Towards Solving the Gilbert-Pollak Conjecture via Large Language Models

The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times that of the Euclidean minimum spanning tree (the Steiner ratio). A sequence of improvements through the 1980s culminated in a lower bound of $0.824$, with no substantial progress reported over the past three decades. Recent advances in LLMs have demonstrated strong performance on contest-level mathematical problems, yet their potential for addressing open, research-level questions remains largely unexplored. In this work, we present a novel AI system for obtaining tighter lower bounds on the Steiner ratio. Rather than directly prompting LLMs to solve the conjecture, we task them with generating rule-constrained geometric lemmas implemented as executable code. These lemmas are then used to construct a collection of specialized functions, which we call verification functions, that yield theoretically certified lower bounds of the Steiner ratio. Through progressive lemma refinement driven by reflection, the system establishes a new certified lower bound of 0.8559 for the Steiner ratio. The entire research effort involves only thousands of LLM calls, demonstrating the strong potential of LLM-based systems for advanced mathematical research.

Mirage2Matter: A Physically Grounded Gaussian World Model from Video

The scalability of embodied intelligence is fundamentally constrained by the scarcity of real-world interaction data. While simulation platforms provide a promising alternative, existing approaches often suffer from a substantial visual and physical gap to real environments and rely on expensive sensors, precise robot calibration, or depth measurements, limiting their practicality at scale. We present Simulate Anything, a graphics-driven world modeling and simulation framework that enables efficient generation of high-fidelity embodied training data using only multi-view environment videos and off-the-shelf assets. Our approach reconstructs real-world environments into a photorealistic scene representation using 3D Gaussian Splatting (3DGS), seamlessly capturing fine-grained geometry and appearance from video. We then leverage generative models to recover a physically realistic representation and integrate it into a simulation environment via a precision calibration target, enabling accurate scale alignment between the reconstructed scene and the real world. Together, these components provide a unified, editable, and physically grounded world model. Vision Language Action (VLA) models trained on our simulated data achieve strong zero-shot performance on downstream tasks, matching or even surpassing results obtained with real-world data, highlighting the potential of reconstruction-driven world modeling for scalable and practical embodied intelligence training.

CoMoVi: Co-Generation of 3D Human Motions and Realistic Videos

In this paper, we find that the generation of 3D human motions and 2D human videos is intrinsically coupled. 3D motions provide the structural prior for plausibility and consistency in videos, while pre-trained video models offer strong generalization capabilities for motions, which necessitate coupling their generation processes. Based on this, we present CoMoVi, a co-generative framework that couples two video diffusion models (VDMs) to generate 3D human motions and videos synchronously within a single diffusion denoising loop. To achieve this, we first propose an effective 2D human motion representation that can inherit the powerful prior of pre-trained VDMs. Then, we design a dual-branch diffusion model to couple human motion and video generation process with mutual feature interaction and 3D-2D cross attentions. Moreover, we curate CoMoVi Dataset, a large-scale real-world human video dataset with text and motion annotations, covering diverse and challenging human motions. Extensive experiments demonstrate the effectiveness of our method in both 3D human motion and video generation tasks.

InfoDCL: Informative Noise Enhanced Diffusion Based Contrastive Learning

Contrastive learning has demonstrated promising potential in recommender systems. Existing methods typically construct sparser views by randomly perturbing the original interaction graph, as they have no idea about the authentic user preferences. Owing to the sparse nature of recommendation data, this paradigm can only capture insufficient semantic information. To address the issue, we propose InfoDCL, a novel diffusion-based contrastive learning framework for recommendation. Rather than injecting randomly sampled Gaussian noise, we employ a single-step diffusion process that integrates noise with auxiliary semantic information to generate signals and feed them to the standard diffusion process to generate authentic user preferences as contrastive views. Besides, based on a comprehensive analysis of the mutual influence between generation and preference learning in InfoDCL, we build a collaborative training objective strategy to transform the interference between them into mutual collaboration. Additionally, we employ multiple GCN layers only during inference stage to incorporate higher-order co-occurrence information while maintaining training efficiency. Extensive experiments on five real-world datasets demonstrate that InfoDCL significantly outperforms state-of-the-art methods. Our InfoDCL offers an effective solution for enhancing recommendation performance and suggests a novel paradigm for applying diffusion method in contrastive learning frameworks.

TrackingWorld: World-centric Monocular 3D Tracking of Almost All Pixels

Monocular 3D tracking aims to capture the long-term motion of pixels in 3D space from a single monocular video and has witnessed rapid progress in recent years. However, we argue that the existing monocular 3D tracking methods still fall short in separating the camera motion from foreground dynamic motion and cannot densely track newly emerging dynamic subjects in the videos. To address these two limitations, we propose TrackingWorld, a novel pipeline for dense 3D tracking of almost all pixels within a world-centric 3D coordinate system. First, we introduce a tracking upsampler that efficiently lifts the arbitrary sparse 2D tracks into dense 2D tracks. Then, to generalize the current tracking methods to newly emerging objects, we apply the upsampler to all frames and reduce the redundancy of 2D tracks by eliminating the tracks in overlapped regions. Finally, we present an efficient optimization-based framework to back-project dense 2D tracks into world-centric 3D trajectories by estimating the camera poses and the 3D coordinates of these 2D tracks. Extensive evaluations on both synthetic and real-world datasets demonstrate that our system achieves accurate and dense 3D tracking in a world-centric coordinate frame.

AdLift: Lifting Adversarial Perturbations to Safeguard 3D Gaussian Splatting Assets Against Instruction-Driven Editing

Recent studies have extended diffusion-based instruction-driven 2D image editing pipelines to 3D Gaussian Splatting (3DGS), enabling faithful manipulation of 3DGS assets and greatly advancing 3DGS content creation. However, it also exposes these assets to serious risks of unauthorized editing and malicious tampering. Although imperceptible adversarial perturbations against diffusion models have proven effective for protecting 2D images, applying them to 3DGS encounters two major challenges: view-generalizable protection and balancing invisibility with protection capability. In this work, we propose the first editing safeguard for 3DGS, termed AdLift, which prevents instruction-driven editing across arbitrary views and dimensions by lifting strictly bounded 2D adversarial perturbations into 3D Gaussian-represented safeguard. To ensure both adversarial perturbations effectiveness and invisibility, these safeguard Gaussians are progressively optimized across training views using a tailored Lifted PGD, which first conducts gradient truncation during back-propagation from the editing model at the rendered image and applies projected gradients to strictly constrain the image-level perturbation. Then, the resulting perturbation is backpropagated to the safeguard Gaussian parameters via an image-to-Gaussian fitting operation. We alternate between gradient truncation and image-to-Gaussian fitting, yielding consistent adversarial-based protection performance across different viewpoints and generalizes to novel views. Empirically, qualitative and quantitative results demonstrate that AdLift effectively protects against state-of-the-art instruction-driven 2D image and 3DGS editing.

HunyuanWorld 1.0: Generating Immersive, Explorable, and Interactive 3D Worlds from Words or Pixels

Creating immersive and playable 3D worlds from texts or images remains a fundamental challenge in computer vision and graphics. Existing world generation approaches typically fall into two categories: video-based methods that offer rich diversity but lack 3D consistency and rendering efficiency, and 3D-based methods that provide geometric consistency but struggle with limited training data and memory-inefficient representations. To address these limitations, we present HunyuanWorld 1.0, a novel framework that combines the best of both worlds for generating immersive, explorable, and interactive 3D scenes from text and image conditions. Our approach features three key advantages: 1) 360{\deg} immersive experiences via panoramic world proxies; 2) mesh export capabilities for seamless compatibility with existing computer graphics pipelines; 3) disentangled object representations for augmented interactivity. The core of our framework is a semantically layered 3D mesh representation that leverages panoramic images as 360{\deg} world proxies for semantic-aware world decomposition and reconstruction, enabling the generation of diverse 3D worlds. Extensive experiments demonstrate that our method achieves state-of-the-art performance in generating coherent, explorable, and interactive 3D worlds while enabling versatile applications in virtual reality, physical simulation, game development, and interactive content creation.

An AI-native experimental laboratory for autonomous biomolecular engineering

Autonomous scientific research, capable of independently conducting complex experiments and serving non-specialists, represents a long-held aspiration. Achieving it requires a fundamental paradigm shift driven by artificial intelligence (AI). While autonomous experimental systems are emerging, they remain confined to areas featuring singular objectives and well-defined, simple experimental workflows, such as chemical synthesis and catalysis. We present an AI-native autonomous laboratory, targeting highly complex scientific experiments for applications like autonomous biomolecular engineering. This system autonomously manages instrumentation, formulates experiment-specific procedures and optimization heuristics, and concurrently serves multiple user requests. Founded on a co-design philosophy of models, experiments, and instruments, the platform supports the co-evolution of AI models and the automation system. This establishes an end-to-end, multi-user autonomous laboratory that handles complex, multi-objective experiments across diverse instrumentation. Our autonomous laboratory supports fundamental nucleic acid functions-including synthesis, transcription, amplification, and sequencing. It also enables applications in fields such as disease diagnostics, drug development, and information storage. Without human intervention, it autonomously optimizes experimental performance to match state-of-the-art results achieved by human scientists. In multi-user scenarios, the platform significantly improves instrument utilization and experimental efficiency. This platform paves the way for advanced biomaterials research to overcome dependencies on experts and resource barriers, establishing a blueprint for science-as-a-service at scale.

Linearly Solving Robust Rotation Estimation

Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear and non-convex optimization problem that requires careful design. However, in this paper, we provide some new perspectives that solving a rotation estimation problem can be reformulated as solving a linear model fitting problem without dropping any constraints and without introducing any singularities. In addition, we explore the dual structure of a rotation motion, revealing that it can be represented as a great circle on a quaternion sphere surface. Accordingly, we propose an easily understandable voting-based method to solve rotation estimation. The proposed method exhibits exceptional robustness to noise and outliers and can be computed in parallel with graphics processing units (GPUs) effortlessly. Particularly, leveraging the power of GPUs, the proposed method can obtain a satisfactory rotation solution for large-scale($10^6$) and severely corrupted (99$\%$ outlier ratio) rotation estimation problems under 0.5 seconds. Furthermore, to validate our theoretical framework and demonstrate the superiority of our proposed method, we conduct controlled experiments and real-world dataset experiments. These experiments provide compelling evidence supporting the effectiveness and robustness of our approach in solving rotation estimation problems.

Voyager: Long-Range and World-Consistent Video Diffusion for Explorable 3D Scene Generation

Real-world applications like video gaming and virtual reality often demand the ability to model 3D scenes that users can explore along custom camera trajectories. While significant progress has been made in generating 3D objects from text or images, creating long-range, 3D-consistent, explorable 3D scenes remains a complex and challenging problem. In this work, we present Voyager, a novel video diffusion framework that generates world-consistent 3D point-cloud sequences from a single image with user-defined camera path. Unlike existing approaches, Voyager achieves end-to-end scene generation and reconstruction with inherent consistency across frames, eliminating the need for 3D reconstruction pipelines (e.g., structure-from-motion or multi-view stereo). Our method integrates three key components: 1) World-Consistent Video Diffusion: A unified architecture that jointly generates aligned RGB and depth video sequences, conditioned on existing world observation to ensure global coherence 2) Long-Range World Exploration: An efficient world cache with point culling and an auto-regressive inference with smooth video sampling for iterative scene extension with context-aware consistency, and 3) Scalable Data Engine: A video reconstruction pipeline that automates camera pose estimation and metric depth prediction for arbitrary videos, enabling large-scale, diverse training data curation without manual 3D annotations. Collectively, these designs result in a clear improvement over existing methods in visual quality and geometric accuracy, with versatile applications.