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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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Provisional trust

This page is a lightweight research summary built from the abstract and metadata while deeper extraction catches up.

Best use

Background context only

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Evidence quality

Provisional

Derived from abstract and metadata only.

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.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

  • This page is still relying on abstract and metadata signals, not a fuller protocol read.
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Should You Rely On This Paper?

Signal extraction is still processing. This page currently shows metadata-first guidance until structured protocol fields are ready.

Best use

Background context only

Use if you need

A provisional background reference while structured extraction finishes.

Main weakness

This page is still relying on abstract and metadata signals, not a fuller protocol read.

Trust level

Provisional

Usefulness score

Unavailable

Eval-fit score is unavailable until extraction completes.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

Usefulness for eval research

Provisional (processing)

Extraction confidence 0%

If you are doing eval pipeline work, start here:

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What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

provisional (inferred)

None explicit

No explicit feedback protocol extracted.

"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

provisional (inferred)

None explicit

Validate eval design from full paper text.

"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 (inferred)

Not reported

No explicit QC controls found.

"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 (inferred)

Not extracted

No benchmark anchors detected.

"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 (inferred)

Not extracted

No metric anchors detected.

"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 (inferred)

Unknown

Rater source not explicitly reported.

"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 Feedback Details

This page is using abstract-level cues only right now. Treat the signals below as provisional.

  • Potential human-data signal: No explicit human-data keywords detected.
  • Potential benchmark anchors: No benchmark names detected in abstract.
  • Abstract highlights: 3 key sentence(s) extracted below.

Evaluation Details

Evaluation fields are inferred from the abstract only.

  • Potential evaluation modes: No explicit eval keywords detected.
  • Potential metric signals: No metric keywords detected.
  • Confidence: Provisional (metadata-only fallback).

Research Brief

Metadata summary

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.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

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

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

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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