The Combinatorial Capacity and Robustness of Hierarchical Concept Coding in the Human Medial Temporal Lobe

Abstract

The human brain encodes a virtually infinite repertoire of semantic concepts using a finite number of neurons, a feat that defies the capacity limits of classical attractor networks. While "Concept Cells" in the medial temporal lobe (MTL) exhibit extreme sparsity, the information-theoretic principles governing their collective robustness remain elusive. Here, we present a hierarchical coding framework that resolves this paradox. We rigorously prove that while uniform sparse coding is bound by a polynomial "Exclusion Volume" limit--leading to catastrophic interference--a hierarchically partitioned architecture unlocks an exponential combinatorial capacity. We demonstrate that this "locally dense, globally sparse" topology mirrors the distance-dependent connectivity of the hippocampal CA3 region. Crucially, we derive a "Supply-Demand" theoretical model for Cognitive Reserve, which quantitatively predicts the "Silent Phase" of neurodegeneration and the mathematical inevitability of the clinical "Cliff Edge" collapse in Alzheimers Disease. Furthermore, our findings identify the lack of topological sparsity as the root cause of catastrophic forgetting in artificial neural networks, offering a blueprint for next-generation, biologically plausible AI architectures.