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Center for Nonlinear Studies |
Large language models should theoretically produce identical perplexities regardless of token ordering (forward, backward, or permuted), yet empirical evidence reveals systematic deviations. We formally prove perplexity invariance under any factorization and demonstrate that models trained on different token orders exhibit consistent violations of this theoretical expectation. These inconsistencies, traceable to positional biases in self-attention mechanisms, suggest fundamental gaps between theoretical foundations and practical implementations. Our findings suggest that probability consistency violations could serve as diagnostic metrics for identifying unreliable model behaviors, offering a principled approach to evaluating model trustworthiness in scientific applications. I'll end by considering how LLMs trained on forward and backward temporal orders can be used to reason about physical systems using test-time compute.
Host: Harsha Nagarajan, Michael McCann, William Taitano, and Svetlana Tokareva