The “Brain-State-in-a-Box” neural model is a gradient descent algorithm

Journal of Mathematical PsychologyPublished 1 March 1986

Richard M. Golden

DOI10.1016/0022-2496(86)90043-x

Source URL

Citations85

SJR quartileQ2

SJR score0.74

SNIP1.10

TL;DR

A formal proof that all trajectories of the BSB algorithm in state vector space approach the set of system equilibrium points, under certain specific conditions, is presented.

Abstract

The Brain-State-in-a-Box (BSB) neural model (J. A. Anderson, J. W. Silverstein, S. A. Ritz, & R. S. Jones, 1977, Psychological Review, 84, 413–451) is a pattern categorization device inspired by neurophysiological considerations. This model has additionally been applied to a fairly diverse range of psychological phenomena. In this paper, the BSB model is demonstrated to be a deterministic constrained gradient descent algorithm that minimizes a quadratic cost function. A formal proof that all trajectories of the BSB algorithm in state vector space approach the set of system equilibrium points, under certain specific conditions, is presented. Some conditions regarding the existence of global energy minima are also briefly discussed.

Keywords

Computer ScienceNeuroscience

Pattern classification and scene analysis

12,643 Citations1973Richard O. Duda, Peter E. Hart

Mathematics and Computers in SimulationLinear and nonlinear programming.

4,850 Citations1986

The linear and nonlinear programming is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.

Psychological ReviewToward a modern theory of adaptive networks: Expectation and prediction.

1,457 Citations1981Richard S. Sutton, Andrew G. Barto

The adaptive element presented learns to increase its response rate in anticipation of increased stimulation, producing a conditioned response before the occurrence of the unconditioned stimulus, and is in strong agreement with the behavioral data regarding the effects of stimulus context.

Mathematics and Computers in SimulationIntroduction to dynamic systems: theory, models and applications

1,144 Citations1981

This introduction to dynamic systems theory models and applications helps people to read a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their laptop.

IEEE Transactions on Pattern Analysis and Machine IntelligenceOn the Foundations of Relaxation Labeling Processes

891 Citations1983Robert A. Hummel, Steven W. Zucker

It is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality, and a procedure nearly identical to the relaxation operator derived under restricted circum-stances serves in the more general setting.

Psychological ReviewDistinctive features, categorical perception, and probability learning: Some applications of a neural model.

860 Citations1977James A. Anderson, Jack W. Silverstein +2 more

The model can predict overshooting, recency data, and probabilities occurring in systems with more than two events with reasonably good accuracy and applies the model to "categorical perception" and probability learning.

IEEE Transactions on Systems Man and CyberneticsCognitive and psychological computation with neural models

342 Citations1983James A. Anderson

A simulation is presented which can learn partial information, integrate it with other material, and use that information to reconstruct missing information and educate the resulting systems and the use of error correcting techniques.

Acta PsychologicaA neural network model of multistable perception

113 Citations1985Alan H. Kawamoto, James A. Anderson

A neural network model based on state vectors, feedback and Hebbian synaptic modification is suggested which can be made to account for a number of the experimental findings.