Progressive Semantic Illusions

• Progressive semantic illusions are characterized by incremental, locally plausible cues that culminate in globally anomalous outcomes.
• They are modeled through dual-constraint optimization in vector sketching and evaluated using perplexity metrics in language models.
• The study highlights challenges in compositionality and iterative reanalysis for AI systems, suggesting a need for hybrid architectures.

Progressive semantic illusions are phenomena in language, vision, and reasoning where local or incremental cues elicit a coherent interpretation at each stage of processing, yet the global composition yields an anomalous or conflicting outcome. In such illusions, the semantic inconsistency is not detectable until a critical threshold—such as full compositional integration or the final step in a sequence—is reached, often resulting in robust misinterpretations by both humans and artificial neural models. These illusions pervade domains ranging from vector sketching to natural language, challenging models that rely on local, sequential, or probabilistic heuristics rather than deep compositional or structural understanding (Cheng et al., 12 Feb 2026, Zhang et al., 2023, Ma et al., 14 Jan 2026).

1. Formal Characterization of Progressive Semantic Illusions

Progressive semantic illusions arise when sequences—of strokes, tokens, or semantic operators—admit locally plausible but globally incoherent interpretations. In visual sketching, a progressive semantic illusion is constructed by additive steps: an initial drawing depicts object A, and continued accretion (without erasure) transforms it unambiguously into object B, exploiting semantic reinterpretation only upon completion (Cheng et al., 12 Feb 2026). In language, they manifest in sentences such as comparative and depth-charge illusions, where early segments compose conventionally, but full assembly exposes a semantic anomaly only after later material is integrated (Zhang et al., 2023).

A defining attribute is the incremental build-up of semantic context: intermediate representations are each locally coherent under the system’s parsing or perception mechanism, and the illusion is detectable only as the compositional load exceeds the capacity of simple local heuristics. In formal terms, these illusions exploit the gap between the system's prediction $P(y_t\mid y_{<t})$ and the valid global interpretation $P(Y)$, where $Y$ denotes the full structure.

2. Illustrative Cases: Visual and Linguistic Progressive Illusions

Vector Sketching

In "Stroke of Surprise," progressive semantic illusions are operationalized in a generative sketching paradigm. A sketch is encoded as a stroke sequence $S = \{s_1, \ldots, s_N\}$ with partitioning $S_p$ (prefix) and $S_\Delta$ (delta):

• $S_p$ alone depicts semantic prompt $p_1$ (e.g., "duck"),
• $S_p \cup S_\Delta$ must depict $p_2$ (e.g., "sheep") (Cheng et al., 12 Feb 2026).

The challenge is to ensure $P(Y)$0 is not overwritten by $P(Y)$1, inducing a temporal semantic flip strictly by augmentation rather than mutual occlusion or destructive editing.

Comparative and Depth-Charge Illusions in Language

Progressive semantic illusions in language are prototypified by sentences such as:

• Comparative illusion: "More people have been to Russia than I have."
• Depth-charge illusion: "No head injury is too trivial to be ignored" (Zhang et al., 2023).

In both, semantic composition proceeds in plausible stages—subject, predicate, modifier—until the full assembly produces an interpretation at odds with any literal or pragmatically likely meaning. The illusion "progresses" incrementally: partial parses do not expose the anomaly, which emerges only at sentence-final integration.

3. Mechanisms and Computational Formulations

Dual-Constraint Optimization in Sketching

In vector sketching, the progressive semantic illusion is formalized as a dual-constraint optimization problem:

• Loss$P(Y)$2: Ensures prefix $P(Y)$3 matches $P(Y)$4 under score distillation sampling (SDS) guidance.
• Loss$P(Y)$5: Ensures full sketch $P(Y)$6 matches $P(Y)$7.
• Combined guidance: $P(Y)$8, where $P(Y)$9 denotes the stroke parameters.

Crucially, optimization is sequence-aware and joint: all $Y$0 are updated simultaneously under both constraints, enabling the discovery of a "common structural subspace" for $Y$1 to satisfy both semantic targets (Cheng et al., 12 Feb 2026).

Overlay Loss

A geometric overlay loss penalizes pixel-level occlusion between $Y$2 and $Y$3:

$Y$4

where $Y$5 and $Y$6 are Gaussian-blurred binary masks of prefix and delta strokes, respectively. This enforces complementarity and minimizes visual interference (Cheng et al., 12 Feb 2026).

Semantic Illusions in LLMs

LLMs are evaluated for their capacity to detect progressive semantic illusions using minimal triplets (acceptable control, unacceptable control, illusion sentence), and measuring whether the model's acceptability estimates (via perplexity or surprisal) erroneously classify the illusion as more acceptable than the unacceptable control (Zhang et al., 2023). Failures often result from:

• Incremental decoding: LMs commit to local-semantic hypotheses at each step, impeding global anomaly detection.
• Probabilistic heuristics: LMs rely on distributional acceptability, not compositional logic.

For event semantics, the Imperfective Paradox exemplifies this: LLMs systematically infer goal-completion from process expressions ("was building a house" $Y$7 "built a house"), overriding explicit contextual negation, due to robust teleological priors (Ma et al., 14 Jan 2026). This constitutes a class of progressive semantic illusion at the event-structure level.

4. Empirical Assessment and Quantitative Results

Vector Sketching Evaluation

Metrics for progressive semantic illusions in sketching include:

• CLIP score (minimum across phases): Assesses semantic alignment.
• Structural concealment: $Y$8 (for $Y$9), quantifies genuine reuse of prefix rather than overwriting.
• Semantic concealment: $S = \{s_1, \ldots, s_N\}$0 measures hidden semantics across phases.
• Coverage: Proportion of prompt pairs achieving successful progressive illusion.

The dual-constraint, joint-SDS approach outperforms state-of-the-art vector and raster baselines (SketchDreamer, SketchAgent, Nano Banana Pro), achieving highest semantic and structural concealment, with 100% coverage in the test set (Cheng et al., 12 Feb 2026).

LLM Assessment

For language illusions, models are scored using minimal-pair acceptability (perplexity and surprisal) and regression modeling to detect illusion effects; higher similarity of illusion to acceptable control implies the model is "tricked." Notably:

• NPI (syntactic) illusions are robustly detected across BERT, RoBERTa, GPT-2, and GPT-3.
• Semantic (comparative, depth-charge) illusions show highly inconsistent or minimal illusion effects—suggesting LMs lack incremental compositionality for global anomaly detection (Zhang et al., 2023).

For the Imperfective Paradox, teleological bias rates ($S = \{s_1, \ldots, s_N\}$1) and the aspectual awareness gap ($S = \{s_1, \ldots, s_N\}$2) quantify the illusion's prevalence. LLMs display near-perfect Group D accuracy (atelic entailment) but fail on Group C (telic non-entailment), yielding $S = \{s_1, \ldots, s_N\}$3, $S = \{s_1, \ldots, s_N\}$4 in zero-shot regimes (Ma et al., 14 Jan 2026).

5. Cognitive and Computational Underpinnings

Progressive semantic illusions exploit the gap between surface-level predictivity and global compositional logic. In human cognition, these illusions align with rational noisy-channel models:

$S = \{s_1, \ldots, s_N\}$5

where high prior $S = \{s_1, \ldots, s_N\}$6 (plausibility) biases interpretation until the full utterance $S = \{s_1, \ldots, s_N\}$7 forces reanalysis. LMs are similarly driven by local next-token likelihood, with limited capacity for backward revision or explicit world-knowledge integration (Zhang et al., 2023). In sketching, progressive transformation leverages the constraints of monotonicity: the impossibility of erasure compels prefix strokes to serve dual roles, requiring the discovery of a shared representational basis between semantic states (Cheng et al., 12 Feb 2026).

6. Limitations, Challenges, and Prospects

Current architectures, both in language and visual modalities, systematically fail to robustly handle progressive semantic illusions:

• LMs lack mechanisms for iterative reanalysis: once a plausible interpretation is committed, constraints arising from later tokens are rarely propagated backward (Zhang et al., 2023).
• Prompt-based interventions (definition-aware prompting, chain-of-thought, counterfactual simulation) offer limited trade-offs, either mitigating teleological bias at the expense of correct entailment or yielding calibration crises (Ma et al., 14 Jan 2026).
• In sketching, reliance on pre-trained diffusion priors (e.g., Stable Diffusion v1.5) constrains applicability to objects with common structural priors; unusual concepts yield weak gradients and poor optimization (Cheng et al., 12 Feb 2026). Runtime constraints also inhibit real-time generation for longer sequences.

A plausible implication is that bridging these gaps will require hybrid and recurrent architectures: the integration of semantic parsers, modules for explicit plausibility, neuro-symbolic memory systems, and support for backward revision or re-scoring. For visual domains, extensions to multi-phase narratives, colored and thick-path vector representations, and more efficient optimization pipelines represent viable directions.

7. Theoretical and Practical Significance

Progressive semantic illusions constitute a unique probe for evaluating the compositional and event-structural fidelity of both human and artificial intelligence systems. Their resistance to surface-level heuristics and requirement for deep, context-sensitive interpretation makes them critical testbeds for next-generation language understanding and generative systems. The study and modeling of these illusions illuminate foundational limits in one-pass neural computation, and inform the design of architectures that aspire to genuine semantic understanding through explicit integration of structure, world knowledge, and backward compositionality (Cheng et al., 12 Feb 2026, Zhang et al., 2023, Ma et al., 14 Jan 2026).