The Illusion of Latent Generalization: Bi-directionality and the Reversal Curse

Autoregressive language models (ARMs) suffer from the reversal curse: after learning ''$A$ is $B$,'' they often fail on the reverse query ''$B$ is $A$.'' Masked diffusion language models (MDMs) exhibit this failure in a much weaker form, but the underlying reason has remained unclear. A common explanation attributes this mitigation to their any-order masked training objective. However, observing ''$[\mathbf{M}]$ is $B$'' during training teaches recovery of $A$ from $B$ in one positional configuration, and does not by itself explain why the learned evidence should transfer to the reverse prompt ''$B$ is $[\mathbf{M}]$.'' We provide a theoretical analysis showing that this transfer arises from a parameter-level coupling between forward and reverse positional conditionals: shared Transformer parameters store token-pair evidence, while relative positional encodings route attention through queries and keys without changing the value-side evidence being retrieved. In a one-layer MDM, we prove that forward masked training strengthens evidence that is reusable in reverse queries, induces correlated forward--reverse attention routes, and yields a positively aligned shared-storage gradient component that decreases the reverse loss to first order. Controlled one-layer experiments and large-scale LLaDA/Dream experiments verify these signatures and show that they translate into improved reverse prediction.

Large language models (LLMs) have achieved strong performance on text-to-knowledge graph generation and related tasks. Nevertheless, it is still unclear whether they accurately model the direction-dependent semantics of inverse relations, in which reversing the order of the arguments alters the meaning of a relation (e.g., mother versus child). To the best of our knowledge, this work presents the first systematic study of inverse relation directionality in LLMs, using a benchmark consisting of 5,457 instances spanning 27 distinct inverse relation labels. We evaluate five open-source LLMs under a multiple-choice prompting framework and further examine the influence of relation descriptions and entity representations by substituting the original entities with synthetic and masked entities. Our findings reveal systematic asymmetries in inverse relation classification across LLMs, indicate that relation descriptions do not consistently improve performance, and show that model performance can be sensitive to variations in entity representations.

Splitting a bidirectional LSTM's contextual representation into a forward-only $F_i$ (strictly a function of tokens $1..i$) and a backward-only $B_i$ (strictly a function of tokens $i..n$) beats either alone and beats a fused self-attention representation for dependency relation-type classification. But a specific, natural extension of this idea -- pairing a token's forward state against a candidate's backward state (``cross-direction'' pairing, $F_i$ vs.\ $B_j$) -- consistently underperforms same-direction pairing, and the penalty grows, not shrinks, with token distance, both paired-bootstrap significant. We diagnose why using a frozen-trunk methodology: architectural information leakage between directions is impossible by construction (a single-layer BiLSTM, verified by code inspection); 93% of the same-vs-cross gap survives freezing the trunk and training only fresh heads, ruling out training-co-adaptation as the primary cause; linear regression shows partial representational redundancy between $F_i$ and $B_i$ ($R^2{=}0.324$ vs.\ $0.028$ for a shuffled control) and a linear probe shows partial anticipatory encoding of upcoming tokens in $F_i$ (36.5% vs.\ 17.2% majority baseline) -- real effects, but neither alone, nor combined, cleanly explains the full gap. Extended frozen-trunk diagnostics (a positional probe and a distance-decay probe) show directional information is genuinely stored but not exactly positioned, and propagates only a few tokens before decaying to baseline -- consistent with, and mechanistically underneath, the distance-growth finding.