Comparative Illusion (CI) Overview

• Comparative Illusion (CI) is a phenomenon where perceived attributes systematically diverge from physical properties due to contextual influences.
• In vision, CI manifests as size, color, and motion distortions quantified by neuro-mathematical models that explain context-driven perceptual errors.
• In language, CI appears in seemingly well-formed yet semantically anomalous comparatives, modeled through Bayesian inference and noisy-channel effects.

Comparative Illusion (CI) refers to instances where the perceived attributes of stimuli deviate systematically from their physical properties due to the presence and arrangement of other contextual elements. In both visual and linguistic domains, comparative illusions reveal how biological and artificial systems leverage context when interpreting and representing sensory or structured input, resulting in errors—or informative mismatches—that illuminate underlying inductive biases and computational constraints.

1. Comparative Illusion in Visual Perception

In vision science, CI is defined as the systematic mismatch between physical stimulus properties and their perceived attributes when two or more elements are juxtaposed. CIs demonstrate that perception is not a direct mapping of sensory input but is modulated by contextual inference. In the human visual system, this inference arises from early contrast enhancement, mid-level grouping, and high-level priors that influence perceptual encoding. Furthermore, AI vision systems trained on comparable visual tasks also exhibit CIs: architectural biases or learned statistical shortcuts lead to misestimation of relative features, such as brightness, size, or orientation, in the presence of contextual distractors (Yang et al., 17 Aug 2025).

Classic examples include the Ebbinghaus illusion (perceived size distortion from surrounding circles), Munker–White illusion (context-dependent color shift), and motion illusions (e.g., Rotating Snakes). In all such cases, errors are not random but are systematically driven by the spatial, chromatic, or dynamical arrangement of contexts.

A detailed neuro-mathematical model by Franceschiello, Sarti, and Citti demonstrates that size-contrast CIs such as Ebbinghaus and Delboeuf illusions can be quantitatively predicted by combining isotropic cortical encoding of scale (via Laplacian-of-Gaussian filters) with a small-strain deformation theory. Local stimulus size signals are propagated via an isotropic lateral kernel:

$K(x, x') = \exp(-c\,|x-x'|),\quad c>0,$

which modulates the effective Riemannian metric on the retinal plane, producing perceptual distortions that closely match human psychophysical data (root-mean-square error on the order of a few percent of target size across classic datasets) (1908.10162). This model unifies both geometric and size-based illusions as metric deformations induced by contextual inducers.

2. Comparative Illusion in Language Comprehension

In language processing, the Comparative Illusion denotes sentences that superficially resemble well-formed comparatives but are semantically anomalous, as in "More students have been to Russia than I have." These sentences elicit strong initial acceptability despite their lack of interpretable comparison. Empirically, CIs are judged nearly as natural as felicitous controls but far more natural than outright semantic anomalies. Graded variation in illusion strength is systematically tied to surface features, such as the pronominal vs. noun phrase subject in the than-clause (Zhang et al., 18 Nov 2025).

Quantitative behavioral studies reveal that:

• Pronoun-singular CIs elicit the strongest illusion;
• Pronoun-plural and noun phrase variants show weaker effects;
• Paraphrase/forced-choice tasks elicit structured distributions over plausible repairs (event comparison, individual comparison, negation), reflecting the graded illusion.

The dominant theoretical account frames the phenomenon as rational Bayesian inference in a noisy channel. Listeners attribute the ill-formed input to noise (production, perception, or transmission), inferring the most plausible intended utterance $s_i$ given the observed illusory sentence $s_p$:

$P(s_i \mid s_p) \propto P(s_i)\,P(s_p \mid s_i),$

where $P(s_i)$ is the prior (approximated by LLMs such as GPT-2 or OPT) and $P(s_p \mid s_i)$ is exponentially sensitive to the word-level Damerau-Levenshtein distance.

Empirically, the strength of the illusion is best predicted not by the probability of a single most likely repair but by the average posterior across multiple plausible repairs, mirroring human acceptability gradients (Zhang et al., 18 Nov 2025).

3. Taxonomies and Formal Models of Comparative Illusion

Comparative illusions in vision are organized into five principal categories (Yang et al., 17 Aug 2025):

• Color/Brightness: Context-induced hue/brightness shifts (e.g., Munker–White).
• Geometric-Optical: Context-driven errors in size/orientation perception (e.g., Ebbinghaus, Zöllner).
• Depth/Space: Contextual cues alter perceived spatial relationships (e.g., Ponzo, Slope).
• Motion: Illusory motion driven by local luminance or spatial frequency structure (e.g., Fraser–Wilcox).
• Cross-Domain: Paradoxical or impossible geometry, composite distortions (e.g., Penrose Triangle).

Quantitative models often employ psychometric functions for human data and define similar metrics for AI models. For geometric illusions, the size error is typically expressed as

$$\epsilon_{\text{size}} = \frac{L_{\text{perceived}} - L_{\text{physical}}}{L_{\text{physical}}},$$

with magnitudes of $\approx 0.15$–$0.25$ in the Ebbinghaus illusion depending on context (Yang et al., 17 Aug 2025).

In linguistic CIs, the noisy-channel Bayesian model underpins formal predictions, using LLM priors over string probabilities and random-edit likelihoods based on Damerau-Levenshtein distance. Empirical validation relies on open-ended paraphrase collection and regression models linking posterior probabilities to acceptability ratings (Zhang et al., 18 Nov 2025).

4. CI in AI Systems: Alignment, Failure Modes, and Quantitative Metrics

AI vision systems, notably deep convolutional networks and vision-LLMs, exhibit both human-like CIs and unique failure modes. CNNs trained without explicit supervision on classic illusions reproduce certain human biases (e.g., Mach-band–like activations, color constancy errors) but tend to overestimate effect magnitude by factors of $\approx$1.3 and show higher error rates in fine perceptual discrimination ($e_{\text{color}}\approx0.12$, $e_{\text{size}}\approx0.18$, $e_{\text{motion}}\approx0.25$ in CLIP-based zero-shot tests) (Yang et al., 17 Aug 2025).

Targeted training on illusion-rich datasets (e.g., IllusionVQA) enables models to answer structured queries about illusion location, mechanism, and magnitude, though alignment gaps persist:

• Coarse localization accuracy $\approx87\%$ with GPT-4V;
• Fine-comparison accuracy drops to $\approx62\%$ (human ceiling $\approx95\%$);
• “Illusion of Illusion” misclassification rates remain substantial.

Alignment between human and AI perceptual distributions is quantified via Kullback–Leibler divergence and an alignment index

$$A = 1 - \frac{1}{2}(D_{\text{KL}} + |\mu_h - \mu_{\text{AI}}|/\sigma_h),$$

with $A_{\text{color}}\approx0.78$, $A_{\text{size}}\approx0.65$, $A_{\text{motion}}\approx0.52$, highlighting category-dependent gaps (Yang et al., 17 Aug 2025).

AI-specific CIs include:

• Pixel-level adversarial sensitivity: imperceptible perturbations ($||\Delta x||_\infty < \epsilon$) can flip predictions; related to high input-gradient loss formulations.
• Hallucinations in vision-LLMs: confident but factually incorrect outputs, quantified by hallucination rates (e.g., $H\approx0.27$ for GPT-4V on MS COCO).
• Constructive Apraxia: VLMs failing spatial reasoning in analogy to clinical apraxia (success rates below 40\% on simple compositional tasks).

5. Methodologies for Quantitative Assessment and Model Comparison

Comparative evaluation relies on parallel protocols for human and AI subjects:

• Human:
  • Just-noticeable differences (JNDs), psychometric curves, and $d'$ from signal detection theory for judgment tasks.
  • Acceptability scaling and structure-elicitation for language illusions.
• AI:
  • Standardized benchmarking on the same stimulus sets;
  • Confusion matrices and $d'_{\text{AI}}$ from model forced-choice behavior;
  • Calculation of $D_{\text{KL}}$ and alignment indices $A$.

Tables summarizing core metrics:

Illusion Category	Human-AI Alignment Index $A$	CLIP Zero-Shot Error Rate ($e$)
Color	0.78	0.12
Size	0.65	0.18
Motion	0.52	0.25

In the linguistic domain, predictive regression compares mean-link ($f_{\mathrm{mean}}$) and max-link ($f_{\max}$) functions from the Bayesian model against acceptability ratings, with empirical support for $f_{\mathrm{mean}}$ as the superior summary predictor (Zhang et al., 18 Nov 2025).

6. Implications, Unification, and Future Research

CIs across visual and linguistic domains demonstrate that perception and comprehension are not passively faithful but are actively shaped by inductive biases, priors, and architectural constraints. In vision, the metric-modulation paradigm unifies size and geometry illusions through V1-scale hypercolumns and isotropic lateral connectivity, negating the necessity for high-level Bayesian world priors (1908.10162). In language, the noisy-channel Bayesian inference model predicts both the presence and gradation of CI effects, quantitatively linking surface structure to behavioral ratings (Zhang et al., 18 Nov 2025).

For AI, these findings motivate:

• The introduction of human-aligned inductive biases (e.g., contrast normalization, geometric regularizers) in AI architectures.
• Multi-task loss functions explicitly encouraging alignment with human psychometric functions, alongside robustification to adversarial and hallucination-type errors.
• Systematic perceptual auditing using standardized illusion benchmarks, and dynamic context-weighting modules for improved alignment (Yang et al., 17 Aug 2025).

A plausible implication is that future vision and language systems will require co-design with human experiments, leveraging joint modeling of biological and artificial CIs to achieve better alignment not just in accuracy but in higher-order behavioral signatures.

Broader consequences include the extension of these models to multi-modal illusions (audio-visual), examination of developmental trajectories in AI-perceptual biases, and the systematic mapping of which inductive biases foster beneficial versus hazardous distortions in artificial systems.