The variance theory of the mirror effect in recognition memory

The mirror effect refers to a rather general empirical finding showing that , for two classes of stimuli, the class with the higher hit rates also has a lower false alarm rate. In this article, a parsimonious theory is propose d to account for the mirror effect regarding, specifically, high- and low-f requency items and the associated receiver-operating curves. The theory is implemented in a recurrent network in which one layer represents items and the other represents contexts. It is shown that the frequency mirror effect is found in this simple network if the decision is based on counting the n umber of active nodes in such a way that performance is optimal or near opt imal. The optimal performance requires that the number of active nodes is l ow, only nodes active in the encoded representation are counted, the activa tion threshold is set between the old and the new distributions, and normal ization is based on the variance of the input. Owing to the interference ca used by encoding the to-be-recognized item in several preexperimental conte xts, the variance of the input to the context layer is greater for high-tha n for low-frequency items, which yields lower hit rates and higher false al arm rates for high- than for low-frequency items. Although initially the th eory was proposed to account for the mirror effect with respect to word fre quency, subsequent simulations have shown that the theory also accounts for strength-based mirror effects within a list and between lists. In this cas e, consistent with experimental data, the variance theory suggests that foc using attention to the more difficult class within a list affects the hit r ate, but not the false alarm rate and not the standard deviations of the un derlying density, leading to no mirror effect.