Is Inference Mediated by Distinct Semantic Structures in LLMs? A Mechanistic Interpretation

Predicting a label correctly does not necessarily require representing the operation that produces it. Transformer representations are known to carry label-level information, but whether they encode semantic operations producing those labels is unclear. We investigate this in Natural Language Inference using controlled premise-hypothesis pairs that differ by a single semantic transformation. Using layer-wise activations, we estimate operation-level subspaces via SVD and test their causal relevance through activation steering in four open-weight decoder models. Transformation effects are decodable with $84.8$-$99\%$ accuracy and occupy partially distinct but overlapping subspaces, exceeding random-subspace baselines. Steering experiments show that these directions causally influence predictions, though steerability varies across models; cross-operation steering further reveals structured interference and a dissociation between subspace selectivity and cross-operation independence. These findings indicate that the models encode not only that a hypothesis relates to a premise but also, in part, how it does so, implying that mechanistic analysis and control should operate at the level of semantic operations rather than predicted labels alone.