Language Models are Injective and Hence Invertible
This establishes injectivity as a fundamental property of language models, enabling exact input recovery for improved transparency and safe deployment, representing a novel theoretical and practical advancement.
The paper proves that transformer language models are injective, meaning different inputs map to different representations, and introduces SipIt, an algorithm that reconstructs exact input text from hidden activations with linear-time guarantees, validated through billions of collision tests on six models with no collisions observed.
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.