Introduction to a Theoretical Mechanics of Neural Networks

MacGregor, Ronald J.

doi:10.1016/b978-0-08-092441-0.50005-2

Cited by 14 publications

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“…The effects of varying transfer functions are illustrated along with the resulting variations in possible synaptic weights. Graphic presentations in 3-D space of the relationship between transfer functions and synaptic weights suggest neural analogies of cell-firingrate and network control.The back propagation strategy used in neural modeling is generally considered to be a poor approximation ofthe real biological events that change neurons during learning (Harvey, 1994;MacGregor, 1993). In particular, the strategy of retroflexively affecting a presynaptic membrane, which is the sine qua non of back propagation, is contrary to long-standing biological evidence.…”

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confidence: 55%

“…The back propagation strategy used in neural modeling is generally considered to be a poor approximation ofthe real biological events that change neurons during learning (Harvey, 1994;MacGregor, 1993). In particular, the strategy of retroflexively affecting a presynaptic membrane, which is the sine qua non of back propagation, is contrary to long-standing biological evidence.…”

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confidence: 99%

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The biological efficacy of the transfer function

Collins

Bremner

1996

Behavior Research Methods, Instruments, & Computers

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The most popular neural network strategy is back propagation. This strategy initiated general interest in neural networks among researchers. Whileback propagation can solve nonlinear problems, it is considered to be a poor example of neuron functioning. Recently, Gardner (1993) has made a strong case for a back propagating phenomenon in networks of livingneurons. In this paper, we present a few simple computational examples that investigate another component of the typical back propagation network. The effects of varying transfer functions are illustrated along with the resulting variations in possible synaptic weights. Graphic presentations in 3-D space of the relationship between transfer functions and synaptic weights suggest neural analogies of cell-firingrate and network control.The back propagation strategy used in neural modeling is generally considered to be a poor approximation ofthe real biological events that change neurons during learning (Harvey, 1994;MacGregor, 1993). In particular, the strategy of retroflexively affecting a presynaptic membrane, which is the sine qua non of back propagation, is contrary to long-standing biological evidence. Nevertheless, evidenceelegantlypresented by Gardner (1993) makes a strong case for a retrograde effect of the postsynaptic cell membrane on the presynaptic membrane in a way analogous to back propagation. Inthe light ofthis new evidence, it seems that back propagation is more neuromorphic than was originally believed.Gardner's (1993) insight into the neural analogy ofback propagation has prompted us to reconsider the neuromorphology of other mathematical components used by the back propagation strategy. This paper focuses on the transfer function and the relationship of synaptic weights generated via back propagation. The transfer function bounds the output of the simulated neuron by adjusting the activation function. In the typical back propagation computer program, the activation function is a multiplication of the incoming signal by the potency of the synapses (the weight, Wj;)' and the addition of a value generated by a limiting function (the threshold). The resultant of these equations is then squashed by the transfer function, which sets upper, lower, and rate-of-change limits on the transmitted signal (Mpitsos, Burton, & Creech, 1988). Similarly, the biological neuron is bounded by its rate of firing, changes in firing rate, and its pattern. Although the maximum firing rate of a neuron is considered to be 1000 Hz, few neurons, if any, fire at their maximum rate (Bremner & Denham, 1993;Hinton & Anderson, 1981).The purpose of this experiment was to investigate two transfer functions representing the neuron's manipulation ofthe incoming signal to produce the biological outCorrespondenceshould be addressed to F.1.Bremner,Department of Psychology, Trinity University, 715 Stadium Dr., San Antonio, TX 78212-7200. put. One of these transfer functions was linear and the other was sigmoid. These two transfer functions were applied to two chaotic data sets, one in...

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confidence: 99%

The biological efficacy of the transfer function

Collins

Bremner

1996

Behavior Research Methods, Instruments, & Computers

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“…These techniques can assist the anatomical, physiological, and theoretical study of such significant questions as: How should we think of and picture the presumed 156 multiunit neuroelectric signals by which meanings are represented and communicated in these junctions (Sherringten 1906;Kubie 1930;Hebb 1949;Mountcastle 1957;Lashley 1960;Eccles 1970;John 1972;Braitenberg 1978;Palm 1981;Abeles 1982;MacGregor 1991MacGregor ,1993a? What patterns or principles of intrinsic local topography and multiunit microconnectivity exist in diffuse and discrete junctions, if any?…”

Section: Introductionmentioning

confidence: 99%

Characterization, scaling, and partial representation of neural junctions and coordinated firing patterns by dynamic similarity

1995

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This paper presents a dynamic-similarity-based system for mathematically characterizing the functional connectivity and information flow of neural junctions. This approach allows for quantitative comparison of operations of neural junctions across systems, and an interpretation of their connectivity parameters in terms of the flow of multiunit firing patterns. The paper further uses this characterization to show how to rationally construct reduced operational models of neural junctions. Both uniformly proportional scaling and partial fragmentary representations are developed. The uniformly scaled models are better adapted to overall capacities and broader theoretical conceptualizations; the partial representations are better adapted to direct comparison with microelectrode experimentation. The characterization of information flow is based on coordinated multiunit patterns such as synfire chains or sequential configurations. The system can be applied to component parts of large composite networks including junctions with topographical patchiness and other irregularities. The characterization should be of use to anatomists, physiologists, modelers, and theorists. The theory predicts that the necessity for cooperative confluence of synaptic potentials in sending and receiving sequential configurations across topographically constrained projection fields requires the existence of functional 'pattern modules' within the topographical synaptology of the junction.

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“…This theoretical model of information representation in local neural circuits considers sensory information to be maintained in coordinated, spatiotemporal firing patterns (Hebb 1949;Gerstein et al 1986;Abeles 1991;MacGregor and Gerstein 1991;MacGregor 1993). In general, the way in which these assemblies come about and their size and spatial characteristics have not yet been fully elucidated.…”

Section: Model Hypothesismentioning

confidence: 99%

Inhibitory control of sensory gating in a computer model of the CA3 region of the hippocampus

Moxon

Gerhardt

Gulinello

et al. 2003

Biological Cybernetics

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A model of the CA3 region of the hippocampus was used to simulate the P50 auditory-evoked potential response to repeated stimuli in order to study the neuronal circuits involved in a sensoryprocessing deficit associated with schizophrenia. Normal subjects have a reduced P50 auditoryevoked potential amplitude in response to the second of two paired auditory click stimuli spaced 0.5 s apart. However, schizophrenic patients do not gate or reduce their response to the second click. They have equal auditory-evoked response amplitudes to both clicks. When schizophrenic patients were medicated with traditional neuroleptics, the evoked potential amplitude to both clicks increased, but gating of the second response was not restored or improved. Animal studies suggest a role for septohippocampal cholinergic activity in sensory gating. We used a computational model of this system in order to study the relative contributions of local processing and afferent activity in sensory gating. We first compared the effect of information representation as average firing rate to information representation as cell assemblies in order to evaluate the best method to represent the response of hippocampal neurons to the auditory click. We then studied the effects of nicotinic cholinergic input on the response of the network and the effect of GABA B receptor activation on the ability of the local network to suppress the test response. The results of our model showed that nicotinic cholinergic input from the septum to the hippocampus can control the flow of sensory information from the cortex into the hippocampus. In addition, postsynaptic GABA B receptor activation was not sufficient to suppress the test response when the interstimulus interval was 500 ms. However, presynaptic GABA B receptor activity may be responsible for the suppression of the test response at this interstimulus interval.

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Introduction to a Theoretical Mechanics of Neural Networks

Cited by 14 publications

References 0 publications

The biological efficacy of the transfer function

The biological efficacy of the transfer function

Characterization, scaling, and partial representation of neural junctions and coordinated firing patterns by dynamic similarity

Inhibitory control of sensory gating in a computer model of the CA3 region of the hippocampus

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