Nearest neighbor is a popular nonparametric method for classification and regression with many appealing properties. In the big data era, the sheer volume and spatial/temporal disparity of big data may prohibit centrally processing and storing the data. This has imposed considerable hurdle for nearest neighbor predictions since the entire training data must be memorized. One effective way to overcome this issue is the distributed learning framework. Through majority voting, the distributed nearest neighbor classifier achieves the same rate of convergence as its oracle version in terms of the regret, up to a multiplicative constant that depends solely on the data dimension. The multiplicative difference can be eliminated by replacing majority voting with the weighted voting scheme. In addition, we provide sharp theoretical upper bounds of the number of subsamples in order for the distributed nearest neighbor classifier to reach the optimal convergence rate. It is interesting to note that the weighted voting scheme allows a larger number of subsamples than the majority voting one. Our findings are supported by numerical studies.

Reinforcement Learning (RL) has emerged as a powerful paradigm for advancing Large Language Models (LLMs), achieving remarkable performance in complex reasoning domains such as mathematics and code generation. However, current RL methods face a fundamental scalability bottleneck due to their heavy reliance on human-curated preference data or labeled datasets for reward modeling. To overcome this limitation, we explore RL on unlabeled data where models learn autonomously from continuous experience streams. The core challenge in this setting lies in reliable reward estimation without ground-truth supervision. Existing approaches like Test-Time RL address this through self-consistent consensus, but risk reinforcing incorrect pseudo-labels derived from majority voting. We introduce COMPASS (Composite Path and Answer Self-Scoring), a novel test-time reward mechanism that operates without external supervision. COMPASS integrates two complementary components: the Dual-Calibration Answer Reward (DCAR), which stabilizes training by establishing trustworthy pseudo-labels through confidence and credibility calibration, and the Decisive Path Reward (DPR), which directly optimizes the reasoning process quality beyond mere outcome supervision. By jointly reinforcing trustworthy consensus answers and highly decisive reasoning chains, the COMPASS systematically enhances the model's analytical capabilities. Extensive experiments show that COMPASS achieves significant and consistent performance gains across diverse reasoning tasks and model architectures, advancing a more scalable direction for LLMs to learn from continuous experience.

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Majority voting has proven effective for close-ended question answering by aggregating parallel reasoning traces. However, it is not directly applicable to open-ended reasoning, such as code generation and web-based deep research, where a "majority" over complete solutions is ill-defined. Empirically, it matches or surpasses majority voting on AIME and GPQA, while delivering consistent gains on open-ended coding tasks: on LiveCodeBench (hard), pass@1 improves by +8.28% for DeepCoder-14B-Preview and +7.58% for Qwen3-8B. These results demonstrate that parallel test-time scaling can benefit open-ended reasoning without relying on voting over complete outputs. Recent advances in Large Language Models (LLMs) have been driven by test-time compute scaling. As evidenced by OpenAI's o1 (OpenAI, 2024), DeepSeek-R1 (Guo et al., 2025), etc., models generate extended "think" segments that reflect intermediate hypotheses, derivations, and self-corrections prior to emitting the final answer (Chen et al., 2025b; Y ang et al., 2025c). Such sequential test-time scaling has established a new paradigm: increasing the inference-time computation (e.g., longer reasoning traces) often leads to improved accuracy and problem-solving capability. Y et simply lengthening the chain has diminishing returns and can even hurt, e.g., overthinking (Chen et al., 2024; Cuadron et al., 2025), with studies showing that correct answers often appear in shorter traces (Zeng et al., 2025).

This paper presents a unified study of four distinct modeling approaches for classifying dysarthria severity in the Speech Analysis for Neurodegenerative Diseases (SAND) challenge. All models tackle the same five class classification task using a common dataset of speech recordings. We investigate: (1) a ViT-OF method leveraging a Vision Transformer on spectrogram images, (2) a 1D-CNN approach using eight 1-D CNN's with majority-vote fusion, (3) a BiLSTM-OF approach using nine BiLSTM models with majority vote fusion, and (4) a Hierarchical XGBoost ensemble that combines glottal and formant features through a two stage learning framework. Each method is described, and their performances on a validation set of 53 speakers are compared. Results show that while the feature-engineered XGBoost ensemble achieves the highest macro-F1 (0.86), the deep learning models (ViT, CNN, BiLSTM) attain competitive F1-scores (0.70) and offer complementary insights into the problem.

Its color represents the class label prediction of the corresponding classifier. The sequential querying of classifiers in the ensemble can be seen as draws without replacement from the urn. An analysis of this classical urn model based on the hypergeometric distribution makes it possible to estimate the confidence on the outcome of majority voting when only a fraction of the individual predictions is known. These estimates can be used to speed up the prediction by the ensemble. Specifically, the aggregation of votes can be halted when the confidence in the final prediction is sufficiently high. If one assumes a uniform prior for the distribution of possible votes the analysis is shown to be equivalent to a previous one based on Dirichlet distributions.

We study community detection in the \emph{symmetric $k$-stochastic block model}, where $n$ nodes are evenly partitioned into $k$ clusters with intra- and inter-cluster connection probabilities $p$ and $q$, respectively. Our main result is a polynomial-time algorithm that achieves the minimax-optimal misclassification rate \begin{equation*} \exp \Bigl(-\bigl(1 \pm o(1)\bigr) \tfrac{C}{k}\Bigr), \quad \text{where } C = (\sqrt{pn} - \sqrt{qn})^2, \end{equation*} whenever $C \ge K\,k^2\,\log k$ for some universal constant $K$, matching the Kesten--Stigum (KS) threshold up to a $\log k$ factor. Notably, this rate holds even when an adversary corrupts an $η\le \exp\bigl(- (1 \pm o(1)) \tfrac{C}{k}\bigr)$ fraction of the nodes. To the best of our knowledge, the minimax rate was previously only attainable either via computationally inefficient procedures [ZZ15] or via polynomial-time algorithms that require strictly stronger assumptions such as $C \ge K k^3$ [GMZZ17]. In the node-robust setting, the best known algorithm requires the substantially stronger condition $C \ge K k^{102}$ [LM22]. Our results close this gap by providing the first polynomial-time algorithm that achieves the minimax rate near the KS threshold in both settings. Our work has two key technical contributions: (1) we robustify majority voting via the Sum-of-Squares framework, (2) we develop a novel graph bisection algorithm via robust majority voting, which allows us to significantly improve the misclassification rate to $1/\mathrm{poly}(k)$ for the initial estimation near the KS threshold.

The BLP-2025 Task 1A requires Bengali hate speech classification into six categories. Traditional supervised approaches need extensive labeled datasets that are expensive for low-resource languages. We developed PromptGuard, a few-shot framework combining chi-square statistical analysis for keyword extraction with adaptive majority voting for decision-making. We explore statistical keyword selection versus random approaches and adaptive voting mechanisms that extend classification based on consensus quality. Chi-square keywords provide consistent improvements across categories, while adaptive voting benefits ambiguous cases requiring extended classification rounds. PromptGuard achieves a micro-F1 of 67.61, outperforming n-gram baselines (60.75) and random approaches (14.65). Ablation studies confirm chi-square-based keywords show the most consistent impact across all categories.