1978).

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The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a given synapse depends not only on instantaneous pre- and postsynaptic activities but also on a slowly varying time-averaged value of the postsynaptic activity. Assuming an appropriate nonlinear form for this dependence, development of selectivity is obtained under quite general conditions on the sensory environment. One does not require nonlinearity of the neuron's integrative power nor does one need to assume any particular form for intracortical circuitry. This is first illustrated in simple cases, e.g., when the environment consists of only two different stimuli presented alternately in a random manner. The following formal statement then holds: the state of the system converges with probability 1 to points of maximum selectivity in the state space. We next consider the problem of early development of orientation selectivity and binocular interaction in primary visual cortex. Giving the environment an appropriate form, we obtain orientation tuning curves and ocular dominance comparable to what is observed in normally reared adult cats or monkeys. Simulations with binocular input and various types of normal or altered environments show good agreement with the relevant experimental data. Experiments are suggested that could test our theory further.

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A single-cell theory for the development of selectivity and ocular dominance in visual cortex has been generalized to incorporate more realistic neural networks that approximate the actual anatomy of small regions of cortex. In particular, we have analyzed a network consisting of excitatory and inhibitory cells, both of which may receive information from the lateral geniculate nucleus (LGN) and then interact through cortico–cortical synapses in a mean-field approximation. Our investigation of the evolution of a cell in this mean-field network indicates that many of the results on existence and stability of fixed points that have been obtained previously in the single-cell theory can be successfully generalized here. We can, in addition, make explicit further statements concerning the independent effects of excitatory and inhibitory neurons on selectivity and ocular dominance. For example, shutting off inhibitory cells lessens selectivity and alters ocular dominance (masked synapses). These inhibitory cells may be selective, but there is no theoretical necessity that they be so. Further, the intercortical inhibitory synapses do not have to be very responsive to visual experience. Most of the learning process can occur among the excitatory LGN–cortical synapses.

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The functional organization of the cerebral cortex is modified dramatically by sensory experience during early postnatal life. The basis for these modifications is a type of synaptic plasticity that may also contribute to some forms of adult learning. The question of how synapses modify according to experience has been approached by determining theoretically what is required of a modification mechanism to account for the available experimental data in the developing visual cortex. The resulting theory states precisely how certain variables might influence synaptic modifications. This insight has led to the development of a biologically plausible molecular model for synapse modification in the cerebral cortex.

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1. The aim of this work was to assess whether a form of synaptic modification based on the theory of Bienenstock, Cooper, and Munro (BCM) can, with a fixed set of parameters, reproduce both the kinetics and equilibrium states of experience-dependent modifications that have been observed experimentally in kitten striate cortex.

2. According to the BCM theory, the connection strength of excitatory geniculocortical synapses varies as the product of a measure of input activity (d) and a function (φ) of the summed postsynaptic response. For all postsynaptic responses greater than spontaneous but less than a critical value called the “modification threshold” (θ), φ has a negative value. For all postsynaptic responses greater than θ, φ has a positive value. A novel feature of the BCM theory is that the value of θ is not fixed, but rather “slides” as a nonlinear function of the average postsynaptic response.

3. This theory permits precise specification of theoretical equivalents of experimental situations, allowing detailed, quantitative comparisons of theory with experiment. Such comparisons were carried out here in a series of computer simulations.

4. Simulations are performed by presenting input to a model cortical neuron, calculating the summed postsynaptic response, and then changing the synaptic weights according to the BCM theory. This process is repeated until the synaptic weights reach an equilibrium state.

5. Two types of geniculocortical input are simulated: “pattern” and “noise.” Pattern input is assumed to correspond to the type of input that arises when a visual contour of a particular orientation is presented to the retina. This type of input is said to be “correlated” when the two sets of geniculocortical fibers relaying information from the two eyes convey the same patterns at the same time. Noise input is assumed to correspond to the type of input that arises in the absence of visual contours and, by definition, is uncorrelated.

6. By varying the types of input available to the two sets of geniculocortical synapses, we simulate the following types of visual experience: 1) normal binocular contour vision, 2) monocular deprivation, 3) reverse suture, 4) strabismus, 5) binocular deprivation, and 6) normal contour vision after a period of monocular deprivation.

7. The constraints placed on the set of parameters by each type of simulated visual environment, and the effects that such constraints have on the evolution of the synaptic weights, are investigated in detail.

8. It was discovered that the exact form and dependencies of the sliding modification threshold are critical in obtaining a set of simulations that are consistent with the experimentally observed kinetics of synaptic modification in visual cortex. In particular, to account for observed changes during reverse suture and binocular deprivation, the value of θ could approach zero only when the synaptic strengths were driven to very low values. In the present model, this was achieved by including in the calculation of θ the postsynaptic responses generated by spontaneous input activity.

9. It is concluded that the modification of excitatory geniculocortical synapses according to rules derived from the BCM theory can account for both the outcome and kinetics of experience-dependent synaptic plasticity in kitten striate cortex. The understanding that this theory provides should be useful for the design of neurophysiological experiments aimed at elucidating the molecular mechanisms in play during the modification of visual cortex by experience.

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In this paper, we present an objective function formulation of the Bienenstock, Cooper, and Munro (BCM) theory of visual cortical plasticity that permits us to demonstrate the connection between the unsupervised BCM learning procedure and various statistical methods, in particular, that of Projection Pursuit. This formulation provides a general method for stability analysis of the fixed points of the theory and enables us to analyze the behavior and the evolution of the network under various visual rearing conditions. It also allows comparison with many existing unsupervised methods. This model has been shown successful in various applications such as phoneme and 3D object recognition. We thus have the striking and possibly highly significant result that a biological neuron is performing a sophisticated statistical procedure.

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We tested a theoretical prediction that patterns of excitatory input activity that consistently fail to activate target neurons sufficiently to induce synaptic potentiation will instead cause a specific synaptic depression. To realize this situation experimentally, the Schaffer collateral projection to area CA1 in rat hippocampal slices was stimulated electrically at frequencies ranging from 0.5 to 50 Hz. Nine hundred pulses at 1–3 Hz consistently yielded a depression of the CA1 population excitatory postsynaptic potential that persisted without signs of recovery for >1 hr after cessation of the conditioning stimulation. This long-term depression was specific to the conditioned input, ruling out generalized changes in postsynaptic responsiveness or excitability. Three lines of evidence suggest that this effect is accounted for by a modification of synaptic effectiveness rather than damage to or fatigue of the stimulated inputs. First, the effect was dependent on the stimulation frequency; 900 pulses at 10 Hz caused no lasting change, and at 50 Hz a synaptic potentiation was usually observed. Second, the depressed synapses continued to support long-term potentiation in response to a high-frequency tetanus. Third, the effects of conditioning stimulation could be prevented by application of NMDA receptor antagonists. Thus, our data suggest that synaptic depression can be triggered by prolonged NMDA receptor activation that is below the threshold for inducing synaptic potentiation. We propose that this mechanism is important for the modifications of hippocampal response properties that underlie some forms of learning and memory.

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Activity-dependent synaptic plasticity in the superficial layers of juvenile cat and adult rat visual neocortex was compared with that in adult rat hippocampal field CA1. Stimulation of neocortical layer IV reliably induced synaptic long-term potentiation (LTP) and long-term depression (LTD) in layer III with precisely the same types of stimulation protocols that were effective in CA1. Neocortical LTP and LTD were specific to the conditioned pathway and, as in the hippocampus, were dependent on activation of N-methyl-D-aspartate receptors. These results provide strong support for the view that common principles may govern experience-dependent synaptic plasticity in CA1 and throughout the superficial layers of the mammalian neocortex.

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The Bienenstock, Cooper, and Munro (BCM) theory of synaptic plasticity has successfully reproduced the development of orientation selectivity and ocular dominance in kitten visual cortex in normal, as well as deprived, visual environments. To better compare the consequences of this theory with experiment, previous abstractions of the visual environment are replaced in this work by real visual images with retinal processing. The visual environment is represented by 24 gray-scale natural images that are shifted across retinal fields. In this environment, the BCM neuron develops receptive fields similar to the fields of simple cells found in kitten striate cortex. These fields display adjacent excitatory and inhibitory bands when tested with spot stimuli, orientation selectivity when tested with bar stimuli, and spatial-frequency selectivity when tested with sinusoidal gratings. In addition, their development in various deprived visual environments agrees with experimental results.

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In this paper we realistically model a two-eye visual environment and study its effect on single cell synaptic modification. In particular, we study the effect of image misalignment on receptive field formation after eye opening. We show that binocular misalignment effects PCA and BCM learning in different ways. For the BCM learning rule this misalignment is sufficient to produce varying degrees of ocular dominance, whereas for PCA learning binocular neurons emerge in every case. Such differences should help us distinguish between these learning rules.

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We present a general neural model for supervised learning of pattern categories which can resolve pattern classes separated by nonlinear, essentially arbitrary boundaries. The concept of a pattern class develops from storing in memory a limited number of class elements (prototypes). Associated with each prototype is a modifiable scalar weighting factor (λ) which effectively defines the threshold for categorization of an input with the class of the given prototype. Learning involves (1) commitment of prototypes to memory and (2) adjustment of the various λ factors to eliminate classification errors. In tests, the model ably defined classification boundaries that largely separated complicated pattern regions. We discuss the role which divisive inhibition might play in a possible implementation of the model by a network of neurons.

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The study of distributed memory systems has produced a number of models which work well in limited domains. However, until recently, the application of such systems to real-world problems has been difficult because of storage limitations, and their inherent architectural (and for serial simulation, computational) complexity. Recent development of memories with unrestricted storage capacity and economical feedforward architectures has opened the way to the application of such systems to complex pattern recognition problems. However, such problems are sometimes underspecified by the features which describe the environment is often non-specific. We will review current work on high density memory systems and their network implementations. We will discuss a general learning algorithm for such high density memories and review its application to separate point sets. Finally, we will introduce an distributions of non-separate point sets.

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We present a relaxation model for memory based on a generalized coulomb potential. The model has arbitrarily large storage capacity and, in addition, well-defined basins of attraction about stored memory states. The model is compared with the Hopfield relaxation model.

The Coulomb Potential Learning (CPL) algorithm (Bachmann et al., 1987), which derives its name from its functional form's likeness to a coulomb charge potential, was originally motivated by the short-comings of the Perceptron (Rosenblatt, 1962) and the original Hopfield net (Hopfield, 1979). In the case of the Perceptron, it was clear almost from the outset that the linear-separability provided by the perceptron would not be sufficient to perform complex tasks. In the case of the original Hopfield model, the recall capacity of the network is low due. to non-orthogonal memories and the existence of spurious memories. The CPL algorithm addresses both of these problems by providing a simple network which is capable of both storing an arbitrarily large number of memories with perfect recall and no spurious memories; and also constructing arbitrary nonlinear boundaries for classification tasks. In addition the CPL algorithm is easy to implement in hardware and is readily adaptable to parallel computation.

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This paper extends our previous results for averaged regression estimators (Perrone and Cooper, 1993b). We prove that averaged regression estimates always perform as good or better that their unaveraged counterparts. We show that this result derives from the notion of convexity and in this way demonstrate that a wide variety of optimization algorithms can benefit from averaging including: Mean Square Error, a general class of L_P-norm cost functions, Maximum Likelihood Estimation, Maximum Entropy, Maximum Mutual Information, the Kullback-Leibler Information, Penalized Maximum Likelihood Estimation and Smoothing Splines.

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An unsupervised neural network model inductively acquires the ability to distinguish categorically the stop consonants of English, in a manner consistent with prenatal and early postnatal auditory experience, and without reference to any specialized knowledge of linguistic structure or the properties of speech. This argues against the common assumption that linguistic knowledge, and speech perception in particular, cannot be learned and must therefore be innately specified.

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In this paper we present a new version of the standard multilayer perceptron (MLP) algorithm for the state-of-the-art in neural network VLSI implementations: the Intel Ni1000. This approach enables the standard MLP to utilize the parallel architecture of the Ni1000 to achieve on the order of 40000, 256-dimensional classifications per second. Due to the compact size and affordable price of the Ni1000, this classification speed could be available for the average personal computer.

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The following sections are included:

• A Final Few Words

• Monet's Sunrise