Plausibility–Validity Gap

• The plausibility–validity gap is a phenomenon where outputs appear reasonable or human-convincing but fail to satisfy strict criteria of correctness, logical soundness, or domain-grounded truth.
• It manifests across diverse domains such as reinforcement learning, language modeling, explainable AI, and predictive inference, revealing a divergence between soft plausibility assessments and hard validity guarantees.
• Mitigation strategies include structural redesign of uncertainty sets, disentanglement of representational features, and objective recalibration to align optimization targets with domain-specific validity requirements.

Searching arXiv for papers on the plausibility–validity gap and closely related formulations. The plausibility–validity gap denotes a recurrent dissociation between outputs that appear reasonable, likely, or human-convincing and outputs that satisfy a stricter criterion of correctness, faithfulness, logical soundness, or domain-grounded truth. Across reinforcement learning, LLMs, explainable AI, conformal prediction, question answering, commonsense benchmarks, and counterfactual explanation, the term names structurally similar phenomena: a system can be optimized to produce or prefer what is plausible without thereby guaranteeing what is valid. In reinforcement learning, the gap appears between overly broad plausibility sets and valid optimism guarantees (Russel et al., 2019). In language modeling, it appears when models rank plausible future facts well but do not thereby achieve factual accuracy (Yuan et al., 2024), or when they conflate semantic plausibility with logical validity in internal representations (Bertolazzi et al., 8 Oct 2025). In XAI, plausibility with respect to human rationales can diverge from explanation faithfulness (Jin et al., 2023). In predictive inference, the issue motivates a distinction between Type-1 and Type-2 validity and the use of consonant plausibility measures (Cella et al., 2020). The common pattern is not merely terminological: plausibility is typically relative, graded, and often human- or posterior-facing, whereas validity is tied to a target guarantee.

1. Conceptual structure across fields

The central distinction is domain-specific but stable in form. In PRobELM, plausibility is a relative notion: given a fixed context, one asks how likely scenario $A$ is versus scenario $B$, and the benchmark operationalizes this as a ranking task over a “most plausible” future triple and less plausible alternatives (Yuan et al., 2024). Factual validity, by contrast, means correspondence to a ground-truth fact. The gap is therefore defined as the phenomenon that a model’s ability to choose plausible but not yet known scenarios does not necessarily track its ability to retrieve or generate true facts (Yuan et al., 2024).

A closely related distinction appears in reasoning research. In the VAIR setting, one separates the task of reasoning production from the task of reasoning evaluation. Let $T_{\mathrm{prod}}$ denote solving a problem and $T_{\mathrm{eval}}$ denote grading a supplied solution. With $A_{\mathrm{prod}}$ the probability of a correct final answer on production and $A_{\mathrm{eval}}$ the probability of a correct grade on evaluation, the production–evaluation gap is

$$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$

This is a plausibility–validity gap in a strong sense: the final answer is valid, yet the reasoning chain is invalid, and models often endorse it anyway (Sun et al., 31 May 2026).

In XAI, plausibility and validity are defined even more explicitly. Let $h(x)\subseteq F$ be a human rationale and $e(x)\subseteq F$ an explanation from method $M$. Plausibility is agreement with human rationales,

$B$0

often instantiated as Intersection-over-Union,

$B$1

Validity, by contrast, requires that the explanation genuinely reflect the inner workings of the predictor $B$2 (Jin et al., 2023). This makes the gap especially stark: an explanation can be highly plausible to humans while being unfaithful to the model.

In question answering, PlausibleQA formalizes the distinction by assigning each candidate answer $B$3 for question $B$4 a plausibility score $B$5, while validity is binary: $B$6 The gap is precisely the possibility that high $B$7 co-occurs with $B$8 (Mozafari et al., 22 Feb 2025).

These formulations differ in ontology—states, explanations, candidate answers, reasoning traces, future world events—but share a common architecture. Plausibility is usually a softer, ranking- or similarity-based notion. Validity is a guarantee-bearing notion. A plausible implication is that the gap is best understood as a mismatch between optimization targets and downstream desiderata.

2. Reinforcement learning: from plausibility sets to valid optimism

In finite-horizon MDPs $B$9, a plausibility set is a family of per-state-action sets

$T_{\mathrm{prod}}$0

such that, with high confidence, the true transition $T_{\mathrm{prod}}$1 for every $T_{\mathrm{prod}}$2 (Russel et al., 2019). An OFU-style method then solves the robust optimistic Bellman equations

$T_{\mathrm{prod}}$3

so that $T_{\mathrm{prod}}$4 upper-bounds the true optimal $T_{\mathrm{prod}}$5 with high probability (Russel et al., 2019).

The plausibility–validity gap in this setting arises because standard confidence-interval constructions are sufficient but not necessary for valid optimism. A common distribution-free choice centers $T_{\mathrm{prod}}$6 on the empirical frequency $T_{\mathrm{prod}}$7 and uses an $T_{\mathrm{prod}}$8-ball

$T_{\mathrm{prod}}$9

This ensures $T_{\mathrm{eval}}$0 with probability $T_{\mathrm{eval}}$1, but the radius grows like $T_{\mathrm{eval}}$2, which is conservative and can produce overly large optimistic values (Russel et al., 2019).

OFVF, “Optimism in the Face of sensible Value Functions,” replaces this with a Bayesian posterior construction and then optimizes the geometry of each ambiguity set to be just large enough to maintain valid optimism (Russel et al., 2019). For each candidate value function $T_{\mathrm{eval}}$3 in a growing set $T_{\mathrm{eval}}$4, it computes

$T_{\mathrm{eval}}$5

that is, the $T_{\mathrm{eval}}$6-quantile of $T_{\mathrm{eval}}$7 under the posterior (Russel et al., 2019). It then solves, for each $T_{\mathrm{eval}}$8, the LP

$T_{\mathrm{eval}}$9

and uses the resulting $A_{\mathrm{prod}}$0-ball of radius $A_{\mathrm{prod}}$1 around the minimizer (Russel et al., 2019).

The validity theorem states that, with probability at least $A_{\mathrm{prod}}$2, the policy $A_{\mathrm{prod}}$3 obtained from the robust Bellman recursion on OFVF sets satisfies

$A_{\mathrm{prod}}$4

The proof is by induction on the horizon; OFVF preserves the classical OFU line of argument while tightening the sets (Russel et al., 2019).

The paper explicitly distinguishes two sources of looseness: the “plausibility gap,” in which $A_{\mathrm{prod}}$5 is chosen too large in order to make $A_{\mathrm{prod}}$6 easy to guarantee, and the “validity gap,” in which even conditioned on $A_{\mathrm{prod}}$7, the quantity $A_{\mathrm{prod}}$8 can significantly overstate $A_{\mathrm{prod}}$9 (Russel et al., 2019). OFVF reduces both by using posterior information and value-function-sensitive geometry. The stated regret scaling is

$A_{\mathrm{eval}}$0

with the improvement attributed to $A_{\mathrm{eval}}$1 being typically much smaller than the frequentist radius $A_{\mathrm{eval}}$2 (Russel et al., 2019). This suggests a general principle: plausibility objects that are only as large as required by the downstream validity criterion reduce exploration cost.

3. LLMs and reasoning systems

PRobELM frames plausibility as ranking rather than truth retrieval. Each evaluation instance consists of one “most plausible” scenario—a new Wikidata triple added immediately after the model’s knowledge cutoff—and ten less plausible alternatives, yielding eleven candidates (Yuan et al., 2024). Ranking metrics include accuracy,

$A_{\mathrm{eval}}$3

mean reciprocal rank,

$A_{\mathrm{eval}}$4

and NDCG@11 (Yuan et al., 2024). The empirical finding central to the plausibility–validity gap is that rankings on PRobELM diverge strongly from TruthfulQA, COPA, ARC, and related factual benchmarks. Pythia-14M is reported as #1 on TruthfulQA at $A_{\mathrm{eval}}$5 but #9 on PRobELM at $A_{\mathrm{eval}}$6, while Pythia-2.8B is #1 on PRobELM at $A_{\mathrm{eval}}$7 but only #4 on TruthfulQA at $A_{\mathrm{eval}}$8 (Yuan et al., 2024). Across ten models, Spearman’s $A_{\mathrm{eval}}$9 between PRobELM plausibility and TruthfulQA accuracy is near zero or slightly negative (Yuan et al., 2024). The result is not a small calibration issue but a skill dissociation.

The VAIR study shows an analogous dissociation for reasoning evaluation. VAIR contains 1,001 instances in which the final answer is correct but the reasoning is flawed through Missing Premises, Missing Reasoning, Shuffled Reasoning, or Circular Reasoning (Sun et al., 31 May 2026). Frontier LRMs achieve near-perfect $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$0 yet often fail on $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$1. Reported values include GPT 5.4 with $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$2, $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$3, and $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$4, and Claude Sonnet 4.6 with $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$5, $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$6, and $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$7 (Sun et al., 31 May 2026). Humans, by contrast, show production $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$8, VAIR evaluation $$\Delta_{\mathrm{gap}} = A_{\mathrm{prod}} - A_{\mathrm{eval}_{\mathrm{VAIR}}}.$$9, and $h(x)\subseteq F$0 (Sun et al., 31 May 2026).

Mechanistically, the VAIR paper attributes the gap to an answer confirmation bias. Chain-of-thought analysis identifies two workflow modes—Independent Solving and Step Tracing—and three justification behaviors—Blind Endorsement, Forced Rationalization, and Strict Rejection (Sun et al., 31 May 2026). On VAIR, $h(x)\subseteq F$1–$h(x)\subseteq F$2 of CoTs use Independent Solving, followed by Blind Endorsement or Forced Rationalization (Sun et al., 31 May 2026). Linear probes trained on hidden states show that while models encode some representation of valid reasoning, they fail to robustly represent VAIR solutions as invalid; a static probe peaks at $h(x)\subseteq F$3 on concordant VAVR/IAIR but falls below chance on VAIR (Sun et al., 31 May 2026). Causal patching of answer-token representations flips verdicts at high rates—for example, $h(x)\subseteq F$4 for Qwen3-0.6B when patching across all layers (Sun et al., 31 May 2026). These results indicate that valid-answer cues override internal signals of invalid reasoning.

A third language-model formulation addresses logical validity directly. The representational analysis of content effects defines binary validity labels $h(x)\subseteq F$5 and plausibility labels $h(x)\subseteq F$6, then computes layerwise difference-of-means vectors

$h(x)\subseteq F$7

Their alignment is measured by

$h(x)\subseteq F$8

Across steerable layers, this cosine typically lies in $h(x)\subseteq F$9, which the paper interprets as strong positive alignment (Bertolazzi et al., 8 Oct 2025). Cross-task steering shows that plausibility vectors can flip validity judgments and vice versa, establishing causal entanglement (Bertolazzi et al., 8 Oct 2025).

The same work defines a content effect using the four subsets $e(x)\subseteq F$0: $e(x)\subseteq F$1

$e(x)\subseteq F$2

For Qwen2.5-32B zero-shot, original accuracy is $e(x)\subseteq F$3 and $e(x)\subseteq F$4; after adding $e(x)\subseteq F$5 with $e(x)\subseteq F$6, accuracy becomes $e(x)\subseteq F$7 and $e(x)\subseteq F$8 (Bertolazzi et al., 8 Oct 2025). For Qwen3-14B, accuracy improves from $e(x)\subseteq F$9 to $M$0 and $M$1 falls from $M$2 to $M$3 (Bertolazzi et al., 8 Oct 2025). This is a direct representational mitigation of the gap.

4. Explainable AI, counterfactuals, and uncertainty quantification

In XAI, the plausibility–validity gap has a normative dimension. Jin, Li, and Hamarneh argue that plausibility, usually quantified by feature localization or feature correlation with human rationales, is invalid as a criterion for explainability (Jin et al., 2023). The hidden assumptions are: first, that an explanation faithfully reflects the reasoner’s true decision process; second, that plausible explanations indicate correct decisions and vice versa (Jin et al., 2023). Plausibility metrics verify neither. The paper gives a formal counterexample: if an XAI method maximizes $M$4 with no constraint relating explanations to the model $M$5, it can achieve $M$6 while faithfulness is $M$7 (Jin et al., 2023).

The consequences are listed explicitly: misleading explanations that manipulate users, deteriorating trust, undermining autonomy, inability to achieve complementary human-AI task performance, and abandonment of other approaches for enhancing understandability (Jin et al., 2023). The proposed remedy is validity-centered evaluation: perturbation or gradient-based checks for faithfulness, the correlation between explanation plausibility and model correctness, and end-user utility as the ultimate criterion (Jin et al., 2023). A notable proposed quantity is

$M$8

intended to restore a link between plausible explanations and reliable predictions (Jin et al., 2023).

Time-series counterfactual explanations instantiate the gap differently. The goal is to generate a perturbed series $M$9 such that $B$00, while maintaining proximity, sparsity, and realism (Kostrzewa et al., 9 Mar 2026). The total loss is

$B$01

The novelty is the plausibility term

$B$02

which aligns the generated counterfactual with target-class nearest neighbors under soft-DTW (Kostrzewa et al., 9 Mar 2026). Validity is enforced via

$B$03

This makes plausibility an optimization constraint rather than a post-hoc screening criterion (Kostrzewa et al., 9 Mar 2026).

On eight UCR/UEA benchmarks, the reported method achieves near-perfect validity on all datasets while substantially improving plausibility measured by standard DTW, e.g. on TwoLeadECG, $B$04 versus $B$05 for Glacier and $B$06 for M-CELS, and on Cricket, $B$07 versus $B$08 for M-CELS (Kostrzewa et al., 9 Mar 2026). The paper states that this comes at the cost of larger perturbations in $B$09 and $B$10, explicitly characterizing a plausibility–proximity trade-off (Kostrzewa et al., 9 Mar 2026). This suggests that the gap can be narrowed, but not eliminated, without confronting competing objectives.

In predictive inference, the gap is not between human judgment and truth but between two kinds of validity. Cella and Martin distinguish Type-1 validity, which controls coverage of prediction sets,

$B$11

from Type-2 validity, which controls the event that an assertion $B$12 is assigned small upper probability even though it is true,

$B$13

They show that ordinary predictive distributions generally cannot satisfy Type-2 validity except in degenerate cases, whereas consonant plausibility measures can (Cella et al., 2020).

A consonant plausibility measure is determined by a contour $B$14 with

$B$15

The key connection to conformal prediction comes from interpreting the conformal $B$16-value

$B$17

as the plausibility contour itself (Cella et al., 2020). This yields both Type-1 and strong Type-2 validity under exchangeability. Here the gap is closed by replacing precise predictive probabilities with an imprecise but coherent and calibrated plausibility formalism.

5. Benchmarks, annotation regimes, and empirical signatures

Several datasets operationalize the plausibility–validity gap by directly measuring disagreement between graded plausibility and gold-labeled correctness.

In multiple-choice commonsense reasoning, Palta et al. define, for each question $B$18 with answer options $B$19, mean plausibility scores

$B$20

where each $B$21 is a 5-point Likert judgment on the isolated plausibility of $B$22 (Palta et al., 2024). Let

$B$23

and let $B$24 be the index of the benchmark gold answer. The per-question gap is

$B$25

A question is “plausibly problematic” exactly when $B$26, equivalently $B$27 (Palta et al., 2024).

On 250 items sampled from Social-IQa and CommonsenseQA, $B$28 in $B$29 of the sampled MCQs in both datasets (Palta et al., 2024). The paper reports that in 87% of cases a new majority-vote annotation procedure matches the original gold, but the subset with positive plausibility–validity gap shows higher rates of ambiguity, semantic mismatch, incoherence, and absence of any good answer choice (Palta et al., 2024). LLMs perform markedly worse on this subset: averaged over all tested LLMs, SIQA accuracy is $B$30 on problematic items versus $B$31 on non-problematic ones; CSQA accuracy is $B$32 versus $B$33 (Palta et al., 2024). The paper therefore treats plausibility judgments as a diagnostic for benchmark quality.

PlausibleQA measures the same dissociation in open-domain QA but shifts the unit of analysis from benchmark items to candidate wrong answers (Mozafari et al., 22 Feb 2025). The dataset contains 10,000 questions and 100,000 candidate answers, each annotated with plausibility scores and justifications, plus 900,000 pairwise-comparison justifications (Mozafari et al., 22 Feb 2025). Candidate plausibility is first elicited listwise on a 1–100 scale, then refined through pairwise comparisons aggregated with Bradley–Terry and Plackett–Luce models (Mozafari et al., 22 Feb 2025). Reported agreement between listwise and pairwise-derived scores is substantial: Spearman $B$34–$B$35, Pearson $B$36–$B$37, and KL-Divergence $B$38–$B$39 (Mozafari et al., 22 Feb 2025).

For robustness evaluation, PlausibleQA defines the rejection indicator

$B$40

and the question-level robustness score

$B$41

Overall QARA is the mean of $B$42 over questions whose gold answers are known by the model (Mozafari et al., 22 Feb 2025). The paper reports that QARA is largely independent of ExactMatch or Contains, with Spearman $B$43 and Pearson correlations from $B$44 to $B$45 (Mozafari et al., 22 Feb 2025). It also reports monotonic decline in robustness as candidate plausibility rises, showing that highly plausible wrong answers are the most difficult to reject (Mozafari et al., 22 Feb 2025). In MCQA experiments, average accuracy drops by $B$46–$B$47 percentage points from easy to hard distractor settings (Mozafari et al., 22 Feb 2025). This is a direct behavioral signature of the gap.

The benchmark literature therefore uses plausibility–validity disagreement in two ways: as a psychometric signal that a benchmark item may be defective, and as an adversarial continuum that reveals failure modes hidden by binary correctness alone.

6. Mechanisms, harms, and mitigation strategies

Across domains, the gap is typically attributed to objective mismatch or representational entanglement. In LRMs, current RL-based and outcome-focused training is said to reward correct final answers without penalizing the production or acceptance of flawed reasoning steps, thereby encouraging answer confirmation bias (Sun et al., 31 May 2026). In content-effect studies, validity and plausibility are represented by strongly aligned concept vectors, and this geometric alignment predicts the magnitude of behavioral bias across models, with mixed-effects regression coefficient $B$48 and $B$49 (Bertolazzi et al., 8 Oct 2025). In chemistry-focused scientific assistants, the core issue is that LLMs are trained to maximize the plausibility of outputs rather than scientific validity, yielding well-formed but chemically invalid molecules or reaction schemes (Malikussaid et al., 9 Jul 2025).

The chemistry study makes this especially concrete. It defines plausibility rate

$B$50

validity rate

$B$51

and the gap

$B$52

The fine-tuned Magistral Small model is reported to reach FAR $B$53, CVR $B$54, and SFR $B$55 on a 500-task evaluation set, compared with baseline Ministral 8B at $B$56, $B$57, and $B$58, respectively (Malikussaid et al., 9 Jul 2025). The paper also reports overall validity precision $B$59, recall $B$60, and F1 $B$61 (Malikussaid et al., 9 Jul 2025). The mitigation strategy is a combination of a reasoning-centric base model and LoRA fine-tuning on a “dual-domain dataset” of molecular properties and reactions (Malikussaid et al., 9 Jul 2025).

The same study highlights hierarchical learning: format adherence improves first, chemical validity next, and synthesis feasibility last (Malikussaid et al., 9 Jul 2025). This suggests that bridging the gap is not a single-step calibration problem but a staged acquisition of syntactic, rule-based, and integrative competencies. Persistent limitations remain in stereochemistry, knowledge cutoff, and reference hallucinations (Malikussaid et al., 9 Jul 2025). This suggests that closing the gap requires more than local fine-tuning when the validity criterion depends on external, evolving, or three-dimensional constraints.

In XAI, the harms are explicitly user-centered. High-plausibility explanations can manipulate users into accepting wrong predictions, erode trust when the coupling between plausible explanations and correctness fails, and prevent complementary human-AI performance (Jin et al., 2023). In reasoning systems, the broader impact is described as the risk of proliferating misleading or invalid arguments even as models autonomously generate more complex proofs and scientific content (Sun et al., 31 May 2026). In QA and commonsense evaluation, the consequence is a distorted sense of benchmark reliability and robustness (Palta et al., 2024, Mozafari et al., 22 Feb 2025).

Mitigation strategies vary by domain but cluster around three families. The first is structural redesign of the plausibility object: OFVF reshapes ambiguity sets (Russel et al., 2019), conformal prediction reinterprets $B$62-values as consonant plausibility contours (Cella et al., 2020), and time-series counterfactuals incorporate soft-DTW plausibility directly in the loss (Kostrzewa et al., 9 Mar 2026). The second is representation-level disentanglement: task-difference vectors reduce content effects in logical validity judgments (Bertolazzi et al., 8 Oct 2025). The third is training-objective correction: process rewards, step-level adversarial supervision, debate or critique frameworks for reasoning (Sun et al., 31 May 2026), and domain-specific fine-tuning with curated data in chemistry (Malikussaid et al., 9 Jul 2025).

7. Interpretation and open problems

A unifying interpretation is that plausibility and validity are rarely interchangeable because they answer different epistemic questions. Plausibility usually asks whether an object is consistent with priors, world knowledge, posterior mass, or human expectations. Validity asks whether it satisfies a task-specific criterion that often depends on causal influence, logical form, hidden process, or external ground truth. When systems are optimized for the former and evaluated by the latter, the gap becomes visible.

Several recurrent misconceptions are rejected by the cited literature. One is that higher factual accuracy should imply better plausibility inference; PRobELM shows that the correlation can be near zero or slightly negative (Yuan et al., 2024). Another is that plausible explanations are adequate stand-ins for faithful explanations; the XAI position paper argues that plausibility is invalid as an explainability criterion (Jin et al., 2023). A third is that correct answers imply sound reasoning; VAIR shows that models can have near-perfect production while failing badly at evaluation (Sun et al., 31 May 2026). A fourth is that benchmark gold labels necessarily coincide with the most plausible human answer; commonsense MCQ analysis finds mismatch rates above one in five (Palta et al., 2024).

Open problems recur as well. PRobELM identifies sensitivity to relation type, the approximate character of co-occurrence-based negative sampling, and the need for retrieval, reasoning chains, or temporal conditioning to ground plausibility judgments in current facts (Yuan et al., 2024). The VAIR study calls for training schemes that reward skepticism and counter-argumentation rather than answer consistency alone (Sun et al., 31 May 2026). The representational analysis of content effects indicates that disentangling validity from plausibility may be possible without parameter updates, but only after identifying the shared subspace (Bertolazzi et al., 8 Oct 2025). In time-series counterfactuals, computational cost and multimodal class structure limit nearest-neighbor plausibility terms (Kostrzewa et al., 9 Mar 2026). In chemistry, persistent stereochemistry errors and a static knowledge cutoff remain unresolved (Malikussaid et al., 9 Jul 2025).

This suggests that the plausibility–validity gap is not a single pathology but a general pattern of misalignment between soft, inferential, or human-facing criteria and hard, task-grounded guarantees. Its importance lies in making that misalignment explicit, measurable, and, in some settings, optimizable.