[GRFM26] #
Search Efficiency Drives Reference Production Across Modalities, But Colour Is Special. Open Mind: Discoveries in Cognitive Science 10, 236–260.
Core Argument #
Overinformativeness is communicatively efficient: speakers use redundant modifiers to help listeners search for the referent. The rate of overinformativeness tracks the search efficiency gained by adding the modifier — the interaction of discriminability (ease of perceptual search along the redundant attribute) and sufficiency (difficulty of search using the sufficient attribute alone).
Experiments #
Exp 1 (N = 72, bat factory director task): Manipulates discriminability (high vs low via psychophysical staircases) and sufficiency (which attribute identifies the target) across two modalities — visual colour and auditory material. Results: overinformativeness tracks the discriminability × sufficiency interaction in both modalities, but colour is overinformed more than material even with equalized discriminability.
Exp 2 (N = 97, shape array director task): Compares redundant colour (high-frequency and low-frequency terms) vs redundant orientation, controlling for discriminability, salience (contextual distinctiveness), production effort (button-click), and word frequency. Result: colour is overinformed significantly more than orientation, ruling out salience, frequency, and effort as explanations.
Key Findings #
| # | Finding | Evidence | β | 95% CI |
|---|---|---|---|---|
| 1 | Search efficiency: S-Low/R-High > S-High/R-Low | Exp 1 | −1.09 | [−1.35, −0.83] |
| 2 | Search efficiency: S-Low/R-High > Baseline | Exp 1 | −0.94 | [−1.20, −0.68] |
| 3 | Colour > material (cross-modal) | Exp 1 | −1.43 | [−1.65, −1.20] |
| 4 | Colour HF > orientation | Exp 2 | −0.97 | [−1.20, −0.75] |
| 5 | Colour LF ≈ Colour HF (frequency doesn't explain) | Exp 2 | −0.20 | [−0.44, 0.03] |
Theoretical Implications #
The noise discrimination model (RSA.Noise) correctly predicts
Finding 1–2 (discriminability drives overinformativeness) and
Finding 3 (colour > material from gap ordering). But it incorrectly
predicts that colour and orientation should be overinformed equally
(since both have discrimination ≈ 0.98). Finding 4 falsifies this:
colour has a residual privilege beyond discriminability.
Verified Data #
Regression coefficients verified against Tables 1 and 2 of the paper.
The experimental conditions of Exp 1, defined by the sufficiency × discriminability interaction: which attribute identifies the target (sufficient vs. redundant) crossed with how easy each attribute is to search (high vs. low discriminability, set via psychophysical staircases).
- sHighRLow : DisplayType
Sufficient attribute: high discriminability, Redundant attribute: low discriminability.
- sLowRHigh : DisplayType
Sufficient attribute: low discriminability, Redundant attribute: high discriminability.
- baseline : DisplayType
Both attributes: high discriminability.
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- GilesEtAl2026.instReprDisplayType = { reprPrec := GilesEtAl2026.instReprDisplayType.repr }
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- GilesEtAl2026.instDecidableEqDisplayType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
The search efficiency view's prediction: overinformativeness is high exactly when the sufficient attribute is hard to search and the redundant attribute facilitates search. When the sufficient attribute is already search-efficient, redundancy adds no benefit.
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A regression coefficient from a Bayesian mixed-effects logistic model with 95% credible interval.
- β : ℚ
- se : ℚ
- ci_lower : ℚ
- ci_upper : ℚ
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The 95% CI excludes zero (evidence of a reliable effect).
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- c.IsSignificant = (0 < c.ci_lower ∨ c.ci_upper < 0)
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Intercept (Table 1).
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- GilesEtAl2026.exp1_intercept = { β := -2.50, se := 0.41, ci_lower := -3.34, ci_upper := -1.70 }
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Material-Redundant vs Colour-Redundant (Table 1). Negative β: colour is overinformed MORE than material even with equalized discriminability via psychophysical staircases.
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- GilesEtAl2026.exp1_material_redundant = { β := -1.43, se := 0.11, ci_lower := -1.65, ci_upper := -1.20 }
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Baseline vs S-Low/R-High (Table 1). Negative β: overinformativeness is LOWER at baseline (both attributes high-discriminability) than when the sufficient attribute is hard.
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- GilesEtAl2026.exp1_baseline = { β := -0.94, se := 0.13, ci_lower := -1.20, ci_upper := -0.68 }
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S-High/R-Low vs S-Low/R-High (Table 1). Negative β: overinformativeness is LOWER when the sufficient attribute is already search-efficient.
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- GilesEtAl2026.exp1_sHighRLow = { β := -1.09, se := 0.13, ci_lower := -1.35, ci_upper := -0.83 }
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Intercept (Table 2).
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- GilesEtAl2026.exp2_intercept = { β := 0.97, se := 9e-2, ci_lower := 0.80, ci_upper := 1.14 }
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Low-frequency colour terms (Table 2, sum contrasts). Small negative β relative to grand mean; CI includes zero → frequency does NOT explain colour's disproportionate use.
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- GilesEtAl2026.exp2_lf_colour = { β := -0.20, se := 0.12, ci_lower := -0.44, ci_upper := 3e-2 }
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Orientation-redundant (Table 2, sum contrasts). Large negative β relative to grand mean; CI excludes zero → colour is overinformed SIGNIFICANTLY MORE than orientation.
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- GilesEtAl2026.exp2_orientation = { β := -0.97, se := 0.12, ci_lower := -1.20, ci_upper := -0.75 }
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All Exp 1 effects are significant (95% CI excludes zero).
The colour vs orientation effect is significant.
The low-frequency colour effect is NOT significant.
The search efficiency ordering: S-Low/R-High > S-High/R-Low. When the sufficient attribute is hard to search and the redundant attribute facilitates search, speakers overinform more.
The search efficiency ordering: S-Low/R-High > Baseline. Speakers don't just mention all high-discriminability attributes; they selectively overinform to help difficult searches.
Colour is overinformed more than material (Exp 1), extending [KD21]'s finding cross-modally.
[KD21] showed colour > material with visual stimuli. This study confirms the asymmetry persists when material is presented in the auditory modality via impact sounds, with discriminability equalized via psychophysical staircases.
Converging evidence with [KD21]: both studies find colour used redundantly more than material. The present study adds cross-modal generalisation.
The noise model's discrimination ordering (colour > size > material) is consistent with the search efficiency results of Exp 1: higher discrimination → more overinformativeness when redundant.
The noise model predicts colour = orientation (both discrimination 0.98), but the data shows colour >> orientation (β = −0.97). This is the central dissociation: search efficiency (noise discrimination) is necessary but not sufficient to explain overinformativeness patterns. Colour has a residual privilege.
Possible explanations (General Discussion):
- Colour categories are optimised for perceptual communication ([RKK07]), making colour inherently more search-efficient than orientation across naturalistic contexts.
- Speakers learn from experience that colour is a reliable referential strategy and deploy it even when its search efficiency advantage is controlled away.
Word frequency does not explain the colour privilege: low-frequency colour terms (teal, jade) produce overinformativeness rates indistinguishable from high-frequency terms (green, blue).
The cs-RSA model ([DHG+20]) explains redundant modification via noisy perception. This study provides perceptual grounding for the noise parameters: discriminability measured via psychophysical staircases maps to the noise gap.
The cs-RSA prediction — that higher noise gap produces more overinformativeness — is confirmed for the discriminability × sufficiency interaction (Exp 1 display type effects).
Both this study and [EBF06] demonstrate that speakers routinely over-describe. The search efficiency view reinterprets these violations of Gricean Q2 as communicatively efficient: the "extra" information facilitates listener search.
The search efficiency prediction for each display type matches the empirical ordering from Exp 1.
Algebraic biconditional: In a cs-RSA scene with one target and two distractors (cf. [DHG+20] §2), L0 prefers the overmodified form iff the redundant modifier's noise gap is positive.
Scene structure: size is sufficient (only target is small), color is redundant (one distractor shares the target's color).
- L0(target | sufficient) = sM / (sM + 2·sMM)
- L0(target | sufficient+redundant) = sM·cM / (sMM·cM + sMM·cMM + sM·cM)
Proved algebraically over free variables — a general property of the Product of Experts architecture, not a finite data check.
d' predicts overmodification: The SDT sensitivity d' for the redundant feature is positive iff the cs-RSA L0 prefers the overmodified form. This unifies three levels of linglib:
- Psychophysics (
Core.SDTModel): d' measures perceptual sensitivity - Noise channel (
RSA.Noise): match/mismatch are hit/false-alarm rates - Pragmatics (cs-RSA PoE): L0 posterior determines speaker choice
The match/mismatch noise parameters ARE the observer's hit rate and false alarm rate for feature verification. Positive d' means the observer can discriminate match from mismatch above chance — exactly when the redundant modifier carries useful information through the noise channel.
[GRFM26] provide the perceptual grounding: discriminability measured via psychophysical staircases (d') maps to the noise parameters that drive overinformativeness in reference production.
Instantiation: for the standard [DHG+20] noise parameters (color match = 0.99, mismatch = 0.01), the redundant color modifier's d' is positive, so L0 prefers "small blue" over "small."
This connects the concrete cs-RSA demonstration to the general
dprime_iff_overmodification theorem.
Monotonicity in likelihood ratio: For two redundant features with noise channels (cM₁, cMM₁) and (cM₂, cMM₂), the first produces a higher L0 posterior from overmodification iff its likelihood ratio cM₁/cMM₁ exceeds cM₂/cMM₂.
The likelihood ratio — not the noise gap (cM − cMM) or d' alone — is the quantity that determines the strength of overmodification. Two features with equal d' but different likelihood ratios produce different overmodification rates.
For the one-parameter noise family (x, 1−x) used in BDA fitting, the likelihood ratio ordering reduces to the parameter ordering: x₁ > x₂ iff x₁·(1−x₂) > x₂·(1−x₁). Combined with probit monotonicity, this gives: higher d' → stronger overmodification.
This is the one-parameter specialization where d', noise gap, and likelihood ratio are all monotonically related — the only regime where "higher d'" unambiguously predicts "more overmodification."
The d'/likelihood-ratio model's monotonicity is correct within a feature (higher d' → more overmod, §14) but incomplete across features: two features with equal d' can have different overmod rates.
[GRFM26] propose two accounts for the residual colour privilege:
Category optimality: Colour naming systems are near-optimal partitions of perceptual space ([RKK07], [ZKTR19]). Colour categories maximise discriminability across natural contexts, making colour inherently more search-efficient than orientation even when within-trial d' is equalized.
Learned strategy: Speakers learn from experience that colour is a reliable referential cue and deploy it as a default strategy even when its perceptual advantage is controlled away.
Both accounts locate the symmetry-breaking outside the single-trial noise channel — in the ecological statistics of feature reliability across contexts.
The cs-RSA Product of Experts architecture — φ(u, o) = ∏ features,
noiseChannel_f(u, o) — is the UNIQUE factoring consistent with
[Luc59]'s dimension independence axiom, as proven by
Core.multidimensional_decomposition in Psychophysics.lean.
The argument chain:
- Dimension independence ([Luc59] §2.C): the ratio v(a[d↦s])/v(a) depends only on dimension d and the old/new values
- Decomposition theorem: under independence, v(a) = C · ∏ scale_d(a_d)
- cs-RSA instantiation: scale_color(match) = colorMatch = 0.99, scale_color(mismatch) = colorMismatch = 0.01, etc.
- [GRFM26] ground the scale parameters in d' measured via psychophysical staircases
[DHG+20] builds the factoring into the concrete φ (the
Product-of-Experts construction of DegenEtAl2020.φ). This bridge
connects to the ABSTRACT infrastructure that shows the factoring is
forced by independence — not an ad hoc modelling choice.
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Map each world to its (sizeMatch?, colorMatch?) feature vector, relative to the "small blue" target from [DHG+20].
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- GilesEtAl2026.worldStimulus DegenEtAl2020.World.bigBlue = ![true, true]
- GilesEtAl2026.worldStimulus DegenEtAl2020.World.bigRed = ![true, false]
- GilesEtAl2026.worldStimulus DegenEtAl2020.World.smallBlue = ![false, true]
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The cs-RSA PoE φ function, expressed as a multidim_luce model.
The score for each world is ∏ d, scale_d(stimulus(w)(d)), which
equals sizeParam × colorParam — exactly the Product of Experts.