GCPO: Diagnosing and Constraining Subspace Geometry in Rollout RL for LLMs

On-policy rollout methods such as GRPO are central to post-training of large language models, yet they frequently suffer from training instabilities, cross-task capability degradation, and response-length inflation. Although prior work has characterized the subspace geometry of aggregate updates, the stepwise variation of this geometry and its relationship to model performance remain unclear. We introduce Principal-Subspace Overlap, a dimension-corrected measure of individual rollout updates relative to the dominant singular subspaces of pretrained weights. Despite low average overlap, transient spikes often precede performance degradation. To address this, we propose GCPO (Geometrically Constrained Policy Optimization), which applies hard bilateral orthogonal projections to constrain updates to the complementary subspaces, preventing such excursions by construction. Across mathematical reasoning, code generation, and tool-use tasks on Qwen3-8B and GLM4-9B, GCPO consistently outperforms GRPO and recent variants, including DAPO and GSPO, improving over the base models and the strongest baseline by up to 27.69 and 2.37 points, respectively. Furthermore, GCPO preserves general capabilities, eliminates response-length inflation, and stabilizes policy entropy. Our findings provide a new diagnostic lens and a principled design perspective for stable reinforcement learning post-training.

Hunyuan3D-Buffalo 1.0: A Unified Multimodal Model for Scalable 3D Generation, Understanding, and Editing

Recent advances in image generation have demonstrated the potential of unified multimodal models that integrate understanding, generation, and editing. However, unified 3D modeling remains constrained by scarce multimodal data, particularly the lack of large-scale and geometrically consistent editing data. To address this limitation, we propose Hunyuan3D-Buffalo 1.0, a unified framework supporting 3D understanding, text-to-3D generation, instruction-guided 3D editing, and text-grounded part generation within a single architecture. To enable scalable training, we construct an 87M-scale 3D multimodal corpus, comprising 25M understanding samples, 50M text-to-3D pairs, and 12M editing pairs generated using Nano3D-v2. Architecturally, the framework combines Hunyuan3D-VLM for semantic, structural, and spatial understanding with Hunyuan3D DiT for high-fidelity 3D synthesis. The VLM provides multimodal semantic conditions for generation, while editing and part generation additionally condition the diffusion process on the source object representation to preserve its overall structure and unedited regions. Extensive experiments show that Hunyuan3D-Buffalo 1.0 achieves state-of-the-art or leading performance on text-to-3D generation and 3D editing benchmarks, while exhibiting strong understanding and part-generation capabilities. Our analysis further shows that both generation and understanding improve editing, demonstrating the effectiveness of unified 3D multimodal training. Project Page: https://tencent-hunyuan.github.io/Hunyuan3D-Buffalo1.0/

Pointer-CAD v2: Plan-Then-Construct CAD Generation with Dimension-Aware Parametric Precision

Computer-aided design (CAD) plays a fundamental role in modern manufacturing by providing the high precision required for industrial production. Recent large language model based approaches formulate CAD generation as a sequence prediction problem and have achieved promising results. However, existing methods and evaluation protocols primarily emphasize visual similarity, while overlooking precise geometric parameters and correct metric scale. Small numerical deviations that are negligible at the shape-level may still violate industrial tolerance requirements, a problem further compounded by current autoregressive paradigms that utilize command sequence representations, aggressively quantize numerical parameters to ease LLM prediction. In this work, we present Pointer-CAD v2. Compared with v1 (arXiv:2603.04337), this version directly predicts continuous values, bypassing the need for quantized numerical parameters and thereby eliminating quantization errors. Specifically, we propose a unified framework that decouples parameter reasoning from geometric construction through a Plan-Then-Construct paradigm. Our method first produces a structured design plan with explicit metric scale parameters. These parameters are organized into a dictionary and directly referenced during sequence generation via a pointer mechanism, eliminating discretization errors and ensuring dimensionally consistent execution. In addition, we construct a new large-scale dataset with plan-level annotation and introduce three hierarchical geometry accuracy metrics to evaluate parametric fidelity at the vertex, edge, and face levels. Extensive experiments demonstrate that Pointer-CAD v2 consistently outperforms existing baselines and achieves substantial improvements in geometric accuracy, enabling reliable CAD generation for precision-critical engineering applications.

Trajectory-Consistent Calibration for Cache-Accelerated Diffusion Models

Diffusion Transformers require repeated denoiser evaluations during iterative sampling, making inference computationally expensive. Cache-based acceleration reduces this cost by reusing intermediate representations across denoising steps, but can introduce representation deviations and degrade generation quality. In this paper, we analyze these deviations and show that effective calibration should consider both the direct mismatch caused by reuse and the subsequent trajectory shift induced by earlier corrections. To address this challenge, we propose Trajectory-Consistent Calibration (TCC), a training-free method that calibrates cached representations toward their full-computation counterparts. Specifically, rather than estimating all calibration priors from a single uncorrected cache trajectory, TCC uses an offline iterative procedure so that each prior accounts for the trajectory shift induced by preceding calibrations. Experiments on PixArt-alpha and DiT-XL/2 show that TCC consistently improves FID across representative cache-based acceleration methods while preserving their underlying reuse policies. Notably, in a representative PixArt-alpha cache-acceleration setting based on FORA, TCC reduces FID from 29.83 to 27.35, slightly surpassing the full-computation baseline.

Rethinking Supervision Granularity: Segment-Level Learning for LLM-Based Theorem Proving

Automated theorem proving with large language models in Lean 4 is commonly approached through either step-level tactic prediction with tree search or whole-proof generation. These two paradigms represent opposite granularities for constructing supervised training data: the former provides dense local signals but may fragment coherent proof processes, while the latter preserves global structure but requires complex end-to-end generation. In this paper, we revisit supervision granularity as a training set construction problem over proof trajectories and propose segment-level supervision, a training data construction strategy that extracts locally coherent proof segments for training policy models. We further reuse the same strategy at inference time to trigger short rollouts for existing step-level models. When trained with segment-level supervision on STP, LeanWorkbook, and NuminaMath-LEAN, the resulting policy models achieve proof success rates of 64.84%, 60.90%, and 66.31% on miniF2F, respectively, consistently outperforming both step-level and whole-proof baselines. Goal-aware rollout further improves existing step-level provers while reducing inference costs. It increases the proof success rate of BFS-Prover-V2-7B from 68.77% to 70.74% and that of InternLM2.5-StepProver from 59.59% to 60.33%, showing that appropriate supervision granularity better aligns model learning with proof structure and search. Code and models are available at https://github.com/NJUDeepEngine/SEG-ATP.

Pointer-CAD: Unifying B-Rep and Command Sequences via Pointer-based Edges & Faces Selection

Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command sequences. But these methods struggle in practical scenarios because command sequence representation does not support entity selection (e.g. faces or edges), limiting its ability to support complex editing operations such as chamfer or fillet. Further, the discretization of a continuous variable during sketch and extrude operations may result in topological errors. To address these limitations, we present Pointer-CAD, a novel LLM-based CAD generation framework that leverages a pointer-based command sequence representation to explicitly incorporate the geometric information of B-rep models into sequential modeling. In particular, Pointer-CAD decomposes CAD model generation into steps, conditioning the generation of each subsequent step on both the textual description and the B-rep generated from previous steps. Whenever an operation requires the selection of a specific geometric entity, the LLM predicts a Pointer that selects the most feature-consistent candidate from the available set. Such a selection operation also reduces the quantization error in the command sequence-based representation. To support the training of Pointer-CAD, we develop a data annotation pipeline that produces expert-level natural language descriptions and apply it to build a dataset of approximately 575K CAD models. Extensive experimental results demonstrate that Pointer-CAD effectively supports the generation of complex geometric structures and reduces segmentation error to an extremely low level, achieving a significant improvement over prior command sequence methods, thereby significantly mitigating the topological inaccuracies introduced by quantization error.

LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of $60.74\%$ on MiniF2F and $21.18\%$ on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

FUSION: Fully Integration of Vision-Language Representations for Deep Cross-Modal Understanding

We introduce FUSION, a family of multimodal large language models (MLLMs) with a fully vision-language alignment and integration paradigm. Unlike existing methods that primarily rely on late-stage modality interaction during LLM decoding, our approach achieves deep, dynamic integration throughout the entire processing pipeline. To this end, we propose Text-Guided Unified Vision Encoding, incorporating textual information in vision encoding to achieve pixel-level integration. We further design Context-Aware Recursive Alignment Decoding that recursively aggregates visual features conditioned on textual context during decoding, enabling fine-grained, question-level semantic integration. To guide feature mapping and mitigate modality discrepancies, we develop Dual-Supervised Semantic Mapping Loss. Additionally, we construct a Synthesized Language-Driven Question-Answer (QA) dataset through a new data synthesis method, prioritizing high-quality QA pairs to optimize text-guided feature integration. Building on these foundations, we train FUSION at two scales-3B, 8B-and demonstrate that our full-modality integration approach significantly outperforms existing methods with only 630 vision tokens. Notably, FUSION 3B surpasses Cambrian-1 8B and Florence-VL 8B on most benchmarks. FUSION 3B continues to outperform Cambrian-1 8B even when limited to 300 vision tokens. Our ablation studies show that FUSION outperforms LLaVA-NeXT on over half of the benchmarks under same configuration without dynamic resolution, highlighting the effectiveness of our approach. We release our code, model weights, and dataset. https://github.com/starriver030515/FUSION

FastMap: Fast Queries Initialization Based Vectorized HD Map Reconstruction Framework

Reconstruction of high-definition maps is a crucial task in perceiving the autonomous driving environment, as its accuracy directly impacts the reliability of prediction and planning capabilities in downstream modules. Current vectorized map reconstruction methods based on the DETR framework encounter limitations due to the redundancy in the decoder structure, necessitating the stacking of six decoder layers to maintain performance, which significantly hampers computational efficiency. To tackle this issue, we introduce FastMap, an innovative framework designed to reduce decoder redundancy in existing approaches. FastMap optimizes the decoder architecture by employing a single-layer, two-stage transformer that achieves multilevel representation capabilities. Our framework eliminates the conventional practice of randomly initializing queries and instead incorporates a heatmap-guided query generation module during the decoding phase, which effectively maps image features into structured query vectors using learnable positional encoding. Additionally, we propose a geometry-constrained point-to-line loss mechanism for FastMap, which adeptly addresses the challenge of distinguishing highly homogeneous features that often arise in traditional point-to-point loss computations. Extensive experiments demonstrate that FastMap achieves state-of-the-art performance in both nuScenes and Argoverse2 datasets, with its decoder operating 3.2 faster than the baseline. Code and more demos are available at https://github.com/hht1996ok/FastMap.

CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM

This paper aims to design a unified Computer-Aided Design (CAD) generation system that can easily generate CAD models based on the user's inputs in the form of textual description, images, point clouds, or even a combination of them. Towards this goal, we introduce the CAD-MLLM, the first system capable of generating parametric CAD models conditioned on the multimodal input. Specifically, within the CAD-MLLM framework, we leverage the command sequences of CAD models and then employ advanced large language models (LLMs) to align the feature space across these diverse multi-modalities data and CAD models' vectorized representations. To facilitate the model training, we design a comprehensive data construction and annotation pipeline that equips each CAD model with corresponding multimodal data. Our resulting dataset, named Omni-CAD, is the first multimodal CAD dataset that contains textual description, multi-view images, points, and command sequence for each CAD model. It contains approximately 450K instances and their CAD construction sequences. To thoroughly evaluate the quality of our generated CAD models, we go beyond current evaluation metrics that focus on reconstruction quality by introducing additional metrics that assess topology quality and surface enclosure extent. Extensive experimental results demonstrate that CAD-MLLM significantly outperforms existing conditional generative methods and remains highly robust to noises and missing points. The project page and more visualizations can be found at: https://cad-mllm.github.io/