A New Learning Algorithm for Mean Field Boltzmann Machines
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
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This paper presents a study on associative mental arithmetic with mean-field Boltzmann Machines. We examined the role of number representations, showing theoretically and experimentally that cardinal number representations (e.g., numerosity) are superior to symbolic and ordinal representations w.r.t. learnability and cognitive plausibility. Only the network trained on numerosities exhibited the problem-size effect, the core phenomenon in human behavioral studies. These results urge a reevaluation of current cognitive models of mental arithmetic.