With technological advances in neuroanatomy and neurophysiology, neuroscience of multi-regional brain-wide neural circuits is taking off. However, recent studies have renewed the debate on local versus global neural information encoding and processing. Here, I will propose a mechanism for functional specificity in a cortex made of repeated canonical local circuits à la Kevan Martin and Rodney Douglas. I will introduce large-scale modeling of cortex based on connectomic data for monkeys and mice, and highlight macroscopic gradients of synaptic excitation and inhibition as a general principle of the large-scale cortical organization. Then, I will discuss findings about a hierarchy of timescales, distributed working memory and simple decision-making. This line of work suggests that the new concept of “bifurcation in space” can explain functional modularity/specialization compatible with distributed neural representations in the neocortex.