Extended Data Fig. 9: Size and performance analysis of logic circuits for pattern recognition.

a, Logic circuits that determine whether a 9-bit pattern is more similar to ‘L’ or ‘T’. b, Logic circuits that recognize 100-bit handwritten digits. To find a logic circuit that produces correct outputs for a given set of inputs, with no constraint on other inputs, we first created a truth table including all experimentally tested inputs and their corresponding outputs. The outputs for all other inputs were specified as ‘don’t care’, meaning the values could be 0 or 1. The truth table was converted to a Boolean expression and minimized in Mathematica, and then minimized again jointly for multiple outputs and mapped to a logic circuit in Logic Friday (https://download.cnet.com/Logic-Friday/3000-20415_4-75848245.html). In the minimized truth tables shown here, ‘X’ indicates a specific bit of the input on which the output does not depend. For comparison, minimized logic circuits were also generated from training sets with a varying total number of random examples from the MNIST database. The performance of each logic circuit, defined as the percentage of correctly classified inputs, was computed using all examples in the database. To make the minimization and mapping to logic gates computable in Logic Friday, the size of the input was restricted to the 16 most significant bits, determined on the basis of the weight matrix of the neural networks.