“…Although other studies have examined translation invariance and related properties (rotation and reflection invariance) in artificial networks (Ranzato et al, 2007; Goodfellow et al, 2009; Lenc and Vedaldi, 2014; Zeiler and Fergus, 2013; Fawzi and Frossard, 2015; Güçlü and van Gerven, 2015 , Shang et al, 2016; Shen et al, 2016; Tsai and Cox, 2015), we are unaware of any study that has quantitatively documented a steady layer-to-layer increase of translation invariant form selectivity, measured for single units, across layers throughout a network like AlexNet. For example, using the invariance metric of Goodfellow et al (2009), Shang et al (2016), their Figure 4c) averaged over multiple types of invariance (e.g., translation, rotation) and over all units within a layer and found a weak, non-monotonic increase in invariance across layers in a CNN similar to AlexNet.…”