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 (CRC) 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 CRC and is robust across DG implementation; (ii) the spiking CA3 exhibits a runaway transition whose boundary is set by the product (active fraction x CRC), 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 CRC; spiking runs away at high active-fraction x CRC) 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 and Feigelman, 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 {approx} 0.02-0.05) is the condition that lets a highly recurrent network perform stable autoassociation. Significance StatementHow densely CA3 pyramidal neurons interconnect is contested, with functional and anatomical estimates differing roughly tenfold. In a dentate-gyrus[->]CA3 model run across two DG and two CA3 implementations, we show this need not be a contradiction: whether higher recurrent connectivity helps or harms pattern completion depends on the CA3 computational mode and, above all, on how sparse CA3 activity is. A spiking attractor collapses once the product of active fraction and recurrent in-degree exceeds an approximately size-invariant threshold, whereas a hard-sparsity network is immune. Whether neurogenesis helps or harms depends on whether young neurons recruit inhibition: without it they destabilise an E/I CA3; with it they protect it. Sparse coding is thus the control variable for stable memory.