Embedded Conditional Independence Tests for Large Language Model Generated Text with an Application to German Parliament Speeches
Marco Simnacher, Georg Keilbar, Benjamin König, Christoph Lippert, Sonja Greven
stat.ML · cs.AI · cs.LG · math.ST · stat.ME
Quick verdict
eCITs embed text for CI tests of LLM bias; theory is careful, but unverifiable embedding sufficiency, non-iid data and no code temper the claims.
Summary
This method paper introduces embedded conditional independence tests (eCITs) for a question standard CITs cannot handle: does an LLM output X carry information about an attribute Y beyond the source text Z it was generated from? X and Z are mapped to feature representations, and an existing test — the projected covariance measure, extended here to categorical outcomes with a precision-weighted projection direction — is applied to the representations. The authors prove that when the embedding of Z is sufficient, meaning it retains what Z carries about Y or about the representation of X, the null hypothesis transfers between text and representation levels; they also characterize when the two hypotheses are equivalent and show that sufficiency weakens to mean sufficiency for conditional-mean-independence tests. A semi-synthetic design resampling German Parliament speech–summary pairs assesses type I error and power for concrete embedding stacks before application. On speeches summarized by Gemma 4 and Qwen 3.6, all sixteen test settings reject at α=0.05 (T between 3.5 and 51.3): summaries contain information about speaker faction (seven classes, n≈53,978) and gender (n≈50,839) beyond the speech. Key limitations: embedding sufficiency is unverifiable, the i.i.d. assumption is violated through speaker recurrence, nuisance regression conditions are asserted but not verified, embedder training-corpus overlap with LLM data cannot be excluded, and no code release is stated.
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Assessment at a glance
5
risk flags identified
● high 0
● medium 3
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- If the embedding of the conditioning text Z is (mean-)sufficient, a CIT valid at the representation level is valid for the hypothesis stated on the texts (Theorems 3/5/14, Corollaries 7/15).
- For categorical Y under i.i.d. laws, testing conditional mean independence with the adapted PCM is equivalent to testing full conditional independence (Remark 16), and the precision-weighted projection direction is optimal (Proposition 22).
- The semi-synthetic design detects both regimes on the actual dataset: sufficient embedding arms stay calibrated while insufficient arms show type I error inflation growing with n (e.g., 6%->48%->86% for one Qwen-DGM arm at n=1,000/5,000/10,000).
- Summaries of both Gemma 4 and Qwen 3.6 contain information about the speaker's faction and gender beyond the source speech: all sixteen application settings reject at α=0.05 (Table 1, T from 3.513 to 51.317).
- Defining LLM bias as conditional dependence of the output on a protected attribute given the source text yields a reference-free bias criterion with type I error guarantees, a conditional version of Gentzkow et al. (2019) partisanship measurement.
Strengths
Rigorous null-transfer theory beyond prior work
Because Z itself is embedded, the marginal-law argument of Simnacher et al. (2026) breaks (Remark 6); the authors instead use an almost-sure conditional formulation and disintegration lemmas (Lemmas 17-20) that tolerate non-product null classes under in-sample estimated parameters, with Theorems 3/5 (CI) and 12/14 (mean) plus equivalence conditions (Theorem 9, Corollary 10).
Disciplined treatment of alternative explanations
Section 4.3 probes four rival explanations via designed Table 1 settings: adding learned pred-hidden representations (setting 2) sharply reduces T, exposing insufficiency of the pretrained-only conditioning set; holding X=pred-hidden and swapping Z-embedders (settings 3-4) barely moves T, arguing against residual insufficiency dominating.
Reusable pre-application diagnostic with both regimes exhibited
Categorical PCM extension properly derived
Reference-free bias definition with guarantees
Weaknesses
Calibration evidence does not cover the application regime
i.i.d. violated by construction, unquantified
Validity conditions of the categorical PCM asserted, not verified
Embedder-LLM training overlap cannot be excluded
No code/data release; coarse simulation replication count
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Scope & Claims
The paper targets a concrete gap: conditional independence tests (CITs) cannot run on raw text, yet the authors want to test H0: Y independent of X given Z, where X is an LLM summary and Z its source speech - defining LLM bias as information about a protected attribute Y beyond the source. Claimed contributions: (i) CI testing justified as a reference-free bias criterion (Section 2, with Example 1 showing in-sample kNN memorization, k=2,5,10, produces detectable conditional dependence while out-of-sample predictions stay null-calibrated); (ii) embedded CITs (eCITs) embedding both X and Z; (iii) a sufficiency characterization for the embedding of Z under which the textual null transfers to the embedded null (Theorems 3/5), with equivalence conditions (Theorem 9, Corollary 10) and weakening to mean sufficiency for conditional-mean-independence tests (Theorems 12/14, Corollary 15); (iv) a categorical adaptation of the PCM (Appendix D); (v) a semi-synthetic pre-application diagnostic and the real-data finding that Gemma 4 and Qwen 3.6 summaries carry faction (L=7) and gender information beyond the speech.
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
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Frequently asked questions
What did this paper find about LLM bias in German Parliament speeches?
It tested whether LLM-generated summaries of Bundestag speeches reveal the speaker's faction or gender beyond what the speech itself contains. For summaries by Gemma 4 and Qwen 3.6, all 16 test settings rejected the null of conditional independence at α=0.05 (test statistics T from 3.5 to 51.3), meaning the summaries carry extra attribute information - consistent with memorization of training data, though the test cannot prove that mechanism.
What is an embedded conditional independence test (eCIT)?
A procedure that embeds two text variables (an LLM output X and its source text Z) into feature vectors and applies a standard conditional independence test to the representations and the attribute Y. Theory shows the textual null hypothesis transfers to the embedded one when the embedding of Z is sufficient - i.e., keeps everything Z carries about Y or about the representation of X; otherwise type I error can inflate with sample size.
Does the test guarantee its type I error in the application?
Only conditionally: under (mean-)sufficiency of the Z-embedding, embedding parameters estimated independently of the test sample, i.i.d. observations, and verified nuisance conditions. The paper's own simulations show sufficient arms stay calibrated while insufficient arms inflate (up to 86% at n=10,000), and the i.i.d. assumption is violated in the parliament application (speakers recur), so the guarantees are partial.
Is code available for this paper?
The paper text contains no code or data availability statement. The underlying corpus (Open Discourse) and the models are public and named, but no repository, summaries or embeddings are released.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figures 1-6 are available only as caption/prose descriptions; arm-level rejection-rate values beyond those quoted in the text cannot be checked from the extraction.
- The running header 'CI Testing for LLMs' interleaves with body text at page breaks; no content loss observed, and the full abstract appears in the body despite the truncated metadata abstract.
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