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When Model Priors Conflict with Visual Evidence: Mitigating Commonsense-Driven Hallucinations by Selective Prior Calibration
Kesheng Chen, Yamin Hu, Wenjian Luo
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
Last extracted: 8/3/2026, 2:49:18 AM
Summary
The paper addresses Commonsense-Driven Hallucination (CDH) in vision-language models, where model priors override visual evidence. The authors propose Selective Prior Calibration (SPC), a method that estimates candidate-level prior preferences via text-only scoring and subtracts these from image-conditioned scores with an instance-dependent strength. SPC selectively revises predictions only when the adjusted scores strongly support an alternative, thereby repairing counterfactual errors while preserving accuracy on commonsense-consistent images.
Entities (8)
Relation Signals (6)
Selective Prior Calibration → mitigates → Commonsense-Driven Hallucination
confidence 95% · We therefore propose Selective Prior Calibration (SPC)... Extensive experiments demonstrate that SPC substantially improves accuracy on CF images while largely preserving accuracy on matched CS images.
Selective Prior Calibration → evaluatedon → CDH-Bench
confidence 93% · To investigate these questions, we use CDH-Bench... We evaluate Qwen3-VL-32B... and LLaVA-1.6-34B... SPC raises CF accuracy... on the MC test set.
Selective Prior Calibration → appliedto → Qwen3-VL-32B
confidence 90% · We evaluate Qwen3-VL-32B... SPC raises CF accuracy by 7.8... for Qwen...
Selective Prior Calibration → appliedto → LLaVA-1.6-34B
confidence 90% · We evaluate... LLaVA-1.6-34B... SPC raises CF accuracy by... 7.0... for LLaVA...
Commonsense-Driven Hallucination → characterizedby → Counterfactual Image
confidence 88% · In a counterfactual (CF) image, an atypical visual state conflicts with the model’s commonsense prior... CDH highlights the dual role of commonsense priors...
NoLan → comparedwith → Selective Prior Calibration
confidence 85% · NoLan is the strongest existing baseline, but SPC achieves the highest utility in all four model–task settings.
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Abstract
Abstract:In vision--language models, commonsense-driven hallucination (CDH) occurs when a model's commonsense prior overrides clear visual evidence of an atypical state. For example, a model may report that a visibly six-fingered hand has five fingers. We show that these errors are systematically directed: when a model answers a question about a counterfactual (CF) image incorrectly, its answer often coincides with the candidate it prefers without access to the image. Suppressing this prior indiscriminately can repair CF errors, but may also disrupt correct answers on matched commonsense (CS) images, where the same prior is helpful. We therefore propose Selective Prior Calibration (SPC), which subtracts candidate-level prior-preference estimates from image-conditioned scores with an instance-dependent strength and revises the original prediction only when the resulting score pattern strongly supports an alternative. Extensive experiments demonstrate that SPC substantially improves accuracy on CF images while largely preserving accuracy on matched CS images. Furthermore, these gains generalize across CDH categories, candidate-answer permutations, and other conflict benchmarks, while SPC rarely alters predictions on benchmarks without such conflicts.
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- Source: https://arxiv.org/abs/2607.29240v1
- Canonical: https://arxiv.org/abs/2607.29240v1
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When Model Priors Conflict with Visual Evidence: Mitigating Commonsense-Driven Hallucinations by Selective Prior Calibration Kesheng Chen, Yamin Hu, Wenjian Luo Abstract In vision–language models, commonsense-driven hallucination (CDH) occurs when a model’s commonsense prior overrides clear visual evidence of an atypical state. For example, a model may report that a visibly six-fingered hand has five fingers. We show that these errors are systematically directed: when a model answers a question about a counterfactual (CF) image incorrectly, its answer often coincides with the candidate it prefers without access to the image. Suppressing this prior indiscriminately can repair CF errors, but may also disrupt correct answers on matched commonsense (CS) images, where the same prior is helpful. We therefore propose Selective Prior Calibration (SPC), which subtracts candidate-level prior-preference estimates from image-conditioned scores with an instance-dependent strength and revises the original prediction only when the resulting score pattern strongly supports an alternative. Extensive experiments demonstrate that SPC substantially improves accuracy on CF images while largely preserving accuracy on matched CS images. Furthermore, these gains generalize across CDH categories, candidate-answer permutations, and other conflict benchmarks, while SPC rarely alters predictions on benchmarks without such conflicts. Code: https://github.com/MiLab-HITSZ/2026ChenSPC 1 Introduction Commonsense-driven hallucination (CDH) (Chen et al. 2026) occurs when a vision–language model’s commonsense prior overrides clear visual evidence of an atypical state. For example, consider a commonsense (CS) image of a one-headed dog and a counterfactual (CF) image of a visibly two-headed dog, both queried with the same question: “How many heads does the dog have?” On the CS image, visual evidence and the model’s prior both favor one, and the model answers correctly. On the CF image, however, the model again answers one, exemplifying CDH: visual evidence supports two, whereas the model’s prior favors the ordinary answer one. Such atypical states also occur in real-world images, including those depicting rare anatomical variations (Chen et al. 2026). Consequently, mitigating CDH is essential for ensuring that models correctly interpret unusual but valid visual evidence. CDH is related to, but distinct from, object hallucination. Object-hallucination benchmarks evaluate unsupported objects, attributes, and relations (Rohrbach et al. 2018; Li et al. 2023; Wang et al. 2023; Sun et al. 2024; Zheng et al. 2025). Existing object-hallucination mitigation methods modify token decoding (Leng et al. 2024; Favero et al. 2024; Huang et al. 2024; Chen et al. 2024), strengthen attention to visual evidence (Liu et al. 2024b), or steer latent representations (Wu et al. 2026). More directly related to CDH, prior studies examine language bias and conflicts between visual evidence and world knowledge (Goyal et al. 2017; Agrawal et al. 2018; Cadène et al. 2019; Chen et al. 2020; Niu et al. 2021; Selvaraju et al. 2019; Zhou et al. 2023; Lee et al. 2025; Zhou et al. 2025; Liu et al. 2025b; Golovanevsky et al. 2025). Most closely related to our work, NoLan contrasts multimodal and text-only token distributions to suppress language priors in object hallucination (Ren et al. 2026). Taken together, existing work leaves two questions unresolved: whether erroneous responses systematically converge on the ordinary answer favored by the model’s prior, and how this error direction can be mitigated without harming cases in which that answer is visually correct. To investigate these questions, we use CDH-Bench (Chen et al. 2026), which consists of matched CF–CS image pairs. The two images in each pair share the same question and candidate answer set. The CF image depicts a state that conflicts with ordinary-world expectations, whereas the matched CS image depicts the corresponding ordinary state. To estimate the model’s prior preference, we score the candidate answers without the image and identify the highest-scoring candidate. We find that incorrect predictions on CF images systematically converge on this prior-favored candidate, a pattern we call directed prior attraction. Notably, this candidate frequently matches the ground-truth answer for the paired CS image, indicating that the errors are generally directed toward the answer associated with the ordinary state. The observed direction of CF errors suggests a simple intervention: subtracting prior preferences from image-conditioned candidate scores. Applying this correction indiscriminately, however, can harm performance on CS images, where the prior reinforces the answer indicated by visual evidence. Effective CDH mitigation must therefore balance CF repair against CS retention. We address this trade-off by proposing Selective Prior Calibration (SPC), which learns an instance-dependent strength for subtracting candidate-level prior-preference estimates and revises the original prediction only when the adjusted score pattern provides sufficient support for an alternative. Notably, SPC processes each image independently during online inference, without access to its matched counterpart or a label indicating whether the current image is CF or CS. To our knowledge, SPC is the first method specifically designed to exploit the answer-level direction of CDH while explicitly balancing CF repair and CS retention. Our contributions are threefold. First, we show that incorrect CF predictions systematically converge on the prior-favored candidate, revealing directed prior attraction. Second, we propose SPC, which learns how strongly to subtract candidate-level prior-preference estimates from image-conditioned scores and selectively revises the original prediction. Third, extensive experiments show that SPC substantially improves accuracy on CF images while largely preserving accuracy on matched CS images. These gains generalize across CDH categories, candidate-answer permutations, models, and related conflict benchmarks, while SPC rarely alters predictions on benchmarks without prior–evidence conflict. 2 Preliminaries CDH Mitigation Objective CDH highlights the dual role of commonsense priors in visual understanding. In a counterfactual (CF) image, an atypical visual state conflicts with the model’s commonsense prior, so a correct response requires the model to prioritize visual evidence over the ordinary-state answer favored by that prior. In a commonsense (CS) image, visual evidence and the prior agree, allowing the same prior to support a correct prediction. Indiscriminately weakening the prior may therefore repair CF errors while introducing new errors on CS images. Effective CDH mitigation must reduce harmful prior influence under conflict while preserving correct predictions when the prior agrees with visual evidence. CDH-Bench CDH-Bench, constructed by Chen et al. (Chen et al. 2026), provides a controlled setting for studying CDH mitigation. It contains 300 instances spanning 14 subcategories, grouped into three broad categories: counting, attributes, and relations. Each instance consists of a matched CF–CS image pair. Each pair is associated with a question evaluated in two tasks: four-option multiple-choice QA and binary yes/no QA, hereafter denoted MC and QA, respectively. Let Y denote the task-specific candidate set: A,B,C,D\A,B,C,D\ for MC and yes,no\yes,no\ for QA. Within each instance, the CF and CS images share the same question and candidate set. Only the depicted state and, consequently, the visually correct answer differ. This pairing enables us to test whether CF errors systematically converge on a prior-favored answer, indicating directed prior attraction. It also allows us to assess whether a mitigation method repairs errors under prior–evidence conflict without disrupting correct predictions when the prior agrees with visual evidence. 3 Selective Prior Calibration Directed prior attraction motivates candidate-level correction based on estimated prior preference: when a candidate receives strong estimated prior support, its image-conditioned score is reduced accordingly. Based on this idea, we propose Selective Prior Calibration (SPC) to perform this correction adaptively and selectively. During development, we use paired CF and CS data to fit the parameters that determine the correction strength for each instance. This paired learning promotes CF repair while discouraging unnecessary changes to correct predictions on CS images. During online inference, SPC first scores each candidate with and without the image. It then uses the learned parameters to determine the correction strength, adjust the candidate scores, and form a corrected proposal. Finally, it replaces the original answer only when the proposal satisfies the predefined support conditions. Figure 1 illustrates the directed prior attraction and the overall procedure. Figure 1: From directed prior attraction to selective prior calibration. (a) On the CS image, visual evidence aligns with the model’s prior. On the CF image, they conflict, and the same prior biases the model toward the prior-favored answer. (b) SPC scores candidates with and without the image, adjusts their scores using a learned correction strength, and adopts the corrected proposal only when it is sufficiently supported. Candidate-Level Score Correction Given an image–question pair and candidate set Y, SPC scores each candidate y∈y both with and without the image, using the log-probability of its corresponding answer token. Scoring with the image yields the image-conditioned score sI(y)s_I(y), whereas repeating the same procedure without the image yields the text-only score sP(y)s_P(y). We use sP(y)s_P(y) as an operational estimate of the model’s prior preference for candidate y. It captures preferences arising from the model’s learned knowledge and should be interpreted as a proxy rather than a direct measure of its latent prior (Favero et al. 2024; Ren et al. 2026). We mean-center sIs_I and sPs_P separately across candidates, obtaining s¯I s_I and s¯P s_P; this preserves candidate rankings and pairwise score differences while standardizing the score levels used for calibration. SPC then adjusts each candidate’s score according to its estimated prior preference: sC(y)=s¯I(y)−λs¯P(y),y∈,s_C(y)= s_I(y)-λ s_P(y), y , (1) where λ≥0λ≥ 0 controls the correction strength. In a CDH case, the incorrect ordinary-state candidate typically receives strong support from the text-only score s¯P s_P. Equation (1) therefore subtracts more from this candidate than from alternatives, weakening its prior-driven advantage. If another candidate retains sufficient support in the image-conditioned scores, it can become the highest-scoring candidate after correction. SPC thus mitigates CDH by discounting candidate support that persists even when the image is removed. However, the same correction can be harmful on a CS example, where the prior-favored candidate is also visually correct. To explain this trade-off, let y∗y^* denote the visually supported answer and y a competing candidate. Their corrected relative score is sC(y∗)−sC(y)=s¯I(y∗)−s¯I(y)+λ[s¯P(y)−s¯P(y∗)]. splits_C(y^*)-s_C(y)=& s_I(y^*)- s_I(y)\\ &+λ [ s_P(y)- s_P(y^*) ]. split (2) When the prior estimate favors an incorrect ordinary-state candidate y, as often occurs in CF errors, the final term is positive and increases the score of y∗y^* relative to y. When the prior instead favors the visually correct answer y∗y^*, as is common on CS examples, the final term is negative and reduces its relative score. A strong fixed correction may therefore repair CF errors while introducing new CS errors. SPC must instead adapt the correction strength to each instance rather than apply a fixed strength universally. Learning the Correction Strength SPC predicts an instance-dependent correction strength from 13 features computed from the image-conditioned scores, text-only scores, original prediction, and candidate-set size. These features include distribution entropy, peak scores, differences between the two highest scores, Jensen–Shannon divergence, and indicators of agreement among the predictions. The complete feature definition is provided in the appendix. We learn the mapping from these features to the correction strength based on a development set. To support fitting with limited paired development data, we parameterize this mapping with a low-capacity function: λθ(u)=minsoftplus(u⊤θ),λmax, _θ(u)= \! \softplus(u θ), _ \, (3) where u is the 13-dimensional feature vector and θ is the learned parameter vector. The softplussoftplus function constrains the correction strength to be positive, while λmax _ prevents excessively large adjustments. We learn θ by minimizing a regularized cross-entropy loss over the corrected candidate scores. Specifically, we place an isotropic Gaussian prior on θ, θ∼(0,ρ−1I)θ (0,ρ^-1I), and obtain its maximum a posteriori (MAP) estimate by minimizing ℓi(θ) _i(θ) =−log[softmax(s¯I,i−λθ(ui)s¯P,i)]yi, =- \! [softmax\! ( s_I,i- _θ(u_i) s_P,i ) ]_y_i, θ θ =argminθ∑i∈Dℓi(θ)+ρ2∥θ∥22, = _θ _i∈ D _i(θ)+ ρ2 θ _2^2, (4) where D denotes the development instances and yiy_i is the ground-truth answer for instance i. We fit one shared parameter vector θ jointly using paired CF and CS development data from both the MC and QA tasks. Each development instance in CDH-Bench contributes four training instances: one CF and one CS instance for each task. The CF instances provide supervision for removing harmful prior preference, whereas the CS instances penalize excessive correction when the prior supports the correct answer. The appendix provides the complete fitting details and analyzes when the learned correction recovers the visually supported answer. Selective Answer Revision Equation (1) with adaptive correction strength always produces a highest-scoring candidate, but this candidate is not necessarily a reliable correction. For example, subtraction may reverse the order of two nearly tied candidates, causing an alternative to rank first by only a small amount. These corrections are particularly risky when the original answer is already correct, as is often the case for CS images. SPC therefore treats the highest-scoring candidate after correction as a proposal rather than an automatic replacement. It changes the original answer only when the proposal is sufficiently separated from the remaining candidates and the score pattern is consistent with one of the predefined support conditions. To define the change rule, we introduce the following notation. Let ib∈i_b denote the model’s original prediction, obtained by parsing its standard response to the image–question prompt containing the candidate set Y. We denote the highest-scoring candidates under image-conditioned and text-only scoring by iI=argmaxy∈s¯I(y),iP=argmaxy∈s¯P(y),i_I= _y s_I(y), i_P= _y s_P(y), (5) respectively. Here, iPi_P is the prior-favored candidate and often corresponds to the ordinary-state answer in the CDH cases. The corrected candidate probabilities and the resulting proposal are qC=softmax(sC),zM=argmaxy∈qC(y),q_C=softmax(s_C), z_M= _y q_C(y), (6) where zMz_M denotes the proposed corrected answer. We quantify its support by its probability gap over the strongest alternative: m=qC(zM)−maxy∈,y≠zMqC(y).m=q_C(z_M)- _y ,\,y≠ z_Mq_C(y). (7) SPC restricts answer changes to two predefined support conditions. The first is d=(iI≠iP)∧(zM=iI)d=(i_I≠ i_P) (z_M=i_I), where the image-conditioned and text-only scores favor different candidates, and the corrected scores select the image-conditioned candidate. The second is a=(ib=iI=iP)∧(zM≠ib)a=(i_b=i_I=i_P) (z_M≠ i_b), where the original prediction and both scoring conditions initially favor the same candidate, but prior subtraction promotes an alternative. The corrected proposal is adopted only if it differs from the original answer, has sufficient support, uses a candidate-set size observed during development, and satisfies either support condition. Define the Boolean change decision as gM=(zM≠ib)∧(m≥mmin)∧(K∈D)∧(d∨a).g_M=(z_M≠ i_b) (m≥ m_ ) (K _D) (d a). (8) The final answer is y^=zM,if gM,ib,otherwise. y= casesz_M,&if g_M,\\ i_b,&otherwise. cases (9) Here, mminm_ is selected on the development set, and DK_D contains the candidate-set sizes observed during development. Notably, during online inference, the change rule uses only the input image, question, candidate set, original prediction, and the corresponding image-conditioned and text-only scores. It does not require the matched image, ground-truth answer, or information about whether the input image is a CF or CS image. 4 Experimental Setup We organize our experiments around five research questions. RQ1: Do CDH errors systematically converge on a prior-favored candidate? We analyze the direction of incorrect CF predictions. RQ2: How effectively does SPC repair CF errors while preserving correct predictions on matched CS images? We evaluate CF repair, CS retention, and performance relative to existing methods. RQ3: Which components drive SPC’s performance? We examine candidate-specific prior subtraction, instance-dependent correction strength, and selective answer revision. RQ4: How well does SPC generalize beyond its fitting setting? We test held-out CDH categories, unseen candidate-answer orders, and external benchmarks. RQ5: Under what conditions is prior-based correction effective? We examine its sensitivity to question form and claim order. Benchmarks and models. We reserve five instances from each of the 14 subcategories of CDH-Bench (Chen et al. 2026) to form a development set of 70 instances. The remaining 230 instances form the test set. We evaluate Qwen3-VL-32B (Bai et al. 2025) and LLaVA-1.6-34B (Liu et al. 2024a) on both MC and QA tasks. SPC requires a fixed candidate set and does not currently support open-ended generation. We evaluate generalization on Visual CounterFact (Golovanevsky et al. 2025), HallusionBench (Guan et al. 2024), ConflictVIS (Liu et al. 2025b), POPE (Li et al. 2023), and POPEv2 (Li et al. 2026). Evaluation metrics. To evaluate both CF repair and CS retention, let b denote the original model and m a mitigation method. We compute ΔCF=AccCFm−AccCFb _CF=Acc^m_CF-Acc^b_CF and ΔCS=AccCSm−AccCSb _CS=Acc^m_CS-Acc^b_CS. Here, ΔCF _CF measures whether mitigation recovers answers supported by atypical visual evidence, whereas ΔCS _CS measures whether it preserves accuracy when visual evidence agrees with the commonsense prior. A useful method should increase ΔCF _CF while keeping ΔCS _CS close to zero or positive. We also report the number of repairs and harms, which count corrected errors and newly introduced errors, respectively. We additionally report absolute CF and CS accuracy (CF-Acc and CS-Acc). Following CDH-Bench (Chen et al. 2026), we also report CFAD, RPD, and CCR. We assess paired accuracy changes using exact McNemar tests and estimate their variability using 10,000 pair-level bootstrap resamples. Baselines and model selection. We compare Focus on Vision (Liu et al. 2025b), VCD (Leng et al. 2024), MFCD (Liu et al. 2025a), PAI (Liu et al. 2024b), NoLan (Ren et al. 2026), and REVIS (Wu et al. 2026). We retain their released interventions and settings. Implementation details are in the appendix. We select the hyperparameter configurations of SPC by maximizing ΔCF+0.5ΔCS _CF+0.5 _CS. A configuration is considered only if it satisfies ΔCF≥0 _CF≥ 0 and ΔCS≥−ϵCS _CS≥- _CS, where ϵCS _CS denotes the maximum permitted CS accuracy decrease. Tunable baselines use the same development data, selection objective, and CS-loss constraint. 5 Results RQ1: Directed Prior Attraction Figure 2 reports the prior-attraction rate among incorrect CF predictions across subcategories, models, and tasks, with n denoting the number of CF errors in each cell. Across most cells, incorrect CF predictions tend to select the candidate preferred without the image. This pattern is particularly pronounced for counting and relation categories. Notably, in most cases, the text-only preferred candidate matches the ground-truth answer for the paired CS image, indicating that the errors are directed toward the answer associated with the ordinary CS state rather than an arbitrary frequent answer. Figure 2: Prior attraction by CDH subcategory. Each cell reports the fraction of original CF errors that select the no-image prior winner. Rows represent CDH subcategories, and columns represent model–task settings. RQ2: Comparison with Existing Methods Table 1 reports the performance of SPC on the MC test set. SPC raises CF accuracy by 7.8 and 7.0 points for Qwen and LLaVA, respectively, while changing CS accuracy by only +0.4 and -0.4 points. Repairs substantially outnumber harms (21/3 and 17/1). Consistent with these gains, CFAD and RPD decrease, indicating a narrower CF–CS performance gap, while the lower CCR shows that fewer remaining CF errors converge on the paired CS answer. SPC therefore repairs atypical cases while largely preserving correct predictions on matched CS images. Model Method CF-Acc CS-Acc CFAD↓ RPD↓ CCR↓ ΔCF _CF/ΔCS(%) _CS(\%) #Repairs/harms Qwen3-VL-32B Original model 0.665 0.965 0.300 0.311 0.857 – – SPC 0.743 0.970 0.226 0.233 0.695 +7.8/+0.4 21/3 LLaVA-1.6-34B Original model 0.565 0.917 0.352 0.384 0.830 – – SPC 0.635 0.913 0.278 0.305 0.750 +7.0/-0.4 17/1 Table 1: Performance of SPC on MC data with ϵCS=0.04 _CS=0.04. “#Repairs/harms” gives the numbers of corrected errors and new errors. The 95% intervals for ΔCF _CF/ΔCS _CS are [3.9, 12.2]/[-2.2, 3.0] for Qwen and [3.5, 10.4]/[-2.6, 1.7] for LLaVA. Table 2 compares SPC with existing mitigation methods using U0.5=ΔCF+0.5ΔCSU_0.5= _CF+0.5 _CS to summarize the repair–retention trade-off. For fairness, the same development objective is used to select every tunable method. The baselines vary substantially across models and tasks: some provide little CF repair, while others reduce CF accuracy or incur notable CS loss. NoLan is the strongest existing baseline, but SPC achieves the highest utility in all four model–task settings. The ϵCS=0.04 _CS=0.04 setting performs best on Qwen MC, while ϵCS=0.10 _CS=0.10 performs best in the other three settings, demonstrating a more consistent balance between CF repair and CS retention. Paired significance tests are reported in the appendix. Qwen3-VL-32B LLaVA-1.6-34B Method MC QA MC QA Focus on Vision -0.9/+0.4 +8.7/-0.4 -12.6/+3.0 -13.0/+2.2 VCD -0.9/+0.0 +1.3/+0.0 +2.6/-1.7 -0.4/+0.0 MFCD -2.2/+0.4 +1.7/+0.0 +3.5/-2.2 -3.0/-0.4 PAI +0.4/-0.4 +3.0/+0.0 +1.3/+0.0 +3.9/-0.4 REVIS -1.3/+0.0 -2.2/-0.4 -1.3/+0.9 +14.8/-3.0 NoLan +4.8/-1.7 +15.2/-0.9 +11.7/-3.5 +24.8/-8.7 SPC (ϵCS=0.04 _CS=0.04, ours) +7.8/+0.4 +22.2/-1.7 +7.0/-0.4 +23.9/-4.8 SPC (ϵCS=0.10 _CS=0.10, ours) +8.3/-0.9 +23.9/-4.3 +12.6/-2.2 +30.0/-9.1 Table 2: Comparison of CF repair and CS retention across mitigation methods. Each cell is ΔCF _CF/ΔCS _CS in percentage points. Bold marks the highest U0.5=ΔCF+0.5ΔCSU_0.5= _CF+0.5 _CS in each model–task column. RQ3: Component Analysis of SPC Table 3 compares SPC with three variants: No prior subtraction directly selects the highest-scoring image-conditioned candidate; Fixed correction strength uses λ=0.8λ=0.8 for every instance and directly outputs the highest-scoring corrected candidate; and Ungated adaptive subtraction uses the learned instance-dependent correction strength but directly adopts every proposal. Qwen3-VL-32B LLaVA-1.6-34B Variant MC QA MC QA No prior subtraction (λ=0λ=0) -0.9/-1.3 -22.6/-0.4 -1.3/+1.7 -3.5/+0.9 Fixed correction strength (λ=0.8λ=0.8) +10.4/-2.2 +17.4/-0.9 +11.3/-0.9 +33.0/-13.9 Ungated adaptive subtraction +9.6/-2.6 +22.6/-4.8 +10.9/-0.9 +30.9/-10.4 Full SPC (ϵCS=0.04 _CS=0.04) +7.8/+0.4 +22.2/-1.7 +7.0/-0.4 +23.9/-4.8 Table 3: Component analysis of SPC. Each cell is ΔCF _CF/ΔCS _CS in percentage points. No prior subtraction. The original prediction is produced through standard decoding and parsed into candidate set Y, whereas this variant ranks all candidates using their image-conditioned teacher-forced scores. The appendix details these procedures and explains why they may yield different predictions. As shown in Table 3, candidate rescoring without prior subtraction reduces CF accuracy in all four model–task settings, most substantially on Qwen QA. Thus, the gains of SPC do not come simply from changing free-form generation into candidate comparison: prior subtraction provides the corrective effect. Fixed correction strength. As shown in Table 3, a fixed coefficient can be competitive, confirming that candidate-specific prior subtraction is itself an effective correction direction. However, its performance is less consistent across model–task settings, and excessive subtraction can remove useful prior support from matched CS instances. The appendix provides additional comparisons under more challenging settings, including reduced development sets and CDH-category holdouts. Adaptive correction achieves higher average utility than the corresponding fixed-strength variant across both models in these settings (Appendix Table A9). It also yields positive average CF gains at every development-set size (Appendix Table A10). These results show that instance-dependent correction is particularly valuable when fitting data are limited or the test distribution differs from the fitting distribution. Ungated adaptive subtraction. This variant tests whether adapting the correction strength is sufficient without selective answer revision. It adopts the highest-scoring corrected candidate for every instance. Compared with full SPC, it generally achieves more CF repair but incurs larger losses on matched CS images, particularly in QA. Therefore, the two components serve complementary roles: the learned correction strength determines how strongly to adjust the candidate scores, whereas selective answer revision prevents weak proposals from replacing correct predictions. We conduct additional ablations to test three design choices: matching each prior score to its corresponding candidate, fitting with both CF and CS instances, and estimating prior preference by removing the image. Replacing the current candidate-specific prior scores with the mean prior over the development set, prior scores borrowed from another question, or a random permutation of the current prior scores across candidates removes nearly all MC repair, as shown in Figure 3. Fitting with CF instances alone increases repair but causes substantial loss on matched CS images, confirming the importance of paired CF–CS fitting. Replacing the image-removed condition with white or black images yields similar prior rankings and retains positive gains, showing that the results do not depend on a single prior-estimation procedure. Full results are provided in the appendix. Figure 3: Effect of prior-direction controls on Qwen3-VL-32B under MC. Box plots show the distributions over 10,000 pair-level bootstrap resamples. RQ4: Generalization of SPC We evaluate whether SPC generalizes to held-out CDH categories, unseen candidate-answer orders, and external benchmarks. For CDH category generalization, we exclude one CDH category during fitting and evaluate on the held-out category. For candidate-answer order generalization, we fit using the original candidate order and evaluate on candidate-answer permutations. For generalization to external benchmarks, we select all configurations on CDH-Bench and apply them to other benchmarks without retuning. Generalization to held-out CDH categories. Table 4 reports the category-holdout results. SPC achieves positive CF gains in every model–task setting, showing that the correction transfers to held-out CDH categories. CS performance remains stable on MC, whereas QA retention varies more across held-out categories. This greater variation motivates testing SPC’s sensitivity to QA question forms and claim orders in RQ5. Qwen3-VL-32B LLaVA-1.6-34B Held-out CDH Category MC QA MC QA Attribute +9.3/+0.0 +10.7/-9.3 +5.3/+0.0 +5.3/-1.3 Counting +10.0/+0.0 +33.8/-3.8 +10.0/-1.2 +41.2/-5.0 Relation +6.7/+4.0 +29.3/+0.0 +10.7/-1.3 +36.0/-12.0 Table 4: Generalization to held-out CDH categories. Each cell reports ΔCF/ΔCS _CF/ _CS in percentage points. Generalization to alternative candidate orders. Across three unseen orderings of the same MC candidates, Qwen3-VL-32B and LLaVA-1.6-34B retain positive CF gains with similar absolute accuracy. Thus, the gains do not depend on a particular A–D ordering. Detailed results are provided in the appendix. Generalization to external benchmarks. Table 5 evaluates whether SPC configured and fitted on CDH-Bench generalizes to external conflict and object-hallucination benchmarks without retuning. CDH-Bench results and NoLan are included as references. SPC achieves positive gains across the external conflict benchmarks. Notably, SPC changes almost no predictions on POPE or POPEv2, whereas NoLan changes substantially more. These results indicate that SPC generalizes selectively when visual evidence conflicts with an identifiable ordinary-state answer, rather than to object-hallucination benchmarks in general. Detailed results are provided in the appendix. SPC (ϵCS=0.04 _CS=0.04, ours) SPC (ϵCS=0.10 _CS=0.10, ours) NoLan Benchmark Reported change #Instances #Changed #Repairs/harms Effect #Changed #Repairs/harms Effect #Changed #Repairs/harms Effect Conflict benchmarks CDH-Bench MC ΔCF _CF/ΔCS _CS 460 40 26/7 +7.8/+0.4 49 29/12 +8.3/-0.9 53 24/17 +4.8/-1.7 CDH-Bench QA ΔCF _CF/ΔCS _CS 460 59 53/6 +22.2/-1.7 69 57/12 +23.9/-4.3 42 37/4 +15.2/-0.9 Visual CounterFact ΔCF _CF/ΔCS _CS 2440 45 40/5 +3.1/-0.2 56 44/12 +3.4/-0.8 46 33/11 +2.5/-0.7 HallusionBench ΔCF _CF/ΔCS _CS 656 34 24/10 +5.2/-0.9 45 28/17 +6.1/-2.7 109 36/56 -2.4/-3.7 ConflictVIS MC Δaccuracy _accuracy 374 8 8/0 +2.1 8 8/0 +2.1 8 8/0 +2.1 ConflictVIS QA Δaccuracy _accuracy 374 96 96/0 +25.7 96 96/0 +25.7 97 97/0 +25.9 Object-hallucination benchmarks POPE Δaccuracy _accuracy/ΔF1 _F1 9000 17 6/11 -0.1/+0.0 18 6/12 -0.1/+0.0 572 299/273 +0.3/+1.0 POPEv2 Δabsent _absent/Δpresent _present 140 1 0/1 -1.4/+0.0 1 0/1 -1.4/+0.0 12 0/12 -17.1/+0.0 Table 5: Performance of SPC and NoLan on CDH-Bench and external conflict and object-hallucination benchmarks. Within each benchmark, bold marks nondominated results among the compared methods. RQ5: Scope of Prior-Based Correction Using the binary QA task, Table 6 examines the scope of prior-based correction by varying the question form and claim order and measuring how the estimated prior’s preference for the ordinary answer relates to CF repair. Question form Prior favors ordinary (%) ΔCF _CF when prior favors ordinary ΔCF _CF otherwise Qwen3-VL-32B Contrastive 57.4 +46.2/+22.7 +22.4/-3.1 Instead 46.1 +25.5/+21.7 +9.7/+0.0 Choice 49.1 +8.0/+23.0 -1.7/-0.9 Reject second 24.3 +55.4/+26.8 +44.3/-6.3 LLaVA-1.6-34B Contrastive 46.5 +52.3/+14.0 +41.5/-14.6 Instead 14.3 +60.6/+9.1 +56.3/-14.7 Choice 5.7 +23.1/+7.7 +21.2/-15.2 Reject second 0.0 –/– +82.2/-43.0 Table 6: Effect of question form and claim order on prior preference and CF repair. The percentage column reports instances for which the estimated prior favors the ordinary answer under both claim orders. The last two columns report ΔCF _CF when this condition holds and otherwise, with results under the ordinary-first and atypical-first claim orders separated by a slash. Effect of question form. We express the same question in four forms: Contrastive asks whether the image supports “five rather than six”, Instead uses “five instead of six”, Choice asks which of the two answers is supported by the image, and Reject second asks whether choosing “six” is incorrect because “five” is correct. Only the Contrastive form is used during fitting; the other three forms are unseen. Table 6 shows that the estimated prior favors the ordinary answer less frequently for some unseen forms, particularly for LLaVA. Thus, question forms affect how reliably the no-image scores estimate the model’s preference for the ordinary answer. Effect of claim order. Each question form is evaluated under two claim orders: ordinary-first places the ordinary claim first, whereas atypical-first places the atypical claim first. We classify an instance as having an ordinary-state prior preference only when the no-image condition predicts “yes” in the ordinary-first order and “no” in the atypical-first order. This criterion distinguishes a preference for the ordinary claim from a fixed preference for either “yes” or “no”. Table 6 reports the percentage of instances satisfying this criterion and the corresponding ΔCF _CF within and outside this group. When the estimated prior consistently favors the ordinary state, SPC improves CF accuracy under both claim orders. Outside this group, the gains are concentrated in the ordinary-first order and generally disappear or become negative when the claims are reversed, particularly for LLaVA. Thus, prior-based correction is reliable only when the estimated prior remains associated with the ordinary state. Additional statistics are provided in the appendix. 6 Discussion Relation to NoLan. NoLan and SPC both contrast model scores obtained with and without the image, but differ in two respects. First, NoLan modifies token probabilities during generation using a hand-designed rule, whereas SPC adjusts candidate-answer scores over a fixed candidate set using a learned instance-dependent correction strength. Second, SPC retains the original prediction when the corrected answer lacks sufficient support, while NoLan applies its correction directly during decoding. Empirically, NoLan achieves more CF repair in some settings but shows less consistent CS retention and changes substantially more predictions on POPE and POPEv2. Overall, SPC provides a more conservative correction that explicitly balances CF repair against CS retention. Limitations. SPC requires a fixed candidate set, access to candidate-level probabilities, and model-specific paired CF–CS development data. During inference, it scores each candidate both with and without the image, making it more expensive than one-pass decoding and incompatible with interfaces that expose only generated text. The current method therefore does not support open-ended generation. Table 6 further reveals a limitation on binary QA: the no-image preference may reflect a fixed yes/no bias or claim position rather than a preference for the ordinary state. Although the final decision rule can reject weak corrections, it cannot compensate for a misaligned prior estimate. Future work will extend SPC to open-ended generation, reduce its scoring cost, and improve the stability of prior estimation across question forms and claim orders. 7 Conclusion This work identifies directed prior attraction as a systematic error pattern in commonsense-driven hallucination (CDH) and introduces SPC to mitigate it. Experiments show that SPC effectively reduces CDH while largely preserving correct predictions on ordinary cases. Further analysis demonstrates its generalization and clarifies that reliable prior estimation is essential for successful correction. Supplementary Material When Model Priors Conflict with Visual Evidence: Mitigating Commonsense-Driven Hallucinations by Selective Prior Calibration Kesheng Chen, Yamin Hu, Wenjian Luo Contents 1 Introduction 2 Preliminaries CDH Mitigation Objective CDH-Bench 3 Selective Prior Calibration Candidate-Level Score Correction Learning the Correction Strength Selective Answer Revision 4 Experimental Setup 5 Results RQ1: Directed Prior Attraction RQ2: Comparison with Existing Methods RQ3: Component Analysis of SPC RQ4: Generalization of SPC RQ5: Scope of Prior-Based Correction 6 Discussion 7 Conclusion A Benchmark and Evaluation Benchmark Composition and Data Split Tasks and Evaluation Settings Prompts, Decoding, and Candidate Scoring Inputs During Online Inference B Why Correction Strength Depends on the Example C How SPC Is Fitted and Applied Learning the Correction Strength Uncertainty-Aware Revision under Distribution Shift Selecting Settings on Development Data Applying SPC During Online Inference D RQ1: Directed Prior Attraction E RQ2: Comparison with Existing Methods Compared Methods Baseline Performance on CDH-Bench Why REVIS’s LLaVA QA Gain Does Not Transfer to MC F RQ3: Component Analysis of SPC Why Candidate-Specific Prior Scores Matter Alternative Prior Estimates Why Paired CF and CS Fitting Matters Candidate Scoring Does Not Explain the Gain Correction Strength and Selective Answer Revision Performance with Less or Shifted Development Data Contribution of the Two Support Conditions Effect of Development-Set Size Fitting One SPC Model for MC and QA G RQ4: Generalization of SPC Generalization Across CDH Categories Stability Across Data Splits Generalization Across MC Candidate-Answer Orders Transfer to Other Hallucination Benchmarks H RQ5: Scope of Prior-Based Correction Unequal Yes/No Answers in the Original Questions Transfer Across Question Forms When the Estimated Prior Favors the Ordinary Answer I Statistical Tests and Computational Cost References Appendix A Benchmark and Evaluation Benchmark Composition and Data Split CDH-Bench contains 300 matched counterfactual (CF) and commonsense (CS) pairs in 14 subcategories (Chen et al. 2026). We reserve five pairs from each subcategory for fitting and model selection. This gives 70 development pairs and 230 test pairs. This section describes the data and the information available to every method. We use the same terms as the main paper. The prior-favored candidate is the candidate ranked highest by the text-only scores. Directed prior attraction is the tendency of incorrect CF responses to move toward this candidate. In CDH, the prior-favored candidate often expresses the ordinary state. Counting (100 pairs) Body Parts Animal Parts Everyday Objects Plant Structure Attributes (100 pairs) Color Material Temperature Physical State Luminescence/Transparency Relations (100 pairs) Animal Behavior Object Function Spatial Causality Size Scale Figure A1: Representative CDH pairs from all 14 subcategories. Within every cell, the matched CS image is on the left and the CF image is on the right. The three categories change what must be recovered from the image: counts, visual attributes, or the relation between entities and events. Every test prediction still receives only one of the two images. Figure A1 shows examples beyond counting. Counting contains four subcategories with 25 pairs each. Attributes contain Color and Material with 25 pairs each, Temperature with 20 pairs, and Physical State and Luminescence/Transparency with 15 pairs each. Relations contain five subcategories with 20 pairs each. Each pair keeps the queried concept fixed. It changes whether the image agrees with the ordinary state. The trade-off between CF repair and CS retention therefore covers counts, attributes, and relations. The 70 development pairs are chosen by a fixed rule. We take the first five numbered pairs in each of the 14 subcategories. The remaining 230 pairs form the test set. Both images and both answer formats from a pair always stay in the same split. The split is fixed before fitting or selecting any setting. Tasks and Evaluation Settings Multiple choice (MC) is the primary test of answer-level correction because candidate positions can change without changing their meaning. Binary QA serves a different role. Its original wording strongly favors “no” on CF images and “yes” on CS images. We therefore use QA to test whether a gain survives changes in claim order and question form. As in the main paper, ϵCS _CS denotes the largest allowed CS accuracy decrease on development data. Most results use ϵCS=0.04 _CS=0.04. We also report ϵCS=0.10 _CS=0.10, which allows a larger CS decrease. A second version accounts for uncertainty in the learned correction strength. Qwen3-VL-32B (Bai et al. 2025) and LLaVA-1.6-34B (Liu et al. 2024a) are evaluated on MC, QA, the balanced claim-order test, and external transfer benchmarks. We also evaluate Qwen3-VL-30B-A3B (Bai et al. 2025) on MC. For this model, we test error direction, paired repair and retention, and transfer to CDH categories excluded from fitting. We use the same 70/230 split. RQ5 introduces a balanced claim-order test. It asks the same visual question with the ordinary and atypical answers in both orders. This test separates a preference for the ordinary answer from a fixed preference for “yes” or “no.” Section H gives the full construction and question forms. Prompts, Decoding, and Candidate Scoring Original MC predictions use the benchmark question followed by its four options and the instruction “Answer with a single letter (A, B, C, or D).” Original QA predictions use the benchmark question followed by “Answer with yes or no.” Decoding is greedy with temperature zero and at most 64 new tokens. We remove any completed thinking block and parse the first valid answer: A–D for MC or yes/no for QA. An output with no valid answer is incorrect. Candidate scoring keeps the same question, options, and answer instruction. It then adds “Final answer:” and scores the supplied continuations A, B, C, and D for MC or yes and no for QA. A candidate score is the sum of its teacher-forced token log-probabilities. In the text-only condition, we omit the image content from the same chat template; the text is unchanged. Qwen images are resized to 512×512512× 512 pixels. LLaVA uses its model-provided image processor. Inputs During Online Inference Every example is evaluated independently. At inference, SPC receives one image, its question, and the candidates supplied by MC or QA. It cannot access the paired image, CF/CS identity, category, pair identifier, or test answer. Removing the image creates the text-only scoring condition for that example. A white, black, or mean image gives an alternative prior estimate. None of these conditions provides a second view of the scene. Appendix B Why Correction Strength Depends on the Example SPC subtracts a prior-preference estimate for each candidate. The useful correction strength depends on how strongly the prior affects that decision. Too little leaves a prior-favored candidate dominant when it conflicts with the image. Too much can erase useful support on a CS example. The following analysis makes this trade-off explicit. Let Y be a fixed set of possible answers, and let y∗y^* be the answer supported by visual evidence. We model the centered image-conditioned score with three terms: visual evidence v(y)v(y), prior contribution αp(y)α p(y), and residual error ϵ(y)ε(y), where α≥0α≥ 0: s¯I(y)=v(y)+αp(y)+ϵ(y),s¯P(y)=p(y). s_I(y)=v(y)+α p(y)+ε(y), s_P(y)=p(y). (A1) This is an idealized decomposition used for intuition. In practice, s¯P s_P is a text-only proxy for p. Any difference between that proxy and the latent prior is included in ϵε. SPC ranks sλ(y)=s¯I(y)−λs¯P(y)s_λ(y)= s_I(y)-λ s_P(y). In the ideal case, ϵ(y)=0ε(y)=0 and λ=αλ=α. Candidate-specific subtraction then removes the prior term exactly. We next ask how far λ can differ from α while preserving the visually supported answer. When subtraction recovers the visual answer. Define Δv _v =miny≠y∗[v(y∗)−v(y)], = _y≠ y^* [v(y^*)-v(y) ], (A2) Rp R_p =maxy≠y∗|p(y∗)−p(y)|, = _y≠ y^*|p(y^*)-p(y)|, (A3) Re R_e =maxy≠y∗|ϵ(y∗)−ϵ(y)|. = _y≠ y^*|ε(y^*)-ε(y)|. (A4) If Δv>Re _v>R_e, Rp>0R_p>0, and |λ−α|<(Δv−Re)/Rp,|λ-α|<( _v-R_e)/R_p, (A5) then y∗y^* is the unique top candidate under SPC. For every y≠y∗y≠ y^*, the corrected pairwise margin satisfies sλ(y∗)−sλ(y) s_λ(y^*)-s_λ(y) =v(y∗)−v(y) =v(y^*)-v(y) (A6) +(α−λ)[p(y∗)−p(y)] +(α-λ)[p(y^*)-p(y)] (A7) +ϵ(y∗)−ϵ(y) +ε(y^*)-ε(y) (A8) ≥Δv−|λ−α|Rp−Re>0. ≥ _v-|λ-α|R_p-R_e>0. (A9) When Rp=0R_p=0, prior subtraction cannot alter any pairwise ranking and the condition reduces to Δv>Re _v>R_e. Why one correction strength cannot work for every example. For sample j with Δv,j>Re,j _v,j>R_e,j and Rp,j>0R_p,j>0, let δj=(Δv,j−Re,j)/Rp,j _j=( _v,j-R_e,j)/R_p,j and Aj=(αj−δj,αj+δj)∩[0,∞)A_j=( _j- _j, _j+ _j)∩[0,∞). A single fixed correction strength meets the condition for every sample only when ⋂jAj _jA_j is not empty. If these ranges do not overlap, no fixed strength can satisfy this sufficient condition for every sample. A fixed strength may still work outside the bound because the bound is conservative. An instance-dependent model can place each λj _j inside its own AjA_j when the observed scores distinguish the samples. This motivates learning the correction strength instead of assigning one value to every question. The quantities Δv _v, RpR_p, and ReR_e explain the decision, but the model does not expose them separately. SPC does not attempt to recover their true values. Image-conditioned and text-only margins instead describe how sharply the candidates are separated. Entropy describes uncertainty. Differences between the distributions and their top answers indicate how strongly the estimated prior can alter the ranking. The learned feature map uses these observed relations to predict a correction strength. The range analysis explains why this strength should depend on the observed scores. It does not assume that the three score terms can be separated exactly. The same idea can be checked directly from the observed scores. Each condition sλ(y)≥sλ(y′)s_λ(y)≥ s_λ(y ) is linear in λ. Together, these conditions define the exact range over which y is ranked first. SPC uses the strength predicted by its learned correction model. We also evaluate a version that accounts for uncertainty in correction strength. It measures the probability assigned to this range instead of treating the predicted strength as exact. How stable are the corrected proposals? Figure A2 shows how the corrected proposal changes with the correction strength. The median width of the range that keeps the same proposal is 1.10–1.74 across the four model and task combinations. For 15–51% of examples, the range has no upper bound. The selected maximum correction strength stays within the range for 76.5% of Qwen MC examples and 99.6% of LLaVA MC examples. Whenever λθ _θ reaches this maximum, it remains inside the stable range. We also replace λθ(u) _θ(u) with a constant λ∗λ^* selected on the development set. The constants are 0.80 for Qwen and 0.74 for LLaVA. They fall outside the stable ranges on 5.9% and 1.1% of examples. Range width does not distinguish successful repairs from harms. Define the stability radius as r=min(λ−λlo,λhi−λ)r= (λ- _lo, _hi-λ). Repaired and harmed examples have nearly identical median r values, 0.29 and 0.28. Thus, the radius alone does not separate useful changes from harmful ones. Small changes in correction strength leave most proposals unchanged. Selective answer revision still needs information beyond the width of the stable range. Figure A2: Stability of corrected proposals as correction strength changes. Each line is one MC test example. Segments show the range over which the proposal remains unchanged. Examples are sorted by the lower and then upper endpoint of this range. Ranges are shown only up to 1.6. Dots show the fitted λθ(u) _θ(u). The dashed line shows the selected maximum correction strength. The dotted line shows the constant λ∗λ^* selected on development data. Selective answer revision cannot remove every trade-off. Suppose two examples have identical score features, but the same answer change repairs one and harms the other. A fixed rule must treat them alike. Paired development data therefore choose a statistical balance between CF repair and CS retention. These results explain the two decisions in SPC. The learned strength handles variation in prior strength. Selective answer revision handles ambiguity after correction. Paired CF and CS outcomes fit the correction model and select the revision threshold. Appendix C How SPC Is Fitted and Applied SPC learns how strongly to subtract candidate-level prior preference. It selects when to adopt the resulting proposal on development data. This section gives the complete feature map, fitting objective, setting selection, and online inference procedure. Learning the Correction Strength The evaluated implementation uses a regularized linear model. Its inputs describe the candidate score distributions for one example. Fitting uses paired CF and CS examples from a development set D, which show both successful repairs and harmful corrections. At inference, the model uses image-conditioned scores, text-only scores, the original answer, and the candidate count. Let the observable input to the correction model be o=(s¯I,s¯P,ib,K)o=( s_I, s_P,i_b,K). Let K=||K=|Y|, qI=softmax(s¯I)q_I=softmax( s_I), qP=softmax(s¯P)q_P=softmax( s_P), and let mI,mPm_I,m_P be the margins between the two highest scores. Write iI,iP,ibi_I,i_P,i_b for the positions of the answers ranked first by the image-conditioned scores, the text-only scores, and the original prediction, respectively. The feature vector is u=ϕ(o)=[ u=φ(o)=[ 1,logK/log4,(qI)/logK,(qP)/logK, 1, K/ 4, H(q_I)/ K, H(q_P)/ K, maxqI,maxqP,tanh(mI/4),tanh(mP/4), q_I, q_P, (m_I/4), (m_P/4), JS(qI,qP),[iI=iP], JS(q_I,q_P),1[i_I=i_P], [ib=iI],[ib=iP],tanh((mP−mI)/4)]. 1[i_b=i_I],1[i_b=i_P], ((m_P-m_I)/4)]. (A10) Here H denotes entropy. JSJS denotes Jensen–Shannon divergence, which measures the difference between two probability distributions. The first two values are a bias term and the normalized candidate count. The next six describe entropy, peak probability, and the margin between the two highest scores under the two scoring conditions. The remaining values describe distribution disagreement, agreement among the answers ranked first, and the margin gap tanh((mP−mI)/4) ((m_P-m_I)/4). Together, the features summarize candidate count, confidence, and image–prior disagreement. They form the evaluated linear correction model. The control using image-conditioned scores alone removes every input that depends on the prior estimate. We standardize each nonconstant feature using its mean and standard deviation on D; a zero standard deviation is replaced by one. We leave the bias feature unchanged. In the equations below, u denotes this standardized feature vector. The fitting and inference strengths are λθfit(u) _θ^fit(u) =softplus(u⊤θ), =softplus(u θ), (A11) λθ(u) _θ(u) =minλθfit(u),λmax. = \ _θ^fit(u), _ \. For a development set D, SPC fits a regularized correction model with θ∼(0,ρ−1I)θ (0,ρ^-1I) and minimizes ∑i∈D−logsoftmax(s¯I,i−λθfit(ui)s¯P,i)yi+ρ2∥θ∥22. _i∈ D- ( s_I,i- _θ^fit(u_i) s_P,i)_y_i+ ρ2\|θ\|_2^2. (A12) The regularization strength ρ is selected on the development set. The maximum-a-posteriori (MAP) estimate θ θ defines the standard SPC correction model. Uncertainty-Aware Revision under Distribution Shift The category-holdout, candidate-order, and reduced-data experiments change the conditions seen during fitting. For these tests, we use an uncertainty-aware extension of SPC. It averages corrected probabilities over plausible correction strengths. It also checks whether the proposal stays first across those strengths and whether the score pattern resembles the development data. The fitting objective and candidate scores remain unchanged. Let J(θ)J(θ) denote the objective above and H=∇θ2J(θ^)H= _θ^2J( θ). We form a Laplace approximation θ∼(θ^,Σ)θ ( θ, ). Here, Σ is the symmetrized pseudoinverse of H+10−8IH+10^-8I. Its eigenvalues are clipped to [10−8,4][10^-8,4] for numerical stability. For a test vector u, η=u⊤θ∼(μ,σ2),μ=u⊤θ^,σ2=u⊤Σu.η=u θ (μ,σ^2), μ=u θ, σ^2=u u. (A13) We set λ(η)=minsoftplus(η),λmaxλ(η)= \softplus(η), _ \ and compute q~(y)=η[softmax(s¯I−λ(η)s¯P)y] q(y)=E_η\! [softmax ( s_I-λ(η) s_P )_y ] (A14) with 64-point Gauss–Hermite quadrature. The proposal is zU=argmaxyq~(y)z_U= _y q(y), and its margin is mU=q~(zU)−maxy≠zUq~(y)m_U= q(z_U)- _y≠ z_U q(y). We also compute the exact range of strengths for which zUz_U stays first: ℒ(zU)= (z_U)= λ∈[0,λmax]: \λ∈[0, _ ]: (A15) s¯I(zU)−λs¯P(zU)≥s¯I(y)−λs¯P(y),∀y. s_I(z_U)-λ s_P(z_U)≥ s_I(y)-λ s_P(y),\ ∀ y\. Its posterior support is rU=Pr[λ(η)∈ℒ(zU)]r_U= [λ(η) (z_U)]. Each pairwise inequality is linear in λ, so ℒ(zU)L(z_U) is obtained by intersecting its closed half-intervals. The extension can also reject score patterns far from the development data. Let x contain the 12 standardized nonbias features, let CDC_D be their development-set covariance, and define ddev=x⊤(CD+0.1I)+x.d_dev= x (C_D+0.1I)^+x. (A16) We retain the two support conditions from the main paper, replacing the point proposal zMz_M with zUz_U. Thus, d=(iI≠iP)∧(zU=iI)d=(i_I≠ i_P) (z_U=i_I) and a=(ib=iI=iP)∧(zU≠ib)a=(i_b=i_I=i_P) (z_U≠ i_b). The complete decision is gU= g_U= (zU≠ib)∧(K∈D) (z_U≠ i_b) (K _D) ∧(mU≥mmin)∧(ddev≤dmax) (m_U≥ m_ ) (d_dev≤ d_ ) ∧[(d∧rU≥τD)∨(a∧rU≥τA)]. [(d r_U≥ _D) (a r_U≥ _A) ]. (A17) Here, τD _D and τA _A are the minimum posterior support for conditions d and a. The threshold mminm_ is the minimum proposal margin, and dmaxd_ is the largest accepted development distance. The set DK_D contains the candidate counts observed in D. The final answer is zUz_U when gUg_U is true and ibi_b otherwise. Standard SPC uses the point estimate θ θ, no distance check, and the decision in the main paper. Results use standard SPC unless a caption explicitly names the uncertainty-aware extension. Selecting Settings on Development Data For each model, D contains MC and QA data from the same 70 pairs. The CF and CS sides in both tasks contribute four examples per pair. Model selection chooses the highest mean value of ΔCF+0.5ΔCS _CF+0.5 _CS across MC and QA. Each task must have a CF change of at least zero and satisfy ΔCS≥−ϵCS _CS≥- _CS. The fitted model is model-specific but receives no task indicator. Table A1 lists the settings selected for the primary results. Setting Qwen3-VL- 32B LLaVA-1.6- 34B Regularization ρ 0.01 0.01 Maximum correction strength 1.0 0.8 Minimum gap between the top two corrected-answer probabilities 0.3 0.2 Candidate counts accepted at test time 2, 4 2, 4 Table A1: Settings selected for each model with ϵCS=0.04 _CS=0.04. These are the standard point-estimate SPC settings used for the primary results. We select ρ from 0.01,0.1,1,10\0.01,0.1,1,10\. We select the maximum correction strength from 0.8,1,1.2,1.5\0.8,1,1.2,1.5\. Both choices use U0.5=ΔCF+0.5ΔCSU_0.5= _CF+0.5 _CS. The minimum proposal margin is selected from 0,0.05,0.1,0.2,0.3\0,0.05,0.1,0.2,0.3\. For standard SPC with ϵCS=0.10 _CS=0.10, Qwen selects ρ=0.01ρ=0.01, λmax=1.0 _ =1.0, and mmin=0m_ =0. LLaVA selects ρ=1.0ρ=1.0, λmax=1.0 _ =1.0, and mmin=0m_ =0. The uncertainty-aware extension searches τD _D and τA _A over 0.5,0.65,0.8,0.9,0.95,1.01\0.5,0.65,0.8,0.9,0.95,1.01\. It searches dmaxd_ over the 90th, 95th, and 99th percentiles of the development distances. For compactness, define h=(ρ,λmax,τD,τA,mmin,dmax)h=(ρ, _ , _D, _A,m_ ,d_ ). The selected values are: Model ϵCS _CS h Qwen 0.00, 0.02 (0.01,0.8,0.5,1.01,0,6.60)(0.01,0.8,0.5,1.01,0,6.60) 0.04 (0.01,1.0,0.5,0.5,0.3,6.60)(0.01,1.0,0.5,0.5,0.3,6.60) 0.06, 0.10 (0.01,1.0,0.5,0.5,0,6.60)(0.01,1.0,0.5,0.5,0,6.60) LLaVA 0.00 (0.01,0.8,0.5,1.01,0,3.56)(0.01,0.8,0.5,1.01,0,3.56) 0.02 (0.01,0.8,0.5,0.5,0.3,3.56)(0.01,0.8,0.5,0.5,0.3,3.56) 0.04 (0.01,1.0,0.5,0.8,0.2,6.39)(0.01,1.0,0.5,0.8,0.2,6.39) 0.06 (1.0,0.8,0.5,0.5,0.05,6.39)(1.0,0.8,0.5,0.5,0.05,6.39) 0.10 (1.0,1.2,0.5,0.5,0,6.39)(1.0,1.2,0.5,0.5,0,6.39) All values are fixed before test evaluation. Applying SPC During Online Inference During online inference, SPC first records the original answer. It uses teacher forcing to score every supplied answer under the image-conditioned and text-only conditions. It then computes u=ϕ(o)u=φ(o) and predicts λθ(u) _θ(u). Next, it subtracts the estimated prior preference for each answer and forms a corrected proposal. Selective answer revision adopts the proposal only when it satisfies the conditions in the main paper. No parameter fitting or threshold selection occurs on test examples. The uncertainty-aware extension replaces the point proposal and final decision with Eqs. A14 and A17. Otherwise, it follows the same procedure. Appendix D RQ1: Directed Prior Attraction The subcategory matrix in the main paper shows that incorrect CF predictions often select the prior-favored candidate. The overall rates show the same pattern in every model and task combination. For Qwen, the rates are 70.1% on MC and 90.4% on QA. For LLaVA, they are 77.0% and 91.6%. CDH errors therefore follow the same direction across both answer formats and models. The number of errors in each matrix cell matters when reading these rates. Several attribute cells and a few MC counting cells contain very few original CF errors. Their rates are less stable. Outside cells with few errors, the attraction is clear and is strongest for counting and relation QA. In most cells, the prior-favored candidate is also the correct answer for the matched CS image. The direction is therefore tied to the ordinary answer rather than to an arbitrary frequent label. Appendix E RQ2: Comparison with Existing Methods Table A2 reports all CDH metrics for the primary setting. On MC, the paired bootstrap 95% intervals for ΔCF/ΔCS _CF/ _CS are [3.9, 12.2]/[-2.2, 3.0] for Qwen and [3.5, 10.4]/[-2.6, 1.7] for LLaVA. Thus, both models show a clear CF gain and a CS change near zero. On MC, CFAD, RPD, and CCR decrease for both models. On QA, CFAD and RPD decrease, while CCR remains at 1.0. Model Task Method CF Acc. CS Acc. CFAD↓ RPD↓ CCR↓ Qwen3-VL-32B MC Original 0.665 0.965 0.300 0.311 0.857 SPC 0.743 0.970 0.226 0.233 0.695 QA Original 0.591 0.948 0.357 0.376 1.000 SPC 0.813 0.930 0.117 0.126 1.000 LLaVA-1.6-34B MC Original 0.565 0.917 0.352 0.384 0.830 SPC 0.635 0.913 0.278 0.305 0.750 QA Original 0.535 0.922 0.387 0.420 1.000 SPC 0.774 0.874 0.100 0.114 1.000 Qwen3-VL-30B-A3B MC Original 0.635 0.948 0.313 0.330 0.869 SPC 0.730 0.904 0.174 0.192 0.694 Table A2: Complete CDH-Bench metrics with ϵCS=0.04 _CS=0.04. CFAD is CS Acc. minus CF Acc. RPD normalizes CFAD by CS Acc. CCR is the fraction of incorrect CF answers that select the paired CS answer. CCR reaches 1.0 on the original ordinary-first question form. RQ5 therefore evaluates both claim orders separately. Compared Methods All methods follow the protocol in Inputs During Online Inference. Their adjustable parameters are selected on the common 70-pair development set. We compare five types of method. Focus on Vision uses a grounding prompt inspired by vision–knowledge conflict analysis (Liu et al. 2025b). VCD (Leng et al. 2024) and MFCD (Liu et al. 2025a) contrast visual views. PAI (Liu et al. 2024b) modifies visual attention. NoLan suppresses language priors during decoding (Ren et al. 2026). REVIS changes hidden states (Wu et al. 2026). NoLan uses the token-level decoder in Eq. A18. VCD, MFCD, and PAI retain their released token-level equations and fixed parameters in implementations for each evaluated model. SPC subtracts the estimated prior preference for each answer in the current question. NoLan decoding. At generation step t, let ℓtI ^I_t and ℓtP ^P_t be the logits over all tokens from the image-conditioned and text-only decoding runs. NoLan (Ren et al. 2026) computes γt _t =12DKL(qtI∥qtP)+DKL(qtP∥qtI), = 12\D_KL(q^I_t\|q^P_t)+D_KL(q^P_t\|q^I_t)\, αt _t =β[tanh(1/γt)+1],β=0.8, =β[ (1/ _t)+1], β=0.8, ℓtN ^N_t =(1+αt)ℓtI−αtℓtP. =(1+ _t) ^I_t- _t ^P_t. (A18) Each run keeps its own decoder state. Both receive the same selected token, so they keep the same generated prefix. We update γt _t and αt _t after every token. Greedy decoding uses ℓtN ^N_t. NoLan and the matched β=0β=0 reference use the same 64-token limit. We use the released decoding equations and reported parameters. VCD uses α=1.0α=1.0, β=0.1β=0.1, diffusion step 500, and seed 42. MFCD uses Gaussian high/low views with thresholds 0.1/0.9, unit contrast weights, and β=0.3β=0.3, without its JSD or entropy extensions. PAI uses attention weight 0.2, CFG scale 1.1, plausibility threshold 0.1, and the released relative layer span from decoder layer 2 through the final layer. NoLan uses β=0.8β=0.8. Each decoding baseline applies its low-probability token filter before greedy token selection. The two decoding runs share the same generated prefix. Each baseline uses the same prompt and parser as the original model. The fixed grounding prompt prepends the following text to the original benchmark prompt: “Ground your answer in this single image only. Before deciding, silently verify the task-focused visible count, identity, attribute, material, state, relation, cause, or scale. Treat normal commonsense defaults as hypotheses, not facts. If the image conflicts with what is typical, follow the image. Do not use paired examples, dataset labels, reference images, ground-truth claims, or any information outside the task prompt and image.” It then appends the same task-specific output rule used by the original model. The separate CFG score control uses the candidate scores again. VCD, MFCD, and PAI use the token-level decoding rules described above. Our REVIS implementation follows the released direction extraction, layer search, risk calibration, and hidden-state correction (Wu et al. 2026). Direction extraction uses 100 released examples, and risk calibration uses at most 300 released examples. The risk scale is 1.0, and the threshold is the 85th percentile of factual calibration risk. The selected Qwen and LLaVA layers are 46 and 56, with thresholds −0.2178-0.2178 and −0.1068-0.1068. Their paper-reported correction strengths are 1.6 and 1.1. No CDH test label is used for extraction, calibration, or layer selection. We also evaluate the released code default of 2.5. Baseline Performance on CDH-Bench The token-level baselines make smaller and less consistent changes than SPC. On Qwen, VCD changes MC/QA by -0.9/+0.0 and +1.3/+0.0 CF/CS points. MFCD changes them by -2.2/+0.4 and +1.7/+0.0. PAI changes them by +0.4/-0.4 and +3.0/+0.0. On LLaVA, the VCD changes are +2.6/-1.7 and -0.4/+0.0. The MFCD changes are +3.5/-2.2 and -3.0/-0.4. The PAI changes are +1.3/+0.0 and +3.9/-0.4. These methods sometimes repair CDH. Their effects, however, vary across models and answer formats. NoLan (Ren et al. 2026) uses β=0.8β=0.8 without CDH tuning. Every cross-method table measures its changes from the same original predictions as the other methods. Under this comparison, it changes Qwen MC by +0.0/-4.8 CF/CS points and QA by +13.9/-0.9. The corresponding LLaVA changes are +9.6/-2.6 and +24.8/-8.7. We also compare NoLan with a matched decoding loop that sets β=0β=0. This comparison isolates the NoLan token update, although its reference predictions can differ from the common original decoder. The matched changes are +4.8/-1.7 and +15.2/-0.9 on Qwen, and +11.7/-3.5 and +24.8/-8.7 on LLaVA. The grounding prompt changes Qwen MC/QA by -0.9/+0.4 and +8.7/-0.4. For LLaVA, it changes them by -12.6/+3.0 and -13.0/+2.2. The separate CFG control applied to scores for complete answers selects γ=1.1/1.5γ=1.1/1.5 for Qwen MC/QA and γ=2.0γ=2.0 for both LLaVA tasks. It changes Qwen MC/QA by +0.9/-0.9 and -17.8/-0.4. The corresponding LLaVA changes are +6.5/+0.9 and +21.3/-4.3. This control does not include PAI’s attention edit or token-level rule. It tests a fixed contrast between image-conditioned and text-only answer scores. Allowing a larger CS decrease gives the second standard SPC setting in the main paper. With ϵCS=0.10 _CS=0.10, Qwen changes MC/QA by +8.3/-0.9 and +23.9/-4.3. LLaVA changes them by +12.2/-1.3 and +30.0/-9.6. The uncertainty-aware extension gives the same Qwen changes and +12.6/-2.2 and +30.0/-9.1 on LLaVA. The larger CS allowance increases CF repair in all four model–task combinations. Each development-set CS change remains within the selected limit. Why REVIS’s LLaVA QA Gain Does Not Transfer to MC With the selected correction strengths, REVIS changes Qwen by -1.3/+0.0 points on MC and -2.2/-0.4 on QA. On LLaVA, it changes MC by -1.3/+0.9 and QA by +14.8/-3.0. Every changed LLaVA QA answer moves from yes to no. This includes 36 CF answers and seven CS answers. MC repair instead requires changes among different answer options. This directional bias explains why the QA gain does not transfer to MC. Qwen does not show the same QA gain. Appendix F RQ3: Component Analysis of SPC RQ3 follows the three parts of SPC in the main paper: candidate-specific prior subtraction, instance-dependent correction strength, and selective answer revision. It also tests how prior estimation, paired fitting, and candidate scoring affect these parts. Why Candidate-Specific Prior Scores Matter Teacher-forced image scoring alone (λ=0λ=0) replaces the original prediction with the top image-conditioned candidate. It changes Qwen by -0.9/-1.3 points on MC and -22.6/-0.4 on QA. It changes LLaVA by -1.3/+1.7 and -3.5/+0.9. Candidate rescoring alone therefore does not explain SPC’s CF gain. Each control changes the prior scores while keeping the correction model and selection procedure unchanged. Table A3 reports the resulting accuracy changes. MC QA Score used in correction ΔCF _CF ΔCS _CS ΔCF _CF ΔCS _CS No prior subtraction (λ=0λ=0) -0.9 -1.3 -22.6 -0.4 Use image-conditioned scores as the prior estimate 0.0 0.0 0.0 0.0 Mean prior scores from development set +0.4 0.0 +20.9 -5.7 Prior scores from another question -0.7± 1.2 -1.5± 1.1 +17.4± 1.9 -4.0± 1.0 Prior scores shuffled across answers -0.7± 0.8 -0.2± 0.3 0.0± 0.0 0.0± 0.0 SPC +8.3 -0.9 +23.9 -4.3 Table A3: Effect of replacing the prior scores used by SPC on Qwen3-VL-32B. Results use the 230-pair test split. Controls that shuffle scores report mean ± standard deviation over 20 fixed seeds. Entries report ΔCF _CF or ΔCS _CS in percentage points. Every control uses ϵCS=0.10 _CS=0.10. Bold marks the highest U0.5U_0.5 in each task. All Qwen controls fit SPC again with the same search ranges and development data. One control replaces each example’s prior scores with an average for the same task and candidate count. Another uses scores from a different development question with the same task and candidate count. A third randomly changes the order of scores across answers in the current example. The two controls that move scores across examples use 20 seeds. The final control subtracts the image-conditioned score vector. It also removes all features that depend on the prior estimate. Candidate-specific prior scores give +8.3/-0.9 points on MC and +23.9/-4.3 on QA. On MC, they give a larger gain than mean prior scores with paired p=0.001p=0.001. They also outperform every run that uses another question, with p≤0.003p≤ 0.003. Repeating the controls with ϵCS=0.04 _CS=0.04 gives the same ordering. At ϵCS=0.10 _CS=0.10, every replacement has at most a 0.4-point mean MC gain, compared with 8.3 points for SPC. At ϵCS=0.04 _CS=0.04, every replacement has mean MC repair at or below zero. This result shows that the useful direction comes from matching each prior score to the same candidate in the current question. Alternative Prior Estimates SPC targets the model’s language and world knowledge preference over the supplied candidates. Removing the image is one way to estimate this preference. We also test white, black, and mean images. The mean image uses the 140 unique development images. Let p(r)p^(r) be the centered candidate-score vector from prior estimate r, where r is text-only, white, black, or mean image. We normalize each vector by its root-mean-square value. The normalized-median estimate takes the median for each candidate and restores the median scale. The three-input median applies the same operation to text-only, white, and black scores. The 25% adjustment is padj=0.75p(text)+0.25pmed.p_adj=0.75p^(text)+0.25p_med. (A19) The disagreement-weighted version reduces this adjustment for candidates on which the estimates differ. Let p~(r) p^(r) denote a normalized score and let δ(y) δ(y) =medianr|p~(r)(y)−medianr′p~(r′)(y)|, =median_r | p^(r)(y)-median_r p^(r )(y) |, (A20) w(y) w(y) =0.10.1+δ(y). = 0.10.1+δ(y). (A21) It uses p(text)(y)+0.25w(y)[pmed(y)−p(text)(y)]p^(text)(y)+0.25w(y)[p_med(y)-p^(text)(y)] and then centers the resulting vector. Table A4 fixes the SPC settings selected with ϵCS=0.04 _CS=0.04, changing only how prior preference is estimated. Input used to estimate prior preference MC ΔCF/ΔCS _CF/ _CS QA ΔCF/ΔCS _CF/ _CS Text-only (image removed) +7.8/+0.4 +22.2/-1.7 White image +6.5/-0.9 +15.7/-0.4 Black image +6.1/+0.0 +14.8/+0.0 Mean image from development set +3.9/+0.9 +0.9/+0.0 Median of normalized scores +6.1/-0.9 +15.7/+0.0 Median of text-only/white/black +6.5/-1.3 +16.1/-0.4 25% adjustment toward median +7.8/+0.9 +22.2/-2.6 Adjustment weighted by estimate disagreement +7.4/+0.4 +22.2/-2.6 Table A4: Alternative ways to estimate prior preference with Qwen3-VL-32B on 230 test pairs. SPC settings use ϵCS=0.04 _CS=0.04. Entries report ΔCF/ΔCS _CF/ _CS in percentage points. Bold marks the highest U0.5=ΔCF+0.5ΔCSU_0.5= _CF+0.5 _CS in each task. The text-only top answer agrees with the top answer from a white image on 87.4% of examples. It agrees with the top answer from a black image on 88.0%. White and black images agree on 96.3%. The mean development image agrees with text-only scoring on only 76.3%. An image formed by averaging pixels is therefore not a reliable average visual input. Combining the estimates does not improve CF repair. We therefore use text-only scoring as the default prior estimate. Why Paired CF and CS Fitting Matters The main paper separates answer scoring, learned prior subtraction, and selective answer revision. Table A5 tests which paired development outcomes are needed. All three variants use the same image-conditioned and text-only scores. They also use the same correction model and search values. They differ only in the examples used for fitting and setting selection. Test labels are never used for selection. Use of CF and CS development data MC ΔCF/ΔCS _CF/ _CS (CF repairs/harms) QA ΔCF/ΔCS _CF/ _CS (CF repairs/harms) Qwen3-VL-32B Fit and select on CF and CS +7.83/+0.43 (21/3) +22.17/-1.74 (53/2) Fit on CF and CS; select on CF +8.26/-0.87 (24/5) +23.91/-4.35 (57/2) Fit and select on CF +9.57/-58.70 (34/12) +34.35/-83.04 (82/3) LLaVA-1.6-34B Fit and select on CF and CS +6.96/-0.43 (17/1) +23.91/-4.78 (57/2) Fit on CF and CS; select on CF +12.17/-1.30 (29/1) +30.00/-9.57 (71/2) Fit and select on CF +16.96/-38.26 (44/5) +40.87/-79.57 (97/3) Table A5: Effect of CF and CS data during fitting and setting selection. Results use 230 test pairs. Selection with both sides uses ϵCS=0.04 _CS=0.04 for each task. Selection with CF alone does not observe CS correctness. Entries are in percentage points. Fitting only on CF examples makes the method change too many answers. On Qwen, it harms 140 CS examples in MC and 202 in QA while repairing only five and eleven CS examples. On LLaVA, it harms 91 and 192 CS examples while repairing three and nine. Fitting on both CF and CS but selecting settings from CF alone causes less CS harm. It still moves LLaVA from +6.96/-0.43 to +12.17/-1.30 on MC and from +23.91/-4.78 to +30.00/-9.57 on QA. Paired data therefore serve two roles. Both sides shape the model for correction strength. CS outcomes limit the cost of CF repair. Candidate Scoring Does Not Explain the Gain The preceding tests change the source of the prior scores and the data used for fitting. We next check whether the way candidate scores are computed can explain the gain. The teacher-forced score used throughout the paper is s(y)=∑t=1|y|logp(yt∣I,q,y<t),s(y)= _t=1^|y| p(y_t I,q,y_<t), (A22) with I removed in the text-only scoring condition. The scored text is the original answer token (yes/no or A/B/C/D). It is not the answer description. Table A6 compares every answer in all 1,200 examples per fully evaluated model. Task Summed-score ΔCF/ΔCS _CF/ _CS Mean-score ΔCF/ΔCS _CF/ _CS Agreement at fixed strength Selected CF agreement Selected CS agreement Qwen3-VL-32B MC +7.83/+0.43 +7.83/+0.43 100.0 100.0 100.0 QA +22.17/-1.74 +22.17/-1.74 100.0 100.0 100.0 LLaVA-1.6-34B MC +6.96/-0.43 +4.35/+0.87 100.0 96.1 97.4 QA +23.91/-4.78 +23.04/-4.78 100.0 99.1 100.0 Table A6: Comparison of summed and mean token log-probabilities. The three agreement columns compare the predictions from summed and mean scores. They cover a shared fixed correction strength and the CF and CS predictions after separate setting selection. All agreement values are percentages. The two Δ columns report percentage points. No example contains answers of unequal token length. Image-conditioned and text-only token counts always match. Stored sums equal token count times stored means. Answer length therefore cannot favor one candidate within an example. Using mean scores changes the scale and spread of scores across examples. It can therefore change which LLaVA setting is selected. Both selected settings still give positive MC and QA CF gains. The correction direction is unchanged because sum and mean scores agree at every fixed correction strength. Answer length is not the only possible scoring concern. Scoring the supplied answers could also replace the original decoder with a better classifier. Table A7 shows that this does not explain the result. It compares the original answer with the top image-conditioned candidate before prior subtraction. Their agreement is high in every model and task combination except Qwen QA on CF images. The top image-conditioned answer is already correct in only five of the 148 CF repairs made by SPC across the two models and formats. In 143 repairs, the original prediction, image-conditioned scores, and text-only scores initially favor the same wrong answer. SPC repairs these errors by changing the candidate margin. It does not simply select a correct answer already exposed by image-conditioned scoring. Model and task Original=image-scored answer CF/CS (%) CF repairs Image already correct (%) All three chose the same answer (%) Qwen3-VL-32B MC 92.2/97.8 21 19.0 81.0 Qwen3-VL-32B QA 75.7/99.6 53 0.0 100.0 LLaVA-1.6-34B MC 97.0/97.8 17 5.9 94.1 LLaVA-1.6-34B QA 96.5/98.3 57 0.0 100.0 Table A7: Agreement between the original prediction and teacher-forced candidate scoring. Results use ϵCS=0.04 _CS=0.04. “Image already correct” and “all three chose the same answer” are fractions of SPC’s CF repairs. The latter compares the original, image-conditioned, and text-only top answers before correction. Correction Strength and Selective Answer Revision Prior subtraction determines the corrected proposal. Selective answer revision determines whether that proposal replaces the original answer. We first vary the allowed CS decrease to trace this repair–retention balance. Figure A3: MC repair and retention as ϵCS _CS changes. The curves use the SPC version that accounts for uncertainty in the learned correction strength. Point labels give ϵCS _CS. Stars mark ϵCS=0.04 _CS=0.04. Open diamonds use one fixed correction strength selected under the same limit. Figure A3 shows the MC repair–retention curve. On Qwen, ϵCS=0.04 _CS=0.04 gives +7.8/+0.4+7.8/+0.4 CF/CS points. Increasing it to 0.06 gives +8.3/−0.9+8.3/-0.9, and 0.10 selects the same result. Most of the Qwen MC gain therefore appears by 0.04. On LLaVA, repair rises more steadily. It changes from 0.0/0.00.0/0.0 at 0.00 to +12.6/−2.2+12.6/-2.2 at 0.10. The open diamonds compare one fixed correction strength at ϵCS=0.04 _CS=0.04. The fixed result is competitive on this full development split. It gives more Qwen CF repair but less CS retention than the learned correction strength. It improves both test changes for LLaVA at this value. An instance-dependent strength does not always perform best on the full development split. Table A9 shows its clearer benefit for LLaVA when development data are smaller or exclude the tested category. Figure A4: CF repair and CS retention across allowed CS decreases. Results use the uncertainty-aware extension of SPC and ϵCS∈0,0.02,0.04,0.06,0.10 _CS∈\0,0.02,0.04,0.06,0.10\. SPC labels show the same limits in percentage points: 0, 2, 4, 6, and 10. Labels are combined when settings produce the same point. Fixed-strength controls use one correction strength. Controls based on direct subtraction remove text-only scores directly. The two separate answer-revision controls use the same 13 features and 70 development pairs. Figure A4 extends the focused MC curve to QA and adds three proposal and answer-revision controls. It shows the full balance between CF repair and CS retention as ϵCS _CS changes. We then hold ϵCS=0.04 _CS=0.04 fixed. Table A8 compares different ways to form and accept a corrected proposal. The controls separate the correction strength from the final revision rule. The fixed-strength control selects one strength on development data and keeps SPC’s selective answer revision. The learned-revision control instead fits a logistic revision rule from the same 13 score features. We apply this rule to proposals formed by either a fixed correction strength or direct subtraction of the text-only scores. All controls use the same development examples, selection objective, and value of ϵCS _CS as SPC. We search fixed strengths in 0.1,0.2,0.3,0.5,0.8,1.0,1.2,1.5\0.1,0.2,0.3,0.5,0.8,1.0,1.2,1.5\ and logistic-rule ℓ2 _2 penalties in 0.01,0.1,1,10\0.01,0.1,1,10\. The development set also selects the probability threshold. The selected settings (proposal scale, ℓ2 _2, threshold) are (1.2,1,0.469)(1.2,1,0.469) and (1.1,0.01,0.532)(1.1,0.01,0.532) for Qwen’s fixed and direct proposals. They are (0.5,1,0.162)(0.5,1,0.162) and (2.0,1,0.162)(2.0,1,0.162) for LLaVA. Method MC ΔCF/ΔCS _CF/ _CS QA ΔCF/ΔCS _CF/ _CS Qwen3-VL-32B NoLan +0.0/-4.8 +13.9/-0.9 Adaptive strength; always adopt proposal +9.6/-2.6 +22.6/-4.8 SPC +7.8/+0.4 +22.2/-1.7 Fixed λ=0.8λ=0.8; always adopt proposal +10.4/-2.2 +17.4/-0.9 Selected fixed strength; SPC revision rule +9.6/-0.9 +16.5/-0.4 Fixed strength; learned revision rule +6.1/+0.9 +25.2/-4.3 Direct subtraction; learned revision rule +0.9/+0.0 +0.0/+0.0 LLaVA-1.6-34B NoLan +9.6/-2.6 +24.8/-8.7 Adaptive strength; always adopt proposal +10.9/-0.9 +30.9/-10.4 SPC +7.0/-0.4 +23.9/-4.8 Fixed λ=0.8λ=0.8; always adopt proposal +11.3/-0.9 +33.0/-13.9 Selected fixed strength; SPC revision rule +7.8/+0.9 +23.0/-3.9 Fixed strength; learned revision rule +6.1/+0.9 +21.3/-4.3 Direct subtraction; learned revision rule +6.1/+0.9 +21.3/-4.3 Table A8: Effect of correction strength and selective answer revision. Results use ϵCS=0.04 _CS=0.04. Each result is ΔCF/ΔCS _CF/ _CS in percentage points relative to the common original predictions. NoLan is the released dynamic token-level rule with β=0.8β=0.8. The rows differ in how they form a proposal and whether they always adopt it, use SPC’s revision rule, or use a separately learned revision rule. Table A8 separates the corrected proposal from selective answer revision. Always adopting the proposal increases repair and also increases CS loss, especially on LLaVA QA. A fixed correction strength shifts the balance between MC and QA. A separately trained rule for answer revision allows more Qwen QA repair at a larger CS cost. NoLan improves CF in three settings and leaves Qwen MC unchanged, but its CS cost varies across models and answer formats. The fixed λ=0.8λ=0.8 row isolates the effect of using one correction strength without selective answer revision. It gives substantial CF repair, but always adopting its proposal causes a 13.9-point CS loss on LLaVA QA. By contrast, the selected fixed strength retains SPC’s revision rule. The first component row, “Adaptive strength; always adopt proposal,” tests correction without selective revision. The row “Selected fixed strength; SPC revision rule” tests whether one shared strength can replace SPC’s instance-dependent strength. For LLaVA, the fixed-strength and direct-subtraction proposals agree on every development example and all but one test example. The learned revision rule rejects that one difference, so the two LLaVA rows have the same final results. Performance with Less or Shifted Development Data We next repeat this comparison with less development data or with the tested CDH category excluded from development. Development data SPC Fixed strength Learned revision rule Qwen3-VL-32B Target category excluded 11.52 9.89 14.89 14 pairs 10.72 9.41 11.83 LLaVA-1.6-34B Target category excluded 15.43 14.35 12.72 14 pairs 13.91 10.70 11.54 Table A9: Average MC/QA utility U0.5U_0.5 in percentage points with less or shifted development data. Development data either exclude the tested CDH category or contain only 14 pairs. The 14-pair result averages five samples that preserve the category proportions. The SPC column uses the uncertainty-aware extension. Table A9 asks whether these alternatives retain their ordering when fewer development examples are available or one CDH category is excluded. The separately learned revision rule has the highest average U0.5U_0.5 in the two Qwen settings. SPC is best in both LLaVA settings. Candidate-specific prior subtraction transfers in all four conditions. The best form of answer revision differs by model. The selected correction strength varies across examples. For Qwen, the middle 50% ranges from 0.236 to 0.827 on MC and from 0.395 to 1.000 on QA. For LLaVA, it ranges from 0.713 to 0.800 and from 0.550 to 0.735. The LLaVA MC strength reaches its maximum of 0.8 on 62.6% of examples. This explains why a fixed correction strength is competitive for LLaVA MC. Only 8.9% of Qwen MC examples reach their maximum. Table A9 contains four results that either exclude a CDH category or use 14 pairs. SPC exceeds the fixed control by 1.08–3.21 utility points in all four tests. The learned revision rule is stronger on Qwen, while SPC is stronger on LLaVA. These results support adapting the correction strength, but the best final answer rule still depends on the model. Contribution of the Two Support Conditions Removing individual conditions from selective answer revision tests the two cases defined in the main paper. In the Qwen analysis with ϵCS=0.10 _CS=0.10, removing the conflict condition costs 1.7 additional MC CS points without improving QA. Allowing changes only when the image-conditioned and text-only scores prefer different answers produces at most +0.9 CF points. The case in which all scores initially prefer the same answer retains most of the gain. Many repairs therefore begin with agreement on the original wrong answer. Prior subtraction then makes a supported alternative the top answer. Direct disagreement between the two scoring conditions adds a smaller set of repairs. Effect of Development-Set Size The component tests above use all 70 development pairs. We next reduce this set while keeping the same 230 test pairs. Development pairs MC ΔCF _CF MC ΔCS _CS QA ΔCF _CF QA ΔCS _CS Qwen3-VL-32B 14 +5.7±2.5+5.7± 2.5 −1.1±2.2-1.1± 2.2 +22.0±5.1+22.0± 5.1 −3.5±2.9-3.5± 2.9 28 +5.7±2.2+5.7± 2.2 −2.7±2.0-2.7± 2.0 +24.1±3.2+24.1± 3.2 −4.8±2.7-4.8± 2.7 42 +7.8±1.2+7.8± 1.2 −1.1±1.6-1.1± 1.6 +24.4±1.6+24.4± 1.6 −4.2±1.6-4.2± 1.6 56 +8.0±0.5+8.0± 0.5 −0.3±0.9-0.3± 0.9 +23.7±2.2+23.7± 2.2 −3.9±1.2-3.9± 1.2 70 +8.3±0.0+8.3± 0.0 −0.9±0.0-0.9± 0.0 +23.9±0.0+23.9± 0.0 −4.3±0.0-4.3± 0.0 LLaVA-1.6-34B 14 +4.6±1.0+4.6± 1.0 −1.0±0.7-1.0± 0.7 +26.7±2.6+26.7± 2.6 −7.0±1.9-7.0± 1.9 28 +10.1±1.8+10.1± 1.8 −2.4±1.3-2.4± 1.3 +29.7±2.1+29.7± 2.1 −10.5±2.8-10.5± 2.8 42 +10.0±1.3+10.0± 1.3 −1.9±0.8-1.9± 0.8 +29.5±2.3+29.5± 2.3 −10.1±2.9-10.1± 2.9 56 +10.4±1.6+10.4± 1.6 −1.9±0.7-1.9± 0.7 +28.3±2.7+28.3± 2.7 −8.6±2.7-8.6± 2.7 70 +12.6±0.0+12.6± 0.0 −2.2±0.0-2.2± 0.0 +30.0±0.0+30.0± 0.0 −9.1±0.0-9.1± 0.0 Table A10: Effect of development-set size with ϵCS=0.10 _CS=0.10. Every row uses the same 230-pair test set. For each of five seeds, smaller sets are contained in larger sets. They contain one to five pairs from every subcategory. Cells report mean ± standard deviation in points. The 70-pair set is identical across seeds. These results use the uncertainty-aware extension of SPC. Table A10 shows that even one pair per subcategory produces positive mean CF change in both formats and models. More development data mainly strengthen MC and reduce Qwen MC variation. QA produces substantial CF gains with fewer examples, but its CS cost differs by model. The table shows that candidate-specific prior scores are useful early. More data are needed to stabilize answer revision. Fitting One SPC Model for MC and QA The primary SPC model is fitted jointly on MC and QA. To test the effect of this choice, we fit and select a second model using only development MC. Table A11 compares the two fits. Qwen3-VL-32B LLaVA-1.6-34B Fitting data MC QA MC QA MC and QA +7.8/+0.4 +22.2/-1.7 +7.0/-0.4 +23.9/-4.8 MC only +9.1/-0.9 +0.0/+0.0 +11.3/-2.6 +0.0/+0.0 Table A11: Effect of fitting one SPC model for both answer formats. Each entry is ΔCF/ΔCS _CF/ _CS in percentage points. Both rows use ϵCS=0.04 _CS=0.04 on the development tasks available during fitting. The MC-only model gives more MC repair but changes no QA answer. Joint fitting therefore trades some MC repair for a correction that applies to both answer formats. Appendix G RQ4: Generalization of SPC The remaining tests change CDH categories, candidate-answer orders, data splits, and evaluation benchmarks. All settings remain fixed after selection on development data. Generalization Across CDH Categories For each test, we remove one CDH category from the development set. We then evaluate only the test pairs from that category. Combining the predictions from the three held-out-category evaluations covers all 230 test pairs. Qwen obtains +8.7/+1.3 points on MC and +24.8/-4.3 on QA. LLaVA obtains +8.7/-0.9 and +27.8/-6.1. Each held-out category improves in both formats. We also repeat this procedure for each of the 14 subcategories. Aggregating the predictions from the 14 held-out-subcategory evaluations gives +7.0/-0.4 on Qwen MC and +24.3/-3.9 on Qwen QA. MC improves in nine subcategories, stays unchanged in three, and declines in two. QA improves in 13 and stays unchanged in one. No category or subcategory label enters the feature vector or setting selection. Held-out category MC ΔCF/ΔCS _CF/ _CS MC repairs/harms (CF; CS) QA ΔCF/ΔCS _CF/ _CS QA repairs/harms (CF; CS) Qwen3-VL-32B Attribute +9.3/+0.0 7/0;1/1 +10.7/-9.3 10/2;0/7 Counting +10.0/+0.0 8/0;1/1 +33.8/-3.8 27/0;0/3 Relation +6.7/+4.0 7/2;3/0 +29.3/+0.0 22/0;0/0 LLaVA-1.6-34B Attribute +5.3/+0.0 4/0;0/0 +5.3/-1.3 6/2;0/1 Counting +10.0/-1.2 8/0;0/1 +41.2/-5.0 33/0;0/4 Relation +10.7/-1.3 10/2;3/4 +36.0/-12.0 27/0;0/9 Qwen3-VL-30B-A3B Attribute +9.3/-5.3 7/0;1/5 – – Counting +8.8/-2.5 7/0;0/2 – – Relation +6.7/+1.3 7/2;3/2 – – Table A12: Generalization to CDH categories excluded from fitting. Results are in percentage points. Within a repairs/harms cell, the values before the semicolon describe CF and those after it describe CS. These results use the uncertainty-aware extension of SPC. The additional model also shows directed prior attraction. It makes 84 original MC errors on CF images. Of these, 68 (81.0%) select the prior-favored candidate. That candidate is the paired CS answer in 76 cases (90.5%). On all 230 test pairs, SPC changes CF/CS accuracy by +9.6/-4.3 points with 24/2 CF repairs/harms. Every excluded CDH category retains a positive CF change in Table A12. This gives the same qualitative conclusion as the two main models. Stability Across Data Splits Figure A5: Results over ten independent 70/230 data splits. Each split keeps five development pairs from every subcategory, and SPC is fitted again. Every point has positive CF change. CS change varies across splits. These results use the uncertainty-aware extension of SPC. Figure A5 shows the ten independent fits. For each of ten predefined seeds, we sample five pairs from every subcategory. Both image sides and both tasks stay in the same split. SPC is then fitted on 70 pairs and tested on the other 230. Table A13 reports the corresponding means and ranges. Model and task ΔCF _CF mean ± std. [range] ΔCS _CS mean ± std. [range] Qwen MC +7.57±1.01+7.57± 1.01 [6.52, 9.13] −0.83±1.19-0.83± 1.19 [-2.61, 0.87] Qwen QA +21.96±2.53+21.96± 2.53 [16.52, 24.78] −2.78±1.60-2.78± 1.60 [-5.22, -0.87] LLaVA MC +9.96±1.27+9.96± 1.27 [7.83, 11.74] −2.09±0.93-2.09± 0.93 [-3.91, -0.87] LLaVA QA +27.26±2.50+27.26± 2.50 [22.61, 30.43] −6.91±2.06-6.91± 2.06 [-9.57, -3.48] Table A13: Variation across ten independent data splits. All values are percentage points. All 40 CF changes are positive. Generalization Across MC Candidate-Answer Orders Category transfer keeps the original answer order. The next test keeps the answer meanings fixed but rotates or reverses their positions. Rotation 1 changes the old order A/B/C/D to B/C/D/A. Rotation 2 changes it to C/D/A/B. Reversal changes it to D/C/B/A. The answer letters are updated after each change. Table A14 reports the resulting accuracy. Candidate-answer order Original CF/CS Acc. SPC CF/CS Acc. ΔCF/ΔCS _CF/ _CS Qwen3-VL-32B Original 0.665/0.965 0.748/0.957 +8.3/-0.9 Rotation 1 0.665/0.961 0.739/0.939 +7.4/-2.2 Rotation 2 0.678/0.961 0.757/0.922 +7.8/-3.9 Reversal 0.687/0.970 0.739/0.939 +5.2/-3.0 LLaVA-1.6-34B Original 0.565/0.917 0.691/0.896 +12.6/-2.2 Rotation 1 0.561/0.939 0.687/0.917 +12.6/-2.2 Rotation 2 0.530/0.943 0.670/0.891 +13.9/-5.2 Reversal 0.539/0.922 0.674/0.878 +13.5/-4.3 Table A14: MC results after changing candidate-answer positions. SPC uses ϵCS=0.10 _CS=0.10 on the original development data. Answer texts and meanings are unchanged. The final column reports percentage points. These results use the uncertainty-aware extension of SPC. With ϵCS=0.04 _CS=0.04, Qwen’s CF changes range from +5.7 to +7.8 points. Its CS changes range from +0.4 to -3.0. LLaVA’s CF changes range from +6.5 to +10.0, and its CS changes range from -0.9 to -2.6. With ϵCS=0.10 _CS=0.10, the largest CF accuracy difference across orders is 1.7 points for Qwen and 2.2 points for LLaVA. Exact paired tests cover 16 comparisons. These include two models, four candidate-answer orders, and two image sides. Seven of eight CF gains remain significant at 0.05. Only Qwen reversal does not (Holm p=0.136p=0.136). For CS, only LLaVA Rotation 2 remains significant (Holm p=0.0165p=0.0165). The four orders also reveal a limitation. We first map answer letters back to their meanings. The original predictions then agree across all four orders on 86.5/95.2% of Qwen CF/CS pairs and 85.2/91.3% of LLaVA pairs. SPC with ϵCS=0.10 _CS=0.10 obtains 78.7/90.9% and 78.3/84.8%. SPC therefore does not always produce the same answer after candidate positions change. Still, CF accuracy varies little and every paired CF change is positive. The gain therefore survives changes in candidate-answer order. Transfer to Other Hallucination Benchmarks The external benchmarks use different structures. Visual CounterFact provides matched ordinary and counterfactual images (Golovanevsky et al. 2025). HallusionBench pairs easy and hard questions (Guan et al. 2024). We treat the hard question as the conflict side and its matched easy question as the control side. ConflictVIS contains MC and binary QA (Liu et al. 2025b). POPE and POPEv2 test object presence rather than a matched ordinary-state answer (Li et al. 2023, 2026). We report each benchmark in its native subsets and metrics. Open-ended benchmarks such as CHAIR and MMHal-Bench are outside SPC’s current fixed-candidate setting (Rohrbach et al. 2018; Sun et al. 2024). Table A15 shows transfer with settings selected only on CDH development data. The paragraphs that follow give the protocol and analysis for each benchmark. Benchmark Subset Original metric SPC metric ϵCS=0.04 _CS=0.04 SPC metric ϵCS=0.10 _CS=0.10 Repairs/harms ϵCS=0.04 _CS=0.04 Repairs/harms ϵCS=0.10 _CS=0.10 Visual CounterFact (Qwen) CF 0.962 0.993 0.997 38/0 42/0 CS 0.998 0.995 0.989 2/5 2/12 Visual CounterFact (LLaVA) CF 0.939 0.984 0.989 55/0 62/1 CS 0.994 0.993 0.995 1/2 3/2 HallusionBench Hard 0.607 0.659 0.668 20/3 23/3 Easy 0.848 0.838 0.820 4/7 5/14 ConflictVIS MC 0.971 0.992 0.992 8/0 8/0 QA 0.738 0.995 0.995 96/0 96/0 POPE All 0.899/0.893 0.898/0.893 0.898/0.893 6/11 6/12 POPEv2 Absent 0.686 0.671 0.671 0/1 0/1 Present 0.986 0.986 0.986 0/0 0/0 Table A15: Performance on external benchmarks. SPC settings are selected on CDH development data with ϵCS=0.04 _CS=0.04 or 0.100.10. POPE reports accuracy/F1. All other entries report accuracy. Repairs/harms are measured against the same original predictions. Visual CounterFact is evaluated with both listed models; the remaining benchmarks use Qwen3-VL-32B. With ϵCS=0.10 _CS=0.10, the CF gains remain significant on Visual CounterFact (p=4.5×10−13p=4.5× 10^-13) and HallusionBench Hard (p=8.8×10−5p=8.8× 10^-5). Both ConflictVIS gains also remain significant (p=0.0078p=0.0078 and p=2.5×10−29p=2.5× 10^-29). The larger Qwen Visual CounterFact CS change is significant (p=0.0129p=0.0129). HallusionBench Easy is not statistically significant (p=0.0636p=0.0636). POPE is also not statistically significant (p=0.238p=0.238). Neither POPEv2 side changes significantly (p=1.0p=1.0 for both). The 0.10 setting repairs more conflict cases. The 0.04 setting better preserves the matched CS side. We also evaluate NoLan with its published β=0.8β=0.8 rule. Relative to the same original predictions used for SPC, its Qwen changes are +3.1/-0.7 on Visual CounterFact and -2.1/-7.6 on HallusionBench. They are +1.3 and +24.1 on ConflictVIS MC and QA. On POPE, accuracy/F1 changes by +0.0/+0.6. On POPEv2, absent/present accuracy changes by -21.4/+0.0. The answer-token implementation uses full-vocabulary logits. Every value here uses the common original predictions as its reference. Visual CounterFact (Golovanevsky et al. 2025) provides a large paired transfer test. We use all 1,220 released color and size pairs. We retain the published questions and A/B balance. Original images form CS, and the published counterfactual images form CF. SPC settings come only from the 70 CDH development pairs. The text-only scores rank the ordinary attribute first on 92.8% of Qwen pairs and 82.1% of LLaVA pairs. The prior-favored candidate matches 45 of Qwen’s 46 original CF errors and all 75 LLaVA errors. All 121 errors select the ordinary attribute. With ϵCS=0.04 _CS=0.04, Qwen changes CF/CS by +3.11/-0.25 points. LLaVA changes them by +4.51/-0.08. The Qwen CF interval is [2.2, 4.1] points with 38/0 repairs/harms. The LLaVA interval is [3.4, 5.7] points with 55/0. Exact CF tests give p=7.28×10−12p=7.28\!×\!10^-12 and 5.55×10−175.55\!×\!10^-17. The CS changes are not significant. For Qwen, the color and size changes are +1.01/-0.81 and +4.54/+0.14. For LLaVA, they are +4.87/-0.41 and +4.26/+0.14. SPC therefore transfers beyond the CDH categories and benchmark used for fitting. Results with ϵCS=0.10 _CS=0.10 appear in Table A16. Model Method selected on CDH ΔCF _CF ΔCS _CS Qwen3-VL-32B SPC (ϵCS=0.04 _CS=0.04) +3.11 -0.25 SPC (ϵCS=0.10 _CS=0.10) +3.44 -0.82 Fixed correction strength (ϵCS=0.10 _CS=0.10) +2.38 -0.25 Separate answer revision (ϵCS=0.10 _CS=0.10) +3.44 -4.02 LLaVA-1.6-34B SPC (ϵCS=0.04 _CS=0.04) +4.51 -0.08 SPC (ϵCS=0.10 _CS=0.10) +5.00 +0.08 Fixed correction strength (ϵCS=0.10 _CS=0.10) +3.93 -0.16 Separate answer revision (ϵCS=0.10 _CS=0.10) +5.49 -0.33 Table A16: Transfer to Visual CounterFact in accuracy points. Every variant is selected on CDH development data only. Table A16 separates candidate-specific prior subtraction from correction strength and selective answer revision. Transfer remains positive with a fixed strength and with separately learned answer revision. SPC provides the better balance between CF repair and CS retention. Separate answer revision matches or exceeds CF repair but incurs a much larger Qwen CS loss. The HallusionBench transfer (Guan et al. 2024) uses 328 questions. Each question has an exact easy/hard pair with opposite ground truth. With ϵCS=0.04 _CS=0.04, SPC changes CF/CS by +5.18/-0.91 points. CF has 20 repairs and three harms (p=0.00049p=0.00049). CS has four repairs and seven harms (p=0.55p=0.55). REVIS uses its reported Qwen correction value, α=1.6α=1.6. It changes CF/CS by +0.61/-0.91 points. The intervals are [-1.2, 2.4] and [-2.7, 0.9] points. Its risk gate is active on every example and at 33.7% of hidden positions. Both methods use the same BF16 original predictions and image processing. POPE evaluation (Li et al. 2023) uses all 9,000 released questions. Original prediction and candidate scoring use the same 512-by-512 image processing. Baseline accuracy/F1 is 0.917/0.911 on random, 0.898/0.892 on popular, and 0.881/0.877 on adversarial. Across the three splits, SPC with ϵCS=0.04 _CS=0.04 changes 17 answers. These changes include six repairs and 11 harms. Overall accuracy changes by -0.06 points, and F1 changes by -0.04 points (p=0.33p=0.33). For POPEv2, we group the released annotations by image and retain the 70 image IDs selected after shuffling with seed 20260711. The modified image, from which the target object was removed, forms the absent side. Its original COCO image forms the present side. Both use the same native yes/no question. SPC changes one absent-side question and no present-side question. Selective answer revision therefore usually keeps the original prediction on this subset. ConflictVIS evaluation (Liu et al. 2025b) uses every released question with complete candidate scores. It contains 374 QA and 374 MC questions over 374 images. These cover 171 action conflicts and 203 place conflicts. We exclude the open-ended subset because SPC requires a fixed candidate set. No ConflictVIS label is used for fitting or selection. On MC, SPC changes accuracy from 0.971 to 0.992. This is a gain of 2.14 points with eight repairs and no harms (p=0.0078p=0.0078). The CFG score control gains 0.53 points. On QA, SPC changes accuracy from 0.738 to 0.995, while the CFG control reaches 0.997. These QA gains require care because all 374 labels are yes and there is no matched CS control. The MC result is therefore the more informative transfer test. Appendix H RQ5: Scope of Prior-Based Correction Binary QA can reward a method that follows a frequent answer token instead of the visual claim. We first measure the unequal answer directions in the original question form. We then reverse the same claims and vary how the question is written. The balanced claim-order test uses the original MC answer texts for 299 pairs. Pair 222 has identical CF and CS labels in its MC annotation, so its two caption answers provide the two answer texts. These texts appear only in the constructed question. They are not passed to SPC as labels or metadata. Let aCSa_CS and aCFa_CF denote the mutually exclusive ordinary and atypical answers. One question places aCSa_CS first, and the other places aCFa_CF first. Across both orders, each image has one “yes” label and one “no” label. The 70/230 pair split is unchanged. Unequal Yes/No Answers in the Original Questions In the original question form, the two CF answer groups are highly unequal. On the 218 CF examples whose correct answer is no, SPC changes Qwen accuracy by +26.1 points. On the 12 examples whose correct answer is yes, it changes accuracy by -16.7 points. The corresponding LLaVA changes are +32.6 and -16.7 points. On CS, the 218 examples whose correct answer is yes change by -4.6 and -9.6 points for Qwen and LLaVA. Neither model changes accuracy on the 12 examples whose correct answer is no. Overall QA accuracy on this question form therefore cannot show whether the method works in both yes/no answer directions. The balanced claim-order test exchanges the two claims. It keeps the image and visual question fixed. After fitting on the original question form, Qwen changes ordinary-first CF by +37.8 points and atypical-first CF by +4.3. Their 95% intervals are [31.7, 44.3] and [1.3, 7.8] points. After fitting on both claim orders, the gains are +36.1 and +11.7. Their intervals are [30.0, 42.6] and [7.4, 16.5] points. For LLaVA, fitting on the original form gives +33.0 and -1.7 points. The intervals are [27.0, 39.1] and [-6.5, 3.0] points. Fitting on both claim orders gives +46.5 and -1.3 points. The intervals are [40.0, 53.0] and [-6.1, 3.5] points. The smaller LLaVA direction is not statistically resolved. Table A17 reports the corresponding consistency and joint accuracy across both claim orders. Method Image type Consistency after exchanging claims Both claim orders correct Qwen3-VL-32B SPC fitted on original form CF 0.761→ 0.817 0.448→ 0.687 CS 0.983→ 0.939 0.974→ 0.913 SPC fitted on both orders CF 0.761→ 0.917 0.448→ 0.765 CS 0.983→ 0.943 0.974→ 0.926 CFG score control CF 0.761→ 0.422 0.448→ 0.265 CS 0.983→ 0.943 0.974→ 0.935 LLaVA-1.6-34B SPC fitted on original form CF 0.600→ 0.843 0.304→ 0.583 CS 0.922→ 0.961 0.917→ 0.948 SPC fitted on both orders CF 0.600→ 0.800 0.304→ 0.630 CS 0.922→ 0.883 0.917→ 0.870 CFG score control CF 0.600→ 0.730 0.304→ 0.470 CS 0.922→ 0.948 0.917→ 0.939 Table A17: Consistency after exchanging claims. The second measure requires both claim orders to be correct. Results use the 230-pair balanced claim-order test. Every cell reports before→ accuracy. The original prediction and the two candidate scoring conditions show where the difference between claim orders first appears. This analysis comes before selective answer revision. Table A18 asks whether each condition gives opposite predictions after the two claims are exchanged. The original prediction changes appropriately on most CS pairs but less often on CF pairs. The text-only prediction changes on only 58.3% of Qwen pairs and 47.4% of LLaVA pairs. Model Prediction source CF CS Qwen Original answer 0.761 0.983 Image-conditioned scores 0.378 0.917 Text-only scores 0.583 0.583 LLaVA Original answer 0.600 0.922 Image-conditioned scores 0.552 0.891 Text-only scores 0.474 0.474 Table A18: Pre-correction consistency under claim exchange. A prediction is consistent when exchanging the ordinary and atypical claims also reverses its yes/no answer for the same image. For ordinary-first CF questions, the text-only scores favor the ordinary answer on 99.1% of examples for both models. When the atypical claim is placed first, they favor the ordinary answer on only 57.4% of Qwen examples and 46.5% of LLaVA examples. This explains the difference between the two claim orders. Balanced development data improve Qwen’s weaker direction. They do not make LLaVA improve in both directions. In more than half of the LLaVA examples, subtraction no longer moves away from the ordinary answer. The CFG score control tests global prior suppression. On Qwen, its CF change is -19.1 points for ordinary-first questions and +16.5 for atypical-first questions. Accuracy requiring both claim orders to be correct falls to 0.265. On LLaVA, the two changes are +17.4 and +2.6, and joint accuracy rises to 0.470. Neither CFG nor SPC works reliably in both claim orders for every model. On the Contrastive form, SPC improves both directions on Qwen. It also improves consistency after exchanging claims for both models. The LLaVA result shows the remaining QA failure directly. Transfer Across Question Forms We next change the question form, not only the claim order. Every form presents the same two mutually exclusive visual claims. It does not reveal the CF or CS identity. We fit SPC on both claim orders of 70 development pairs using the Contrastive form. We then apply the same model and thresholds to 230 test pairs. The four forms are Contrastive, Instead, Choice, and Reject second. The last three are absent from development. Table A19 gives the exact templates. Question form Template Contrastive For the visual question “Q,” is the correct answer “FIRST” rather than “SECOND”? Instead Looking only at the image, should the question “Q” be answered “FIRST” instead of “SECOND”? Choice Between “FIRST” and “SECOND,” does the image support “FIRST” as the answer to “Q”? Reject second For the image-based question “Q,” would choosing “SECOND” be incorrect because “FIRST” is the right answer? Table A19: Question forms used in the claim-order test. FIRST and SECOND are replaced by the two answer texts. Exchanging them creates the ordinary-first and atypical-first versions. The CFG score control uses one strength selected on the same development split. Neither method uses test labels or separate thresholds for each form. Table A20 reports transfer to all four forms. Question form Text-only answer reverses with claim order (%) SPC ΔCF _CF ordinary/atypical first CFG ΔCF _CF ordinary/atypical first Both claim orders correct Qwen3-VL-32B Contrastive 58.3 +36.1/+11.7 -19.1/+16.5 44.8→ 76.5 Instead 46.5 +17.0/+10.0 -18.7/+19.1 45.7→ 63.0 Choice 52.6 +3.0/+10.9 -11.3/+22.2 54.3→ 63.0 Reject second 24.3 +47.0/+1.7 -27.8/+22.6 30.4→ 65.2 LLaVA-1.6-34B Contrastive 47.4 +46.5/-1.3 +17.4/+2.6 30.4→ 63.0 Instead 14.3 +57.0/-11.3 +18.3/-2.6 28.3→ 59.1 Choice 5.7 +21.3/-13.9 +12.2/-10.4 44.3→ 45.7 Reject second 0.0 +82.2/-43.0 +29.1/-23.9 0.9→ 49.1 Table A20: Transfer across question forms with the same meaning. Settings do not change for each form. The percentage is the fraction of pairs for which exchanging the ordinary and atypical claims also reverses the text-only prediction. Values in the two ΔCF _CF columns list the ordinary claim first and the atypical claim first. They report percentage points. The final column gives accuracy when both claim orders must be correct, before and after correction. Qwen improves CF in all eight combinations of question form and claim order. Its eight CS changes remain between -3.9 and +3.9 points. Six CF changes remain significant after Holm adjustment over 32 comparisons. These cover two models, four question forms, two claim orders, and two image sides. The unresolved ordinary-first Choice result is +3.0 points (p=0.092p=0.092, 95% interval [0.0, 6.1] points). The atypical-first reject second result is +1.7 points (p=0.557p=0.557, interval [-2.6, 6.1] points). As an image-free control, we select among keeping the original answer, always answering yes, always answering no, and reversing yes/no. Development selection chooses the original answer. A rule based only on claim order therefore cannot reproduce the result. The CFG control loses CF on every ordinary-first Qwen form and gains CF on every atypical-first form. LLaVA shows a different failure. Its text-only prediction changes with claim order on 47.4% of examples under the fitted form. This rate falls to 14.3%, 5.7%, and 0.0% on the three unseen forms. SPC then gains on ordinary-first questions but loses on atypical-first questions. The CFG control shows the same split. On Reject second, the two SPC CF changes are +82.2 and -43.0 points. The corresponding CS changes are -33.9 and +67.8 points. Both candidate-specific subtraction and global guidance fail in the same direction. The problem therefore arises in prior estimation. The text-only scores follow syntax instead of the ordinary claim. When the Estimated Prior Favors the Ordinary Answer An overall consistency rate can hide which pairs have a useful prior estimate. We therefore divide the test pairs before measuring accuracy. We say that the estimated prior favors the ordinary answer in both claim orders when two conditions hold. Its top answer is yes for the ordinary-first question. Its top answer is no for the atypical-first question. This definition uses only text-only scores. It does not use the image, CF/CS identity, or correct answer. Table A21 combines the two claim orders in each group. The main paper reports the two directions separately. Estimated prior Pairs ΔCF _CF 95% CI ΔCS _CS Repairs/harms (CF; CS) Qwen3-VL-32B: Contrastive Favors ordinary 132 +34.47 [28.03,41.29] -3.79 91/0;0/10 Does not favor ordinary 98 +9.69 [5.61,14.29] -1.53 22/3;0/3 Qwen3-VL-32B: Instead Favors ordinary 106 +23.58 [17.45,30.19] -0.47 50/0;0/1 Does not favor ordinary 124 +4.84 [2.42,7.66] +0.00 12/0;0/0 Qwen3-VL-32B: Choice Favors ordinary 113 +15.49 [11.06,20.35] +0.00 35/0;0/0 Does not favor ordinary 117 -1.28 [-3.42,0.43] +0.85 1/4;2/0 Qwen3-VL-32B: Reject second Favors ordinary 56 +41.07 [32.14,50.89] -0.89 46/0;0/1 Does not favor ordinary 174 +18.97 [14.94,22.99] +0.29 77/11;10/9 LLaVA-1.6-34B: Contrastive Favors ordinary 107 +33.18 [27.10,39.72] -4.67 71/0;0/10 Does not favor ordinary 123 +13.41 [8.13,18.70] -1.22 51/18;10/13 LLaVA-1.6-34B: Instead Favors ordinary 33 +34.85 [24.24,45.45] -1.52 23/0;0/1 Does not favor ordinary 197 +20.81 [17.01,24.62] -4.57 111/29;13/31 LLaVA-1.6-34B: Choice Favors ordinary 13 +15.38 [0.00,34.62] -11.54 4/0;0/3 Does not favor ordinary 217 +3.00 [-0.23,5.99] -2.53 46/33;10/21 LLaVA-1.6-34B: Reject second Favors ordinary 0 – – – 0/0;0/0 Does not favor ordinary 230 +19.57 [15.22,23.91] +16.96 189/99;156/78 Table A21: Results grouped by whether the estimated prior favors the ordinary answer in both claim orders. The reported Δ values combine both claim orders. They are percentage points. Confidence intervals resample image pairs. The final column gives CF repairs/harms followed by CS repairs/harms. Every group with a prior estimate that favors the ordinary answer improves in both claim orders. These groups also have zero CF harms in the combined analysis. A group without this alignment can still have a positive combined result when its ordinary-first gain is larger than its atypical-first loss. For example, LLaVA Reject second has a combined change of +19.57 even though the two changes are +82.17 and -43.04 points. The combined result must therefore be read with both directions. In this test, SPC is most reliable across both claim orders when the estimated prior favors the ordinary answer. Otherwise, one direction can dominate the average. This is a limit of the prior estimate, not a lack of confidence in the corrected proposal. Raising a confidence threshold cannot fix a score whose meaning changes with question form or claim order. Appendix I Statistical Tests and Computational Cost The main results compare paired predictions before and after correction. Table A22 gives the corresponding exact tests. We then report the resampling procedure and computational cost. Model Comparison Raw p Holm p Qwen3-VL-32B MC CF 0.000277 0.001662 MC CS 1.000000 1.000000 QA CF 8.55×10−148.55\!×\!10^-14 7.70×10−137.70\!×\!10^-13 QA CS 0.125000 0.375000 LLaVA-1.6-34B MC CF 0.000145 0.000870 MC CS 1.000000 1.000000 QA CF 6.14×10−156.14\!×\!10^-15 6.14×10−146.14\!×\!10^-14 QA CS 0.000977 0.004885 Qwen3-VL-30B-A3B MC CF 1.05×10−51.05\!×\!10^-5 8.39×10−58.39\!×\!10^-5 MC CS 0.030884 0.123535 Table A22: Exact two-sided McNemar tests for SPC on the 230-pair comparisons. Holm adjustment covers the ten comparisons in the table. Model generation is greedy. Each fixed setting is evaluated once because decoding is deterministic. We report exact repair/harm counts, exact two-sided McNemar tests, and 10,000 bootstrap resamples of image pairs with seed 20260712. The balanced claim-order test uses 10,000 paired resamples with seed 20260715. Holm adjustment covers 32 comparisons across models, question forms, claim orders, and CF/CS sides. Visual CounterFact also uses 10,000 resamples with seed 20260715. Its Holm adjustment covers four model and side comparisons. Each image pair is one bootstrap sample. Experiments use eight 24GB RTX 3090 GPUs with Python 3.13.9, PyTorch 2.10.0, CUDA 12.8, and Transformers 4.57.6. Median processing time per example is 1.870/3.254 seconds for Qwen QA/MC and 14.278/21.963 seconds for LLaVA QA/MC. SPC uses one original prediction plus image-conditioned and text-only candidate scoring. The evaluation code scores every answer under one condition in a single batch. Predicting the correction strength and applying selective answer revision require no additional model pass. References A. 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