Chiral Symmetry Breaking in Transformers: A Group-Equivariant Framework for Addressing the Reversal Curse via Adjoint Manifold Mappings

The "reversal curse" exposes a critical asymmetry in autoregressive models, where models trained on facts in one direction often fail to access the corresponding inverse relation. This work studies the phenomenon from a representation-level perspective, characterizing it as a form of chiral asymmetry between subject- and object-oriented latent states. We introduce the Chiral Transformer, a lightweight framework that encourages an involutive adjoint mapping operator $\mathcal{T}$ through contrastive regularization. At inference time, Adjoint-Induced Retrieval (AIR) uses this learned map as a structured readout over model-derived entity representations, rather than as an unconstrained autoregressive generation protocol. Empirical validation on inverse-relation benchmarks shows that this symmetry-aware retrieval setting substantially improves inverse factual access, with AIR reaching 65.07% accuracy on Fact-Inv-300. These findings support a representation-access view of the reversal curse: inverse relations may be difficult not only because of missing data, but also because standard autoregressive readout fails to expose useful latent structure.