Hierarchical Neural Circuit Theory of Normalization and Inter-areal Communication

The primate brain exhibits a hierarchical, modular architecture with conserved microcircuits executing canonical computations across reciprocally connected cortical areas. We present a hierarchical neural circuit theory with feedback connections that dynamically implements divisive normalization across its hierarchy. In a two-stage instantiation (V1 {leftrightarrow}V2), increasing feedback from V2 to V1 amplifies responses in both areas. We analytically derive power spectra (V1) and coherence spectra (V1-V2), and validate them against experimental observations: peaks in both spectra shift to higher frequencies with increased stimulus contrast, and power decays as 1/f4 at high frequencies (f). The theory further predicts distinctive spectral signatures of feedback and input gain modulation. Crucially, the theory offers a unified view of inter-areal communication, with emergent features commensurate with empirical observations of both communication subspaces and inter-areal coherence. It admits a low-dimensional communication subspace, where inter-areal communication is lower-dimensional than within-area communication. It further predicts that: i) increasing feedback strength enhances inter-areal communication and diminishes within-area communication, without altering the subspace dimensionality; ii) high-coherence frequencies are characterized by stronger communication (ability to estimate neural activity in one brain area from neural activity in another brain area) and reduced subspace dimensionality; iii) Normalization reduces the subspace dimensionality. Finally, a three-area (V1 {leftrightarrow}V4 and V1{leftrightarrow} V5) instantiation of the theory demonstrates that differential feedback from higher to lower cortical areas dictates their dynamic functional connectivity. Altogether, our theory provides a robust and analytically tractable framework for generating experimentally-testable predictions about normalization, inter-areal communication, and functional connectivity.