GPT, But Backwards: Exactly Inverting Language Model Outputs

arXiv:2507.01693v3 Announce Type: replace-cross Abstract: Recent work shows that distinct inputs produce distinct hidden representations in LLMs, so the input can in principle be recovered from them. Yet, no existing method can reliably do so from the model's output text or logits alone. We introduce Sparse One-hot Discrete Adam (SODA), a white-box search-based algorithm that reconstructs textual inputs from partial knowledge of the output. Given output logits, SODA recovers natural sequences of up to 17 tokens with zero false positives and achieves a 4x improvement in exact-match reconstructi

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