Papers

The temporal generalization matrix (TGM) - train a linear classifier on neural population activity at one time and test it at another - is a standard tool in cognitive neuroscience, where off-diagonal generalization is read as a 'stable, maintained' representation and a diagonal-only pattern as a 'dynamic' code. We show analytically that this interpretation is not identifiable. Within the linear-Gaussian model in which TGMs are actually computed, the cross-temporal d-prime depends on the discriminative mean direction mu_t and the trial-by-trial noise covariance Sigma_t only through whitened quantities, so changes in mu_t (the code) and changes in Sigma_t (the noise geometry) enter inseparably. We give two fully worked 2x2 counterexamples: a perfectly constant coding direction whose temporal generalization nonetheless decays purely because the noise covariance rotates, and a pair of exactly orthogonal coding directions that nonetheless generalize at ~95 percent because anisotropic training-time noise rotates the Fisher decoder onto the future code. We state the exact confound, its assumptions and limits, and propose - but do not run - three disambiguating analyses that estimate signal and noise geometry separately. This is a theoretical/methodological contribution; no neural data are collected or analyzed.