Uncertainty Is Not Enough: Value-of-Information Routing for Mixtures of LoRA Experts

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

Uncertainty-Aware Simulation-Based Inference for Operations Research with Large Language Models

Deploying large language models (LLMs) for operations research (OR) tasks remains challenging because correctness depends on a coherent modeling process, not merely a correct final answer. Standard autoregressive generation operates on a myopic policy, which sometimes fails to anticipate whether a partial formulation can be validly extended into a globally consistent optimization model. Consequently, locally plausible steps may propagate into catastrophic downstream formulation or solver code errors. To address this, we propose an uncertainty-aware, training-free inference framework for OR mathematical modeling. Without updating model parameters, our method evaluates intermediate candidate steps using short lookahead simulations to quantify downstream predictive uncertainty or probability concentration. Candidates that demonstrate a higher likelihood of yielding coherent mathematical formulations are then dynamically selected via importance resampling. Empirical evaluations across multiple OR benchmarks (including NL4OPT, MAMO, and IndustryOR) demonstrate that our framework consistently outperforms both standard and low-temperature baselines, establishing an efficient, training-free paradigm for reliable OR formulation generation.

Reliability Scales Inversely: Hallucinations Snowball Faster in Bigger Language Models

Bigger language models are less reliable. Across three families, three benchmarks and six rungs, including in-the-wild chat logs, scaling closes the start-of-response knowledge gap up to $7\times$ while within-response knowledge degradation grows up to $39\times$. We trace that residual to one variable, the per-position disagreement $δ= \log p_M - \log p_O$ against a stronger oracle, whose second moment splits exactly into bias$^2$ $\mathrm{KL}(p_M \,\|\, p_O)^2$ and decoding risk $\mathrm{Var}[δ]$. That split is an interpretability statement before it is a statistical one: the model's self-readable uncertainty $H(p_M)$ enters only the bias term, so the risk term has no model-readable component. Risk also takes a growing share of the squared error with scale, $31\%$ to $49\%$ from $1.7$B to $14$B. At a fabrication $H(p_M)$ relaxes within one token while risk persists up to $23\times$ longer, leaving a confident-but-precarious regime that bridges consecutive fabrications ($+69\%$ at $14$B). Contracting that risk at fixed $\mathrm{KL}$ removes $35$-$74\%$ of web-verified hallucinations across six rungs and three families. Semantic entropy fires $\approx$$30\%$ less on that branch ($p\!<\!10^{-16}$) though it carries nearly $4\times$ the fabrications. Bigger models snowball mistakes faster, through a failure mode that is dominant, self-perpetuating, causal and invisible to the model itself.

Confident but Conflicted: Internal Uncertainty and Cognitive Dissonance Resolution in LLMs

Large language models (LLMs) frequently encounter inputs that disagree with their prior outputs, through user pushback, retrieved documents, or web search results. While the way they resolve such conflicts -- a process we frame as cognitive dissonance resolution -- has been characterized behaviorally, its connection to internal model uncertainty is not well understood. To study this systematically, we vary persuasion attempts along two dimensions, source authority and evidence quality, across 12 health-science claims of stratified epistemic status. Dissonance can be resolved through persuasion, backfire, or immunity. We introduce Trust Elasticity (TE), an econometrics-inspired measure of how readily a model is persuaded toward conflicting evidence. Across four LLMs, TE varies substantially, while clearly false claims elicit near-zero TE across all models. On two open-weight models, we further find that this variation is associated with two complementary internal uncertainty indicators, Confidence Miscalibration in Qwen and Internal Uncertainty Change in Llama. These results link cross-model behavioral variation to a measurable internal property and point to interventions targeting internal uncertainty as future work.

Calibration of Structured Ignorance Certificates for Diagnosing Unknown Unknowns in Reasoning Models

Large language models frequently fail in a characteristic way: rather than acknowledging ignorance, they produce fluent but incorrect answers to questions that lie beyond their knowledge boundaries. We introduce \textbf{Structured Ignorance Certificates} (SICs), a JSON-formatted output schema that demands a model explicitly name the missing domain intersection, enumerate required concepts, and propose a productive retrieval query rather than hallucinating an answer. To train models to produce high-quality SICs we construct a 7,347-sample \emph{Unknown-Unknown} (UU) dataset by prompting Qwen3-14B to stitch together questions from seven domains (physics, biology, engineering, CS, economics, medical, legal) into novel cross-domain queries that no single-domain expert could answer. We fine-tune a 14B-parameter model with Group Relative Policy Optimization (GRPO) using a composite reward that combines retrieval utility, concept specificity, and output-format validity. A paraphrase-divergence probe trained on model responses confirms that SIC-tuned outputs systematically exhibit higher unknown-unknown probability scores. Evaluation on 735 held-out UU questions achieves a 99.46\% JSON validity rate, a mean Certificate Specificity Score of 0.967, and a 3.6\% ROUGE-L improvement over the base model on retrieval-grounded generation -- demonstrating that explicit epistemic structuring is a learnable and measurable capability.

Staying with the Uncertainty: Uncertainty-Scaffolding Strategies for Artificial Moral Advisors in LLM-to-LLM Simulated Conversations

LLMs are increasingly deployed as Artificial Moral Advisors (AMA) in a variety of contexts: what kind of conversational patterns should they display? In this paper, we study how AMA can help their interlocutors "stay with the uncertainty". We propose three modes of uncertainty (Perspective-Multiplying, Tension-Preserving, Process-Reflecting) and compare them against three control conditions (Baseline, Persuasive, Sycophantic). A user-agent LLM engages in a dialogue on an ethical dilemma with an AMA following a specific uncertainty strategy, and completes pre- and post-conversation questionnaires. We further examine the effect of two persona prompt formats (Declarative and Narrative). We found that (1) no single model dominates as a simulated user agent, with open models aligning with human ambiguity through between-persona divergence and closed models through within-persona hedging; (2) declarative personas better capture initial stance diversity while narrative personas show more realistic belief revision; (3) all six AMA strategies produce distinguishable conversational patterns; and (4) uncertainty strategies differ not in how much stance revision they produce, but in the quality of engagement they sustain.

Reliability-Aware Sexism Detection: Combining DPO with Annotator Agreement and Token-Level Confidence Scoring

The detection of online sexism remains an open problem. Sexism detection is inherently subjective, yet most existing systems reduce multi-annotator labels to a single majority decision and treat all instances uniformly. This ignores two informative signals: annotator agreement and model uncertainty. We propose RA-DPO (Reliability-Aware Direct Preference Optimization), which integrates annotator agreement, model confidence, and a token-level uncertainty signal into a single reliability score. RA-DPO uses this score to select high-value preference pairs during training and to support inference-time abstention, which allows the model to trade coverage for accuracy. We evaluate RA-DPO on 6,920 multilingual posts from EXIST 2023, fine-tune OpenAI gpt-4o base via DPO, and validate on two open-weight 3B models (Llama, Qwen). Results show that training on the top 30% most reliable pairs matches full-data DPO, which indicates that reliability-aware selection can reduce training cost without sacrificing performance. At inference, selective prediction reaches 96.2% accuracy at 50% coverage in the true-agreement setting and 88.7% in the deployable predicted-agreement setting, both exceeding the 85.3% no-agreement baseline. These results suggest that accounting for annotation uncertainty is beneficial for both efficient training and reliable deployment in subjective classification.

What Did They Mean? How LLMs Resolve Ambiguous Social Situations across Perspectives and Roles

People increasingly turn to large language models (LLMs) to interpret ambiguous social situations: a delayed text reply, an unusually cold supervisor, a teacher's mixed signals, or a boundary-crossing friend. Yet in many such cases, no stable interpretation can be verified from the available evidence alone. We study how LLMs respond to these situations across four domains: early-stage romantic relationships, teacher--student dynamics, workplace hierarchies, and ambiguous friendships. Across 72 responses from GPT, Claude, and Gemini, only 9 (12.5\%) genuinely preserved uncertainty. The remaining 87.5% produced interpretive closure through recurring pathways including narrative alignment, narrative reversal, normative advice under uncertainty, and hedged language that still supported a single conclusion. We further find that narrator perspective shapes the path to closure: first-person accounts more often elicited alignment, while third-person accounts invited more detached interpretation, even when the underlying situation remained comparable. Together, these findings show that LLMs do not simply assist interpersonal sensemaking; they tend to resolve ambiguity into coherent and actionable narratives. These results suggest that the central risk is not only that LLMs may misinterpret social situations, but that they may make unresolved situations feel prematurely settled. We frame this tendency as a design challenge for uncertainty-preserving social AI.