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Kai Yang

Publications and source records attributed to Kai Yang.

At least 55 records · Page 3Linked to original sources
arXiv2026

Popular Differences and the Croot--Lev Half-Threshold Problem

Let $A$ be a finite non-empty subset of an abelian group $G$, and let $r_A(d)=|\{(a,a')\in A^2:a-a'=d\}|$. Croot and Lev asked whether the pointwise half-threshold condition $r_A(d)\ge |A|/2$ for every $d\in A-A$ forces $A-A$ to be either a subgroup or a union of three cosets. We resolve this open problem in its sharp general form by identifying the essential obstruction: the statement is false in arbitrary abelian groups, but becomes true after excluding non-zero two-torsion. More precisely, if $G$ is two-torsion-free and the half-threshold condition holds, then either $A-A$ is a finite subgroup of $G$, or there are a finite subgroup $H\le G$ and elements $x,g\in G$ such that \[ A=(x+H)\cup(x+g+H). \] The two-torsion-free hypothesis is essential: for every $r\ge1$ we construct $A\subseteq\F_2^{2r+1}$ with $A-A=\F_2^{2r+1}\setminus\{t\}$ such that every non-zero represented difference has exactly $|A|/2$ representations, giving genuine counterexamples to the Croot--Lev conclusion. The proof of the positive result combines a Kneser quotient reduction with Lev's formulation of Kemperman's critical-pair theory.

math.CO↗
arXiv2026

Odd cycles in symmetric Cayley graphs on prime cyclic groups

Let $p$ be an odd prime and let $S\subseteq \Z_p$ be symmetric with $0\notin S$. Let $\Cay(\Z_p,S)$ be the undirected Cayley graph on $\Z_p$ in which $x$ and $y$ are adjacent if and only if $x-y\in S$. For $1\le \ell\le (p-1)/2$, define \[ \ex_{\Cay}(C_{2\ell+1},\Z_p)=\max\{|S|: S=-S,\ 0\notin S,\ \Cay(\Z_p,S)\text{ contains no }C_{2\ell+1}\}. \] Confirming a conjecture of Cashman and Kelley, we prove that if $p=2\ell+1$, then $\ex_{\Cay}(C_{2\ell+1},\Z_p)=0$, while if $p>2\ell+1$, then \[ \ex_{\Cay}(C_{2\ell+1},\Z_p)=2\floor{\frac{p+2\ell+1}{2(2\ell+1)}}. \] The proof combines a sharp additive zero-sum odd-girth argument with weak odd pancyclicity to transfer the result from odd-girth exclusion to fixed odd-cycle exclusion. We also give a canonical extremal family, an exact extremality criterion in terms of odd zero-sum avoidance, and an example showing that extremizers need not be dilates of the canonical construction.

math.CO↗
arXiv2026

HOTDISK. Finding Massive Protostellar Disks with Water and Refractory Molecular Species

We present high-angular-resolution ($\sim0.05^{\prime\prime}$, $\sim 60-250$ au) ALMA Band~6 observations from the HOTDISK project (Hot-Origin Tracer survey of DISKs of massive protostars) aimed at investigating the "hot-disk" chemical pattern traced by vibrationally excited water, NaCl, SiS, and SiO in the innermost regions around massive protostars. Ten targets were selected based on strong CH$_3$CN emission exhibiting clear rotational signatures and centrally concentrated SiO emission from lower-resolution observations. We detect vibrationally excited water emission toward 7 of the 10 sources. In all detections, the blueshifted and redshifted components are compact and located on opposite sides of the 1.3 mm continuum peak, with velocity gradients approximately perpendicular to the outflow axes, consistent with rotation on disk scales. Emission from NaCl and SiS is detected toward 5 of these 7 sources and exhibits similar kinematics, further supporting the presence of compact rotating structures. In contrast, commonly used hot-core tracers (e.g., CH$_3$CN and SO$_2$) primarily probe larger-scale envelope gas. These results demonstrate that vibrationally excited water, NaCl, and SiS are powerful tracers of disk structures on $\sim$100 au scales, when observed at sufficient angular resolution and sensitivity. The high detection rate suggests that hot-disk chemical patterns -- and thus compact rotating disks -- are common in massive star-forming regions, at least among sources with well-developed rotating envelopes.

astro-ph.GA↗
arXiv2026

RLVR Datasets and Where to Find Them: Tracing Data Lineage for Better Training Data

The proliferation of Reinforcement Learning from Verifiable Rewards (RLVR) datasets has exacerbated provenance collapse due to unclear lineage among existing datasets. To bridge this fragmented RLVR data landscape, we propose Atomic-source Tracing via Lineage-Aware Search (ATLAS), a systematic framework for tracing RLVR datasets back to their atomic sources, attributing over 99.7% of 1.45M instances to 20 atomic sources. Our analysis reveals that most RLVR datasets are variants of a small set of shared upstream sources, with few introducing genuinely new data, and many facing data contamination risks. These findings naturally motivate us to curate a new RLVR dataset, DAPO++, and to benchmark existing datasets from a lineage-aware perspective. To this end, we propose Source-level Counterfactual Attribution (SCA) as a guiding principle to curate a decontaminated training dataset with concentrated learning signals. Essentially, SCA measures a sample's marginal utility by comparing per-atomic-source RL checkpoints against a shared base model. Building upon these attribution signals, we further design a composite dataset quality score Q that strongly correlates with downstream RLVR performance. Experiments on Qwen3 series models verify that DAPO++ consistently improves performance on held-out benchmarks, while Q reliably predicts downstream RLVR training effectiveness. Our code and data is available at https://github.com/Celine-hxy/ATLAS.

cs.LG↗
arXiv2026

FD-RAG: Federated Dual-System Retrieval-Augmented Generation

Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down in edge environments, where knowledge is fragmented across devices, raw data cannot be shared, and repeated LLM calls are prohibitively expensive. We propose FD-RAG, a federated dual-system RAG framework that decouples lightweight memory access from on-demand LLM reasoning for decentralized deployment. Specifically, FD-RAG learns semantic-aware adaptive hypergraphs over local corpora and distills them into compact QA memories. At inference time, it answers well-covered queries via direct memory matching and invokes LLM-based reasoning only when necessary, while tracing retrieved memories to hypergraph-grounded evidence. To mitigate cross-device knowledge fragmentation, FD-RAG aggregates anonymized memories across devices without exposing raw documents. Experiments on QA benchmarks show that FD-RAG improves accuracy by up to 7.8\% while reducing latency by 8.4$\times$ compared with strong local and federated baselines. We also provide theoretical analysis establishing an $\mathcal{O}(1/ε^{2})$ convergence rate for the proposed hypergraph learning, supporting its tractable deployment in edge settings.

cs.IR↗
arXiv2026

Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, existing studies largely attribute this advantage to denser and more stable supervision, while the parameter-level mechanisms underlying OPD's efficiency remain poorly understood. In this work, we argue that OPD's efficiency stems from a form of ``foresight'': it establishes a stable update trajectory toward the final model early in training. This foresight manifests in two aspects. First, at the \textbf{Module-Allocation Level}, OPD identifies regions with low marginal utility and concentrates updates on modules that are more critical to reasoning. Second, at the \textbf{Update-Direction Level}, OPD exhibits stronger low-rank concentration, with its dominant subspaces aligning closely with the final update subspace early in training. Building on these findings, we propose \textbf{EffOPD}, a plug-and-play acceleration method that speeds up OPD by adaptively selecting an extrapolation step size and moving along the current update direction. EffOPD requires no additional trainable modules or complex hyperparameter tuning, and achieves an average training acceleration of $3\times$ while maintaining comparable final performance. Overall, our findings provide a parameter-dynamics perspective for understanding the efficiency of OPD and offer practical insights for designing more efficient post-training methods for large language models.

cs.CL↗
arXiv2026

Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

cs.LG↗
arXiv2026

SafeAlign-VLA: A Negative-Enhanced Safe Alignment Framework for Risk-Aware Autonomous Driving

End-to-end autonomous driving systems excel in common scenarios but struggle with safety-critical long-tail cases. Vision-Language-Action (VLA) models are promising due to their strong reasoning capabilities. However, most VLA-based approaches rely on positive expert demonstrations, rarely exploiting negative samples, leading to insufficient understanding of risky behaviors and safety boundaries. To address this limitation, we propose SafeAlign-VLA, a unified negative-enhanced safe alignment framework that incorporates negative data into supervised learning and reinforcement learning. First, we develop a counterfactual safety pairing paradigm to generate structured safety labels and counterfactual positive trajectories from risky scenarios via counterfactual reasoning. Then, a two-stage training strategy is adopted: negative-enhanced supervised fine-tuning for failure feedback and trajectory correction, followed by anchor-based group relative policy optimization that uses positive and negative trajectories as contrastive anchors to steer sampling and penalize high-risk behaviors via group-relative advantages. Experiments on NAVSIM and DeepAccident validate the proposed framework. SafeAlign-VLA achieves 89.1 PDMS on the NAVSIM v1 testset, improving over the baseline without negative data by 1.3%. On DeepAccident, it reduces the collision rate to 3.36%, while achieving 84.2% language accuracy and 85.8% risk prediction accuracy. These results demonstrate the effectiveness of the proposed negative-enhanced safe alignment framework for safe and robust autonomous driving.

cs.RO↗
arXiv2026

Small Generalizable Prompt Predictive Models Can Steer Efficient RL Post-Training of Large Reasoning Models

Reinforcement learning enhances the reasoning capabilities of large language models but often involves high computational costs due to rollout-intensive optimization. Online prompt selection presents a plausible solution by prioritizing informative prompts to improve training efficiency. However, current methods either depend on costly, exact evaluations or construct prompt-specific predictive models lacking generalization across prompts. This study introduces Generalizable Predictive Prompt Selection (GPS), which performs Bayesian inference towards prompt difficulty using a lightweight generative model trained on the shared optimization history. Intermediate-difficulty prioritization and history-anchored diversity are incorporated into the batch acquisition principle to select informative prompt batches. The small predictive model also generalizes at test-time for efficient computational allocation. Experiments across varied reasoning benchmarks indicate GPS's substantial improvements in training efficiency, final performance, and test-time efficiency over superior baseline methods.

cs.AI↗
arXiv2026

VSPO: Vector-Steered Policy Optimization for Behavioral Control

Modern language models often need to optimize a primary accuracy objective while also accommodating secondary behavioral preferences, such as verbosity, agreeableness, or the level of technical expertise in its response. In practice, a base model may exhibit a desired behavior very rarely or not at all. Thus, endowing the model with a target behavior creates a sparse behavioral reward bottleneck. To address such multi-objective problems, we introduce Vector-Steered Policy Optimization (VSPO) which employs a steering vector associated with the target behavior to control the behavior intensity of the generated rollouts. VSPO is obtained by modifying GRPO to sample rollouts with varying steering intensities. This process can be interpreted as an on-policy latent self-distillation procedure where the model internalizes its steering vector. By varying steering intensities, VSPO upsamples rare behaviors and enriches rollout diversity, which alleviates the sparse reward issue and provably accelerates the policy optimization. Through comprehensive theory and experiments, we establish that VSPO has favorable properties compared to vanilla reward shaping and other alternative approaches. Specifically, under a bandit abstraction, VSPO provably achieves better iteration complexity than reward-shaped GRPO when the steering-induced distributions are sufficiently aligned with the target behavior. We evaluate VSPO across multiple reasoning benchmarks, including MATH and MMLU-Pro, for four target behaviors: explanation expertise, confidence expression, robustness to misleading context, and response verbosity. Our results show that VSPO consistently improves the control along target behavior while maintaining or improving task accuracy compared with reward shaping, teacher-trace distillation, and guidance-based baselines.

cs.LG↗
arXiv2026

Debiased Model-based Representations for Sample-efficient Continuous Control

Model-based representations recently stand out as a promising framework that embeds latent dynamics information into the representations for downstream off-policy actor-critic learning. It implicitly combines the advantages of both model-free and model-based approaches while avoiding the training costs associated with model-based methods. Nevertheless, existing model-based representation methods can fail to capture sufficient information about relevant variables and can overfit to early experiences in the replay buffer. These incur biases in representation and actor-critic learning, leading to inferior performance. To address this, we propose Debiased model-based Representations for Q-learning, tagged DR.Q algorithm. DR.Q explicitly maximizes the mutual information between the representations of the current state-action pair and the next state besides minimizing their deviations, and samples transitions with faded prioritized experience replay. We evaluate DR.Q on numerous continuous control benchmarks with a single set of hyperparameters, and the results demonstrate that DR.Q can match or surpass recent strong baselines, sometimes outperforming them by a large margin. Our code is available at https://github.com/dmksjfl/DR.Q.

cs.LG↗
arXiv2026

C-CoT: Counterfactual Chain-of-Thought with Vision-Language Models for Safe Autonomous Driving

Safety-critical planning in complex environments, particularly at urban intersections, remains a fundamental challenge for autonomous driving. Existing methods, whether rule-based or data-driven, frequently struggle to capture complex scene semantics, infer potential risks, and make reliable decisions in rare, high-risk situations. While vision-language models (VLMs) offer promising approaches for safe decision-making in these environments, most current approaches lack reflective and causal reasoning, thereby limiting their overall robustness. To address this, we propose a counterfactual chain-of-thought (C-CoT) framework that leverages VLMs to decompose driving decisions into five sequential stages: scene description, critical object identification, risk prediction, counterfactual risk reasoning, and final action planning. Within the counterfactual reasoning stage, we introduce a structured meta-action evaluation tree to explicitly assess the potential consequences of alternative action combinations. This self-reflective reasoning establishes causal links between action choices and safety outcomes, improving robustness in long-tail and out-of-distribution scenarios. To validate our approach, we construct the DeepAccident-CCoT dataset based on the DeepAccident benchmark and fine-tune a Qwen2.5-VL (7B) model using low-rank adaptation. Our model achieves a risk prediction recall of 81.9%, reduces the collision rate to 3.52%, and lowers L2 error to 1.98 m. Ablation studies further confirm the critical role of counterfactual reasoning and the meta-action evaluation tree in enhancing safety and interpretability.

cs.CV↗
arXiv2026

PAINET: A Principled Efficient Transformer for 3D Dynamics Modeling

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in object trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant transformer for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory. Our codes, baseline models and datasets are available at https://github.com/Icarus1411/PAINET.

cs.LG↗
arXiv2026

The evolution of C4H and c-C3H2 in molecular cores

Linear C4H and cyclic c-C3H2, as small unsaturated hydrocarbons, are the key precursors to complex organic molecules and are critical components of the interstellar medium. We present on-the-fly mapping observations of C4H 9-8 lines, c-C3H2 2-1, H13CO+ 1-0, and H42 toward a sample of 22 massive star-forming regions using the IRAM 30m telescope. Our aim is to further explore the evolution of these carbon-chain molecules by combining observational results obtained in cold cores. We employed H13CO+ 1-0 and H42 as tracers to probe the positions of molecular cloud cores and ionised hydrogen regions (HII regions), respectively. One chemical model in particular, which includes gas, dust grain surface, and icy mantle phases for C4H and c-C3H2 molecules, was used to make comparisons with observed abundances. From mapping observations targeting 31 regions across 22 sources, C4H 9-8 (J = 19/2-17/2) and C4H 9-8 (J = 17/2-15/2) were detected in only 17 regions, while H13CO+ 1-0 and c-C3H2 2-1 were successfully detected in all 31 regions. We find that the emission of C4H 9-8 and c-C3H2 2-1 is concentrated at the edges of H42 emission regions. The C4H/H13CO+ and c-C3H2/H13CO+ relative abundance ratios range from 0.17 to 1.77 and 1.42 to 6.69, respectively, with a median C4H/c-C3H2 ratio of 0.13. By combining the observational results of cold cores, we find that C4H/H13CO+ and c-C3H2/H13CO+ ratios show a strong decreasing trend as molecular cores evolve. The decreasing trends in C4H/H13CO+ and c-C3H2/H13CO+ ratios imply that small unsaturated hydrocarbons can be consumed and converted into other organic molecules during the evolution of molecular cores. The spatial concentration of C4H and c-C3H2 emission at the edges of H42 regions further supports their role as precursors in the chemical pathways that lead to complex organic molecules in the interstellar medium.

astro-ph.GA↗
arXiv2026

LLM-Enhanced Topical Trend Detection at Snapchat

Automatic detection of topical trends at scale is both challenging and essential for maintaining a dynamic content ecosystem on social media platforms. In this work, we present a large-scale system for identifying emerging topical trends on Snapchat, one of the world's largest short-video social platforms. Our system integrates multimodal topic extraction, time-series burst detection, and LLM-based consolidation and enrichment to enable accurate and timely trend discovery. To the best of our knowledge, this is the first published end-to-end system for topical trend detection on short-video platforms at production scale. Continuous offline human evaluation over six months demonstrates high precision in identifying meaningful trends. The system has been deployed in production at global scale and applied to downstream surfaces including content ranking and search, driving measurable improvements in content freshness and user experience.

cs.IR↗
arXiv2026

Report of the 5th PVUW Challenge: Towards More Diverse Modalities in Pixel-Level Understanding

This report summarizes the objectives, datasets, and top-performing methodologies of the 2026 Pixel-level Video Understanding in the Wild (PVUW) Challenge, hosted at CVPR 2026, which evaluates state-of-the-art models under highly unconstrained conditions. To provide a comprehensive assessment, the 2026 edition features three specialized tracks: the MOSE track for tracking objects within densely cluttered and severely occluded scenarios; the MeViS-Text track for localizing targets via motion-focused linguistic expressions; and the newly inaugurated MeViS-Audio track, which pioneers acoustic-driven object segmentation. By introducing previously unreleased challenging data and analyzing the cutting-edge, multimodal solutions submitted by participants, this report highlights the community's latest technical advancements and charts promising future directions for robust video scene comprehension.

cs.CV↗
arXiv2026

AsyncShield: A Plug-and-Play Edge Adapter for Asynchronous Cloud-based VLA Navigation

While Vision-Language-Action (VLA) models have been demonstrated possessing strong zero-shot generalization for robot control, their massive parameter sizes typically necessitate cloud-based deployment. However, cloud deployment introduces network jitter and inference latency, which can induce severe spatiotemporal misalignment in mobile navigation under continuous displacement, so that the stale intents expressed in past ego frames may become spatially incorrect in the current frame and lead to collisions. To address this issue, we propose AsyncShield, a plug-and-play asynchronous control framework. AsyncShield discards traditional black-box time-series prediction in favor of a deterministic physical white-box spatial mapping. By maintaining a temporal pose buffer and utilizing kinematic transformations, the system accurately converts temporal lag into spatial pose offsets to restore the VLA's original geometric intent. To balance intent restoration fidelity and physical safety, the edge adaptation is formulated as a constrained Markov decision process (CMDP). Solved via the PPO-Lagrangian algorithm, a reinforcement learning adapter dynamically trades off between tracking the VLA intent and responding to high-frequency LiDAR obstacle avoidance hard constraints. Furthermore, benefiting from a standardized universal sub-goal interface, domain randomization, and perception-level adaptation via Collision Radius Inflation, AsyncShield operates as a lightweight, plug-and-play module. Simulation and real-world experiments demonstrate that, without fine-tuning any cloud-based foundation models, the framework exhibits zero-shot and robust generalization capabilities, effectively improving the success rate and physical safety of asynchronous navigation.

cs.RO↗
arXiv2026

AgentRVOS for MeViS-Text Track of 5th PVUW Challenge: 3rd Method

This report describes a Ref-VOS pipeline centered on Sa2VA and organized with explicit agent roles. The key idea is that Sa2VA should provide the first dense semantic hypothesis, while an agent loop decides whether that hypothesis should be accepted, revised, or refined. The pipeline starts with a target-presence judgment stage. If the referred object does not exist in the video, the system directly outputs zero masks. Otherwise, Sa2VA receives the video and referring prompt and produces a coarse mask trajectory over the full video. This trajectory is treated as a semantic prior rather than a final answer. A planner agent decomposes the query, temporal partition agents identify informative blocks, scout agents search for anchor frames, and refinement agents convert reliable Sa2VA masks into boxes and points for SAM3 propagation. A critic scores candidate trajectories, a reflection controller repairs weak hypotheses, and a collaboration controller reconciles multiple agent branches. The result is a Ref-VOS system in which Sa2VA is responsible for dense grounded understanding, while the agent layer handles presence verification, temporal search, confidence-aware revision, and final mask refinement.

cs.CV↗