The m-out-of-n bootstrap, originally proposed by Bickel, Gotze, and Zwet (1992), approximates the distribution of a statistic by repeatedly drawing m subsamples (with m much smaller than n) without replacement from an original sample of size n. It is now routinely used for robust inference with heavy-tailed data, bandwidth selection, and other large-sample applications. Despite its broad applicability across econometrics, biostatistics, and machine learning, rigorous parameter-free guarantees for the soundness of the m-out-of-n bootstrap when estimating sample quantiles have remained elusive. This paper establishes such guarantees by analyzing the estimator of sample quantiles obtained from m-out-of-n resampling of a dataset of size n. We first prove a central limit theorem for a fully data-driven version of the estimator that holds under a mild moment condition and involves no unknown nuisance parameters. We then show that the moment assumption is essentially tight by constructing a counter-example in which the CLT fails. Strengthening the assumptions slightly, we derive an Edgeworth expansion that provides exact convergence rates and, as a corollary, a Berry Esseen bound on the bootstrap approximation error. Finally, we illustrate the scope of our results by deriving parameter-free asymptotic distributions for practical statistics, including the quantiles for random walk Metropolis-Hastings and the rewards of ergodic Markov decision processes, thereby demonstrating the usefulness of our theory in modern estimation and learning tasks.

Recent advancements in Large Language Models (LLMs) and Vision-Language Models (VLMs) have sparked significant interest in developing GUI visual agents. We introduce MONDAY (Mobile OS Navigation Task Dataset for Agents from YouTube), a large-scale dataset of 313K annotated frames from 20K instructional videos capturing diverse real-world mobile OS navigation across multiple platforms. Models that include MONDAY in their pre-training phases demonstrate robust cross-platform generalization capabilities, consistently outperforming models trained on existing single OS datasets while achieving an average performance gain of 18.11%p on an unseen mobile OS platform. To enable continuous dataset expansion as mobile platforms evolve, we present an automated framework that leverages publicly available video content to create comprehensive task datasets without manual annotation. Our framework comprises robust OCR-based scene detection (95.04% F1score), near-perfect UI element detection (99.87% hit ratio), and novel multi-step action identification to extract reliable action sequences across diverse interface configurations. We contribute both the MONDAY dataset and our automated collection framework to facilitate future research in mobile OS navigation.

The paradigm of using Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) as evaluative judges has emerged as an effective approach in RLHF and inference-time scaling. In this work, we propose Multimodal Reasoner as a Judge (MR. Judge), a paradigm for empowering general-purpose MLLMs judges with strong reasoning capabilities. Instead of directly assigning scores for each response, we formulate the judgement process as a reasoning-inspired multiple-choice problem. Specifically, the judge model first conducts deliberate reasoning covering different aspects of the responses and eventually selects the best response from them. This reasoning process not only improves the interpretibility of the judgement, but also greatly enhances the performance of MLLM judges. To cope with the lack of questions with scored responses, we propose the following strategy to achieve automatic annotation: 1) Reverse Response Candidates Synthesis: starting from a supervised fine-tuning (SFT) dataset, we treat the original response as the best candidate and prompt the MLLM to generate plausible but flawed negative candidates. 2) Text-based reasoning extraction: we carefully design a data synthesis pipeline for distilling the reasoning capability from a text-based reasoning model, which is adopted to enable the MLLM judges to regain complex reasoning ability via warm up supervised fine-tuning. Experiments demonstrate that our MR. Judge is effective across a wide range of tasks. Specifically, our MR. Judge-7B surpasses GPT-4o by 9.9% on VL-RewardBench, and improves performance on MM-Vet during inference-time scaling by up to 7.7%.

The learnware paradigm offers a novel approach to machine learning by enabling users to reuse a set of well-trained models for tasks beyond the models' original purposes. It eliminates the need to build models from scratch, instead relying on specifications (representations of a model's capabilities) to identify and leverage the most suitable models for new tasks. While learnware has proven effective in many scenarios, its application to language models has remained largely unexplored. At the same time, large language models (LLMs) have demonstrated remarkable universal question-answering abilities, yet they face challenges in specialized scenarios due to data scarcity, privacy concerns, and high computational costs, thus more and more specialized small language models (SLMs) are being trained for specific domains. To address these limitations systematically, the learnware paradigm provides a promising solution by enabling maximum utilization of specialized SLMs, and allowing users to identify and reuse them in a collaborative and privacy-preserving manner. This paper presents a preliminary attempt to apply the learnware paradigm to language models. We simulated a learnware system comprising approximately 100 learnwares of specialized SLMs with 8B parameters, fine-tuned across finance, healthcare, and mathematics domains. Each learnware contains an SLM and a specification, which enables users to identify the most relevant models without exposing their own data. Experimental results demonstrate promising performance: by selecting one suitable learnware for each task-specific inference, the system outperforms the base SLMs on all benchmarks. Compared to LLMs, the system outperforms Qwen1.5-110B, Qwen2.5-72B, and Llama3.1-70B-Instruct by at least 14% in finance domain tasks, and surpasses Flan-PaLM-540B (ranked 7th on the Open Medical LLM Leaderboard) in medical domain tasks.

Tabular data, a fundamental data format in machine learning, is predominantly utilized in competitions and real-world applications. The performance of tabular models--such as gradient boosted decision trees and neural networks--can vary significantly across datasets due to differences in feature distributions and task characteristics. Achieving top performance on each dataset often requires specialized expert knowledge. To address this variability, practitioners often aggregate the predictions of multiple models. However, conventional aggregation strategies typically rely on static combination rules and lack instance-level adaptability. In this work, we propose an in-context ensemble framework for tabular prediction that leverages large language models (LLMs) to perform dynamic, instance-specific integration of external model predictions. Without access to raw tabular features or semantic information, our method constructs a context around each test instance using its nearest neighbors and the predictions from a pool of external models. Within this enriched context, we introduce Chain of Tabular Thoughts (CoT$^2$), a prompting strategy that guides LLMs through multi-step, interpretable reasoning, making still further progress toward expert-level decision-making. Experimental results show that our method outperforms well-tuned baselines and standard ensemble techniques across a wide range of tabular datasets.

Recent Large Reasoning Models significantly improve the reasoning ability of Large Language Models by learning to reason, exhibiting the promising performance in solving complex tasks. LRMs solve tasks that require complex reasoning by explicitly generating reasoning trajectories together with answers. Nevertheless, judging the quality of such an output answer is not easy because only considering the correctness of the answer is not enough and the soundness of the reasoning trajectory part matters as well. Logically, if the soundness of the reasoning part is poor, even if the answer is correct, the confidence of the derived answer should be low. Existing methods did consider jointly assessing the overall output answer by taking into account the reasoning part, however, their capability is still not satisfactory as the causal relationship of the reasoning to the concluded answer cannot properly reflected. In this paper, inspired by classical mechanics, we present a novel approach towards establishing a CoT-Kinetics energy equation. Specifically, our CoT-Kinetics energy equation formulates the token state transformation process, which is regulated by LRM internal transformer layers, as like a particle kinetics dynamics governed in a mechanical field. Our CoT-Kinetics energy assigns a scalar score to evaluate specifically the soundness of the reasoning phase, telling how confident the derived answer could be given the evaluated reasoning. As such, the LRM's overall output quality can be accurately measured, rather than a coarse judgment (e.g., correct or incorrect) anymore.

Providing personalized, detailed feedback at scale in large undergraduate STEM courses remains a persistent challenge. We present an empirically evaluated practice exam system that integrates AI generated feedback with targeted textbook references, deployed in a large introductory biology course. Our system encourages metacognitive behavior by asking students to explain their answers and declare their confidence. It uses OpenAI's GPT-4o to generate personalized feedback based on this information, while directing them to relevant textbook sections. Through interaction logs from consenting participants across three midterms (541, 342, and 413 students respectively), totaling 28,313 question-student interactions across 146 learning objectives, along with 279 surveys and 23 interviews, we examined the system's impact on learning outcomes and engagement. Across all midterms, feedback types showed no statistically significant performance differences, though some trends suggested potential benefits. The most substantial impact came from the required confidence ratings and explanations, which students reported transferring to their actual exam strategies. About 40 percent of students engaged with textbook references when prompted by feedback -- far higher than traditional reading rates. Survey data revealed high satisfaction (mean rating 4.1 of 5), with 82.1 percent reporting increased confidence on practiced midterm topics, and 73.4 percent indicating they could recall and apply specific concepts. Our findings suggest that embedding structured reflection requirements may be more impactful than sophisticated feedback mechanisms.

Mixture-of-experts (MoE) architectures could achieve impressive computational efficiency with expert parallelism, which relies heavily on all-to-all communication across devices. Unfortunately, such communication overhead typically constitutes a significant portion of the total runtime, hampering the scalability of distributed training and inference for modern MoE models (consuming over $40\%$ runtime in large-scale training). In this paper, we first define collaborative communication to illustrate this intrinsic limitation, and then propose system- and algorithm-level innovations to reduce communication costs. Specifically, given a pair of experts co-activated by one token, we call them "collaborated", which comprises $2$ cases as intra- and inter-collaboration, depending on whether they are kept on the same device. Our pilot investigations reveal that augmenting the proportion of intra-collaboration can accelerate expert parallelism at scale. It motivates us to strategically optimize collaborative communication for accelerated MoE training and inference, dubbed Occult. Our designs are capable of either delivering exact results with reduced communication cost or controllably minimizing the cost with collaboration pruning, materialized by modified fine-tuning. Comprehensive experiments on various MoE-LLMs demonstrate that Occult can be faster than popular state-of-the-art inference or training frameworks (more than $1.5\times$ speed up across multiple tasks and models) with comparable or superior quality compared to the standard fine-tuning. Code is available at $\href{https://github.com/UNITES-Lab/Occult}{https://github.com/UNITES-Lab/Occult}$.

Chain-of-Thought (CoT) reasoning has proven effective in enhancing large language models (LLMs) on complex tasks, spurring research into its underlying mechanisms. However, two primary challenges remain for real-world applications: (1) the lack of quantitative metrics and actionable guidelines for evaluating and optimizing measurable boundaries of CoT capability, and (2) the absence of methods to assess boundaries of unmeasurable CoT capability, such as multimodal perception. To address these gaps, we introduce the Reasoning Boundary Framework++ (RBF++). To tackle the first challenge, we define the reasoning boundary (RB) as the maximum limit of CoT performance. We also propose a combination law for RBs, enabling quantitative analysis and offering actionable guidance across various CoT tasks. For the second challenge, particularly in multimodal scenarios, we introduce a constant assumption, which replaces unmeasurable RBs with scenario-specific constants. Additionally, we propose the reasoning boundary division mechanism, which divides unmeasurable RBs into two sub-boundaries, facilitating the quantification and optimization of both unmeasurable domain knowledge and multimodal perception capabilities. Extensive experiments involving 38 models across 13 tasks validate the feasibility of our framework in cross-modal settings. Additionally, we evaluate 10 CoT strategies, offer insights into optimization and decay from two complementary perspectives, and expand evaluation benchmarks for measuring RBs in LLM reasoning. We hope this work advances the understanding of RBs and optimization strategies in LLMs. Code and data are available at https://github.com/LightChen233/reasoning-boundary.

We introduce TimeSeriesGym, a scalable benchmarking framework for evaluating Artificial Intelligence (AI) agents on time series machine learning engineering challenges. Existing benchmarks lack scalability, focus narrowly on model building in well-defined settings, and evaluate only a limited set of research artifacts (e.g., CSV submission files). To make AI agent benchmarking more relevant to the practice of machine learning engineering, our framework scales along two critical dimensions. First, recognizing that effective ML engineering requires a range of diverse skills, TimeSeriesGym incorporates challenges from diverse sources spanning multiple domains and tasks. We design challenges to evaluate both isolated capabilities (including data handling, understanding research repositories, and code translation) and their combinations, and rather than addressing each challenge independently, we develop tools that support designing multiple challenges at scale. Second, we implement evaluation mechanisms for multiple research artifacts, including submission files, code, and models, using both precise numeric measures and more flexible LLM-based evaluation approaches. This dual strategy balances objective assessment with contextual judgment. Although our initial focus is on time series applications, our framework can be readily extended to other data modalities, broadly enhancing the comprehensiveness and practical utility of agentic AI evaluation. We open-source our benchmarking framework to facilitate future research on the ML engineering capabilities of AI agents.