Neural Selectivity as a Compatibility Problem: From Latent Coordinates to Explicit Features

Whether a neuron is called purely selective, linearly mixed, or nonlinearly mixed is usually decided under a feature set fixed in advance by the experimenter. This label belongs to the pair of neuron and description, not to the neuron alone. Information-preserving re-descriptions of the same inputs can turn nonlinear dependence into linear dependence. We therefore treat the feature description itself as the object of discovery, organized by neural compatibility, the degree to which a feature description supports prediction of a target neural population through a specified simple-readout class. We introduce compatibility-guided feature discovery. A shared population encoder learns a response-predictive representation, and a sparse autoencoder (SAE) provides candidate activation patterns. Language-model-assisted feature proposals and shallow decision trees turn these patterns into binary features defined by executable sensory and behavioral rules. These rule-defined features are selected for their contribution to linear neural prediction. Across 575 neurons from 22 mouse primary somatosensory cortex sessions, full-data discovery produced a descriptive catalog of 164 rule-defined features. Under four-fold nested cross-validation, with encoder training and feature discovery restricted to outer-training trials, adding fold-specific prediction-selected features to inputs already augmented with input-informed LLM features increased mean linear prediction $R^2$ from 0.1079 to 0.1254. On these recordings, previously analyzed for nonlinear sensory integration, the discovered features made part of the nonlinear predictive structure linearly accessible, reducing the nonlinear-over-linear $R^2$ gap by 54.2%. Even with trial time in the baseline, these features retained 92% of their original $R^2$ gain, which was 2.4 times the gain from random features matched in vocabulary, tree structure, and prevalence. Features discovered and fixed in 15 sessions also improved held-out linear prediction in each of seven excluded sessions after within-session readout calibration. Treating descriptions as discoverable turns a known caveat of selectivity analysis into a procedure for discovering and testing interpretable features.