The ability to compare two magnitudes is observed in naïve animals in the absence of learning (Rugani 2016; McCrink 2007), but how this cognitive function emerges without training remains elusive. In monkeys, neurons in the prefrontal and parietal cortex were observed to respond selectively to the proportion between two magnitudes (Vallentin 2008, 2010), suggesting these units could be fundamental for innate magnitude comparisons. However, details of how these comparison units emerge without any learning also remain unclear. Here, we show that magnitude comparison units can arise spontaneously even in completely untrained deep neural networks. We hypothesized that comparisons on a relative or absolute scale are two main means of magnitude comparison. Thus, we designed a set of images in which the number of white and black dots represents a proportion or difference. We fed these images into a randomly initialized AlexNet and found distinct populations of units responding selectively to a specific proportion or difference, regardless of the total number of dots. We confirmed that these units respond to abstract proportions or differences irrespective of the total area and/or the total number of dots, thus enabling the network to compare the two magnitudes. Next, based on the summation coding model, we hypothesized that a combination of monotonically increasing responses according to the number of white or black dots, observed in a previous layer, can generate proportion and difference units. We found that both types of comparison units can emerge when the observed increasing responses are connected with random weights, implying that distinct functional units may share a qualitatively identical developmental mechanism. Furthermore, using a theoretical model, we found that differences in the shape and concavity of response patterns can determine the proportion or difference selectivity. Our findings suggest that statistical variations of feedforward projections can induce diverse innate cognitive functions.