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

The algorithms that simple feedback neural circuits representing a brain area can rapidly carry out are often adequate to solve only easy problems, and 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.