Riemannian Langevin Dynamics: Strong Convergence of Geometric Euler-Maruyama Scheme

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations (SDEs) on manifolds, which raises the need for convergence theory of numerical schemes for manifold-valued SDEs. In Euclidean space, the Euler--Maruyama (EM) scheme achieves strong convergence with order $1/2$, but an analogous result for manifold discretizations is less understood in general settings. In this work, we study a geometric version of the EM scheme for SDEs on Riemannian manifolds and prove strong convergence with order $1/2$ under geometric and regularity conditions. As an application, we obtain a Wasserstein bound for sampling on manifolds via the geometric EM discretization of Riemannian Langevin dynamics.

Are Multimodal Large Language Models Good Annotators for Image Tagging?

Image tagging, a fundamental vision task, traditionally relies on human-annotated datasets to train multi-label classifiers, which incurs significant labor and costs. While Multimodal Large Language Models (MLLMs) offer promising potential to automate annotation, their capability to replace human annotators remains underexplored. This paper aims to analyze the gap between MLLM-generated and human annotations and to propose an effective solution that enables MLLM-based annotation to replace manual labeling. Our analysis of MLLM annotations reveals that, under a conservative estimate, MLLMs can reduce annotation cost to as low as one-thousandth of the human cost, mainly accounting for GPU usage, which is nearly negligible compared to manual efforts. Their annotation quality reaches about 50\% to 80\% of human performance, while achieving over 90\% performance on downstream training tasks.Motivated by these findings, we propose TagLLM, a novel framework for image tagging, which aims to narrow the gap between MLLM-generated and human annotations. TagLLM comprises two components: Candidates generation, which employs structured group-wise prompting to efficiently produce a compact candidate set that covers as many true labels as possible while reducing subsequent annotation workload; and label disambiguation, which interactively calibrates the semantic concept of categories in the prompts and effectively refines the candidate labels. Extensive experiments show that TagLLM substantially narrows the gap between MLLM-generated and human annotations, especially in downstream training performance, where it closes about 60\% to 80\% of the difference.

VI-CuRL: Stabilizing Verifier-Independent RL Reasoning via Confidence-Guided Variance Reduction

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a dominant paradigm for enhancing Large Language Models (LLMs) reasoning, yet its reliance on external verifiers limits its scalability. Recent findings suggest that RLVR primarily functions by eliciting latent capabilities, motivating the development of verifier-free algorithms. However, in such settings, standard methods like Group Relative Policy Optimization face a critical challenge: destructive gradient variance that often leads to training collapse. To address this issue, we introduceVerifier-Independent Curriculum Reinforcement Learning (VI-CuRL), a framework that leverages the model's intrinsic confidence to construct a curriculum independent from external verifiers. By prioritizing high-confidence samples, VI-CuRL effectively manages the bias-variance trade-off, specifically targeting the reduction of action and problem variance. We provide a rigorous theoretical analysis, proving that our estimator guarantees asymptotic unbiasedness. Empirically, VI-CuRL promotes stability and consistently outperforms verifier-independent baselines across six challenging benchmarks with/without verifiers.

BrokenBind: Universal Modality Exploration beyond Dataset Boundaries

Multi-modal learning combines various modalities to provide a comprehensive understanding of real-world problems. A common strategy is to directly bind different modalities together in a specific joint embedding space. However, the capability of existing methods is restricted within the modalities presented in the given dataset, thus they are biased when generalizing to unpresented modalities in downstream tasks. As a result, due to such inflexibility, the viability of previous methods is seriously hindered by the cost of acquiring multi-modal datasets. In this paper, we introduce BrokenBind, which focuses on binding modalities that are presented from different datasets. To achieve this, BrokenBind simultaneously leverages multiple datasets containing the modalities of interest and one shared modality. Though the two datasets do not correspond to each other due to distribution mismatch, we can capture their relationship to generate pseudo embeddings to fill in the missing modalities of interest, enabling flexible and generalized multi-modal learning. Under our framework, any two modalities can be bound together, free from the dataset limitation, to achieve universal modality exploration. Further, to reveal the capability of our method, we study intensified scenarios where more than two datasets are needed for modality binding and show the effectiveness of BrokenBind in low-data regimes. Through extensive evaluation, we carefully justify the superiority of BrokenBind compared to well-known multi-modal baseline methods.

Bifrost: Steering Strategic Trajectories to Bridge Contextual Gaps for Self-Improving Agents

Autonomous agents excel in self-improvement through reflection and iterative refinement, which reuse successful task trajectories as in-context examples to assist subsequent reasoning. However, shifting across tasks often introduces a context mismatch. Hence, existing approaches either discard the trajectories or manipulate them using heuristics, leading to a non-negligible fine-tuning cost or unguaranteed performance. To bridge this gap, we reveal a context-trajectory correlation, where shifts of context are highly parallel with shifts of trajectory. Based on this finding, we propose BrIdge contextual gap FoR imprOvised trajectory STeering (Bifrost), a training-free method that leverages context differences to precisely guide the adaptation of previously solved trajectories towards the target task, mitigating the misalignment caused by context shifts. Our trajectory adaptation is conducted at the representation level using agent hidden states, ensuring trajectory transformation accurately aligns with the target context in a shared space. Across diverse benchmarks, Bifrost consistently outperforms existing trajectory reuse and finetuned self-improvement methods, demonstrating that agents can effectively leverage past experiences despite substantial context shifts.

Causal Graph Learning via Distributional Invariance of Cause-Effect Relationship

This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of those causes. This insight enables a direct test for potential causal relationships by checking the variance of their corresponding effect-cause conditional distributions across multiple downsampled subsets of the data. These subsets are selected to reflect different prior cause distributions, while preserving the effect-cause conditional relationships. Using this invariance test and exploiting an (empirical) sparsity of most causal graphs, we develop an algorithm that efficiently uncovers causal relationships with quadratic complexity in the number of observational variables, reducing the processing time by up to 25x compared to state-of-the-art methods. Our empirical experiments on a varied benchmark of large-scale datasets show superior or equivalent performance compared to existing works, while achieving enhanced scalability.

Positive-Unlabeled Reinforcement Learning Distillation for On-Premise Small Models

Due to constraints on privacy, cost, and latency, on-premise deployment of small models is increasingly common. However, most practical pipelines stop at supervised fine-tuning (SFT) and fail to reach the reinforcement learning (RL) alignment stage. The main reason is that RL alignment typically requires either expensive human preference annotation or heavy reliance on high-quality reward models with large-scale API usage and ongoing engineering maintenance, both of which are ill-suited to on-premise settings. To bridge this gap, we propose a positive-unlabeled (PU) RL distillation method for on-premise small-model deployment. Without human-labeled preferences or a reward model, our method distills the teacher's preference-optimization capability from black-box generations into a locally trainable student. For each prompt, we query the teacher once to obtain an anchor response, locally sample multiple student candidates, and perform anchor-conditioned self-ranking to induce pairwise or listwise preferences, enabling a fully local training loop via direct preference optimization or group relative policy optimization. Theoretical analysis justifies that the induced preference signal by our method is order-consistent and concentrates on near-optimal candidates, supporting its stability for preference optimization. Experiments demonstrate that our method achieves consistently strong performance under a low-cost setting.

Scalable Oversight via Partitioned Human Supervision

As artificial intelligence (AI) systems approach and surpass expert human performance across a broad range of tasks, obtaining high-quality human supervision for evaluation and training becomes increasingly challenging. Our focus is on tasks that require deep knowledge and skills of multiple domains. Unfortunately, even the best human experts are knowledgeable only in a single narrow area, and will not be able to evaluate the correctness of advanced AI systems on such superhuman tasks. However, based on their narrow expertise, humans may provide a weak signal, i.e., a complementary label indicating an option that is incorrect. For example, a cardiologist could state that "this is not related to cardiology,'' even if they cannot identify the true disease. Based on this weak signal, we propose a scalable oversight framework that enables us to evaluate frontier AI systems without the need to prepare the ground truth. We derive an unbiased estimator of top-1 accuracy from complementary labels and quantify how many complementary labels are needed to match the variance of ordinary labels. We further introduce two estimators to combine scarce ordinary labels with abundant complementary labels. We provide finite-sample deviation guarantees for both complementary-only and the mixed estimators. Empirically, we show that we can evaluate the output of large language models without the ground truth, if we have complementary labels. We further show that we can train an AI system with such weak signals: we show how we can design an agentic AI system automatically that can perform better with this partitioned human supervision. Our code is available at https://github.com/R-Yin-217/Scalable-Oversight-via-Human-Partitioned-Supervision.

LLM Routing with Dueling Feedback

We study LLM routing, the problem of selecting the best model for each query while balancing user satisfaction, model expertise, and inference cost. We formulate routing as contextual dueling bandits, learning from pairwise preference feedback rather than absolute scores, thereby yielding label-efficient and dynamic adaptation. Building on this formulation, we introduce Category-Calibrated Fine-Tuning (CCFT), a representation-learning method that derives model embeddings from offline data using contrastive fine-tuning with categorical weighting. These embeddings enable the practical instantiation of Feel-Good Thompson Sampling for Contextual Dueling Bandits (FGTS.CDB), a theoretically grounded posterior-sampling algorithm. We propose four variants of the categorical weighting that explicitly integrate model quality and cost, and we empirically evaluate the proposed methods on the RouterBench and MixInstruct datasets. Across both benchmarks, our methods achieve lower cumulative regret and faster convergence, with better robustness and performance-cost balance than strong baselines built with a general-purpose OpenAI embedding model.

Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update

We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function, thereby modeling a broad class of reward distributions such as Bernoulli and Poisson. While GLBs are widely applicable to real-world scenarios, their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency. Existing methods typically trade off between two objectives, either incurring high per-round costs for optimal regret guarantees or compromising statistical efficiency to enable constant-time updates. In this paper, we propose a jointly efficient algorithm that attains a nearly optimal regret bound with $\mathcal{O}(1)$ time and space complexities per round. The core of our method is a tight confidence set for the online mirror descent (OMD) estimator, which is derived through a novel analysis that leverages the notion of mix loss from online prediction. The analysis shows that our OMD estimator, even with its one-pass updates, achieves statistical efficiency comparable to maximum likelihood estimation, thereby leading to a jointly efficient optimistic method.