IC-135Linear relational embeddings for factual relations form in OLMo-7B, OLMo-1B, and GPT-J when subject-object co-occurrence frequency exceeds model-specific thresholds, with r=0.82 correlation between log co-occurrence and causality across all pretraining stages
Jack Merullo, Noah A. Smith, Sarah Wiegreffe, Yanai Elazar
The paper measures the quality of linear relational embeddings (LREs) for 25 factual relations across 8 intermediate OLMo checkpoints and the final GPT-J checkpoint. It finds that the causality score of an LRE strongly correlates with the log subject-object co-occurrence frequency in the pretraining corpus (r=0.82), and that once a relation's average co-occurrence exceeds a threshold (1,097 for GPT-J, 1,998 for OLMo-7B, 4,447 for OLMo-1B), the LRE achieves near-perfect causality (>0.9) regardless of how early in training that threshold was crossed. The correlation with co-occurrence (0.82) is higher than with subject frequency alone (0.66) or object frequency alone (0.59), and higher than with 5-shot accuracy (0.74 in OLMo-7B).
Evidence
correlational
Key metric
r=0.82 (log subj-obj co-occurrence vs causality); thresholds for mean causality >0.9: GPT-J 1,097, OLMo-7B 1,998, OLMo-1B 4,447; r=0.66 (subject freq), r=0.59 (object freq); causality vs 5-shot accuracy r=0.74 in OLMo-7B; star-constellation-name: 84% accuracy but 44% causality in OLMo-7B
Caveat
Only three models are tested, so the authors caution that scale effects on the threshold cannot be firmly established. The co-occurrence count is a proxy for relation mention frequency, not an exact count of the full triplet. The finding is correlational; the authors explicitly state they cannot draw causal claims about how exposure affects individual representations.