Source
Lo, Sadrzadeh & Mansfield (2024), “Quantum-Like Contextuality in Large Language Models”, arXiv 2412.16806v1, LIT-844, read in full in NOTE-648. Wang, Sadrzadeh, Abramsky & Cervantes (2021), “On the Quantum-like Contextuality of Ambiguous Phrases”, LIT-842, read in full in NOTE-645, with its journal follow-up for comparison.
What was actually shown
Ambiguous phrases (LIT-842). Each ambiguous word is a measurement, its selected meaning the outcome, a two-word phrase a context.
- Hand-set supports (§5.2). {tap, box} × {pitcher, cabinet} is possibilistically non-signalling and contextual, of Hardy type: two global assignments exist, but the locally possible (tap = touch, pitcher = baseball player) extends to neither.
- Corpus estimates (§6). Every model is signalling, e.g. P(box = put in boxes) is 2/3 in “box leaves” and 7/74 in “box can”. The sheaf criterion cannot be applied to any.
- Contextuality-by-Default (§8.1). Two noun–verb pairs read in both grammatical orders, adopt/boxer and throw/pitcher, come out contextual, with measures 1/30 and 7/30 (recomputed in NOTE-645). The paper’s own parametric bootstrap puts the probability that each is noncontextual above .56 and above .08. The counts have denominators of 3 to 30.
Anaphora in BERT (LIT-844). A three-sentence schema (“the same one”, “the other one”) gives every instance the support of the PR prism, which no global assignment fits. Only one marginal per context comes from BERT; the joints are stipulated. With SF the signalling fraction and Δ the CbD direct influence, an instance is sheaf-contextual iff SF < 1/6 and CbD-contextual iff Δ < 2 (CNT1 = 2 − Δ, NOTE-648’s check). Of 51,966,480 instances, 0.148% are sheaf-contextual and 71.1% CbD-contextual. If the three probabilities are equal at p, Δ = 2|2p − 1|, below 2 for every p strictly between 0 and 1. The tie to embedding distance is the softmax identity ε = tanh((p·Δx + Δb)/2), with correlations of 0.06 to 0.20.
What could have come out otherwise: the corpus models could have been non-signalling, and the CbD verdicts could have survived the bootstrap. Neither happened.
What this does not say
- That language is not contextual. No study here uses human judgements with adequate counts. The proposed tests (Wang and Sadrzadeh’s 2023 human-judgement data; Lo et al.’s crowdsourced Winograd schemas) are not held.
- That BERT is contextual in any sense about BERT. The parity contradiction is in the sentences. Any uncertain resolver yields formally contextual data on this schema.
- That the two signalling-aware criteria agree. On the same data they give 0.148% and 71.1%, and whether the sheaf test of Vallée et al. is necessary as well as sufficient is not settled, so 0.148% may be a lower bound.
- That ambiguity is contextuality. press/box has several readings and global assignments for all of them; ambiguity is the outcome set, not the obstruction.
Connections
- THEORY-013 holds that behavioural, social and word-meaning data
published as contextual show none once signalling is separated. These
two studies are its first language cases. Neither meets its
promote_whenas a robust counterexample. - CLAIM-037 (formal contextuality needs Contextuality-by-Default when marginals shift) is supported: every corpus model and every BERT instance not at P = ½ signals. CLAIM-044 holds here only for strong contextuality: the Hardy-type tap/box model keeps two global assignments. CLAIM-009 is not tested: these are lexical selections and a model’s resolutions, not people’s pragmatic judgements.
- The journal follow-up (LIT-851, THEORY-177) measures direct influence across 90 noun–verb systems and reports no new contextual system.