Science & Mathematics

Quantifying uncertainty in time series forecasting is particularly demanding because sequential data exhibit temporal dependence and are prone to distributional changes. Conformal inference has emerged as a powerful uncertainty quantification approach through the construction of prediction sets. Recent advances have introduced online conformal methods that adaptively adjust prediction thresholds through feedback mechanisms. However, the existing feedback mechanism typically relies solely on miscoverage indicators (actual feedback), whether the true label falls within the interval at each time step, while overlooking the empirical prediction threshold (estimated feedback) that is derived from the oracle conformal method. In this paper, we propose Dynamic Dual-feedback Conformal Inference (DDCI), which incorporates a dual-feedback mechanism consisting of actual feedback and estimated feedback. The former drives the primary adjustment of the intervals based on true observations, while the latter dampens excessive expansions or contractions by leveraging empirical thresholds from conformal inference during updates. By balancing these two signals, DDCI achieves more stable and narrower prediction intervals in sequential settings while maintaining near-nominal coverage in practice.

Modals such as may and must can take on different senses depending on discourse context, alternating between root interpretations (e.g., permission, obligation) and epistemic interpretations (e.g., knowledge, belief). While modals are known to be notoriously difficult for children to acquire, limited research exists on whether language models (LMs) can reliably distinguish between different modal senses. We evaluate seven LMs that vary in architecture, size, and training data type using vector-based similarity and surprisal measures across four datasets. Specifically, we investigate whether LMs can leverage contextual information to disambiguate modal senses and whether their performance reflects the distribution of modal senses in their training data. We show that larger LMs trained on diverse text successfully leverage additional contextual information when available. In the absence of context, they tend to favor the dominant sense based on corpus statistics. Smaller developmentally plausible LMs, including those trained on child-directed language (CDL), fail to show consistent sensitivity to modal sense distinctions and do not benefit from context to the same degree.

Clinical decision-making often begins with underspecified information and requires not only gathering missing information but also knowing when to stop. This calls for judging determinability (whether the available information is sufficient for a decision) by considering whether missing information could change the conclusion, not simply the amount of available decision-relevant information. Reliance on this amount as a cue for determinability, which we term \textit{factor coverage bias}, could undermine the trustworthiness of large language models (LLMs) through premature conclusions or excessive information gathering, such as unnecessary invasive tests. Yet whether LLMs exhibit this bias remains insufficiently studied. To address this gap, we construct a controlled pairwise benchmark in which LLMs identify the determinable case within each determinable--undeterminable pair. We add a decision-relevant factor to either side while keeping each case's determinability unchanged, and similarly add irrelevant text to distinguish this bias from context-length effects. Adding a relevant factor made LLMs more likely to select the augmented case as determinable even when it remained undeterminable, an effect that persisted with increased reasoning effort, while adding irrelevant text made them less likely to select the augmented case, an effect that reasoning substantially reduced. These findings identify factor coverage bias as a failure mode distinct from context-length effects and a potential risk to LLM trustworthiness. Our work provides an evaluation framework for LLM trustworthiness under underspecification.

Testing by betting is a powerful framework that recasts hypothesis testing as a betting game. A popular approach spreads the initial wealth over fixed bets according to a prior distribution, using a universal portfolio algorithm. For suitable priors, this approach achieves the optimal expected rejection time as the error probability goes to zero at a fixed alternative. Yet, priors with this guarantee can behave quite differently near the null. This motivates the question: Which prior should we use in testing-by-betting algorithms? We study bounded scalar payoffs and, under technical conditions, prove a sharp formula for expected rejection time, uniform over all bounded alternatives as the error probability tends to zero. The formula shows how the prior's mass around the zero bet determines the cost of adapting to an unknown alternative. We characterize the priors that attain the best possible leading constant when the error probability and alternative vary together. We also show that no valid test can uniformly improve on this cost across ranges of alternatives near the null. In particular, the uniform prior can require arbitrarily more observations than suitable priors that concentrate around the zero bet. A general inversion argument converts our results into sharp expected times to reach a prescribed confidence-sequence width. We also give a concrete prior choice and an FFT-based algorithm with almost linear computational complexity.

Marketing managers routinely allocate limited budgets across individuals in social networks whose responsiveness and influence vary substantially. We study the problem of Budgeted Generalized Fractional Influence Maximization (BGFIM), which captures the allocation of continuous levels of marketing spend across users in the presence of heterogeneous response and network spillovers. In this framework, adoption probabilities are governed by user-specific response functions that capture both baseline propensity and marginal responsiveness, while incentive costs vary across users. We propose a scalable solution approach based on a discrete greedy procedure with provable approximation guarantees, enabling tractable optimization under realistic budget constraints. Our formulation generalizes prior influence maximization models by allowing heterogeneous response and cost structures, providing a more flexible representation of targeted marketing interventions. Using experiments on multiple large-scale networks, we show that continuous allocation strategies can outperform standard heuristics and improve influence outcomes under heterogeneous conditions, and we illustrate how the framework can support profit-oriented decision making by identifying budget levels that balance marginal returns and costs. Overall, our results highlight the value of fine-grained budget allocation in networked marketing environments and offer a scalable approach for data-driven marketing resource allocation.

Multi-speaker automatic speech recognition (MSASR) has advanced rapidly with end-to-end speech large language models. However, existing benchmarks cover limited ranges of specific multi-speaker conditions and scenarios, making it difficult to reveal system limitations under diverse conditions and scenarios. We introduce MS-Bench\footnote{\href{https://aslp-lab.github.io/MS-Bench/}{Demo page: https://aslp-lab.github.io/MS-Bench/}}, a condition-stratified benchmark for fine-grained MSASR evaluation. MS-Bench integrates both public and internal benchmarks and characterizes each recording along five dimensions: speaker number, overlap ratio, speaker similarity, speaker turn interval, and acoustic quality. We stratify these dimensions into condition ranges and construct MS-Bench with broad coverage of conditions, scenarios, languages, and recording devices. Evaluating representative commercial, open-source, and cascaded systems, we find that overlap affects both lexical recognition and speaker attribution, while other factors exhibit more task-specific effects on recognition, attribution, or temporal prediction. These results demonstrate that aggregate metrics alone obscure important MSASR failure modes and highlight the value of condition-stratified evaluation. MS-Bench aims to reveal condition-specific limitations of current MSASR systems and guide future improvements.

Fault localization (FL) aims to identify code locations responsible for software failures and is commonly evaluated by how accurately it ranks known fault locations. Large language model (LLM) agents are changing program repair and are increasingly used to search and reason over repositories. Although recent LLM-based FL methods have improved localization accuracy, their impact on agentic repair remains unclear. To address this gap, we conduct a systematic empirical study of FL in agentic repair. We evaluate six recent FL methods on SWE-bench Verified and Defects4J with three LLMs under a common repair framework and analyze 16,248 repair trajectories. We also examine gold locations and bug-cause descriptions as forms of FL guidance across different repair contexts. The studied FL methods do not consistently improve repair success, and higher localization accuracy does not consistently lead to larger repair gains. Yet FL guides agents' early search and helps them reach relevant code sooner. Accurate locations can reduce repair token use by up to 39.2\%, but current FL methods often consume more tokens than they save during repair. Experiments with gold guidance suggest that FL has greater potential when bug inputs contain fewer location clues. Providing bug causes can further improve repair success beyond locations alone. We also find that ground truth from a single reference patch does not fully capture the locations used by successful repairs. These findings help clarify the value of FL in agentic repair and inform future work on its design and evaluation.

Language models increasingly use skills that provide reusable instructions and procedures for task execution. After a relevant skill has been selected, the model may need to apply its governing procedure together with retrieved task context. When the retrieved context is useful but contains cues that violate the skill, the model must retain compatible information while rejecting the conflicting cues. We study failures in which the model adopts such cues and produces a retrieval-supported but skill-invalid answer, which we call procedural hallucination. We introduce SourceClash, a matched benchmark with 1,271 bundles and 6,355 prompts across ten procedural domains. Each bundle fixes the task, skill specification, and answer space while varying the relation between the skill and retrieval. Across nine models, valid-answer rates average 25.7% under conflicting retrieval, compared with 78.2% and 72.8% under two supportive retrieval settings. Mechanistic analysis of open-weight models shows that the answer-preference difference typically reaches its maximum shortly after generation begins. Residual replacement moves the model toward valid answers, while attention decomposition attributes most of the repair to value vectors. Intervention at the identified value pathway also improves final answer validity. These results characterize how partly conflicting retrieval changes skill-guided generation.

We watch a computation only at moments chosen by a random clock that can leap ahead, pause, or step back, and we count looks rather than steps. How far can such a clock reliably see with polynomially many looks, and does stepping back help? Rare long leaps reach exponential and doubly exponential time, with infinitely many levels between polynomial and exponential time. A clock that tends to fall back sees only the start of the input, and below polynomial time we find infinitely many incomparable levels. Stepping back can help decisively. For clocks whose long leaps occur only at rare positions, no forward-only clock goes beyond polynomial time, while even single steps back raise the reach to exponential time. Stepping back cannot help, however, when the clock's leaps ignore its position.

Diffusion models have recently achieved encouraging results in real-world image dehazing. However, restoring high-resolution images remains challenging due to spatially non-uniform haze and inconsistent predictions across local patches. To address these issues, we propose Hihaze, a one-step diffusion framework for high-resolution real-world dehazing. Hihaze adopts two haze-aware modulation modules: attentive skip compensation (ASC) and a spatial degradation adapter (SDA). ASC selectively transfers reliable encoder information to the variational autoencoder (VAE) decoder, preserving structural details while suppressing haze-degraded features. SDA extracts multi-scale spatial degradation representations and injects them into the U-Net to guide restoration according to local haze variations. Furthermore, we design a training-free global-guided patch fusion (GPF) method. It uses a global prediction to align patch appearance and downweight unreliable predictions, followed by structure-guided detail compensation. Notably, this training-free design also makes GPF a plug-and-play module for other dehazing models. Experiments across four real-world benchmarks show that Hihaze surpasses state-of-the-art approaches in both visual quality and inference speed. Specifically, it delivers PSNR improvements of 3.62~dB on Dense-Haze and 3.69~dB on NH-HAZE compared with the strongest baselines. Code: https://github.com/zhengchen1999/Hihaze.

Autonomous codebase refactoring requires coding agents to restructure working software while strictly preserving externally observable behavior and prioritizing execution performance and compute efficiency over stylistic preference. Existing benchmarks: refactoring benchmarks assess functional correctness while overlooking runtime regressions, whereas code performance benchmarks target isolated micro-kernels that ignore codebase-scale complexity. We observe that refactoring scale is governed by the scope of the observable contract, the caller-visible interface fixing behavioral invariants while freeing private implementations for optimization. Building on this insight, we introduce FrontierRefactor, a benchmark of 60 qualified engineering tasks spanning four scales, from computational kernels to full repositories, across in-place optimization and cross-language rewriting. Evaluating frontier coding agents through a reference-free cascaded protocol across 1,080 execution runs reveals that correctness and speedup are largely decoupled: 41.2% of submissions satisfy functional equivalence yet fail to deliver verified performance improvements, with 19.3% suffering performance regressions and 21.9% trapped in measurement noise. Refactoring paradigms reveal orthogonal engineering bottlenecks: while cross-language rewrites gain speedups from native compilation after passing functional checks, agents struggle with contract fidelity, with pass rates dropping from 65.0% on modules to 32.6% at package scale; conversely, in-place optimization reliably preserves behavioral contracts at 86.5% but rarely achieves acceleration without physical performance profiling. Trajectory analysis shows that agents fall victim to uncalibrated micro-benchmarking illusions, an operational blind spot that multi-turn execution-timing feedback directly resolves, raising strict success from 16.0% to 40.0%.

Diffusion language models can write several tokens in one forward pass, and they decide during generation how many passes to spend. Two outputs of the same token length can therefore vary a lot in cost. To understand the underlying factors of this cost variation, we analyze two diffusion models across 10 tasks. We find that the number of forward passes per token depends heavily on the task. Text copied or lightly edited from the input is cheap, while open-ended writing is costly. In DiffusionGemma, generating a token for story writing requires more than three times as many forward passes as for grammar correction. Two output properties explain much of this gap: how much of it is new relative to the input, and how rare its words are within the task. The same holds within a single response when thinking is involved. The final answer is cheap when it repeats the model's reasoning trace and costly when it adds something new. In multilingual generation, we find that highly tokenized languages also require more passes per token, adding to the cost they already pay with more tokens. Finally, cost tracks correctness: on the same math problem, wrong answers take more passes per token than correct ones, and weighting candidate answers by decoding speed beats majority voting by up to 4.2 points at no extra cost. Taken together, our results show that diffusion's computational advantage depends on how much of the output is already determined, while its decoding effort offers a practical signal for making inference more efficient and reliable.

Reinforcement learning with verifiable rewards (RLVR) is widely used to improve reasoning in language models, yet growing evidence suggests that it mostly sharpens what the base model can already do. This raises a practical question: when RL fails, what is the base model missing? We look inside the RL policy's own rollouts and find that failures are localized: whether a rollout fails is strongly predicted by a small set of characteristic n-grams, ranging from reflection phrases such as "let's recheck" to specific operations such as "the inverse of A". These failures persist throughout RL training, although they are not beyond the model's reach: other sampled answers to the same question are often correct. Building on this observation, we use the failure $n$-grams to retrieve text from the pretraining corpus and continue pretraining the base model on it before RL. The resulting corpus has only 35M tokens, 3--4 orders of magnitude smaller than typical mid-training. We evaluate this approach on OLMo2 and Qwen3 models trained with RL on (1) GSM8K; (2) a mixture of math, commonsense, and knowledge questions; and (3) general math and science reasoning. Despite its size, the corpus yields consistent gains: our approach outperforms continued pretraining on the same amount of text sampled from the pretraining corpus across 10 out of 11 settings, including by $2.0$ points on GSM8K when inserted before mid-training. The retrieved text also transfers across model families: text retrieved for OLMo2-1B's failures improves Qwen3-4B on the mixture by $1.9$ points over the same baseline. Together, our results suggest that where RL fails is a cheap and effective signal for selecting pretraining data.

Visual document retrieval relies on rich multi-vector representations to capture fine-grained evidence in document pages, but encoding and matching these representations can be computationally expensive. Existing compression and elastic representation methods expose smaller configurations, yet making multiple budgets available does not determine which configuration a query should use. The allocation decision must estimate the retrieval value of alternative representations before incurring their full computation, while accommodating different resource preferences. We introduce FlexVDR, a framework for query-adaptive budget allocation within a single retriever. We construct a joint family of routes over encoder depth, embedding width, and token count. Retrieval supervision and distillation train the compact routes, while a native bypass preserves the full-budget reference. A Budget Allocator predicts route-specific retrieval utility from early query features and combines these predictions with a configurable resource preference to select a route. Experiments across five backbones on ViDoRe V1, V2, and V3 public show that FlexVDR retains much of the native retrieval quality while selecting compact routes for individual queries. A configurable resource preference allows the same retriever to adjust its computation without retraining or switching models.

Fine industrial robotic manipulation requires 6D pose, scale, and an operation-ready 3D model. Existing industrial pose estimation relies on CAD models, object-specific training data, or stable workcells, limiting use with unseen objects; zero-shot methods suffer from single-view occlusion, generative bias, and scale uncertainty. We present OV-PEAR, an observation-verified framework for 3D reconstruction and pose-scale estimation of unknown industrial objects. Its three-stage object-centric pipeline: (1) segments RGB-D instances and generates object-level 3D hypotheses; (2) anchors them to the robot frame via appearance-aware view retrieval, explicit scale search, and visibility-sensitive registration; (3) back-projects multi-view RGB-D evidence into the object-canonical frame to verify voxel occupancy, suppress hallucinations, and produce reusable trusted object models. On BOP-Industrial, OV-PEAR achieves 0.657 average AR and improves pose and voxel-level geometric consistency in real scenes; real-robot connector assembly reaches 99.67% grasp and 84.00% assembly success. The model library and pose-scale log enable short-term object-level state maintenance at 0.02 ms/frame.