Abstract
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.
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Stoianov, I., Zorzi, M., Becker, S., Umilta, C. (2002). Associative Arithmetic with Boltzmann Machines: The Role of Number Representations. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_46
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DOI: https://doi.org/10.1007/3-540-46084-5_46
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