Input Order Sensitivity in Language Models

Many language-model pipelines end in a closed-set decision, such as selecting a tool. Prompting a large language model for it is slow and order-sensitive. We ask how small an encoder for such decisions can be and whether it should read the options jointly or separately. In a three-seed study at 32 million parameters, per-option scoring beats joint scoring on a held-out sample of a 37-benchmark decision suite by 5.8 points of chance-corrected skill at matched optimizer steps and by 2.8 at approximately matched training compute; two external benchmarks agree, though not significantly on their unseen tasks. Crossing reader with initialisation shows that the advantage requires a reranker initialisation, whose query-candidate pair input matches per-option reading; from the raw encoder the two readers are indistinguishable. Per-option scoring needs 5 to 13 times more encoder passes: at most twice the median latency, but more than four times the mean. Of six released joint encoders (17 million to 1 billion parameters), the 68- and 150-million-parameter models exceed a 435-million-parameter DeBERTa-v3 zero-shot classifier by 4.9 and 5.9 accuracy points on 209 overlap-audited System1-Arena tasks and are at least on par with it on the 145 tasks unseen in training. The smallest answers a median request in 14 milliseconds on 16 processor threads, against 728 for the classifier. Reordering options changes 12 to 23% of the joint models' answers (per-option scoring: none). Up to 68 million parameters, they lead their size range on a public leaderboard's private, mainly in-distribution tests.

Running prompt tokens through fewer routed experts during prefill makes mixture-of-experts (MoE) serving cheaper, but what it damages has not been measured. We locate the damage with token-, layer- and attention-path interventions in four MoE families on short-answer question answering. At half the experts the F1 loss is mostly answer form: the model still finds the answer but no longer answers briefly. The loss is made at a few tokens: the two chat-template tokens before the answer in Qwen3-30B-A3B, and the first 8-32 tokens, where the instruction sits, in DeepSeek-V2-Lite. Keeping them at full experts removes most of the F1 loss and about half and a fifth of the increase in answer NLL. These tokens are not the familiar suspects: reduction leaves the first-token sink within 4%, and restoring super experts or massive activations recovers at most a quarter of the loss. On real prompts the localisation becomes a placement rule: with about 4% of tokens at full experts, putting them on the task interface keeps F1 within one point of the unmodified model, while the same budget scattered in the documents is about 3 points worse in both prespecified primary tests of this comparison. Time to first token falls about 14% on 11K-token prompts.

Reordering multiple-choice options can change a model's answer, an effect studied as selection bias (a preference for certain option letters) and as order sensitivity (changes in answers across option orderings). We connect these perspectives through the pooled selection-rate standard deviation (pooled SD), which measures how unevenly option letters are selected across questions and orderings. When every option of each question appears equally often at each position, the pooled SD is exactly the product of two label-free factors: the flip rate and the positional skew. The flip rate is the fraction of questions whose chosen option changes across orderings; the positional skew is the standard deviation of option-letter selection rates among those questions. Across 41 checkpoints and 12 benchmarks, the flip rate tracks accuracy and output uncertainty, while the positional skew tracks the estimated option-symbol prior. Prior correction for selection bias mainly reduces the positional skew. Aggregating each ordering with its reversal, a mitigation for order sensitivity, mainly reduces the flip rate. Both reduce the range of accuracy across correct-answer letters by similar amounts, but aggregation leaves fewer model-rank reversals. Applying prior correction before aggregation reduces both factors and further narrows this accuracy range. However, aggregation lowers the flip rate partly by settling questions on the same wrong option. We therefore recommend reporting both factors to distinguish mitigation effects, alongside accuracy to distinguish stability from correctness.

System One models answer typed questions in a single forward pass and promise the same answer for the same input. For choice questions, this promise fails: the answer depends on the order of the options, increasingly so as they grow in number, and averaging over their cyclic shifts reduces this dependence without removing it. Scoring each option alone, which the order cannot affect, shows that the order changes the answer mostly when the model is unsure among its top few options, even though the listwise answer looks confident. We therefore propose $\textbf{Runoff}$, which considers, then chooses: it scores each option alone to keep a few candidates, then compares them in listings where each candidate takes every position. It needs no training and can run in two forward passes, and its answer does not depend on the option order by construction. On two open models and five datasets, it changes no answer under shuffling, against 9.3% for cyclic averaging, and with 20 options it is about as accurate and three to four times faster. Wrapped around eight System One models, it removes the order dependence of the five benchmarks, while cyclic averaging changes up to 15.4%.

Adaptive computation aims to improve language-model inference by tailoring execution to each input. For layer programs, oracle evaluations use known answers to estimate the potential gain from this flexibility, before a practical selector is available. However, a gain from selection does not by itself explain why the chosen programs help. This study examines this distinction using 32 layer-skipping and repetition programs on two models and 4,413 multiple-choice items. The analysis compares their gains over a fixed action selected without the evaluation prompt with those of input-blind perturbations at the same sites, re-evaluating selections on another prompt. With shared option order, the controls give 10.2-11.8 and 15.6-19.4 percentage points of headroom on Qwen3-4B-Base and Llama-3.1-8B, exceeding the real programs' 9.0 and 10.1 in all three random-direction draws per model. They match answer-change rate only, and the ordering depends on the menu: in post hoc comparisons, real programs lead on Llama's repeat-only menu in every draw. A smaller KL-calibrated comparison, including an input-dependent control, favours real programs in point estimate, with inconclusive corrected tests. Fixed letter offsets produce headroom of similar scale. Rotating options sharply reduces both families' headroom, while leaving positive real-minus-control differences of 1.4-2.3 and 3.7-4.5 points; their magnitudes and statistical support depend on further adjustments and the reference. A supplementary generated-answer test finds that search-selected programs keep a 26.0-point advantage over programs selected for other problems after rewording, without a placebo comparison. These results show that substantial headroom can persist across prompts with shared option order without establishing a benefit specific to the selected layer computation; neither ordering against these controls identifies that benefit.

Multiple-choice question (MCQ) benchmarks are widely used to evaluate large language models, yet a single reported accuracy number is not enough to distinguish a model's latent ability from order sensitivity. Debiasing methods tend to be judged on one axis, which implicitly assumes that fixing order sensitivity and improving accuracy go together. We test this assumption with two proprietary models and two open-weight models on MMLU and ARC-Challenge, across four families of strategies. We measure order sensitivity with flip rate, capturing per-question instability, and recall standard deviation (RStd), capturing aggregate positional imbalance. We find accuracy and order sensitivity do not move together consistently: two-stage prompting reduces both flip rate and RStd for GPT on MMLU without a significant change in accuracy. The two sensitivity metrics also diverge from each other. Adding reasoning to direct answering leaves Llama's MMLU flip rate statistically indistinguishable while RStd falls sharply. A $2\times2$ ablation across generation-then-matching, crossing option visibility with matcher type, shows that withholding options mainly harms semantic matching, which achieves zero flip rate by construction, yet loses significantly in accuracy; the effect is smaller when using an LLM matcher. We recommend reporting flip rate and RStd along with accuracy when evaluating MCQ strategies.

Large language models are increasingly used for ordinal classification, yet semantically equivalent changes to prompt organization can alter their predictions. We conduct systematic experiments to characterize positional bias from label order, demonstration order, and demonstration placement. First, we apply the three probes to ten frontier LLMs on a common ordinal-classification task; every model is sensitive to all three positional sources, showing that the problem is pervasive. Second, we vary eight prompt-, task-, and model-level factors across five datasets; accuracy and stability are often misaligned, and only lower scale cardinality consistently improves both. Third, we compare pointwise, pairwise, and listwise inference, alternative aggregation and debiasing methods, and joint configurations; the tested corrections do not provide a reliable remedy, while a comparison-based listwise formulation offers the best balance but transfers unevenly across models and bias sources. These findings show that positional robustness depends on the full system configuration rather than the model alone. Ordinal-classification systems should therefore be selected jointly for predictive performance and stability.

Large language models (LLMs) increasingly issue judgments read as binary verdicts, and a growing literature reports such judgments shifting under logically irrelevant changes of wording - among them an amplified yes-no bias on moral dilemmas, absent in humans. A single framing cannot say what such a shift is: in a yes/no question the word "no" is at once logical verdict, lexical token, and last-printed option. We introduce a psychometric battery that separates these: crossed symmetrization - every logically irrelevant factor flipped in balanced pairs - across a corpus of question forms. A graded rating across logically equivalent forms recovers a coherent internal moral scale: frontier models' stance $θ$ is nearly format-invariant (cross-form incoherence 0.12-0.21 on a $\pm 1$ axis); small open-weight models fail in model-specific ways. Forcing the verdict through yes/no overlays a decomposable artifact: an order bias toward the last-printed option - opposite to classic human primacy - plus a lexical pull toward the word "no"; the artifact is substantial only in the Claude models (story-averaged -0.32 to -0.86), $\approx 0$ for GPT-5.5 and Gemini, and shrinks under extended reasoning. The word and the verdict share one token; swapping the words for arbitrary labels separates them, and the verdict-attached logical bias proves $\approx 0$ for every frontier model, while model-specific label and order attachments remain: the models are not drawn toward rejecting - the pull follows the printed surface, not the verdict it carries. A minimal model, $P = σ((θ\pm m)/s)$, summarizes any such artifact by a framing susceptibility m and a moral decisiveness s, measurably distinct from sampling temperature. The battery applies unchanged to any dilemma set and binary format: measuring what a model values requires crossing the frames of the question, not asking once.

Standard benchmarks for multimodal large language models (MLLMs) score each item on one canonical ordering and miss whether order-irrelevant shuffling changes the answer, a baseline reliability property called for by emerging AI evaluation guidelines. We introduce Facet-Probe, a five-facet audit (option, evidence-chunk, document-rank, image-set, and mixed-modality ordering) of 18 frontier and open-weight MLLMs. A Bayesian item-response model separates ordering noise from per-facet bias, and a same-ordering control estimates the decoder-stochastic floor for observed flips. We find that none of the 18 MLLMs we audit are order-invariant: screened per-facet panel-mean flip rates span 24-50%. A Gemini same-ordering control at temperature 0 estimates a substantial ordering excess over a same-input decoder-noise floor in verified cells. Capability predicts but does not eliminate flips; the best model still flips on 13.4% of trials. In our Gemini mitigation tests, training-free prompt changes are modality-conditional and do not transfer from text to visual reasoning. These results suggest that prompt-level mitigation alone is unlikely to provide general order robustness, motivating future work on training-time and architectural approaches. We propose cross-ordering flip rate as a standard reporting axis for MLLMs.

Large language models (LLMs) can make clinical decision support more accessible by interpreting free-text documentation, but their direct use as diagnostic engines is limited by sensitivity to prompts, information order, and plausible but incorrect outputs. Structured machine-learning models offer more stable risk prediction, yet they require tabular inputs that are difficult to integrate with narrative clinical workflows. We present ClaMPAPP (Clinical Language-assisted Machine-learning Pipeline for Appendicitis), a hybrid system that uses an LLM as an interface rather than as the final decision-maker. ClaMPAPP extracts schema-constrained clinical features from note-like narratives, applies deterministic plausibility checks, and passes validated features to an XGBoost classifier trained on clinical, laboratory, and ultrasound variables. We evaluated ClaMPAPP on two independent pediatric appendicitis cohorts from German hospitals and compared it with end-to-end LLM baselines, including open-source and proprietary models. To preserve ground truth while testing free-text input, narratives were generated from structured electronic health records through template rendering and constrained LLM rewriting, with additional sentence-order permutation to assess positional robustness. ClaMPAPP achieved the strongest overall diagnostic performance in both internal and external validation while minimizing missed appendicitis cases, the key safety concern in acute triage. End-to-end LLMs showed unstable sensitivity-specificity trade-offs and greater degradation under narrative reordering. These results support an LLM-as-interface, ML-as-predictor design that separates natural-language usability from predictive inference and provides a more auditable pathway for clinical decision support.

Order-agnostic language models (OALMs), including discrete diffusion language models (dLLMs), are trained to predict masked tokens under arbitrary conditioning sets, allowing sequences to be generated or scored under arbitrary reveal orders at inference time. In LLaDA-2.1, we report three findings. First, the learned conditionals are not exact factorizations of a coherent joint distribution: changing only the reveal order shifts target log-likelihood by up to 0.49 nats/token, so likelihood alone mixes content difficulty with path-dependent artifacts. Second, although confidence-first (CF) decoding is order-agnostic, its reveal orders are close to left-to-right (L2R) on content tokens. Third, we propose a complementary diagnostic based on the shape of the confidence trace. A uniform-spreading theorem shows that, at fixed total likelihood, target recoverability is maximized when per-step confidence is spread uniformly; the resulting deviation motivates $\mathrm{Var}(\log q_t)$ as a diagnostic for comparing decoding paths. Across C4 and four downstream benchmarks, low variance separates structured paths from random ordering, and variance is consistently associated with downstream correctness. These results support reporting mean confidence and confidence variance jointly when comparing OALM decoding paths.

Large Language Models (LLMs) suffer from order bias, where their performance is affected by the arrangement order of input elements. This unfairness limits the model's applications in scenarios such as in-context learning and Retrieval-Augmented Generation (RAG). Recent studies attempt to obtain optimal or suboptimal arrangements based on statistical results or using dataset-based search, but these methods increase inference overhead while leaving the model's inherent order bias unresolved. Other studies mitigate order sensitivity through supervised fine-tuning using augmented training sets with multiple order variants, but often at the cost of accuracy, trapping the model in consistent yet incorrect hallucinations. In this paper, we propose Dual Group Advantage Optimization (DGAO), which aims to improve model accuracy and order stability simultaneously. DGAO calculates and balances intra-group relative accuracy advantage and inter-group relative stability advantage, rewarding the policy model for generating order-stable and correct outputs while penalizing order-sensitive or incorrect responses. This marks the first time reinforcement learning has been used to mitigate LLMs' order sensitivity. We also propose two new metrics, Consistency Rate and Overconfidence Rate, to reveal the pseudo-stability of previous methods and guide more comprehensive evaluation. Extensive experiments demonstrate that DGAO achieves superior order fairness while improving performance on RAG, mathematical reasoning, and classification tasks. Our code is available at: https://github.com/Hyalinesky/DGAO.

Large language models (LLMs) excel at semantic understanding, yet their ability to reconstruct internal structure from scrambled inputs remains underexplored. Sentence-level restoration is difficult to evaluate automatically because scrambled sentences often admit multiple valid reorderings. We introduce OrderProbe, a deterministic benchmark for structural reconstruction using fixed four-character expressions in Chinese, Japanese, and Korean, which have a unique canonical order and thus support exact-match scoring. We further propose a diagnostic framework that evaluates models beyond recovery accuracy, including Semantic Accuracy, Logical Validity, Structural Consistency, Robustness, and Information Density. Experiments on twelve widely used LLMs show that structural reconstruction remains difficult even for frontier systems: zero-shot recovery frequently falls below 35%. We also observe a consistent gap between meaning-oriented generation and exact structural reconstruction, suggesting that structural robustness is not an automatic byproduct of semantic competence.

Large audio-language models (LALMs) are often used in tasks that involve reasoning over ordered options. An open question is whether their predictions are influenced by the order of answer choices, which would indicate a form of position bias and undermine their reliability. In this paper, we identify and analyze this problem in LALMs. We demonstrate that no model is immune to this bias through extensive experiments on six LALMs across three widely used benchmarks and their spoken counterparts. Shuffling the order of answer options can cause performance fluctuations of up to 24% and even change model rankings, raising concerns about the reliability of current evaluation practices. We also study permutation-based strategies and show that they can mitigate bias in most cases. Our work represents the first systematic investigation of this issue in LALMs, and we hope it raises awareness and motivates further research in this direction.