Language Models are Injective and Hence Invertible

• URL: http://arxiv.org/abs/2510.15511v3
• Date: Tue, 21 Oct 2025 14:44:49 GMT
• Title: Language Models are Injective and Hence Invertible
• Authors: Giorgos Nikolaou, Tommaso Mencattini, Donato Crisostomi, Andrea Santilli, Yannis Panagakis, Emanuele Rodolà,
• Abstract summary: Transformer components such as non-linear activations and normalization are inherently non-injective.<n>We prove mathematically that transformer language models mapping discrete input sequences to their corresponding sequence of continuous representations are injective.<n>We introduce SipIt, the first algorithm that provably and efficiently reconstructs the exact input text from hidden activations.
• Score: 26.862644074381844
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model's representations. In this paper, we challenge this view. First, we prove mathematically that transformer language models mapping discrete input sequences to their corresponding sequence of continuous representations are injective and therefore lossless, a property established at initialization and preserved during training. Second, we confirm this result empirically through billions of collision tests on six state-of-the-art language models, and observe no collisions. Third, we operationalize injectivity: we introduce SipIt, the first algorithm that provably and efficiently reconstructs the exact input text from hidden activations, establishing linear-time guarantees and demonstrating exact invertibility in practice. Overall, our work establishes injectivity as a fundamental and exploitable property of language models, with direct implications for transparency, interpretability, and safe deployment.

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