Semantic axes in the brain support analogical representations

In vectorial embeddings of word meaning, semantic features often reflect consistent directions--or axes--within a representational space. A classic example is gender: the vector spanning "boy"[->]"girl" can be added to the embedding for "king" to predict "queen." Here we show that the same principle governs semantically driven neural responses in the human brain. We recorded single-neuron activity in three brain regions while participants listened to podcasts. Across fifteen analogical categories --including gender, number, and antonymy--we observed consistent vectorial directions, resulting in parallelogram structure within the neural manifold. Among pronouns, vectors corresponding to grammatical case, number, person, and possession obeyed the principle of commutativity, resulting in a prismatic structure, demonstrating that semantic axes can be factorized. We found parallelogram structure in all three regions, with some regional specialization: noun pluralization was more robust in the hippocampus than in the anterior cingulate cortex (ACC) or orbitofrontal cortex, whereas verbal conjugation effects were more robust in the ACC. Finally, we found evidence for partial functional specialization at the neuron level: neurons most strongly involved in one analogy type were less involved in others. These principles parallel representational structure observed in large language models. Together, these findings support a geometric basis for analogical reasoning.