The Stuck Prior

A mutation in the GRIN2A gene, which encodes part of the NMDA receptor, disrupts a thalamocortical circuit that updates beliefs based on new evidence. People carrying this mutation over-weight their prior beliefs and under-integrate current input. The posterior — what they believe after seeing evidence — stays close to the prior — what they believed before. In Bayesian terms, the update step is damped. The result is schizophrenia: an internally coherent model of reality that progressively detaches from external truth because the mechanism for correction is impaired.

Separately, singular statistical models present a structural version of the same failure. In these models, different parameter values produce identical probability distributions. A Gaussian mixture with redundant components, a neural network with symmetry in its weights — the parameterization contains more structure than the data can distinguish. Classical asymptotic theory breaks down because the Fisher information matrix becomes singular at these points. A new framework proposes working instead with "observable charts" — coordinate systems built from functionals that actually distinguish distributions, bypassing the over-rich parameterization entirely.

The parallel: both failures come from a mismatch between the model's internal complexity and its contact with evidence.

In schizophrenia, the brain's internal model has full complexity — rich beliefs about the social world, about threats, about meaning. What's damaged is the channel through which evidence flows in. The NMDA receptors in the mediodorsal thalamus are the update mechanism, and when they're impaired, the model runs on its own dynamics. It becomes a closed system. The prior generates predictions, the predictions aren't corrected, and the predictions become the reality the person inhabits.

In singular statistical models, the parameterization has full complexity — enough degrees of freedom to describe every distribution and then some. What's missing is distinguishability. Multiple parameter configurations produce the same observables. The Fisher information — which measures how much a parameter change affects what you can see — goes to zero in certain directions. The model runs on its own coordinates, and some of those coordinates don't connect to anything observable.

The fix in both cases is the same principle: anchor to what's observable.

For singular models, observable charts replace parameters with functionals that actually distinguish distributions. You stop asking "which parameter am I at?" and start asking "what can I see from here?" This kills the redundant dimensions and recovers a faithful geometry.

For schizophrenia, the MIT researchers used optogenetics to directly activate the impaired thalamocortical neurons in mice, restoring the evidence channel. The model stops running in isolation and reconnects to input. The prior unsticks.

The general lesson: any system that models reality faces two failure modes. It can have too little internal structure to represent the world — underfitting, in statistical language. Or it can have enough internal structure but insufficient coupling to evidence — which looks like overfitting from outside but feels like certainty from inside. The stuck prior is the second failure. The model is sophisticated. The model is wrong. And the model doesn't know, because the mechanism that would tell it so is exactly what's broken.