The brain's synapses are volatile. They strengthen, weaken, appear, and disappear on timescales that seem incompatible with stable computation. This has always created a puzzle: if the wiring is imprecise, how does the brain reliably transmit information from one processing stage to the next? The standard assumption is that somewhere in the decoding — the way downstream neurons read the upstream signal — there's optimization that compensates for the noise. The system is sloppy at the hardware level but smart at the algorithmic level.
The new result from arXiv:2602.21758 is that this compensation doesn't work in the biologically relevant regime. When synaptic precision is low enough — and the evidence says it is — optimized decoding performs no better than naive population averaging. The ceiling isn't set by the decoder. It's set by the correlated noise in the neural responses themselves.
Three regimes emerge. When synaptic precision is high (weak coarse-tuning), the signal-to-noise ratio scales linearly with population size — more neurons means proportionally better discrimination. Optimized decoding matters here because the decoder can extract structure from the precise weight patterns. When precision is moderate, scaling becomes sublinear — adding neurons helps, but with diminishing returns. When precision is low (strong coarse-tuning, the biologically realistic case), SNR saturates. No amount of additional neurons can improve performance, and the optimal decoder converges to the naive one.
The implication is that the nervous system may be confined to a low-dimensional manifold aligned with the naive decoder — not because the brain chose simplicity, but because the signal quality doesn't support anything more sophisticated. You can't decode information that the upstream noise has already destroyed. The decoder's job isn't to be clever; it's to average.
This reframes synaptic volatility as a feature constraint rather than an engineering problem. The question “how does the brain compensate for imprecise wiring?” may have no answer because the question presumes compensation is necessary. If the performance ceiling is set by input noise, then precise wiring would be wasted — the brain couldn't use the extra precision even if it had it. Sloppy wiring isn't a limitation the system works around. It's the equilibrium: the system is exactly as precise as it needs to be, and no more.