Hierarchical Visual Working Memory: Reducing Natural Scene Parsing from NP-Complete to Polynomial-Time Complexit

Parsing natural scenes into constituent objects by binding multiple visual features is, in its most general formulation, combinatorially intractable. Here we present a theoretical and simulation study showing how a biologically grounded, hierarchical visual working memory (VWM) architecture can render the effective computational cost tractable. Central to our framework is the notion that VWM stores \emph{attentional samples} formed via feedforward processing and top-down recurrent refinement (Selective Tuning framework). We implement VWM units as Cohen–Grossberg (leaky-competitive) neurons and prove four interlocking results: (i) a structural complexity bound that yields $O(N)$ neurons and connections under pyramidal reduction and attenuated feedback; (ii) a contraction-based dynamic convergence guarantee giving feedforward stabilization in $O(L\log(1/\varepsilon))$ time; (iii) an interference-limited SNR capacity bound that quantifies how $p$-lattice clarity and cross-talk constrain resolvable memory samples; and (iv) a task-driven retrieval complexity bound that reduces scene-parsing cost to polynomial time under chunking and hierarchical pooling. Simulations calibrated to biologically plausible parameters validate the analytic bounds and expose a capacity landscape governed primarily by clarity and cross-talk. The model accounts for classic VWM phenomena (limited effective capacity despite large codebooks) and makes testable predictions about how attentional depth, receptive-field overlap, and neuromodulatory gain affect capacity and speed. These results bridge computational complexity theory and neurobiology, suggesting principled mechanisms by which the brain attains rapid, robust scene parsing.