StateSwap: Probing Support-Elimination Hidden States in Multiple-Choice Questions

Large language models often answer the same multiple-choice question inconsistently when it is posed under support-oriented and elimination-oriented framings. We investigate whether these discrepancies arise from different internal representations induced by the two framings. We introduce a dual-framing protocol with minimally varied prompts that use either support- or elimination-oriented framing while keeping the evaluation target fixed. To probe the internal computation, we append an untrained special token, [STATE], and treat its residual-stream activation as an intervention interface. Across both models, the two framings induce separable [STATE] activations concentrated in intermediate layers. Swapping these activations between paired prompts systematically changes predictions and improves cross-framing agreement, providing intervention-based evidence that the activations are behaviorally relevant. Beyond instance-level substitution, mean-difference steering directions derived from the dual-framing contrast exhibit more bounded layer-wise responses than matched contrastive activation addition directions under the evaluated protocol.

Large Language Models Systematically Favor Popular Options: Evidence and Mitigation Across MCQs

Multiple-choice questions (MCQs) are a standard format for evaluating large language models (LLMs), yet the popularity of answer options can confound evaluation. Modern LLMs systematically prefer popular but incorrect options over less popular correct ones, a vulnerability we call \textbf{popularity bias}. This pattern aligns with confidence miscalibration: model confidence remains high even as accuracy collapses for popular options. To systematically isolate this phenomenon, we introduce \textbf{PopMCQ}, a benchmark with six controlled strategies that vary option popularity while keeping the correct answer fixed. In our most adversarial setting, where all distractors are more popular than the correct option, models choose popular but wrong answers 66\% of the time. To mitigate this bias, we propose \textbf{PopDebias}, a lightweight inference-time correction that estimates and removes a popularity prior from model predictions. It requires no fine-tuning, is label-free at test time (using only a small calibration split for parameter fitting), and adds negligible computational cost. Experiments on 22 open-source LLMs (0.5B to 32B parameters) show consistent improvements, with accuracy gains up to 54.1 percentage points under strong popularity pressure. The code and data are available https://github.com/DataScienceUIBK/PopMCQ

Structure-Aware Modeling of Multiple-Choice Questions Improves Automatic Difficulty Estimation

Automatic Question Difficulty Estimation (AQDE) holds growing promise for educational assessment because it has the potential to yield difficulty estimates that are competitive with expert judgment, while helping reduce the time and financial burden associated with pilot administrations and scaling to digital testing contexts. Prior AQDE studies report mixed evidence on whether adding distractors as additional text to the question stem and the correct key consistently improves difficulty prediction. We hypothesize that the effectiveness of distractor information depends on its structural representation, and that explicitly modeling distractors as separate components improves difficulty estimation over baselines that omit this information. To address this, we designed controlled architectures that model MCQ components as distinct inputs to isolate the contribution of distractor content and order. Specifically, we represented distractors by encoding each distractor as its own text input and aggregating their representations either with order-aware concatenation (with positional tags) or with an order-invariant summation. We evaluated these architectures using two Chilean datasets (Natural and Social Sciences, 2016-2020; 4,114 multiple-choice questions). Compared to a simpler model that only used the question stem and the key, our best distractor-aware architecture achieved higher predictive performance, reaching R^2 = 0.83 for Natural Sciences and R^2 = 0.71 for Social Sciences items. An order-invariant variant achieved nearly the same accuracy with approximately half as many parameters, offering a favorable accuracy-efficiency trade-off. These results show that structural information (especially distractor content) drives gains in predictive accuracy, supporting the development of efficient, structure-aware models that are computationally viable for large-scale educational applications.