CA3 sparsity stabilises high-connectivity recurrent autoassociation: complementary binary and spiking computational modes in a DG->CA3 model

The dentate gyrus (DG) decorrelates entorhinal inputs (pattern separation); area CA3 completes partial cues via recurrent autoassociation. The density of CA3 recurrent connectivity is contested, with estimates from ~0.9% (Guzman et al., 2016) to ~9-11% (Sammons et al., 2024). We ask how completion depends on recurrent connectivity (C_RC) and whether the answer is intrinsic to CA3 dynamics or inherited from the DG front-end. Using a trisynaptic model that crosses two DG implementations (a point-LIF network with Santhakumar et al. (2005) topology; an abstract fixed-in-degree spiking network validated size-invariant to N=107) with two CA3 autoassociators (binary k-WTA; spiking excitatory/inhibitory attractor) via burst-gated mossy-fiber detonators, we find: (i) completion in the binary CA3 improves monotonically with C_RC and is robust across DG implementation; (ii) the spiking CA3 exhibits a runaway transition whose boundary is set by the product (active fraction x C_RC), is not rescued by stronger feedback inhibition (8x), is insensitive to input overlap, and is size-invariant (N=104-105); (iii) the two CA3 types have opposite failure modes (binary under-completes at low C_RC; spiking runs away at high active-fraction x C_RC) and a capacity/stability trade-off. Adult neurogenesis flips sign by the same logic: excitability-only young cells densify the code and collapse the spiking attractor, but if they recruit feedback inhibition they instead sparsen it and preserve recall. Consistent with classical sparse-coding attractor theory (Tsodyks & Feigel'man, 1988), we propose that the contested CA3 connectivity is better read as an implementation-mode trade-off, and that the empirically sparse activity of CA3 (a~0.02-0.05) is the condition that lets a highly recurrent network perform stable autoassociation.