Searching for memories, Sudoku, implicit check bits, and the iterative use of not-always-correct rapid neural computation

Neural Computation
J J Hopfield

Abstract

The algorithms that simple feedback neural circuits representing a brain area can rapidly carry out are often adequate to solve easy problems but for more difficult problems can return incorrect answers. A new excitatory-inhibitory circuit model of associative memory displays the common human problem of failing to rapidly find a memory when only a small clue is present. The memory model and a related computational network for solving Sudoku puzzles produce answers that contain implicit check bits in the representation of information across neurons, allowing a rapid evaluation of whether the putative answer is correct or incorrect through a computation related to visual pop-out. This fact may account for our strong psychological feeling of right or wrong when we retrieve a nominal memory from a minimal clue. This information allows more difficult computations or memory retrievals to be done in a serial fashion by using the fast but limited capabilities of a computational module multiple times. The mathematics of the excitatory-inhibitory circuits for associative memory and for Sudoku, both of which are understood in terms of energy or Lyapunov functions, is described in detail.

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Citations

Jan 19, 2010·Proceedings of the National Academy of Sciences of the United States of America·John J Hopfield
Jun 4, 2013·Neural Computation·Carina CurtoJudy L Walker
Jan 7, 2014·PLoS Computational Biology·Gašper TkačikMichael J Berry
May 20, 2015·Neural Networks : the Official Journal of the International Neural Network Society·B BorelandH Kunze
Oct 8, 2011·The American Journal of Psychology·Hye-Sang Chang, Janet M Gibson
Jun 28, 2016·Neural Computation·Asieh Abolpour MofradMohammad H Tadayon
Apr 15, 2017·Neural Computation·Asieh Abolpour Mofrad, Matthew G Parker
Jul 2, 2014·Neural Networks : the Official Journal of the International Neural Network Society·Jiann-Ming WuCheng-Yuan Liou
Jun 27, 2017·IEEE Transactions on Cybernetics·Gyeong-Moon ParkJong-Hwan Kim
Mar 19, 2019·Neural Computation·Heiko Hoffmann
Oct 27, 2015·Neural Computation·Hesham MostafaGiacomo Indiveri
Jan 8, 2020·Materials·Valerio MiloDaniele Ielmini
Jul 28, 2018·Frontiers in Neurorobotics·Giulio SandiniPietro Morasso
Aug 20, 2021·Neural Computation·Asieh Abolpour MofradMatthew Geoffrey Parker

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