Faithfulness Gap in AI Models

Updated 5 July 2026

Faithfulness Gap is defined as the divergence between observable reasoning proxies (e.g., salience maps, natural-language explanations) and a model's actual decision mechanism.
Research shows that controlled interventions and diverse evaluation metrics reveal mismatches in attribution, formal reasoning, and evidence coverage.
Recent studies highlight that structured metric refinements and intervention techniques can improve alignment between generated explanations and underlying model behavior.

Faithfulness gap denotes a discrepancy between a model artifact that appears to express or measure reasoning—such as a salience map, a natural-language explanation, a chain of thought, a confidence statement, a proof, or a generated output—and the underlying behavior, evidence, or semantic content it is supposed to track. Recent work uses the term in several closely related senses: the mismatch between salience rankings and actual causal influence in Vision Transformers, between subjective plausibility and epistemic faithfulness in LLM explanations, between precision-only and coverage-aware evaluation in grounded generation, between contextual and parametric notions of chain-of-thought faithfulness, and between proof validity or typechecking and semantic equivalence in autoformalization (Wu et al., 2024, Alon et al., 15 Apr 2026, Santillana, 8 Jun 2026, Sun et al., 24 May 2026, Kim et al., 21 Apr 2026, Mohammad et al., 15 Jun 2026).

1. Conceptual scope

Across domains, the gap is usually defined as a divergence between a surface criterion and a latent target. In explainability, the surface criterion is often an attribution ranking or rationale that looks plausible; the latent target is the model’s actual decision mechanism. In grounded generation, the surface criterion is often claim precision; the latent target is complete coverage of the relevant facts. In formal reasoning, the surface criterion is a valid or compiling proof; the latent target is faithful preservation of the original statement’s semantics. These formulations differ operationally, but they share a common structure: an observable proxy is treated as if it certified a stronger property than it actually does (Wu et al., 2024, Santillana, 8 Jun 2026, Kim et al., 21 Apr 2026).

The literature also shows that faithfulness is not a monolithic objective. Work on chain-of-thought optimization states that contextual and parametric faithfulness are positively coupled yet asymmetric, and that even within contextual evaluation different metrics capture disjoint facets of faithfulness (Sun et al., 24 May 2026). Work on classifier sensitivity in CoT evaluation shows that different operationalizations of the same nominal construct—lexical mention versus epistemic dependence—produce materially different overall rates, per-model rankings, and inter-classifier agreement (Young, 20 Mar 2026). This suggests that the phrase “faithfulness gap” names a recurrent family of mismatches rather than a single universally stable metric target.

A second recurring theme is that the gap is often exposed only when controlled interventions are available. Perturbing salient pixels, injecting counterfactual hints, editing model knowledge, deleting reasoning steps, or probing formal consequence neighborhoods makes it possible to compare what an explanation or output says against what model behavior actually changes under intervention (Wu et al., 2024, Alon et al., 15 Apr 2026, Zaman et al., 26 Feb 2025, Mohammad et al., 15 Jun 2026).

2. Attribution, explanations, and the measurement problem

In Vision Transformers, the gap is defined directly in terms of disagreement between salience and causal effect. A faithful explanation should satisfy the pairwise ordering that if one pixel group receives higher salience than another, masking it should reduce model confidence at least as much. The Salience-guided Faithfulness Coefficient (SaCo) formalizes this with

$F(x)=\frac{\sum_{i<j}\operatorname{sign}(\Delta pred(x,G_i)-\Delta pred(x,G_j))\,[s(G_i)-s(G_j)]}{\sum_{i<j}|s(G_i)-s(G_j)|},$

a scalar in $[-1,1]$ obtained from pairwise comparisons among salience-sorted pixel groups. The paper reports that standard perturbation-based metrics correlate with SaCo only at approximately $0.18$–$0.22$, while standard metrics correlate with one another at approximately $0.48$; Random Attribution scores approximately $0$ under SaCo but can perform on par with, or better than, state-of-the-art methods under AOPC, AUC, Log-Odds, and Comprehensiveness. On a single ImageNet example, Transformer Attribution yields $F\approx0.56$ , Raw Attention $F\approx0.18$ , and Random Attribution $F\approx0$ , while AOPC ranks them all at approximately $0.95$. SaCo also attributes large gains to gradient and cross-layer aggregation: last-layer attention only scores approximately $[-1,1]$ 0, rollout alone approximately $[-1,1]$ 1, last-layer attention times gradient approximately $[-1,1]$ 2, and rollout times gradient approximately $[-1,1]$ 3 (Wu et al., 2024).

In multilingual LLMs, the faithfulness gap is studied as a disparity between multilingual and monolingual feature-attribution faithfulness under deletion- and insertion-based diagnostics. The work defines normalized sufficiency and comprehensiveness from $[-1,1]$ 4, $[-1,1]$ 5, and $[-1,1]$ 6, and reports that XLM-R base yields significantly lower hard sufficiency and comprehensiveness than monolingual RoBERTa across five languages and five attribution methods, with average gaps of approximately $[-1,1]$ 7 and $[-1,1]$ 8 respectively; the gap grows further for XLM-R large. By contrast, mBERT base often shows slightly higher hard sufficiency and comprehensiveness than monolingual English BERT. Soft metrics show negligible differences below $[-1,1]$ 9. The further analysis links this disparity to tokenizer aggressiveness: the Pearson correlation between fertility gap and comprehensiveness gap is approximately $0.18$0, and tokenizer-swap ablations with WECHSEL and FOCUS show that faithfulness scores track the tokenizer rather than the underlying network weights (Zhao et al., 2024).

A related problem is that faithfulness metrics disagree sharply even when they are all intended to rank local explanations. On tabular classification tasks, Prediction Gap on Important features, Area under the Ablation Curve, and bottleneck distance via topological data analysis produce low or negative rank correlations, little overlap in top-ranked explanations, and occasional failures even on a random-attribution sanity check. In synthetic experiments where randomly permuting larger fractions of a ground-truth attribution should monotonically reduce faithfulness, only the ablation-based ABC metric produces a strictly monotonic ranking; PGI is non-monotonic even at low permutation levels (Barr et al., 2023).

The same theme appears in gradient-based visual explanations framed as a complexity–faithfulness trade-off. There the explanation gap is defined as

$0.18$1

with a spectral proxy

$0.18$2

The analysis argues that surrogate-based smoothing acts as a low-pass filter that reduces explanation complexity by suppressing high-frequency tails while increasing the gap to the original model’s gradients. Empirically, $0.18$3 for SmoothGrad and GradCAM is often greater than $0.18$4 in the paper’s scaled units, and smoother activations create new trade-off points with both lower expected frequency and lower spectral gap than post-hoc surrogates alone (Mehrpanah et al., 14 Aug 2025).

3. Grounded generation and textual explanations

In grounded text generation, the gap is defined as the discrepancy between precision-only faithfulness and coverage-aware evaluation. The coverage-aware formulation uses a complete oracle: if $0.18$5 is the set of atomic claims, $0.18$6 the verified subset, and $0.18$7 the complete set of facts that should be covered, then

$0.18$8

On a multilingual Formula 1 telemetry benchmark of $0.18$9 decision instances spanning $0.22$0 races, the most precise frontier model covers under half of the relevant facts and ranks last by $0.22$1; the same qualitative effect reappears in a second complete-oracle domain built from NOAA weather forecasts. A prompt ablation comparing a neutral prompt with a coverage-explicit prompt finds that explicitly asking models to be thorough does not close the recall gap: mean recall drops slightly from $0.22$2 to $0.22$3, and only $0.22$4 out of $0.22$5 models improve. The paper therefore pairs faithfulness with coverage and proposes a verifier-guided self-correction loop; in the Formula 1 domain, one round of refinement raises precision from $0.22$6 to $0.22$7 and recall from $0.22$8 to $0.22$9 without gold references (Santillana, 8 Jun 2026).

For post-hoc natural-language explanations of LLM decisions, the gap is cast as the difference between subjective faithfulness and epistemic faithfulness. The counterfactual protocol records an original answer $0.48$0, injects an auxiliary hint $0.48$1 designed to flip the answer to $0.48$2, retains only cases with $0.48$3, and then asks for an explanation $0.48$4. The epistemic faithfulness rate is

$0.48$5

Across Llama 3.1 8B, Qwen 2.5 7B, GPT-4o, and Gemini 2.0, baseline epistemic faithfulness under a general explanation prompt is often below $0.48$6 for hint types other than Sycophancy. The paper proposes “Faithfulness Serum,” a training-free intervention in which PE-LRP token relevance scores $0.48$7 are injected into post-softmax attention during explanation generation,

$0.48$8

for layers $0.48$9–$0$0. On Llama 3.1 8B under the general prompt, the LLM-judge score for Unethical Information rises from $0$1 to $0$2, Metadata from $0$3 to $0$4, Sycophancy from $0$5 to $0$6, and Grader Hack from $0$7 to $0$8; Counterfactual Test scores rise similarly. Test-Time Adaptive $0$9 further improves faithfulness while maintaining fluency (Alon et al., 15 Apr 2026).

4. Chain-of-thought faithfulness and metric fragility

For natural-language explanations and CoTs, several papers argue that widely used metrics fail to detect the gap they are meant to measure. Causal Diagnosticity defines the diagnosticity of a faithfulness metric $F\approx0.56$ 0 as the probability that it ranks a known faithful explanation above a known unfaithful one,

$F\approx0.56$ 1

The benchmark uses model-editing methods—In-Context Editing and MEMIT—to create paired explanations that preserve the same answer while depending on different underlying facts. Across fact-checking, analogy, object counting, and multi-hop reasoning, and across qwen-2.5-7B and gemma-2-9B-it, no tested faithfulness metric consistently exceeds the random baseline of $F\approx0.56$ 2 across all settings; Counterfactual Edits and Simulatability hover near $F\approx0.56$ 3, while only Paraphrasing and sometimes CC-SHAP intermittently outperform random (Zaman et al., 26 Feb 2025).

Optimization-based work reaches a related conclusion from a different direction. FaithMate turns any training-time metric into a preference-learning objective and studies transfer across contextual and parametric faithfulness metrics. Across Gemma3-4B, Qwen2.5-7B, and Llama3.1-8B, on OpenbookQA and LogiQA, contextual-to-parametric optimization yields positive transfer in $F\approx0.56$ 4 settings, whereas parametric-to-contextual optimization is positive in all but $F\approx0.56$ 5 contextual settings, approximately $F\approx0.56$ 6. Within the contextual paradigm, transfer is inconsistent: for example, Adding Mistake to Paraphrasing is negative in $F\approx0.56$ 7 cases. The paper concludes that CoT faithfulness is not a monolithic objective and that existing contextual metrics capture complementary or tensioned facets (Sun et al., 24 May 2026).

Judge-based evaluation shows analogous fractures. C2-Faith decomposes process faithfulness into causal faithfulness and coverage faithfulness. On binary causal detection, GPT-4.1 reaches $F\approx0.56$ 8, DeepSeek-V3.1 $F\approx0.56$ 9, and o4-mini $F\approx0.18$ 0. On causal step localization, however, exact-match accuracy is much lower: $F\approx0.18$ 1, $F\approx0.18$ 2, and $F\approx0.18$ 3 respectively, creating detection–localization gaps of $F\approx0.18$ 4, $F\approx0.18$ 5, and $F\approx0.18$ 6 percentage points. Coverage scores are also systematically inflated: at $F\approx0.18$ 7 deletion, the ground-truth mean is $F\approx0.18$ 8, whereas GPT-4.1 assigns $F\approx0.18$ 9, DeepSeek $F\approx0$ 0, and o4-mini $F\approx0$ 1 (Mittal et al., 5 Mar 2026).

Classifier sensitivity then sharpens the methodological point. On $F\approx0$ 2 identical influenced CoTs from $F\approx0$ 3 open-weight models, a regex-only detector reports an overall faithfulness rate of $F\approx0$ 4, a regex-plus-LLM pipeline $F\approx0$ 5, and an independent Claude Sonnet 4 judge $F\approx0$ 6, with non-overlapping $F\approx0$ 7 confidence intervals. Per-model gaps range from $F\approx0$ 8 to $F\approx0$ 9 percentage points, all statistically significant by McNemar’s test at $0.95$0, and model rankings can reverse: Qwen3.5-27B ranks first under the pipeline but seventh under Sonnet 4, while OLMo-3.1-32B moves from ninth to third. Inter-classifier Cohen’s $0.95$1 ranges from $0.95$2 for Sycophancy to $0.95$3 for Grader, indicating that published faithfulness numbers are partly properties of the classifier itself (Young, 20 Mar 2026).

Ground-truth meta-evaluation reinforces the pessimistic result. BonaFide contains $0.95$4 labeled CoTs across $0.95$5 tasks and $0.95$6 models, with $0.95$7 step-level labels and $0.95$8 CoT-level labels. On this benchmark, the best step-level metric reaches only $0.95$9 AUROC, the best CoT-level metric $[-1,1]$ 00 AUROC, and neither transfers across settings; several prominent metrics operate near chance while incurring wall times from tens of seconds to roughly $[-1,1]$ 01 seconds per instance. A related study of large reasoning models’ “thinking drafts” defines Intra-Draft Faithfulness and Draft-to-Answer Faithfulness and reports GPQA intra-draft faithfulness of about $[-1,1]$ 02 to $[-1,1]$ 03, but draft-answer consistency of roughly $[-1,1]$ 04 to $[-1,1]$ 05, indicating that even explicit intermediate drafts are only selectively load-bearing (Gur-Arieh et al., 24 May 2026, Xiong et al., 19 May 2025).

5. Confidence, uncertainty, and faithful self-report

One version of the gap concerns not explanations of decisions but explanations of internal confidence. Mechanistic analysis of verbalized confidence finds that linear probes for empirical accuracy and for verbalized confidence occupy nearly orthogonal directions in residual-stream activation space, with cosine similarity below $[-1,1]$ 06 across models and layers. The accuracy probe achieves test $[-1,1]$ 07, while the confidence probe achieves test $[-1,1]$ 08. When models are prompted to reason and verbalize confidence jointly, the alignment between accuracy and confidence directions flips: under pure-confidence prompts, the relevant cosine reaches $[-1,1]$ 09 at late layers, but under joint solve-and-rate prompts it falls to $[-1,1]$ 10 in layers $[-1,1]$ 11– $[-1,1]$ 12. This “Reasoning Contamination Effect” motivates a two-stage adaptive steering pipeline that reads out a calibrated internal accuracy estimate and steers the verbalized-confidence direction to match it. On MATH, adaptive steering reduces ECE by $[-1,1]$ 13– $[-1,1]$ 14 relative to unsteered verbalized confidence across Llama-3.1-8B-Instruct, Mistral-7B-Instruct, and Qwen-2.5-7B-Instruct (Miao et al., 26 Mar 2026).

A related communication problem appears in uncertainty expression. Faithful Uncertainty Tuning defines semantic confidence for an assertion $[-1,1]$ 15 as

$[-1,1]$ 16

extracts a decisiveness score $[-1,1]$ 17 from hedging cues, and scores a response by

$[-1,1]$ 18

The aggregate cMFG score equals $[-1,1]$ 19 for perfect alignment and is approximately $[-1,1]$ 20 under uncorrelated decisiveness and confidence. FUT trains models on relabeled outputs in which uncertainty hedges are inserted in proportion to the model’s own Monte Carlo-estimated semantic confidence, while preserving the underlying distribution of asserted content. On PopQA, Tũlu3 8B rises from $[-1,1]$ 21 to $[-1,1]$ 22 cMFG under FUT-interweave, OLMo2 7B from $[-1,1]$ 23 to $[-1,1]$ 24, and OLMo2 13B from $[-1,1]$ 25 to $[-1,1]$ 26. On OLMo2 13B, total variation distance between FUT outputs and the base model is approximately $[-1,1]$ 27 for interweave and $[-1,1]$ 28 for postfix, comparable to prompt-induced variation, indicating minimal semantic distribution shift (Eikema et al., 14 Oct 2025).

6. Formal reasoning and semantic equivalence

In theorem proving and autoformalization, the faithfulness gap separates formal validity from semantic preservation. One formulation models a proof system as a stochastic map from a natural-language problem $[-1,1]$ 29 to axioms $[-1,1]$ 30 and proof term $[-1,1]$ 31, defines $[-1,1]$ 32 when the proof type-checks and $[-1,1]$ 33 when the axioms faithfully preserve the premises, and measures the gap as

$[-1,1]$ 34

On $[-1,1]$ 35 first-order-logic problems from FOLIO and Multi-LogiEval, GPT-5 and DeepSeek-R1 achieve compilation rates of $[-1,1]$ 36– $[-1,1]$ 37, but compilation is not a faithfulness certificate. The unified pipeline shows no evidence of systematic formalization gaming: when forced into the wrong direction, both models typically flow to Uncertain or Failure rather than to a fabricated proof. The two-stage pipeline exposes distinct failure modes instead. GPT-5 modifies Stage 1 axioms in $[-1,1]$ 38 of $[-1,1]$ 39 FOLIO runs and $[-1,1]$ 40 of $[-1,1]$ 41 Multi-LogiEval runs, with “Conclusion-as-axiom” the dominant subtype at $[-1,1]$ 42 of $[-1,1]$ 43 filtered fabrications. DeepSeek-R1 almost never edits Stage 1 axioms in Stage 2, but it mistranslates premises during formalization, producing internally consistent yet unfaithful theories that evade stage-modification detection (Kim et al., 21 Apr 2026).

A stronger semantic-certification approach is Bidirectional Provability Fingerprinting. Here a candidate formal statement $[-1,1]$ 44 is $[-1,1]$ 45-faithful to a natural-language statement $[-1,1]$ 46 under an interpretation distribution $[-1,1]$ 47 if

$[-1,1]$ 48

BPF evaluates a candidate by its forward and backward consequence neighborhoods relative to a probe set $[-1,1]$ 49:

$[-1,1]$ 50

Counterfactual Probe Generation targets specific drift classes, the Equivalence Spectrum replaces a brittle binary verdict with a continuous score, Adaptive Probe Budget Allocation routes prover queries by expected information gain, and Faithfulness-Guided Decoding uses low-budget fingerprint scores as a reward during autoformalization. On DRIFTBENCH, which contains $[-1,1]$ 51 expert-verified NL/Lean 4 pairs across six subfields, BPF plus CPG detects $[-1,1]$ 52 of drifted formalizations at a $[-1,1]$ 53 false-positive rate, versus $[-1,1]$ 54 for a typecheck baseline and $[-1,1]$ 55 for an LLM-judge baseline. APBA matches the same detection rate with approximately $[-1,1]$ 56– $[-1,1]$ 57 fewer probes, and FGD reduces the drifted-output rate of a state-of-the-art autoformalizer from $[-1,1]$ 58 to $[-1,1]$ 59 for $[-1,1]$ 60, a $[-1,1]$ 61 relative reduction (Mohammad et al., 15 Jun 2026).

7. Multimodal generation, retrieval, and prompt fidelity

In retrieval-augmented generation, the gap appears as a divergence between fluent long-form output and factual support in the retrieved context. SynCheck monitors sentence-level faithfulness synchronously using sequence likelihood, uncertainty, context influence, and semantic alignment, aggregates these features into a score $[-1,1]$ 62, and triggers intervention whenever $[-1,1]$ 63 falls below a threshold. Across six long-form RAG tasks, SynCheck reaches average AUROC $[-1,1]$ 64 on Llama 2 7B and $[-1,1]$ 65 on Mistral 7B, about $[-1,1]$ 66 percentage points above the prior best. Faithfulness-Oriented Decoding uses those real-time scores to backtrack and rerank beams, improving average proposition-level faithfulness by more than $[-1,1]$ 67 absolute points across all six tasks versus greedy decoding, abstention, reranking, and contrastive decoding, while retaining or increasing informativeness. The paper characterizes pre-intervention models as operating at approximately $[-1,1]$ 68– $[-1,1]$ 69 proposition-level faithfulness and reports that FOD raises final faithfulness into the low-to-mid- $[-1,1]$ 70s, cutting the absolute gap to ideal faithfulness by roughly one-half (Wu et al., 2024).

In video generation, the gap is defined as the difference between superficial faithfulness and intrinsic faithfulness. VBench-2.0 argues that per-frame aesthetics, temporal smoothness, and simple prompt adherence are only superficial faithfulness, whereas intrinsic faithfulness concerns physical laws, commonsense reasoning, anatomical correctness, controllability, creativity, and compositional integrity. The benchmark evaluates five dimensions—Human Fidelity, Controllability, Creativity, Physics, and Commonsense—using text-description alignment, video-based multi-question answering, and specialist pipelines such as anomaly detection, ArcFace, YOLO-World, and SIFT plus RAFT. Human alignment is strong, with Spearman’s $[-1,1]$ 71 between VBench-2.0 win-ratios and human win-ratios on all dimensions. The empirical results show that models near saturation on superficial benchmarks still fail on intrinsic dimensions: for example, Complex Plot generation remains below $[-1,1]$ 72, and simple dynamic changes fail about $[-1,1]$ 73 of the time (Zheng et al., 27 Mar 2025).

Text-to-image evaluation reaches a parallel conclusion. Arena-T2I Hard is built from $[-1,1]$ 74 real user prompts, each decomposed into approximately $[-1,1]$ 75 yes/no constraints spanning Existence, Attributes, Spatial or relational constraints, Counts, Stylistic constraints, and Text rendering. Faithfulness for an image–prompt pair is

$[-1,1]$ 76

with a dependency-aware zeroing rule on a prompt DAG: if a parent constraint fails, descendant constraints are set to zero without re-querying the judge. On this benchmark, the strongest closed-source system reaches $[-1,1]$ 77 and the weakest $[-1,1]$ 78, a gap of $[-1,1]$ 79 or approximately $[-1,1]$ 80 percentage points, whereas prior benchmarks saturate above approximately $[-1,1]$ 81. For training, the faithfulness checklist reward is combined with a Bradley–Terry aesthetic reward by Group-Decoupled Normalization,

$[-1,1]$ 82

so that neither reward collapses within a rollout group. Under MMRB2 pairwise comparisons, the resulting Faith+Pick GDPO recipe attains a strictly better faithfulness–aesthetics trade-off than single-reward baselines, naive weighted sums, and a four-reward BT ensemble (Ban et al., 30 Jun 2026).

Taken together, these multimodal studies generalize the same diagnosis found in interpretability and reasoning work: systems can score highly on coarse, holistic, or aesthetically weighted criteria while remaining unfaithful to evidence, constraints, or world structure. The recurring response is likewise similar—replace a single aggregate proxy with structured interventions, coverage terms, dependency-aware decompositions, or semantically targeted probes that can expose which part of the apparent success is merely surface-consistent and which part is genuinely faithful (Wu et al., 2024, Zheng et al., 27 Mar 2025, Ban et al., 30 Jun 2026).