Prompt Legibility in Sequential Decision Making

• The paper demonstrates that using the PoL-MDP framework for legibility in robotics can boost human goal prediction accuracy to around 85% in maze experiments.
• It operationalizes legibility through Bayesian inference and legibility rewards, reducing complexity by precomputing optimal Q-functions instead of modeling full observer beliefs.
• Prompt legibility extends across domains—from LLM oversight to visual accessibility—emphasizing observer-dependent metrics that improve output clarity and checkability.

Legibility is the extent to which an observer can infer, recognize, or verify intended content from partial evidence. In robotic motion, it is the probability that an observer assigns to the robot’s true goal after seeing a movement snippet; in sequential decision making, it becomes a reward over state–action pairs that makes intent-expressive behavior computable under uncertainty; in LLM oversight, it denotes outputs that are clear, easy to understand, and checkable; and in visual and spatial settings, it denotes the ease with which viewers recognize signs, text, or space identity (Faria et al., 2022, Kirchner et al., 2024, Kushalnagar, 2021, Wang et al., 2019). Across these domains, legibility is consistently treated as distinct from raw correctness, optimality, or efficiency, and is evaluated through observer inference, human judgment, or verification success.

1. Conceptual scope and formalizations

The core robotics formulation defines legibility through Bayesian goal inference. Given a movement snippet $\xi_{x_0 \to x_t}$, the inferred goal is

$$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$

with

$$P(g | \xi_{x_0 \to x_t}) \propto P(\xi_{x_0 \to x_t} | g) P(g).$$

In the sequential-decision extension, PoL-MDP defines a Policy Legible Markov Decision Problem as

$$\left< X, A, P, r_{\rm leg}, \gamma, \beta \right>,$$

where the legibility reward for target goal $r_n$ is

$$r_{\rm leg}(x, a) = P(r_n\mid (x, a)) = P((x, a)\mid r_n),$$

and under a maximum-entropy model,

$$r_{\rm leg}(x, a) = \frac{\exp(\beta Q_n^*(x, a))}{\sum_{m=1}^N \exp(\beta Q_m^*(x, a))}.$$

This makes an action legible when it is much more optimal for the true goal than for alternative goals (Faria et al., 2022).

Outside robotics, the same term is specialized rather than abandoned. In indoor-space analysis, legibility is “the extent to which a space can be easily recognized,” and is quantified through the ease with which a DCNN classifies images from spatial segments (Wang et al., 2019). In prover–verifier work on LLMs, legibility is “clear and easy to check” reasoning, with completeness and soundness defined relative to a weaker verifier (Kirchner et al., 2024). In prediction markets, “settlement legibility” is the degree to which an uncertainty can be worded, sourced, and credibly resolved by third parties, operationalized through template repeatability, settlement determinacy, and closure precision (Adegbenro, 13 Jun 2026).

Setting	Object of inference	Representative operationalization
Sequential decision tasks	True goal from partial behavior	$P(g \mid \xi)$, $r_{\rm leg}(x,a)$
LLM oversight	Correctness from explanation	Checkability, faithfulness, completeness, soundness
Visual and spatial tasks	Recognition of signs, text, or place	Human ratings, OCR metrics, classifier accuracy

This suggests that legibility is not a single modality-specific construct but a family of observer-centered inference criteria whose exact form depends on what must be inferred and who or what performs the inference.

2. Sequential decision tasks and legible robot behavior

PoL-MDP was introduced to extend legibility to general MDPs under uncertainty while avoiding the computational burden of explicit belief-state planning. Instead of maintaining observer beliefs as in L-MDPs or interactive POMDPs, PoL-MDP precomputes optimal $Q$-functions for candidate goals, converts them into a legibility reward, and then solves an ordinary MDP with standard solvers such as value iteration, policy iteration, or linear programming (Faria et al., 2022). The resulting construction preserves uncertainty handling while reducing planning to dynamic programming over a modified reward.

Empirically, the method was compared with L-MDP in maze environments with uncertain transitions. In large mazes, PoL-MDP always solved problems within a tractable time window, whereas L-MDP timed out in up to 40–60% of large-scale cases. Both methods achieved similar legibility, but PoL-MDP found solutions much faster. The same paper also evaluated legible policies as demonstrations for inverse reinforcement learning: when demonstrations were unconnected single decision points, IRL agents inferred the target reward much better and faster from PoL-MDP demonstrations, reaching 80% correct after 5 examples; with full trajectories, both policy types were similar, though PoL-MDP retained a slight edge when few demonstrations were provided (Faria et al., 2022).

Human evaluation produced the same pattern. In a study with 150 participants observing a mobile robot in mazes, the PoL-MDP condition yielded about 85% correct goal predictions versus about 70% for the optimal-policy condition, with faster predictions on average (15.7s versus 18.2s, $$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$0) and higher, more consistent confidence ratings (Faria et al., 2022). The concrete implication is that stochastic legibility can improve human goal inference without requiring the agent to model full observer belief dynamics.

Related work on robot movement emphasizes the same observer-centric criterion at shorter time scales. A 2025 humanoid-robot study used the NICO platform in a pointing task with movements truncated at 60% or 80% of full trajectory length, and tested gaze-only, pointing-only, and combined gaze-plus-pointing conditions. The multimodal superiority and ocular primacy hypotheses were both supported: congruent gaze and pointing produced significantly higher prediction accuracy than unimodal conditions, while gaze-only produced the shortest reaction times (Lúčny et al., 7 Aug 2025). A plausible implication is that legibility in embodied interaction is not only a property of trajectory geometry, but also of cue integration across modalities.

The same tension appears in style-conditioned control. Style-Conditioned Diffusion Policy freezes a pretrained diffusion policy, trains lightweight conditioning modules, and activates legible or efficient conditioning depending on scene ambiguity. In ambiguous settings, SCDP improves adaptive transparency relative to standard diffusion policy; in non-ambiguous settings, it preserves efficiency and avoids the “over-legible” behavior of a fixed legibility style, with task success rates above 98% in all conditions (Crétides et al., 17 Mar 2026). This makes the legibility–efficiency trade-off explicitly conditional on environmental ambiguity rather than globally fixed.

3. Measurement, benchmarking, and datasets

Legibility research has placed unusual emphasis on measurement design, because the object being measured is typically observer-dependent. A framework-independent evaluation method for robot trajectories addresses this directly by using a fixed set of hand-designed trajectories, collecting human baseline data on those trajectories, and then evaluating legibility frameworks by correlating each framework’s scores with the human baseline. This enables direct $$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$1-way comparisons, reuse of human data across future frameworks, and explicit analysis of trajectory progression and viewing angle (Wallkotter et al., 2022). In the reported comparison of 10 frameworks from 6 papers, no framework perfectly matched human perception; most obtained medium correlation, Busch Legibility correlated highest, Bodden Legibility (velocity projection) was the best-performing computational model, and viewing angle as well as trajectory progression materially affected human judgments (Wallkotter et al., 2022).

The manuscript-restoration literature makes the same measurement problem spatially explicit. The SALAMI dataset contains 250 images of 50 manuscript regions, each with mean legibility and uncertainty maps derived from a study with 20 experts in philology and paleography. The study reports high intra- and inter-rater agreement, including ICC(2,1) of 0.668, ICC(3,1) of 0.711, ICC(2,k) of 0.976, and ICC(3,k) of 0.980, with most variance attributed to the image regions rather than participant or test-environment effects (Brenner et al., 2021). The dataset therefore serves as ground truth for quantitative legibility metrics in digital text restoration.

A parallel line of work learns legibility models directly from human judgments on perturbed text. The LEGIT dataset contains about 21,600 word pairs over 7,600 unique words, labeled for relative and absolute legibility under Unicode-based visual perturbations. Using this dataset, TrOCR-MT achieved a classification F1 of 0.905 and ranking accuracy of 0.858, while ByT5 variants also performed strongly (Seth et al., 2023). The same study found that legible perturbations from LEGIT degrade NLP systems more effectively than previously known visual-attack strategies, suggesting that existing attacks underexplore the space of human-readable perturbations (Seth et al., 2023).

Built-environment research treats recognizability itself as the signal. In train stations, a ResNet-based pipeline achieved about 98% top-1 accuracy in classifying spatial segments, and human validation with 4,015 Amazon Mechanical Turk samples showed similar confusion patterns: 54.5% correct matches, 37% selection of the model’s most similar segment, and 8.5% random choices (Wang et al., 2019). Here, differences in classifier confidence and confusion are interpreted as differences in spatial legibility, linking architectural distinctiveness to measurable perceptual separability.

4. Checkability, verification, and legibility in language-model systems

In LLM research, legibility is primarily a property of outputs being verifiable by weaker agents or humans under practical constraints. Prover–Verifier Games operationalize this by training a helpful prover to produce correct solutions that a small verifier accepts, a sneaky prover to produce incorrect but convincing solutions, and a verifier to distinguish them. In grade-school math, the helpful prover’s accuracy and verifier robustness improved over training, and legibility training transferred to time-constrained human evaluators, whose accuracy increased when checking helpful-prover solutions and decreased when checking sneaky-prover solutions (Kirchner et al., 2024). The central claim is not merely that outputs become longer or more explicit, but that they become easier for bounded evaluators to check.

This line of work also identified the “legibility tax”: when a single model is trained to be both correct and checkable, answer accuracy may degrade. Decoupled Prover–Verifier Games address that by fixing a solver trained only for correctness and training a separate translator to convert the solver’s output into a faithful, checkable form. In the reported experiments, the decoupled game recovered solver-level test accuracy at 56.9% versus 57.0% for the solver, with no measurable legibility tax, whereas the coupled baseline collapsed to 22.3%; the faithful translator matched the solver’s answer on 99.8% of test cases (Kim et al., 26 Feb 2026). The paper also proves a Stackelberg equilibrium result under which equilibrium is necessary and sufficient for translator faithfulness and for completeness and soundness of the verifier–translator pair (Kim et al., 26 Feb 2026).

Trusted monitoring extends the same idea to adversarial coding. In the APPS setting, “legibility protocols” require or encourage an untrusted model to document its code through comments, docstrings, and file-level documentation. Contrary to comment-removal baselines, commenting protocols improved safety without sacrificing task performance, and the improvement disproportionately favored honest code: the standard deviation of benign suspicion scores dropped from 1.57 to 0.44, while the malign standard deviation dropped from 1.80 to 1.40 (Sreevatsa et al., 9 Feb 2026). Stronger monitors benefited more from commenting, because better monitors could distinguish genuine justifications from superficially plausible ones (Sreevatsa et al., 9 Feb 2026). This directly contradicts the view that explanations should be suppressed to avoid deception.

A related inference-time intervention is Prompt Highlighter, which allows users to highlight prompt spans or image regions and then guides autoregressive generation using context pairs inspired by classifier-free guidance and attention reweighting on highlighted tokens. Without tuning on LLaVA-v1.5, the method achieved 70.7 on MMBench and 1552.5 on MME-perception, and experiments reported more reliable focus on intended input context (Zhang et al., 2023). Here legibility is partly recast as explicit controllability: the path from selected prompt content to generated output becomes more inspectable.

5. Prompt design, media accessibility, and visual legibility

Prompt legibility in generative systems is often treated as the degree to which prompt structure yields outputs that are semantically aligned, visually clear, and cognitively accessible. A structured prompting study for generating accessible images from simplified text designed five templates—Basic Object Focus, Contextual Scene, Educational Layout, Multi-Level Detail, and Grid Layout—under constraints such as object-count limits, spatial separation, and content restrictions. In Phase 1, Basic Object Focus achieved the highest CLIPScore, 0.211, and the highest composite score, 5.31; in Phase 2, Retro was identified as the most accessible style, and Wikipedia as the most effective source dataset (Souayed et al., 13 Oct 2025). The study further reported that stricter minimalism increased mean CLIPScore by 64% to 0.3465, while human agreement was highest for Text Simplicity and much weaker for Image Quality and Ethics (Souayed et al., 13 Oct 2025).

PromptAid addresses legibility from the user-interface side rather than the output side. It combines keyword perturbations, paraphrasing perturbations, and in-context example selection inside a coordinated visual-analytics workflow with a control panel, prompt canvas, data panel, provenance graph, recommendation panel, and testing panel. In a user study with 10 non-experts, PromptAid significantly reduced cognitive effort, improved tracking of prompt changes and their effects, and increased confidence in final prompt design relative to a baseline interface, with reported statistics including $$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$2, $$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$3, and $$\mathcal{I}_L (\xi_{x_0 \to x_t}) = \arg\max_{g\in G} P(g | \xi_{x_0 \to x_t}),$$4 on key questionnaire items (Mishra et al., 2023). This reframes prompt legibility as legibility of the prompt-engineering process itself.

Visual rendering benchmarks expose a different failure mode: the model may understand the prompt but still fail to render legible text. STRICT evaluates diffusion models on the maximum readable text length they can generate, the correctness and legibility of generated text, and the ratio of not following instructions. It uses OCR extraction and order-preserving comparison with normalized edit distance, character error rate, word error rate, and RNFI. Across languages and prompt lengths, GPT-4o and Gemini 2.0 outperformed other models, but performance degraded sharply beyond 200–300 characters for most systems, and all models struggled more on Chinese text (Zhang et al., 25 May 2025). The benchmark attributes this largely to locality bias and long-range conditioning failures in diffusion-based generation (Zhang et al., 25 May 2025).

Accessibility studies on human viewers place hard perceptual constraints on legibility. For ASL video, the fluent range of signer size was found to be 7° to 20° of visual angle, far larger than the roughly 2° typical for print; at a 16-inch viewing distance on a 5- to 5.5-inch smartphone, this corresponds to a signer height of about 2 to 5 inches, or from one-third to full screen (Kushalnagar, 2021). The paper argues that WCAG G54’s qualitative requirement that a signer be discernible lacks a minimum size guideline, and that practical signer-size recommendations should be grounded in this measured fluent range (Kushalnagar, 2021).

6. Trade-offs, controversies, and broader implications

A recurring result is that legibility is beneficial but not free. In human–robot collaboration, legible motions are often sub-optimal and exaggerated, which is useful in ambiguous scenes but redundant when the goal is already obvious; SCDP explicitly addresses this by switching between legible and efficient styles according to scene ambiguity (Crétides et al., 17 Mar 2026). In LLM oversight, the coupled prover–verifier setting produced a legibility tax, while decoupling correctness from translation removed it (Kim et al., 26 Feb 2026). In code monitoring, commenting was previously avoided for fear of deceptive explanations, yet the reported results favored mandatory documentation over comment removal (Sreevatsa et al., 9 Feb 2026). These findings jointly indicate that the cost of legibility depends strongly on architecture and protocol design rather than being an unavoidable property of explanation.

Another recurring result is that legibility is observer- and context-dependent. Framework-independent robot-trajectory evaluation showed that viewing angle and trajectory progression matter, and that only some frameworks account for angle explicitly (Wallkotter et al., 2022). In papyri enhancement, no single method satisfied all factor configurations; users differed widely by expertise, task, image quality, and interface affordances, and the paper therefore recommends offering a broad choice of enhancement methods rather than a universal filter (Atanasiu et al., 2021). The same work distinguishes “casual vision” from “critical vision,” and proposes four criteria for critical tasks: interpret images skeptically, treat all structures as potential information, make uncertainty explicit both visually and numerically, and approach enhancement as a system problem (Atanasiu et al., 2021).

Legibility can also act as an institutional filter. In prediction markets, settlement legibility orders listed contracts steeply: sports and elections sit near the top of the scale, while conflict sits near the bottom. Using an audited dataset of 6,047 Africa-topic and Latin America-topic contracts, the study reports mean primary legibility scores of 3.99 for sports, 3.98 for elections, 2.52 for politics/governance, 1.36 for foreign policy/diplomacy, and 0.67 for security/conflict (Adegbenro, 13 Jun 2026). African inventory was concentrated overwhelmingly in football, with 77% of observed value in sports and 58.6% in the Africa Cup of Nations alone, whereas Latin American inventory was deeper but dominated by Venezuela-related civic uncertainty (Adegbenro, 13 Jun 2026). The paper’s interpretation is that inventories reflect what platforms can settle as much as what traders believe, so reading them as maps of public importance conflates public salience with settlement constraints (Adegbenro, 13 Jun 2026).

Taken together, these results suggest that legibility is best understood as a relational property: it depends on the observer’s model, the timing and modality of evidence, the costs of disambiguation, and the institutional machinery that converts behavior or output into something inferable, readable, or auditable. In that sense, legibility is not merely an aesthetic refinement of systems already optimized for performance; it is a separate axis along which sequential policies, interfaces, explanations, renderings, and contracts become interpretable to bounded observers.