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 ↔ V2), increasing feedback from V2 to V1 amplifies responses in both areas. We analytically derive power spectra (V1) and coherence spectra (V1-V2) as functions of frequency (f), and compare them with experimental observations: peaks in both spectra shift to higher frequencies with increased stimulus contrast, and power decays as 1/f4 at high frequencies. The closed-form spectra are validated against direct stochastic simulation of the full nonlinear circuit across contrasts. The theory further predicts distinctive spectral signatures of feedback and input gain modulation. Crucially, the theory offers a unified view of inter-areal communication, defined as the ability to linearly predict neural activity in one brain area from neural activity in another, with emergent features consistent 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) communication is strongest, and the subspace dimensionality lowest, at the frequencies at which V1-V2 coherence peaks; iii) normalization reduces the subspace dimensionality. Finally, a three-area (V1 ↔ V4 and V1 ↔ 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.