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Language Models are Injective and Hence Invertible

Giorgos Nikolaou, Tommaso Mencattini, Donato Crisostomi, Andrea Santilli, Yannis Panagakis, Emanuele Rodolà · Oct 17, 2025 · Citations: 0

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Mar 13, 2026, 3:58 PM

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Mar 13, 2026, 3:58 PM

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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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Human Feedback Signal

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Field Provenance & Confidence

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Evidence snippet: 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.

Evaluation Modes

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Evidence snippet: 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.

Quality Controls

provisional

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Evidence snippet: 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.

Benchmarks / Datasets

provisional

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Evidence snippet: 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.

Reported Metrics

provisional

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Confidence: Provisional Source: Persisted extraction inferred

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Evidence snippet: 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.

Rater Population

provisional

Unknown

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Rater source not explicitly reported.

Evidence snippet: 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.

Human Data Lens

Structured extraction is still processing. Below are provisional signals inferred from abstract text only.

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  • Abstract highlights: 3 key sentence(s) extracted below.

Evaluation Lens

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Research Brief

Deterministic synthesis

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.

Generated Mar 13, 2026, 3:58 PM · Grounded in abstract + metadata only

Key Takeaways

  • 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.
  • 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.

Researcher Actions

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Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

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