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.

Large language models can often learn a fact in one direction but fail when asked the same fact in reverse. For example, a model may learn that one entity is related to another, yet struggle to identify the first entity when queried from the second. This paper studies why this happens and argues that the information may sometimes be present inside the model but difficult to access through ordinary text generation. We propose a method that makes the model’s internal representations easier to use for reverse factual queries by adding a structured readout mechanism. Experiments on inverse-relation benchmarks show that this approach improves access to reverse factual information in a controlled retrieval setting. The work suggests that some failures of language models may come not only from missing training data, but also from how models retrieve and express information they have already encoded.