Numerosity-tuned units emerge, untrained, in a real CNN trained only for ImageNet object recognition, with Weber-Fechner logarithmic tuning geometry

A real biologically-inspired deep CNN (8 convolutional layers, 5 max-pooling layers, 1 fully-connected layer) trained only on ILSVRC2012 ImageNet object classification develops units selectively tuned to abstract numerosity, despite never being trained on any numerosity task [nasr-viswanathan-nieder-2019-number-detectors-emerge-in-cnn] These numerosity-tuned units are concentrated in the network's final layers and drive the network's number-discrimination performance when read out [nasr-viswanathan-nieder-2019-number-detectors-emerge-in-cnn] The network's number discrimination shows the characteristic signature of the Weber-Fechner law -- discrimination accuracy depends on the ratio between numerosities rather than their absolute difference, matching human and animal number-discrimination psychophysics and implying a logarithmically-compressed tuning geometry along a discovered numerosity axis [nasr-viswanathan-nieder-2019-number-detectors-emerge-in-cnn]