We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponentially small failure probability, there exists a large fraction of the inliers satisfying this condition.

Here we add the generalization results of the Nu-Net when the object density is outside of the distribution of the training set. Specifically, we run the Nu-Net on test images that are the same as the training images but have 50% greatervariations inobject density. The 85% estimation interval length for each input number is shown in Figure 1. It can be seen that, fornumbers 1,2and4,the85% estimation intervallength is1,meaning thattheNu-Net performs very well on small numbers, i.e., on the task of subitizing.

Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition. This has, if true, far reaching significance to the fields of machine learning and cognitivesciencealike.

We highlight improvementsofbothalgorithms overrunning independent standard MABsacross users.