Reply to comments arXiv:2512.07881 and arXiv:2601.06104 on quantum structure in human and AI-generated language
Massimiliano Sassoli de Bianchi, Roberto Leporini
cs.CL
Quick verdict
Conciliatory reply: concedes LLM protocol limits and BE-fit limits, defends 'entanglement as meaning' conceptually, but offers no quantitative re-analysis.
Summary
This paper is a point-by-point author reply to two critical comments (arXiv:2512.07881 and arXiv:2601.06104) and to one unpublished private manuscript by K. Sienicki, defending prior work on Bose-Einstein statistics in human language and on quantum structure in LLM-generated text. On experimental design, the authors concede that the LLM experiments were exploratory, lacking independent sessions, randomized presentation, explicit resets, and run-to-run variability assessment, and they reframe the reported CHSH violations as a first phenomenological comparison. On marginal laws, they argue that Contextuality-by-Default answers a narrower question and is not a universally decisive entanglement test, citing disputed marginal-law violations in physical Bell experiments. On word shuffling, they agree that a Bose-Einstein fit alone cannot diagnose meaning, quoting their earlier statement that it matters only alongside evidence of semantic adaptation. On energy ordering, they agree an independently motivated Hamiltonian is desirable, sketching production-cost and mean-field semantic contributions, yet assert that assigning lowest energies to the most frequent words is not mere rank convention. On vector spaces, they explicitly disclaim that LLM embeddings are automatically Hilbert spaces. They also correct a Table 3 transcription error (Cat Growls P(A′2,B1)=0.222; Cat Whinnies P(A′2,B2)=0), leaving E(A′,B)=0.556 and CHSH unchanged. No new data or quantitative re-analysis is offered.
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Assessment at a glance
4
risk flags identified
● high 0
● medium 2
● low 2
4 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- Marginal-law violations and failure of the Contextuality-by-Default criterion do not, by themselves, negate entanglement in human and AI language, which the authors ground in meaning-connections rather than in the idealized no-signaling scenario.
- The LLM conceptual-combination experiments are explicitly exploratory, and their CHSH violations constitute a first phenomenological comparison rather than a definitive characterization of LLM cognition.
- A Bose-Einstein frequency fit is only one statistical signature, significant only in combination with independent evidence of dynamic semantic adaptation — a limitation the authors say they had already stated.
- Assigning the lowest energy levels to the most frequent words is meaningful and not merely a rank convention, even though an independently motivated Hamiltonian (production cost plus a mean-field semantic term) remains future work.
- The internal real vector spaces of LLMs are not automatically quantum Hilbert spaces; quantum-inspired modeling of language is a methodological program whose precise relation to quantum state spaces stays open, and the Table 3 transcription error (0.222/0 swap) leaves E(A′,B)=0.556 and the CHSH value unchanged.
Strengths
Candor about limitations
The Experimental design section explicitly concedes the LLM protocol lacked independent sessions, randomized presentation orders, explicit reset conditions, and run-to-run variability assessment, reframing the CHSH results as 'a first phenomenological comparison rather than a definitive experimental characterization.'
Scope discipline on interpretations
The Word shuffling and Vector spaces sections draw precise boundaries: a Bose-Einstein fit is 'not, by itself, a sufficient condition for semantic organization,' and LLM internal vector spaces are 'not automatically Hilbert spaces' — both quotes disclaim stronger readings attributed by critics.
Grounding in physics practice
Checkable, precisely specified erratum
Weaknesses
No quantitative re-analysis of the core objection
Falsifiability gap
Energy claim asserted, not derived
LLM response independence left unquantified
Reliance on non-public and self-referential sources
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Scope & Claims
This is a 4-page author reply with no new experiments, responding to Sienicki & Sienicki (arXiv:2512.07881), which targeted the human-language Bose-Einstein analysis (arXiv:2407.14924; Aerts et al. 2025), and Sienicki (arXiv:2601.06104), which targeted the LLM quantum-structure study (arXiv:2511.21731; Aerts et al. 2026, Entropy 28(6):622). A third, unpublished manuscript (Sienicki, 2026b, privately circulated July 13, 2026) is also addressed. The reply has six sections: Experimental design, Marginal laws, Word shuffling, Energy ordering, Vector spaces, and an Erratum. The claims defended: (i) CHSH-violating correlations in conceptual-combination tests with two LLMs evidence entanglement understood as connection-of-meaning, even though the data are inconsistently connected; (ii) a Bose-Einstein rank-frequency fit is one component of a broader evidential case, not a stand-alone proof of meaning; (iii) the Table 3 error in arXiv:2511.21731 is a transcription slip — Cat Growls should carry P(A′2,B1)=0.222 and Cat Whinnies P(A′2,B2)=0 — leaving E(A′,B)=0.556 and the reported CHSH value unchanged.
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Frequently asked questions
What is this arXiv paper (2609.25797) about?
It is a short author reply by Sassoli de Bianchi and Leporini defending two earlier works — one arguing human word frequencies follow Bose-Einstein statistics (arXiv:2407.14924), another claiming quantum structure such as CHSH violations in LLM-generated text (arXiv:2511.21731) — against critical comments by M. and K. Sienicki (arXiv:2512.07881, 2601.06104). It contains no new experiments, only conceptual arguments and one small table correction.
Did the authors admit any errors in their quantum-language studies?
Partially. They concede the LLM experiments were exploratory, without independent sessions, randomized presentation, explicit resets, or run-to-run variability checks, and they correct a transcription error in Table 3 of arXiv:2511.21731: Cat Growls should carry probability P(A′2,B1)=0.222 and Cat Whinnies P(A′2,B2)=0. They state this does not change the expectation value E(A′,B)=0.556 or the reported CHSH value, and they maintain their entanglement interpretation of the data.
Why do the authors still claim entanglement if the Contextuality-by-Default criterion fails?
They argue the CbD criterion only tests whether contextuality remains after removing direct contextual influences, whereas they define entanglement more broadly as a connection of meaning between concepts, actualized through coincidence measurements. They cite disputed marginal-law violations in physical Bell experiments to argue idealized criteria should not be treated as universally decisive. The reply proposes no alternative quantitative test, which critics would view as a definitional retreat.
Do the authors claim LLM embeddings are Hilbert spaces?
No. The reply explicitly disclaims this: the real vector spaces used internally by LLMs are not automatically Hilbert spaces of quantum theory. Their claim is only that the probabilistic and semantic behavior of language can be modeled with quantum-inspired structures on vector spaces, as in quantum information retrieval and quantum cognition, and that the precise relation to quantum state spaces remains an open problem.
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.
- The two criticized comments (arXiv:2512.07881, 2601.06104) and the original papers were not available; assessments of the dispute rest on the reply's own characterization of the criticisms.
- Table 3 of Aerts et al. (2026) is not reproduced here, so the erratum's internal consistency (E(A′,B)=0.556 unchanged) could not be verified numerically.
- The unpublished manuscript Sienicki (2026b) is cited but unavailable, so those specific objections are known only secondhand.
- Supplementary figures or tables of the original studies, if any, are outside the extracted text.
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