Differentiability Is Not Enough: Inference Near a Dynamical Transition in a Whole-Brain Model

Making a scientific simulator differentiable provides gradients, but those gradients do not necessarily support reliable inference. This problem is especially consequential near a dynamical transition, where long recurrent trajectories amplify sensitivities. We study a stochastic, delayed, 68-region whole-brain model near such a transition using group-averaged magnetoencephalography (MEG) and blood-oxygen-level-dependent (BOLD) connectivity summaries. Replicated forward profiles, finite-difference checks, and evaluation under unused process noise distinguish three outcomes. First, the tested connectivity summaries do not resolve conduction speed reproducibly. Second, BOLD connectivity resolves global coupling in synthetic data, but time-truncated gradients move away from the known value, whereas MEG coherence supports recovery at the same chaotic point. Third, a finite-difference-screened regional-rate fit with 67 free parameters improves MEG alpha-power structure but reveals a trade-off with BOLD connectivity. A dynamical transition does not make every gradient useless: inference depends jointly on the parameter, observable, dynamical regime, and sensitivity estimator, and competing targets may require a richer model rather than another loss weight. This case study asks when gradient checks are worth their cost and when a multimodal Pareto conflict should end fitting and begin model revision.