Connection between geometric memory and the reversal curse

Identify and formalize the relationship between the emergence of geometric memory in in-weights graph tasks and the reversal curse phenomenon in next-token-trained Transformers, including the conditions under which reverse-edge augmentation affects each and whether shared mechanisms underlie both behaviors.

Background

The authors observe that reverse-edge augmentation is important for eliciting implicit reasoning on large path-star graphs and conjecture a connection to the reversal curse, where models fail to recall inverse associations without explicit augmentation.

Understanding whether the same underlying representational or optimization dynamics govern both phenomena could inform mitigation strategies and shed light on how symmetry/asymmetry is encoded in parametric memory.