Recording From Biological Neural Networks

A biologically plausible low-order model (LOM) of biological neural networks is proposed. LOM is a recurrent hierarchical network of models of dendritic nodes and trees; spiking and nonspiking neurons; unsupervised, supervised covariance and accumulative learning mechanisms; feedback connections; and a scheme for maximal generalization. These component models are motivated and necessitated by making LOM learn and retrieve easily without differentiation, optimization, or iteration, and cluster, detect, and recognize multiple and hierarchical corrupted, distorted, and occluded temporal and spatial patterns. Four models of dendritic nodes are given that are all described as a hyperbolic polynomial that acts like an exclusive-OR logic gate when the model dendritic nodes input two binary digits. A model dendritic encoder that is a network of model dendritic nodes encodes its inputs such that the resultant codes have an orthogonality property. Such codes are stored in synapses by unsupervised covariance learning, supervised covariance learning, or unsupervised accumulative learning, depending on the type of postsynaptic neuron. A masking matrix for a dendritic tree, whose upper part comprises model dendritic encoders, enables maximal generalization on corrupted, distorted, and occluded data. It is a mathematical organization and idealization of dendritic trees with overlapped and nested input vectors. A model nonspiking neuron transmits inhibitory graded signals to modulate its neighboring model spiking neurons. Model spiking neurons evaluate the subjective probability distribution (SPD) of the labels of the inputs to model dendritic encoders and generate spike trains with such SPDs as firing rates. Feedback connections from the same or higher layers with different numbers of unit-delay devices reflect different signal traveling times, enabling LOM to fully utilize temporally and spatially associated information. Biological plausibility of the component models is discussed. Numerical examples are given to demonstrate how LOM operates in retrieving, generalizing, and unsupervised and supervised learning.

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Decoding neuronal firing and modelling neural networks

Quarterly Reviews of Biophysics ◽

10.1017/s0033583500003024 ◽

1994 ◽

Vol 27 (3) ◽

pp. 291-331 ◽

Cited By ~ 81

Author(s):

L. F. Abbott

Keyword(s):

Neural Networks ◽

Time Scales ◽

Neuronal Firing ◽

Biological Neural Networks ◽

Large Systems

Biological neural networks are large systems of complex elements interacting through a complex array of connexions. Individual neurons express a large number of active conductances (Connors et al. 1982; Adams & Gavin, 1986; Llinás, 1988; McCormick, 1990; Hille, 1992) and exhibit a wide variety of dynamic behaviours on time scales ranging from milliseconds to many minutes (Llinás, 1988; Harris-Warrick & Marder, 1991; Churchland & Sejnowski, 1992; Turrigiano et al. 1994).

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