Recognition: 2 theorem links
· Lean TheoremCan You Keep a Secret? Involuntary Information Leakage in Language Model Writing
Pith reviewed 2026-05-12 03:59 UTC · model grok-4.3
The pith
Frontier language models leak prompted secrets thematically in their writing even when told not to reveal them.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
When given a secret word and told to write a story without revealing it, language models produce text from which a separate model can recover the secret at rates significantly above chance through thematic choices rather than literal mention. Instructing the model to hide the secret causes it to write away from the secret, and this avoidance pattern itself becomes a detectable signal. The leakage transfers across model families, increases sharply with scale, and is absent in short-form tasks.
What carries the argument
Thematic leakage channel: attending to a secret word influences topic, imagery, and setting in generated stories even under explicit non-disclosure instructions, allowing cross-model recovery without literal mention.
If this is right
- Models leak information about hidden prompts through thematic choices in long-form writing such as stories.
- Actively instructing a model to hide a secret produces a detectable avoidance pattern in its output.
- The leakage is readable by other models and increases with model size within tested families.
- No detectable leakage occurs in short-form tasks like joke writing.
- Providing a decoy concept partially shifts the leakage toward the decoy instead of the original secret.
Where Pith is reading between the lines
- Compartmentalization of system prompts or chain-of-thought may require changes beyond simple instructions.
- The same channel could affect other hidden information such as internal reasoning steps.
- Decoy strategies might be refined to reduce leakage further, but they do not eliminate it.
Load-bearing premise
That above-chance guessing by the second model indicates leakage of the specific secret rather than general stylistic or content biases that would appear even without any secret prompt.
What would settle it
Running the same story-writing task with no secret word given to the first model and checking whether the second model still discriminates above chance, or testing with secret words that have no thematic overlap with typical story elements.
Figures
read the original abstract
Language models are deployed in settings that require compartmentalization: system prompts should not be disclosed, chain-of-thought reasoning is hidden from users, and sensitive data passes through shared contexts. We test whether models can keep prompted information out of their writing. We give each model a secret word with instructions not to reveal it, then ask it to write a story. A second model tries to identify the secret from the story in a binary discrimination test. The secret word never appears literally in any output, but all five frontier models we test leak it thematically -- through topic choice, imagery, and setting--6hy-at rates significantly different from chance, up to 79\%. When told to actively hide the secret, models write \emph{away from} it, and this avoidance is itself detectable. The leakage is cross-model readable, scales sharply with model size within two model families, and disappears entirely for short-form writing like jokes. Giving the model a decoy concept to ``focus on instead'' partially redirects the leakage from the real secret to the decoy. Attending to a secret appears to open up an information channel that frontier LLMs cannot close, even when instructed to.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that language models leak secret information thematically into their generated stories even when explicitly instructed not to reveal it. Through experiments with five frontier models, a second model can discriminate the secret word from the story output at rates significantly above chance (up to 79%), via topic, imagery, and setting. The leakage scales with model size, is cross-model, can be partially redirected with decoys, and is detectable even when models try to avoid the secret. It does not occur in short-form writing.
Significance. If the central empirical result holds after controlling for potential confounds in story generation, it would highlight a fundamental limitation in LLMs' ability to compartmentalize information, with implications for AI security and prompt engineering in sensitive applications. The scaling trend and cross-model consistency are notable strengths of the experimental design.
major comments (2)
- [Experimental Design] The experimental setup lacks a no-secret baseline condition in which stories are generated under neutral instructions (without any secret prompt) and then subjected to the same binary discrimination procedure using the same word pairs. This control is necessary to rule out that discrimination success arises from stable stylistic or thematic generation biases correlated with the secret-word distribution rather than specific leakage opened by attending to the secret.
- [Results] The results report consistent above-chance discrimination and a scaling trend across five models, but the manuscript provides no details on the exact prompt wordings, the sampling distribution of secret words, the statistical tests establishing significance, or additional controls for topic/imagery biases independent of the secret. These omissions make it difficult to assess whether the discrimination test isolates the claimed information channel.
minor comments (2)
- [Abstract] The abstract contains an apparent typographical error ('setting--6hy-at rates' should read 'setting at rates').
- [Abstract] The claim that leakage 'disappears entirely for short-form writing like jokes' would be strengthened by explicit comparison of prompt templates and output lengths between the story and joke conditions.
Simulated Author's Rebuttal
We thank the referee for their constructive review and for identifying key areas where additional controls and methodological transparency would strengthen the work. We have revised the manuscript to incorporate a no-secret baseline condition and to provide the requested details on prompts, word sampling, statistics, and bias controls.
read point-by-point responses
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Referee: [Experimental Design] The experimental setup lacks a no-secret baseline condition in which stories are generated under neutral instructions (without any secret prompt) and then subjected to the same binary discrimination procedure using the same word pairs. This control is necessary to rule out that discrimination success arises from stable stylistic or thematic generation biases correlated with the secret-word distribution rather than specific leakage opened by attending to the secret.
Authors: We agree that this baseline is important for isolating the effect of the secret prompt from any pre-existing generation biases tied to the word-pair distribution. In the revised manuscript we have added the requested no-secret condition: stories were generated from neutral prompts containing no secret word, then evaluated with the identical binary discrimination procedure and word pairs. Discrimination accuracy fell to chance levels under this baseline, supporting that the above-chance performance in the main experiments arises from attending to the secret rather than stable stylistic biases. These results are reported in a new subsection of the Results and in an updated Figure 2. revision: yes
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Referee: [Results] The results report consistent above-chance discrimination and a scaling trend across five models, but the manuscript provides no details on the exact prompt wordings, the sampling distribution of secret words, the statistical tests establishing significance, or additional controls for topic/imagery biases independent of the secret. These omissions make it difficult to assess whether the discrimination test isolates the claimed information channel.
Authors: We acknowledge these reporting gaps. The revised manuscript now includes: (1) the exact prompt templates for both story generation and the binary discrimination task (new Appendix A); (2) the sampling procedure for secret words (100 nouns drawn uniformly from a balanced list of common English nouns, stratified by semantic category); (3) the statistical tests (two-sided binomial tests against 50% chance, with Holm-Bonferroni correction for multiple comparisons across models and conditions); and (4) additional controls consisting of shuffled word-pair assignments and unrelated decoy concepts to isolate thematic leakage from general topic preferences. These elements are presented in the Methods section and a new Appendix B. revision: yes
Circularity Check
No circularity: purely empirical experimental results
full rationale
The paper describes a series of LLM prompting experiments (secret word + story generation, followed by binary discrimination by a second model) with no equations, derivations, fitted parameters, or self-referential definitions. All claims rest on direct empirical measurements of output distributions and discrimination accuracy; the discrimination test is independent of the generation process and does not reduce to any input by construction. No load-bearing self-citations or uniqueness theorems appear in the provided text.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption The second model can accurately detect thematic leakage without other biases.
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
Attending to a secret appears to open up an information channel that frontier LLMs cannot close, even when instructed to.
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IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
finite entropy budget—the unpredictability a model can express in its outputs
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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