Negative Candidate-included Question (NCQ)

• NCQ is a framework that embeds explicitly included negative candidates (e.g., decoys, rejected questions) into various QA setups to guide model inference.
• It enforces design constraints such as neutrality, question-only unresolvability, and image-only unresolvability to prevent shortcut exploitation.
• NCQ applications span visual QA, conversational search, and reinforcement learning, improving model calibration, negation reasoning, and policy-level performance.

Negative Candidate-included Question (NCQ) denotes a class of question-answering or prompting setups in which the decision is made in the presence of explicitly included negative candidates. In the original visual question answering usage, an NCQ is a multiple-choice item containing one target answer and several decoys; later work maps the same idea onto conversational search with previously rejected clarifying questions, binary decision prompts that explicitly include a negative token such as “No,” and reinforcement-learning reformulations that aggregate a model’s wrong rollouts into a prompt (Chao et al., 2017, Bi et al., 2021, Yu et al., 2024, Lee et al., 16 Jun 2026). Across these settings, the recurrent issue is not simply whether negatives are present, but whether they are informative, balanced, and semantically controlled enough to prevent shortcut exploitation.

1. Conceptual scope and core formulations

The NCQ concept is used most explicitly in multiple-choice visual QA, where each item comprises a target $T$ and decoys $D$ (Chao et al., 2017). Related literatures do not always use the same term, but they instantiate closely aligned mechanisms. In conversational search, the next yes/no clarifying question is selected relative to a negative set $Q_h$ of previously rejected questions (Bi et al., 2021). In binary reasoning prompts, the instruction itself includes answer candidates such as “Yes” and “No,” making the negative option part of the prompt’s control structure (Yu et al., 2024). In ZPPO, an NCQ is a prompt reformulation that aggregates wrong student rollouts, explicitly lists their wrong final answers, and presents compressed wrong reasoning traces in <candidate> tags (Lee et al., 16 Jun 2026).

Setting	Negative candidate form	Operational role
Visual QA	Decoy answers alongside the target	Prevents answer-prior and single-modality shortcuts
Conversational search	Previously rejected clarifying questions	Pushes selection away from known negatives
Binary reasoning prompts	Explicit “No” or equivalent negative token	Can induce systematic negative bias
RL post-training	Wrong rollouts and wrong final answers	Exposes shared failure modes on hard questions

This broader scope suggests that NCQ is best understood as a design pattern for structuring errorful alternatives. The negative candidate may be a decoy answer, a rejected prior question, a negated proposition, or a compressed trace of prior failures. What remains invariant is that the negative candidate is included explicitly enough to shape either inference, training, or evaluation.

2. Visual QA: decoy design, annotation artifacts, and constructive negatives

The most influential early analysis of NCQ design was carried out for multiple-choice visual question answering, where weak decoys were shown to create strong annotation artifacts (Chao et al., 2017). On Visual7W test, a simple frequency-based target-likelihood diagnostic already reached $48.73\%$ accuracy, close to a trained answers-only model. For an answer candidate $C$, the diagnostic was defined as

$P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$

The empirical pattern was stark. On Visual7W, which is 4-way multiple choice with random accuracy $25\%$, the answers-only model achieved $52.9\%$, image+answers $62.4\%$, question+answers $58.2\%$, and full image+question+answers $D$0, while humans reached $D$1 (Chao et al., 2017). On VQA, which used 18-way candidate sets with random accuracy about $D$2, answers-only was $D$3, image+answers $D$4, question+answers $D$5, and full image+question+answers $D$6, with human performance about $D$7 (Chao et al., 2017). These results showed that learners could ignore the image, the question, or both and still perform well.

The remedy was a principled decoy-generation framework governed by three constraints: Neutrality, Question-only Unresolvable (QoU), and Image-only Unresolvable (IoU) (Chao et al., 2017). Neutrality required sourcing decoys from the pool of target answers so that answer priors were rebalanced. QoU required decoys to be plausible given the question alone, so that the image had to be consulted. IoU required decoys to be plausible given the image alone, so that the question had to be consulted. QoU decoys were retrieved from similar questions using average word2vec embeddings and cosine similarity,

$D$8

followed by string-containment filtering and WordNet Wu–Palmer filtering with threshold $D$9. IoU decoys were harvested from targets of other questions associated with the same image and passed through the same filters. The main model used for analysis was a one-hidden-layer MLP with ResNet-200 image features and average word2vec text features, trained with binary logistic loss (Chao et al., 2017).

The resulting “constructive” negatives materially changed what models had to learn. On Visual7W with combined IoU+QoU decoys, answers-only fell to $Q_h$0, image+answers to $Q_h$1, question+answers to $Q_h$2, and full image+question+answers to $Q_h$3, while human performance remained $Q_h$4 (Chao et al., 2017). On qaVG, the new multiple-choice dataset built from Visual Genome, IoU+QoU evaluation yielded $Q_h$5 for MLP-IQA, $Q_h$6 for an attention model, and $Q_h$7 for humans (Chao et al., 2017). The paper also introduced qaVG from Visual Genome, with $Q_h$8 images and $Q_h$9 IQT triplets, making it the largest dataset created in that study for this task. A central conclusion was that better negatives reveal model differences that original decoys had masked.

3. Conversational search: negative feedback as an NCQ state variable

In conversational search, the NCQ idea is recast as next-question selection conditioned on negative feedback (Bi et al., 2021). The task assumes an ambiguous or faceted topic $48.73\%$0 and a conversation history

$48.73\%$1

where $48.73\%$2 and, in the training histories used in the paper, all answers are “no” until success. The negative candidate set is

$48.73\%$3

Candidate questions are labeled with $48.73\%$4 if they cover the user’s true intent, $48.73\%$5 if they are relevant but not the true intent, and $48.73\%$6 if they are irrelevant. The goal is to identify a $48.73\%$7 question within a turn limit $48.73\%$8 (Bi et al., 2021).

The key mechanism is Maximum Marginal Relevance. In generic form,

$48.73\%$9

with intent anchor $C$0 and negative set $C$1 (Bi et al., 2021). The proposed MMR-BERT model implemented this with BERT pairwise encodings and a MaxPool aggregation over negatives:

$C$2

This separated relevance to the topic from dissimilarity to previously rejected questions. Training used bert-base-uncased, domain pre-fine-tuning for 3 epochs, BERT-INIT training for 5 epochs, then model-specific heads trained for 10 epochs with Adam at learning rate $C$3; transformer layers were frozen for MMR-BERT to improve stability on Qulac (Bi et al., 2021).

On the refined Qulac setting, which contained 198 topics, 762 facets, 2,639 questions, 10,277 question-answer pairs, and 8,962 expanded conversations, MMR-BERT achieved the best intent-identification results across most metrics (Bi et al., 2021). MRR over label-2 questions was $C$4 versus $C$5 for BERT-GT; NDCG@3 over label-2 was $C$6 versus $C$7; NDCG@5 over label-2 was $C$8 versus $C$9 (Bi et al., 2021). Success rates were $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$0 by 3 turns, $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$1 by 4 turns, and $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$2 by 5 turns. The same conversations also improved downstream document retrieval, with MRR $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$3 versus $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$4, P@1 $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$5 versus $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$6, and NDCG@1 $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$7 versus $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$8 (Bi et al., 2021).

The limitations are equally informative. Aggressive diversification away from negatives can miss sibling facets under the same meaning, and navigational facets are fewer and phrased differently, so candidate coverage can become the bottleneck (Bi et al., 2021). This indicates that NCQ design in conversational search is not simply a diversity problem: it is a constrained negative-conditioning problem in a small intent space.

4. Negation-centered NCQs in multimodal and reading-comprehension benchmarks

Negation-oriented benchmarks turn NCQ into a direct test of whether models can distinguish a proposition from its negation. MAQA formulates this in multimodal QA with fixed candidates $P(\text{correct}\mid C)= \begin{cases} 0.5, & \text{if C is never seen in training,}\[3pt] \frac{\#\text{times C as target}}{\#\text{times C as target} + (\#\text{times C as decoy})/K}, & \text{otherwise.} \end{cases}$9 and questions that may be positive or negated (Li et al., 2023). It is derived from the music portion of AudioSet, using 141 music attributes across instruments, genres, moods, and roles, with $25\%$0 unique training clips and $25\%$1 evaluation clips. The benchmark includes ASBaseTrain with $25\%$2 non-negated QA pairs and ASNegationTrain, which adds $25\%$3 negated counterparts (Li et al., 2023).

The principal result was that standard fine-tuning on non-negated questions did not yield negation competence. When trained only on ASBaseTrain-PaLM and evaluated on ASNegationEval, models achieved AUC about $25\%$4–$25\%$5, average accuracy about $25\%$6, non-negated accuracy about $25\%$7–$25\%$8, and negated accuracy only about $25\%$9–$52.9\%$0 (Li et al., 2023). Increasing model size from MT5-Base to MT5-XL or swapping audio encoders between VGGish and MuLan did not fix this. By contrast, training on ASNegationTrain-PaLM yielded AUC about $52.9\%$1–$52.9\%$2 and average, negated, and non-negated accuracies all around $52.9\%$3–$52.9\%$4 (Li et al., 2023). Template-based augmentation helped but remained weaker, with AUC about $52.9\%$5–$52.9\%$6, average accuracy about $52.9\%$7–$52.9\%$8, and negated accuracy about $52.9\%$9–$62.4\%$0. The study attributed the gap to linguistic distribution mismatch and to PaLM-generated negations being more natural than rigid templates.

CONDAQA addresses a related problem in reading comprehension by centering questions on the implications of negated statements in paragraphs rather than on surface negation alone (Ravichander et al., 2022). It contains $62.4\%$1 question-answer pairs, $62.4\%$2 negation cues in total, and $62.4\%$3 test-set cues unseen in training. Most items, over $62.4\%$4, are Yes/No/Don’t know, and each question can be paired with up to four passage variants: the original, a paraphrase of the negated statement, a scope-changed edit, and a negation-reversed affirmative edit (Ravichander et al., 2022). This supports both accuracy and a stricter consistency metric computed over contrastive groups.

The benchmark remained difficult for current models. Human performance was $62.4\%$5 accuracy and $62.4\%$6 consistency on the ALL metric, whereas the best fully finetuned model, UnifiedQA-v2-3B, reached $62.4\%$7 accuracy and only $62.4\%$8 consistency (Ravichander et al., 2022). Edit-level consistency for that model was $62.4\%$9 on paraphrase, $58.2\%$0 on scope, and $58.2\%$1 on affirmative edits. The dataset also exposed systematic underprediction of Don’t know and a bias toward No (Ravichander et al., 2022). Together with MAQA, this establishes that NCQ competence under negation depends on exposure to negated compositions, sensitivity to scope, and evaluation protocols that do not let strong performance on non-negated cases mask systematic failure on negated ones.

5. Binary NCQ prompts and negative bias in LLMs

A distinct line of work studies NCQ not as dataset construction but as prompt-induced model bias (Yu et al., 2024). Here the NCQ is a binary decision prompt that explicitly lists answer candidates, including a negative token such as “No.” Across StrategyQA, MuSiQue, GSM8K, MATH, and AR-LSAT transformed into yes/no or verification settings, the reported pattern was that precision was much higher than recall, and negative responses were both more frequent and more confident than positive ones (Yu et al., 2024). The authors linked this to attention heads that attend disproportionately to the negative candidate token in the instruction regardless of question semantics.

To quantify this, the paper introduced the Negative Attention Score (NAS). For layer $58.2\%$2, head $58.2\%$3, prompt $58.2\%$4, instruction length $58.2\%$5, prompt length $58.2\%$6, and instruction token positions $58.2\%$7 and $58.2\%$8, the score is

$58.2\%$9

Higher NAS indicates stronger negative preference among heads that attend to both candidate tokens (Yu et al., 2024). On a 1,500-sample test set, correlations between NAS and negative confidence were positive across all tested models: LLaMA3-8B showed Pearson $D$00 and Spearman $D$01; Mistral-7B $D$02 and $D$03; Gemma-7B $D$04 and $D$05; Qwen2-7B $D$06 and $D$07 (Yu et al., 2024). Negative heads identified by NAS were also query-agnostic, with overlap across three domains ranging from $D$08 to $D$09.

The mitigation method, NASA, is a parameter-efficient fine-tuning procedure that updates only the query and key projection matrices of selected negatively biased heads (Yu et al., 2024). Training uses false-negative probing examples whose correct answer token is “Yes,” with gradients applied only to the selected head at each tuning stage. The method includes head-wise sequential tuning, early stopping based on SingleHeadNAS and ModelNAS, update cancellation if tuning worsens validation NAS, and an overall halting threshold $D$10 derived from the true-positive subset. The reported hyperparameters were learning rate $D$11, batch size $D$12, maximum $D$13 epochs per head, warmup ratio $D$14, and hardware of $D$15 NVIDIA A40 GPUs with about 3 hours per run (Yu et al., 2024).

The quantitative effect was a substantial narrowing of the precision–recall gap. For LLaMA3-8B on StrategyQA, accuracy changed from $D$16 to $D$17, precision from $D$18 to $D$19, recall from $D$20 to $D$21, F1 from $D$22 to $D$23, and NAS from $D$24 to $D$25 (Yu et al., 2024). On MuSiQue, the same model moved from accuracy $D$26 to $D$27, recall $D$28 to $D$29, F1 $D$30 to $D$31, and NAS $D$32 to $D$33. Calibration also improved: for Mistral-7B, Expected Calibration Error decreased on every reported dataset, including $D$34 on rephrased MuSiQue and $D$35 on rephrased AR-LSAT (Yu et al., 2024). The gains generalized across candidate token choices such as True/False and Correct/Wrong, and across paraphrased instructions. The main limitation noted was that on some math datasets recall could exceed precision after tuning, suggesting sensitivity that might require additional regularization.

6. Reinforcement learning, informative negatives, and resource construction

ZPPO introduces NCQ into reinforcement-learning post-training as a prompt-side mechanism for extracting signal from all-wrong groups (Lee et al., 16 Jun 2026). In GRPO-style on-policy RL, hard questions can yield zero advantage because every rollout is wrong. ZPPO defines a hard question as one whose mean rollout accuracy is below half, $D$36, and for such questions constructs an NCQ that aggregates all wrong student rollouts. The prompt explicitly lists the wrong final boxed answers and appends compressed wrong reasoning traces in <candidate> tags, followed by an instruction requiring > ... reasoning and a boxed final answer (Lee et al., 16 Jun 2026). Candidate compression is performed by a frozen teacher with a 512-token cap per candidate; the student group size is $D$37; there is no top-$D$38 filtering or clustering; replay uses $D$39 with buffer capacity $D$40 and FIFO eviction; augmentation is capped at $D$41 of new questions per step (Lee et al., 16 Jun 2026). Because only student-generated response tokens enter the policy gradient, the method preserves on-policy learning at the response level.

Component ablations showed that NCQ alone provided consistent gains over replay-buffer baselines, and that its relative contribution increased with model size (Lee et al., 16 Jun 2026). On 16 VLM benchmarks, the 0.8B student improved from $D$42 under GRPO† to $D$43 with NCQ, while the 9B student improved from $D$44 to $D$45. On held-out LLM suites, 0.8B improved from $D$46 to $D$47, 4B from $D$48 to $D$49, and 9B from $D$50 to $D$51 with NCQ alone (Lee et al., 16 Jun 2026). The paper also reported that BCQ+NCQ together were strongest, especially for small students, while NCQ became relatively more important when teacher-correct candidates became scarce at higher capability.

A separate but complementary line of work addresses how to build high-quality negative knowledge resources that can serve as negative candidates in QA and chatbots (Arnaout et al., 2022). UnCommonSense starts from an open-world commonsense KB and imposes a local closed-world assumption over comparable concepts. Comparable concepts are selected by shared hypernyms and cosine similarity over Wikipedia2Vec embeddings, retaining the top $D$52 siblings. Candidate negatives are generated when a comparable concept has a fact $D$53 but the target concept lacks $D$54, and are then filtered by SBERT similarity with threshold $D$55, BERT masked-LM probing with top-$D$56, and a genericity threshold $D$57 (Arnaout et al., 2022). Remaining candidates are ranked by strict and relaxed sibling frequency. The released resource contains up to top-1k negations per primary Ascent concept, totaling $D$58 million negative statements across about $D$59 concepts (Arnaout et al., 2022).

The reported gains indicate that informative negatives are materially different from arbitrary absences. In intrinsic evaluation, UnCommonSense-S achieved informativeness $D$60, compared with $D$61 for Quasimodo and $D$62 for GPT-3neg, while maintaining false negatives at $D$63 (Arnaout et al., 2022). Relaxed recall@10 against ConceptNet-neg was $D$64, far above the cited baselines. In an extrinsic multiple-choice QA study on a CommonsenseQA subset aligned with Ascent, UnCommonSense produced 108 helpful eliminations of wrong options, versus 35 for NegatER and 17 for Quasimodo, although it also made 22 unhelpful eliminations of correct options (Arnaout et al., 2022). This suggests that NCQ construction benefits when negative candidates are not merely incorrect, but contextually informative and semantically near the target.

Taken together, these results define a common technical doctrine for NCQ design. Negative candidates should be balanced against answer priors, semantically plausible under some restricted view of the input, and informative enough to force the model to use the intended evidence. When negatives are poorly designed, models exploit frequency, scope insensitivity, or prompt-token bias; when negatives are constructive, they expose genuine multimodal grounding, intent discrimination, negation reasoning, calibration behavior, or policy-level failure modes.