Feng, B.; Gao, R.; Li, N.; Shouval, H.

Neural integrators convert brief inputs into persistent firing and underlie functions such as working memory, evidence accumulation, and gaze holding. Classical integrator models typically rely on finely tuned recurrent connectivity. Here we identify a biologically plausible route by which randomly connected noisy spiking networks can approximate integration over a finite region of parameter space. Mean-field theory (MFT) reveals surprisingly simple dynamics in such networks, governed by the mean recurrent weight and mean feedforward weight, and shows that linear integration critically depends on noise. We further show that this regime can be reached through a local, reward-modulated two-trace plasticity rule. Comparing the model with new experimental results from a delay-switching tactile decision-making task, we find that it reproduces key features of adaptive ramp-to-threshold cortical dynamics during timing-related learning. The same framework further connects to oculomotor persistence and evidence accumulation, providing a mechanistic realization of single-boundary drift--diffusion dynamics.