@cite{schlotterbeck-wang-2023} — Incremental RSA for Adjective Ordering #

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

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.

The Model #

The incremental sequence speaker (S1^inc) produces adjective–noun sequences word-by-word. At each step the utility is the incremental listener's posterior. The trajectory score accumulates utility across all prefixes:

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

where U(w⃗; r) = exp(β · log L0^inc(r | w⃗)) and the paper sets β = 1 in all reported simulations. With β = 1, no cost, and uniform language prior, this simplifies to:

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

The model uses continuous/noisy semantics (@cite{degen-etal-2020}) where each word applies with reliability v (correct application) or 1 − v (noise).

Key insight: With strictly positive noisy semantics, the prefix meaning is a product of per-word terms, and multiplication commutes. Therefore the full-sequence L0 posterior is order-independent: L0(r | w₁, w₂) = L0(r | w₂, w₁). In the paper's batch-normalized model, where S1^inc scores are normalized once over all trajectories, the ordering preference ratio S1^inc(adj₁,adj₂,n|r) / S1^inc(adj₂,adj₁,n|r) reduces entirely to the first-word L0 posterior ratio L0(r|adj₁) / L0(r|adj₂).

Formalization #

This uses RSAConfig's sequential infrastructure (following @cite{cohn-gordon-goodman-potts-2019} and @cite{waldon-degen-2021}):

Ctx = List Word — the prefix produced so far
transition ctx w = ctx ++ [w] — append the next word
initial = [] — start with empty prefix
meaning uses continuous/noisy semantics (lexContinuousQ) with scene-dependent reliability parameters

Predictions use trajectoryProb for ordering preferences and S1_at for first-word informativity, proved via rsa_predict.

Findings #

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

Connections #

Noise theory: lexContinuousQ instantiates the unified noise channel from RSA.Core.Noise. See lexContinuous_as_noiseChannel.
PoE structure: prefix_meaning_product shows two-word prefix meaning decomposes as a product of per-word semantics, matching @cite{degen-etal-2020}'s Product of Experts.
Incremental RSA: Extends @cite{cohn-gordon-goodman-potts-2019} with scene-parameterized continuous semantics.
Psychophysics: The paper's size perception noise is parameterized by Weber fractions — the just-noticeable size difference is proportional to absolute size (@cite{luce-1959}). Core.Agent.PsychophysicalChoice derives Weber-like intensity ratios from Stevens power law + JND thresholds (stevens_jndL_intensity_ratio). A deeper integration could derive the sRel reliability parameter from a StevensScale exponent rather than stipulating it, grounding the noise in the psychophysical theory layer.

Simplifications #

The paper's full model includes components not formalized here:

Gaussian+binomial perception: The paper models size via Gaussian distributions with Weber fractions and color via binomial noise ε (@cite{degen-etal-2020}). Core.Agent.Psychophysics formalizes the Stevens power law and multidimensional decomposition that underlie Weber's law; a future integration could derive size reliability from this framework. We currently use a simpler noise model with flat reliability parameters sRel and cRel.
Language model P_Lang: The paper constrains the S1 vocabulary at each step to grammatically valid continuations (noun vs adjective). Our S1 distributes over all 6 words at each step. This does not affect the qualitative ordering predictions.
S1^{inc_utt} vs S1^inc: The paper defines both a word-level speaker (S1^inc, used for data fitting with β = 1) and an utterance-level speaker (S1^{inc_utt}). We formalize S1^inc.
Bias parameter b: The paper includes a prior bias b for size-first ordering (to account for language-specific defaults). We omit this.

The specific reliability values (sRel, cRel) are chosen to demonstrate the qualitative predictions — they are not taken from the paper's fitted values.