Do Transformers Have the Ability for Periodicity Generalization?

Large language models (LLMs) based on the Transformer have demonstrated strong performance across diverse tasks. However, current models still exhibit substantial limitations in out-of-distribution (OOD) generalization compared with humans. We investigate this gap through periodicity, one of the basic OOD scenarios. Periodicity captures invariance amid variation. Periodicity generalization represents a model's ability to extract periodic patterns from training data and generalize to OOD scenarios. We introduce a unified interpretation of periodicity from the perspective of abstract algebra and reasoning, including both single and composite periodicity, to explain why Transformers struggle to generalize periodicity. Then we construct Coper about composite periodicity, a controllable generative benchmark with two OOD settings, Hollow and Extrapolation. Experiments reveal that periodicity generalization in Transformers is limited, where models can memorize periodic data during training, but cannot generalize to unseen composite periodicity. We release the source code to support future research.

KOCO-BENCH: Can Large Language Models Leverage Domain Knowledge in Software Development?

Large language models (LLMs) excel at general programming but struggle with domain-specific software development, necessitating domain specialization methods for LLMs to learn and utilize domain knowledge and data. However, existing domain-specific code benchmarks cannot evaluate the effectiveness of domain specialization methods, which focus on assessing what knowledge LLMs possess rather than how they acquire and apply new knowledge, lacking explicit knowledge corpora for developing domain specialization methods. To this end, we present KOCO-BENCH, a novel benchmark designed for evaluating domain specialization methods in real-world software development. KOCO-BENCH contains 6 emerging domains with 11 software frameworks and 25 projects, featuring curated knowledge corpora alongside multi-granularity evaluation tasks including domain code generation (from function-level to project-level with rigorous test suites) and domain knowledge understanding (via multiple-choice Q&A). Unlike previous benchmarks that only provide test sets for direct evaluation, KOCO-BENCH requires acquiring and applying diverse domain knowledge (APIs, rules, constraints, etc.) from knowledge corpora to solve evaluation tasks. Our evaluations reveal that KOCO-BENCH poses significant challenges to state-of-the-art LLMs. Even with domain specialization methods (e.g., SFT, RAG, kNN-LM) applied, improvements remain marginal. Best-performing coding agent, Claude Code, achieves only 34.2%, highlighting the urgent need for more effective domain specialization methods. We release KOCO-BENCH, evaluation code, and baselines to advance further research at https://github.com/jiangxxxue/KOCO-bench.

DALD-PCAC: Density-Adaptive Learning Descriptor for Point Cloud Lossless Attribute Compression

Recently, deep learning has significantly advanced the performance of point cloud geometry compression. However, the learning-based lossless attribute compression of point clouds with varying densities is under-explored. In this paper, we develop a learning-based framework, namely DALD-PCAC that leverages Levels of Detail (LoD) to tailor for point cloud lossless attribute compression. We develop a point-wise attention model using a permutation-invariant Transformer to tackle the challenges of sparsity and irregularity of point clouds during context modeling. We also propose a Density-Adaptive Learning Descriptor (DALD) capable of capturing structure and correlations among points across a large range of neighbors. In addition, we develop a prior-guided block partitioning to reduce the attribute variance within blocks and enhance the performance. Experiments on LiDAR and object point clouds show that DALD-PCAC achieves the state-of-the-art performance on most data. Our method boosts the compression performance and is robust to the varying densities of point clouds. Moreover, it guarantees a good trade-off between performance and complexity, exhibiting great potential in real-world applications. The source code is available at https://github.com/zb12138/DALD_PCAC.

Open-Vocabulary 3D Instruction Ambiguity Detection

In safety-critical domains, linguistic ambiguity can have severe consequences; a vague command like "Pass me the vial" in a surgical setting could lead to catastrophic errors. Yet, most embodied AI research overlooks this, assuming instructions are clear and focusing on execution rather than confirmation. To address this critical safety gap, we are the first to define Open-Vocabulary 3D Instruction Ambiguity Detection, a fundamental new task where a model must determine if a command has a single, unambiguous meaning within a given 3D scene. To support this research, we build Ambi3D, the large-scale benchmark for this task, featuring over 700 diverse 3D scenes and around 22k instructions. Our analysis reveals a surprising limitation: state-of-the-art 3D Large Language Models (LLMs) struggle to reliably determine if an instruction is ambiguous. To address this challenge, we propose AmbiVer, a two-stage framework that collects explicit visual evidence from multiple views and uses it to guide an vision-language model (VLM) in judging instruction ambiguity. Extensive experiments demonstrate the challenge of our task and the effectiveness of AmbiVer, paving the way for safer and more trustworthy embodied AI. Code and dataset available at https://jiayuding031020.github.io/ambi3d/.

VideoCuRL: Video Curriculum Reinforcement Learning with Orthogonal Difficulty Decomposition

Reinforcement Learning (RL) is crucial for empowering VideoLLMs with complex spatiotemporal reasoning. However, current RL paradigms predominantly rely on random data shuffling or naive curriculum strategies based on scalar difficulty metrics. We argue that scalar metrics fail to disentangle two orthogonal challenges in video understanding: Visual Temporal Perception Load and Cognitive Reasoning Depth. To address this, we propose VideoCuRL, a novel framework that decomposes difficulty into these two axes. We employ efficient, training-free proxies, optical flow and keyframe entropy for visual complexity, Calibrated Surprisal for cognitive complexity, to map data onto a 2D curriculum grid. A competence aware Diagonal Wavefront strategy then schedules training from base alignment to complex reasoning. Furthermore, we introduce Dynamic Sparse KL and Structured Revisiting to stabilize training against reward collapse and catastrophic forgetting. Extensive experiments show that VideoCuRL surpasses strong RL baselines on reasoning (+2.5 on VSI-Bench) and perception (+2.9 on VideoMME) tasks. Notably, VideoCuRL eliminates the prohibitive inference overhead of generation-based curricula, offering a scalable solution for robust video post-training.

Video Spatial Reasoning with Object-Centric 3D Rollout

Recent advances in Multi-modal Large Language Models (MLLMs) have showcased remarkable capabilities in vision-language understanding. However, enabling robust video spatial reasoning-the ability to comprehend object locations, orientations, and inter-object relationships in dynamic 3D scenes-remains a key unsolved challenge. Existing approaches primarily rely on spatially grounded supervised fine-tuning or reinforcement learning, yet we observe that such models often exhibit query-locked reasoning, focusing narrowly on objects explicitly mentioned in the prompt while ignoring critical contextual cues. To address this limitation, we propose Object-Centric 3D Rollout (OCR), a novel strategy that introduces structured perturbations to the 3D geometry of selected objects during training. By degrading object-specific visual cues and projecting the altered geometry into 2D space, OCR compels the model to reason holistically across the entire scene. We further design a rollout-based training pipeline that jointly leverages vanilla and region-noisy videos to optimize spatial reasoning trajectories. Experiments demonstrate state-of-the-art performance: our 3B-parameter model achieves 47.5% accuracy on VSI-Bench, outperforming several 7B baselines. Ablations confirm OCR's superiority over prior rollout strategies (e.g., T-GRPO, NoisyRollout).

PointMapPolicy: Structured Point Cloud Processing for Multi-Modal Imitation Learning

Robotic manipulation systems benefit from complementary sensing modalities, where each provides unique environmental information. Point clouds capture detailed geometric structure, while RGB images provide rich semantic context. Current point cloud methods struggle to capture fine-grained detail, especially for complex tasks, which RGB methods lack geometric awareness, which hinders their precision and generalization. We introduce PointMapPolicy, a novel approach that conditions diffusion policies on structured grids of points without downsampling. The resulting data type makes it easier to extract shape and spatial relationships from observations, and can be transformed between reference frames. Yet due to their structure in a regular grid, we enable the use of established computer vision techniques directly to 3D data. Using xLSTM as a backbone, our model efficiently fuses the point maps with RGB data for enhanced multi-modal perception. Through extensive experiments on the RoboCasa and CALVIN benchmarks and real robot evaluations, we demonstrate that our method achieves state-of-the-art performance across diverse manipulation tasks. The overview and demos are available on our project page: https://point-map.github.io/Point-Map/

Polysemous Language Gaussian Splatting via Matching-based Mask Lifting

Lifting 2D open-vocabulary understanding into 3D Gaussian Splatting (3DGS) scenes is a critical challenge. However, mainstream methods suffer from three key flaws: (i) their reliance on costly per-scene retraining prevents plug-and-play application; (ii) their restrictive monosemous design fails to represent complex, multi-concept semantics; and (iii) their vulnerability to cross-view semantic inconsistencies corrupts the final semantic representation. To overcome these limitations, we introduce MUSplat, a training-free framework that abandons feature optimization entirely. Leveraging a pre-trained 2D segmentation model, our pipeline generates and lifts multi-granularity 2D masks into 3D, where we estimate a foreground probability for each Gaussian point to form initial object groups. We then optimize the ambiguous boundaries of these initial groups using semantic entropy and geometric opacity. Subsequently, by interpreting the object's appearance across its most representative viewpoints, a Vision-Language Model (VLM) distills robust textual features that reconciles visual inconsistencies, enabling open-vocabulary querying via semantic matching. By eliminating the costly per-scene training process, MUSplat reduces scene adaptation time from hours to mere minutes. On benchmark tasks for open-vocabulary 3D object selection and semantic segmentation, MUSplat outperforms established training-based frameworks while simultaneously addressing their monosemous limitations.

EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning

Reinforcement learning with verifiable reward (RLVR) has become a promising paradigm for post-training large language models (LLMs) to improve their reasoning capability. However, when the rollout accuracy is low on hard problems, the reward becomes sparse, limiting learning efficiency and causing exploration bottlenecks. Existing approaches either rely on stronger LLMs for distillation or filter out difficult problems, which limits scalability or restricts reasoning improvement through exploration. We propose EvoCoT, a self-evolving curriculum learning framework based on two-stage chain-of-thought (CoT) reasoning optimization. EvoCoT constrains the exploration space by self-generating and verifying CoT trajectories, then gradually shortens them to expand the space in a controlled way. This enables LLMs to stably learn from initially unsolved hard problems under sparse rewards. We apply EvoCoT to multiple LLM families, including Qwen, DeepSeek, and Llama. Experiments show that EvoCoT enables LLMs to solve previously unsolved problems, improves reasoning capability without external CoT supervision, and is compatible with various RL fine-tuning methods. We release the source code to support future research.

RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimization

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its inherently on-policy strategy with LLM's immense action space and sparse reward. Further, RLVR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel approach that synergizes internal exploitation (i.e., Thinking) with external data (i.e., Learning) to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components: Multiple Importance Sampling to address for distributional mismatch from external data, and an Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. The results show that RL-PLUS achieves state-of-the-art performance compared with existing RLVR methods on six math reasoning benchmarks and exhibits superior performance on six out-of-distribution reasoning tasks. It also achieves consistent and significant gains across diverse model families, with average relative improvements ranging from 21.1\% to 69.2\%. Moreover, Pass@k curves across multiple benchmarks indicate that RL-PLUS effectively resolves the capability boundary collapse problem.