Artifacts or Abduction: How Do LLMs Answer Multiple-Choice Questions Without the Question? — part 2/4

Cleaned-text code points [15689, 31503). Bibliography omitted here; source.md includes it.

Figure 3 shows no strong evidence that our LLMs memorized the test sets, as the prompts only barely surpass the majority baseline once. While impossible to rule out memorization entirely, we believe that more complex strategies lead to high choices-only accuracy, motivating our ensuing analyses on choice dynamics ( section 5 ) and question inference ( section 6 ).

## 5 Hypothesis 2: Choice Dynamics

With no evidence of memorization in section 4 , we study choice dynamics in MCQA. We define two properties of answer choices that could account for the LLMs’ high accuracy in choices-only prompts:

1) Individual Priors: LLMs may learn strong priors over specific choices from in-context learning or pretraining. For instance, an LLM may believe a priori that “Albert Einstein” is often correct, or subtly that choices containing “not” are often wrong, informing its decision in the choices-only setting.

2) Group Dynamics: LLMs may also ground the evaluation of the correctness of a choice based on its relation to surrounding choices. For example, if an LLM is given a math question with three odd choices and one even choice, the model may reason that the even choice is correct, as it has distinct parity. We define these processes as meta-strategies , where the LLM reasons or makes decisions over a group of choices beyond assessing a single choice, such as inferring the original question ( section 6 ) or eliminating similar options Balepur et al. (2023) .

In this section, we tease apart these two factors of choice dynamics. We first design a prompt format that tasks LLMs with classifying the individual correctness of choices ( section 5.1 ), isolating the effect of individual priors on choices-only accuracy. Next, we develop a scoring system to make these binary classification scores directly comparable to the accuracy of the choices-only prompt ( section 5.2 ). Finally, we assess the relation of individual priors and meta-strategies to choices-only accuracy ( section 5.3 ).

### 5.1 Prompt Design

In a full (Prompt 2.1 ) or choices-only (Prompt 3.1 ) prompt, the LLMs’ accuracy can be explained by both individual priors and group dynamics, since these prompts include all of the choices in 𝒞 \mathcal{C} . To isolate how individual priors alone affect choices-only accuracy, we prompt the LLMs to classify the correctness of each choice c ∈ 𝒞 c\in\mathcal{C} separately. Since these prompts only include a single choice, LLMs cannot use group dynamics. We create two versions of this prompt, when the question q q is present or absent, mirroring the full and choices-only prompts:

Our other few-shot prompts include all choices, using n n MCQA questions as exemplars for an n n -shot prompt, but the above individual prompts must be adapted to manage the increase of 4 ​ n 4n total exemplars (4 choices c c per n n questions). Thus, to keep an n n -shot format, we segment the exemplars such that ⌈ n 2 ⌉ \lceil\frac{n}{2}\rceil classify a random distractor as False and ⌊ n 2 ⌋ \lfloor\frac{n}{2}\rfloor classify the gold answer as True , balancing exposure to both True and False labels.

### 5.2 Converting Individual Scores

To study MCQA when LLMs can use individual priors and group dynamics versus only individual priors, we seek to compare the accuracies of the group full and choices-only prompts (Prompts 2.1 , 3.1 ) against their individual counterparts (Prompts 5.1 , 5.1 ). But the group setting is four-way classification, while the individual setting is binary classification, preventing a direct comparison of the tasks.

Thus, we introduce a function that converts the binary accuracy in the individual setting to a score comparable to the four-way accuracy in the group setting. Based on elimination testing Ben-Simon et al. (1997) , we define s ​ c ​ o ​ r ​ e ​ ( 𝒞 t ​ r ​ u ​ e , c g ) score(\mathcal{C}_{true},c_{g}) , returning the chance the LLM picks the gold choice c g ∈ 𝒞 c_{g}\in\mathcal{C} given the choices 𝒞 t ​ r ​ u ​ e ⊆ 𝒞 \mathcal{C}_{true}\subseteq\mathcal{C} it classifies as True : s ​ c ​ o ​ r ​ e ​ ( 𝒞 t ​ r ​ u ​ e , c g ) = { 0.25 if ​ | 𝒞 t ​ r ​ u ​ e | = 0 0 elif ​ c g ∉ 𝒞 t ​ r ​ u ​ e 1 | 𝒞 t ​ r ​ u ​ e | elif ​ c g ∈ 𝒞 t ​ r ​ u ​ e score(\mathcal{C}_{true},c_{g})=\begin{cases}0.25&\text{if }|\mathcal{C}_{true}|=0\\ 0&\text{elif }c_{g}\notin\mathcal{C}_{true}\\ \frac{1}{|\mathcal{C}_{true}|}&\text{elif }c_{g}\in\mathcal{C}_{true}\end{cases} If the LLM predicts False for all choices (i.e. | 𝒞 t ​ r ​ u ​ e | = 0 |\mathcal{C}_{true}|=0 ), it implies uncertainty and equates to random guessing, giving a score of 0.25. Otherwise, if the LLM does not classify the gold answer c g c_{g} as True (i.e. c g ∉ 𝒞 t ​ r ​ u ​ e c_{g}\notin\mathcal{C}_{true} ), the LLM would not select c g c_{g} when given 𝒞 \mathcal{C} , resulting in a score of 0. Lastly, when c g ∈ 𝒞 t ​ r ​ u ​ e c_{g}\in\mathcal{C}_{true} , the LLM’s ability to pick c g c_{g} is akin to guessing among 𝒞 t ​ r ​ u ​ e \mathcal{C}_{true} , yielding a score of 1 | 𝒞 t ​ r ​ u ​ e | \frac{1}{|\mathcal{C}_{true}|} . With this scoring, we can directly compare the group and individual prompt accuracies.

### 5.3 Results

In Figure 4 , on ARC and MMLU, both the group full prompt and its individual counterpart lead in accuracy, followed by the group choices-only prompt and its individual counterpart. The individual full prompt bests the group choices-only prompt, implying that seeing the question is more helpful than seeing all the choices on these datasets. Further, the individual choices-only prompts underperform the group choices-only prompts. Thus, the LLMs’ individual priors alone do not fully explain the choices-only accuracy, suggesting the use of meta-strategies and group dynamics in choices-only settings.

On HellaSwag, the trend varies by model. For LLaMA, the order mirrors ARC/MMLU, but the group choices-only prompt bests the individual full prompt. Hence, for LLaMA, seeing all choices is more informative than the question, and the LLM may still use meta-strategies. In contrast, for Mixtral and Phi, the individual prompts surpass their group versions. This implies that these LLMs may: 1) mainly use individual priors in the choices-only setting; and 2) struggle with the context present in group prompts, due to the dataset’s longer choices.

Takeaway: Partial-input models are often linked to simple shortcuts Du et al. (2023) , such as using statistical cues in individual choices, but we find that LLMs may reason over groups of choices. To study when meta-strategies can effectively be used by LLMs, future works can try to manually control specific properties of distractors (e.g. parity).

## 6 Hypothesis 3: Question Inference

Given the potential use of meta-strategies ( section 5 ), we see if LLMs can use abductive reasoning—giving the best rationale for an observation Peirce (1974) —in choices-only settings. Inspired by work using LLMs to verbalize inferences Hoyle et al. (2023) , we test this via abductive question inference (AQI) . Below, we design ( section 6.1 ), evaluate ( section 6.2 ), and qualitatively analyze ( section 6.3 ) AQI.

### 6.1 Prompt Design

We implement AQI via the two-step process of: 1) generating a question q g ​ e ​ n q_{gen} using the choices 𝒞 \mathcal{C} ; and 2) asking the LLM to pick the correct answer a a to its own question q g ​ e ​ n q_{gen} . Step 1 uses the prompt:

We extract q g ​ e ​ n q_{gen} from Prompt 6.1 5 5 5 The LLM also outputs “ Answer: a \texttt{Answer:}\;a ” after q g ​ e ​ n q_{gen} . We initially wanted AQI to be 1 step where q g ​ e ​ n q_{gen} acts as a chain-of-thought (i.e. merge steps one and two of AQI), but this 1-step process is less effective (see Appendix B.5 ). to perform step two of AQI, where the LLM answers q g ​ e ​ n q_{gen} :

In Prompt 6.1 , the LLM may ignore q g ​ e ​ n q_{gen} , treating it like the choices-only prompt (Prompt 3.1 ). To test this, we design a baseline where the LLM must answer q r ​ a ​ n ​ d q_{rand} , a randomly sampled question from the test set unrelated to the current choices 𝒞 \mathcal{C} :

If the self-ask prompt outperforms the random question prompt, the generated question q g ​ e ​ n q_{gen} provides more useful information than a random question q r ​ a ​ n ​ d q_{rand} , suggesting that the LLM is using q g ​ e ​ n q_{gen} .

### 6.2 Quantitative Results

AQI always results in an accuracy near the choices-only prompt on ARC and MMLU (Figure 5 ). One hypothesis is that the LLMs ignore the generated question q g ​ e ​ n q_{gen} in the self-ask prompt (Prompt 6.1 ), but in 11/12 cases, using the random question q r ​ a ​ n ​ d q_{rand} underperforms q g ​ e ​ n q_{gen} . Thus, q g ​ e ​ n q_{gen} is of higher average quality 6 6 6 It is also possible for q r ​ a ​ n ​ d q_{rand} to be misleading and q g ​ e ​ n q_{gen} to just be irrelevant/non-misleading. However, our qualitative analysis ( section 6.3 ) reveals that q g ​ e ​ n q_{gen} is often answerable by the choices, and thus we claim that it is higher quality than q r ​ a ​ n ​ d q_{rand} . than q r ​ a ​ n ​ d q_{rand} , meaning our LLMs can extract information from q g ​ e ​ n q_{gen} relevant to answering the question. Further, on HellaSwag for Falcon, Phi, and Mixtral, AQI bests the choices-only prompt. AQI is a reasoning-based strategy and thus, future works can try to reason with other strategies Huang and Chang (2023) to see if LLMs can obtain even higher accuracy in choices-only settings.

Since the choices-only prompt and AQI perform similarly, the choices-only prompt may effectively function as the two-step process of AQI. To test this, we use Cohen’s κ \kappa Cohen (1960) to quantify if the choices-only prompt and AQI answer similar questions correctly and incorrectly. The two strategies exhibit moderate agreement (average κ \kappa of 0.32), much higher than a random baseline near 0 (Table 1 ). Thus, while LLMs may implicitly perform AQI in choices-only prompts, we speculate that they may also employ other strategies jointly, such as reasoning over multiple inferred questions.

### 6.3 Qualitative Analysis

In our qualitative analysis, we study the behavior of AQI grouped into three research questions below. We use ARC, as MMLU has questions requiring expert knowledge, and HellaSwag contains multi-sentence questions that are hard to interpret. We study LLaMA’s outputs, but show other LLMs and examples of inferred questions in Appendix B.6 .

Q1—Why can AQI fail : We study when AQI ends up picking the correct (gold) or incorrect (non-gold) choice, sampling 50 cases of each. The two errors of AQI we examine are: 1) generating a question q g ​ e ​ n q_{gen} that cannot be answered by any choice; and 2) selecting a choice a a that does not answer q g ​ e ​ n q_{gen} . We compute IP (Ans), the proportion where q g ​ e ​ n q_{gen} is answerable by one of the choices, and for each answerable q g ​ e ​ n q_{gen} , if the model correctly answers q g ​ e ​ n q_{gen} ( IP (Corr | Ans)). In Table 2 (left), IP (Ans) and IP (Corr | Ans) are high (over 0.8), even when AQI leads to an incorrect answer. Thus, AQI errors with LLaMA mostly stem from inferring questions related to non-gold choices, rather than generating an unanswerable q g ​ e ​ n q_{gen} or incorrectly answering q g ​ e ​ n q_{gen} .

Q2—Can LLMs infer the original question: For each answerable q g ​ e ​ n q_{gen} studied in Q1, we annotate if it matches the meaning of the original question ( IP (Match | Ans)). When a a is incorrect, q g ​ e ​ n q_{gen} never matches the original question, but remarkably, in 43 cases when q g ​ e ​ n q_{gen} is answerable and a a is correct, it matches the original question 42% of the time (Table 2 , right). None of the matches are identical, leading us to believe that this ability is not due to exact memorization. The high rate of matched questions suggests that LLMs may have the ability to verbalize MCQA inferences via abductive reasoning, motivating future works to study the faithfulness of these rationales Turpin et al. (2023) .

Q3— When is AQI effective: We explore the effectiveness of AQI based on the nature of the inferred question q g ​ e ​ n q_{gen} . We sample 100 AQI cases with LLaMA on ARC and mark each q g ​ e ​ n q_{gen} as: 1) unanswerable; 2) answerable and not matching the original question q q ; or 3) answerable and matching q q . To isolate the efficacy of question inference from LLaMA’s ability to answer questions, we have one “oracle” annotator read each q g ​ e ​ n q_{gen} and mark all correct choices 𝒞 a ​ n ​ s ⊆ 𝒞 \mathcal{C}_{ans}\subseteq\mathcal{C} with access to Google. The annotator can mark multiple options as correct to account for when q g ​ e ​ n q_{gen} is ambiguous. The score of this human/LLM team is 0 if the gold answer is not in 𝒞 a ​ n ​ s \mathcal{C}_{ans} , and 1 | 𝒞 a ​ n ​ s | \frac{1}{|\mathcal{C}_{ans}|} if the gold answer is in 𝒞 a ​ n ​ s \mathcal{C}_{ans} .

Table 3 shows that, as expected, the average human/LLM score is 0 when q g ​ e ​ n q_{gen} is unanswerable and 1 when q g ​ e ​ n q_{gen} matches q q . However, when q g ​ e ​ n q_{gen} is answerable and does not match q q , it obtains a score of 0.293—above random guessing (0.25). Thus, even when LLaMA generates a question distinct from the original, it still often pertains to the gold answer, indicating an ability to infer questions relevant to the gold answer beyond random chance.

Takeaway: In some cases, LLMs can use reasoning to reconstruct the question from the choices. AQI is more impressive than the surface-level shortcuts linked with artifacts Du et al. (2023) , but it cannot fully explain choices-only accuracy, meaning that the rest of the choices-only accuracy could be attributed to artifacts and surface-level shortcuts. Thus, while we support artifact-robust evaluations to test LLMs as intended, we also urge researchers to not fully dismiss successful partial-input models Srikanth and Rudinger (2022) , as such models may still employ impressive, unexpected reasoning.

## 7 Related Work

### 7.1 Dataset Artifacts

Data collection protocols can introduce artifacts exploitable by models Du et al. (2023) . Artifacts stem from many sources, such as biases in crowdworkers Gururangan et al. (2018) ; Geva et al. (2019) ; Parmar et al. (2023) or models in synthetic data Yu et al. (2023) . Model reliance on artifacts poses risks, leading to performance overestimation and generalization issues Wiegreffe and Marasović (2021) .

One approach to uncover artifacts is partial-input models Poliak et al. (2018) , which omit parts of inputs. Such models include hypothesis-only models in NLI Poliak et al. (2018) ; Herlihy and Rudinger (2021) ; Srikanth and Rudinger (2022) , passage-only models in reading comprehension Kaushik and Lipton (2018) ; Shah et al. (2020) , and question-only models in visual QA Goyal et al. (2017) .

Other methods to find artifacts include text perturbations Feng et al. (2019) ; Sugawara et al. (2019) ; Gardner et al. (2020) , adversarial data Jia and Liang (2017) ; Wallace et al. (2019) ; Morris et al. (2020) , and probing experiments Glockner et al. (2018) ; McCoy et al. (2019) . To limit artifacts and reliably assess models, works have used special training objectives Belinkov et al. (2019) ; Mersinias and Valvis (2022) , debiasing procedures Ravichander et al. (2023) , human-AI data collection Liu et al. (2022) , and context altering to flip model decisions Srikanth and Rudinger (2022) ; Elazar et al. (2023) .

Conversely, we show that LLMs can obtain high partial-input MCQA accuracy with few examples.

### 7.2 MCQA Decision Making

We study three facets of MCQA decision making: memorization, choice dynamics, and question inference. Each has been explored in prior works.