A geometric foundation for word meaning in the brain

In language models of word meaning, directions in the embedding space often correspond to semantic features that can be reused across different words. For example, a single direction corresponding to gender may differentiate word pairs like boy/girl, uncle/aunt, and king/queen. Here we show that the same principle governs semantically driven neural responses in the human brain. We recorded populations of single neurons during podcast listening and identified word sets with consistent meaning differences. Across fifteen sets, including gender, plural, and negation, we observed consistent vectorial directions, resulting in parallelogram structures within the neural manifold. Deviation from parallelism in large language models (LLMs) predicted corresponding deviations in brain-derived parallelism. Among pronouns, vectors corresponding to case, number and person exhibited parallelogram structures individually and, collectively, obeyed the principle of commutativity, resulting in a prismatic structure. Finally, different semantic variables were preferentially associated with discrete groups of neurons, consistent with energy-efficiency theories. Together, these results establish a geometric foundation for the neural encoding of word meaning.