We have focused on the formation of maps of “simple cells,” that is, cells containing only a single RF subunit representing a particular shape feature. In reality, many or most cells in visual cortex, beginning already in V1, are “complex” (Gilbert,
1977; Hubel & Wiesel,
1962). Complex cells pool over multiple spatially displaced RF subunits (Chen, Han, Poo, & Dan,
2007; Hubel & Wiesel,
1962; Mel,
1997), which is thought to be the main mechanism responsible for increasing spatial invariance from stage to stage in the ventral visual processing stream (Cadieu et al.,
2007; Fukushima,
1980; Hubel & Wiesel,
1962; Lee, Grosse, Ranganath, & Ng,
2009; Mel,
1997; Nandy, Sharpee, Reynolds, & Mitchell,
2013; Ranzato, Huang, Boureau, & LeCun,
2007; Riesenhuber & Poggio,
1999; Rust & DiCarlo,
2010; Serre, Wolf, & Poggio,
2005; Sharpee, Kouh, & Reynolds,
2013; Ullman, Vidal-Naquet, & Sali,
2002; Wallis & Rolls,
1997). Our focus here on multimap formation involving simple rather than complex cells was justified by the assumption that the same two rules need to be followed whether the cells involved in the map formation process are simple or complex. In particular, a representational unit—whether the lone RF subunit of a simple cell, or one of the several subunits within a complex cell RF—should learn a stimulus only when (a) the subunit lies within a strongly activated cortical neighborhood, and (b) the subunit is itself strongly activated by the stimulus. What differs about training a map containing complex cells is that an additional mechanism must be included that ties together the multiple subunits contained within a complex cell's RF. The most commonly proposed mechanism to do this is a temporal trace rule (Berkes & Wiskott,
2005; Földiák,
1991; Wallis & Rolls,
1997). While this is clearly an important part of a full understanding of map formation in extrastriate visual areas, the process that encourages the multiple RF subunits of a complex cell to differentiate into distinct spatial variants of the same basic stimulus can occur after the process that differentiates cells into separate feature maps, and so, we argue, can be studied separately.