Abstract
The reversal curse describes a failure of autoregressive language models to retrieve a fact in reverse order (e.g., training on ``A > B'' but failing on ``B < A''). Recent work shows that objectives with bidirectional supervision (e.g., bidirectional attention or masking-based reconstruction for decoder-only models) can mitigate the reversal curse. We extend this evaluation to include a vanilla masked language modeling (MLM) objective and compare it to decoder-only masking-based training across four reversal benchmarks and then provide a minimal mechanistic study of \emph{how} these objectives succeed. We show that reversal accuracy requires training signal that explicitly makes the source entity a prediction target, and we find little evidence that success corresponds to a single direction-agnostic representation of a fact. Instead, representation distances and linear probes are consistent with storing forward and reverse directions as distinct entries, with different indexing geometry for MLM versus decoder-only masking-based training. Our results caution that objective-level ``fixes'' can improve reversal behavior without necessarily inducing the kind of latent generalization one might expect from a unified concept.
