Tracking the Fidelity of Internal Neural Representations with Error-In-Variables Regression

Internal neural representations can systematically deviate from externally measured sensory and behavioral variables, yet neuroscientists lack a principled statistical framework to quantify these mismatches. Here we introduce a nonlinear error-in-variables regression framework that explicitly models neural activity as a function of latent internal variables that deviate from measured sensory and behavioral variables. This approach uses a flexible basis expansion and a sampling-based inference scheme to jointly infer neuron-specific tuning functions, latent trajectories, and a representational fidelity parameter{kappa} that controls the strength of coupling between latent and measured variables. On synthetic datasets, the model accurately recovers latent dynamics, tuning curves, and identifies the true fidelity regime via cross-validated marginal likelihood. Applied to population recordings from mouse anterodorsal thalamic nucleus and rat medial entorhinal cortex across distinct sensory and behavioral conditions, the framework reveals condition-dependent changes in representational fidelity, tuning gain and profile, and uncovers latent population manifolds that are obscured in conventional tuning analyses. These results establish error-in-variables regression as a powerful and computationally tractable tool for tracking the fidelity of internal neural representations in systems neuroscience experiments.