@cite{schlotterbeck-wang-2023} — Incremental RSA for Adjective Ordering (sanity-check slice) #

@cite{cohn-gordon-goodman-potts-2019} @cite{degen-etal-2020} @cite{waldon-degen-2021}

Schlotterbeck, F. & Wang, H. (2023). An incremental RSA model for adjective ordering preferences in referential visual context. Proceedings of the Society for Computation in Linguistics (SCiL) 6, 121–132.

SCOPE WARNING. This file formalizes the symmetric-PoE sanity-check slice of S&W 2023, not their main asymmetric model. The paper documents (page 6) that with symmetric per-class continuous semantics the incremental listener's order-independence holds as a sanity check; their predictive results come from the asymmetric semantics + sequence speaker that this file does not formalize.

What this file does formalize: the order-independence headline at the listener level, plus discrimination-driven ordering preferences at the speaker level using linglib's trajectoryProb (chain-rule product of per-step normalized softmaxes). Note that linglib's trajectoryProb is not literally S&W's S1^inc (which accumulates utilities with a single global normalization rather than per-step softmaxes); see Composition.trajectoryProb_eq_compose_chain for the deferred A≡C equivalence statement.

What this file does not formalize:

Asymmetric per-class semantics (k%-threshold for size dimensions à la Schmidt et al. 2009 / Cremers 2022 / Franke et al. 2019, vs binomial-ε for color à la @cite{degen-etal-2020})
The language model P_Lang constraining S1's per-step vocabulary to grammatical continuations
The utterance-prior bias b for size-first defaults

The model (formalized slice) #

The incremental sequence speaker S1^inc produces adjective–noun sequences word-by-word. With β = 1, no cost, and uniform language prior, the trajectory score reduces to a per-prefix product of literal-listener posteriors:

S1^inc(w₁,...,wₙ | r) ∝ ∏ₖ L0(r | w₁,...,wₖ)

The L0 meaning is the Product-of-Experts noisy semantics (@cite{degen-etal-2020}): each word contributes an independent ℚ-valued factor lex(w, r), and the prefix meaning is their product. With strictly positive lex, the product commutes (RSA.prefixMeaning_perm), so the full-sequence L0 posterior is order-independent.

Substrate use #

This file plugs RSA.NoisyLex (Theories/Pragmatics/RSA/Noisy.lean) into RSAConfig's sequential machinery. Each scene becomes a NoisyLex value plus a scene predicate; NoisyLex.toRSAConfigSeq produces the incremental RSAConfig. The PoE prefix-product order-independence lemmas live in RSA.Sequential and are inherited (no per-study reproof).

Variable-name note (α vs β) #

S&W's α is the utterance-level speaker softmax temperature (Table 1 row 6, varied 5/1/1 across Fig. 3a–c); their β is the utility/word-level speaker temperature (Table 1 row 7, set to 1 in all reported simulations). This file's RSAConfig.α field corresponds to S&W's β = 1. The α-field-name in the substrate predates S&W and is not renamed here.

Findings #

#	Finding	Theorem
1	Prefix meaning is order-independent	`prefix_meaning_swap`
2	Size-discriminatory scene → size-first preferred	`size_first_when_size_discriminates`
3	Equal discrimination + reliable color → color-first	`color_first_when_color_reliable`
4	Both orderings identify the target (Scene A)	`both_orderings_identify_target_A`
5	Both orderings identify the target (Scene B)	`both_orderings_identify_target_B`