arXiv subjects

Chen Cao

Publications and source records attributed to Chen Cao.

At least 19 recordsLinked to original sources

arXiv2026

New criteria for upper bounds on the number of limit cycles in Liénard systems

We establish criteria for at most one or at most two limit cycles of generalized Liénard systems in a single potential well. Two independent uniqueness tests use modified quotients of the damping and restoring forces; both allow a degenerate restoring force, and one extends to continuous potential profiles with corners. Opposite convexity of the two branches of the damping quotient in the potential coordinate gives an upper bound of two. Further criteria apply to weak damping with an analytic normalized profile on a bounded potential interval under an explicit smallness condition, to small profile perturbations vanishing near the equilibrium on a bounded range of half-widths, and to parameter families satisfying curvature, monotonicity and boundary conditions. Applications give another proof of the classical quartic bound. For Selkov systems, we obtain a two-cycle bound in a specified negative-parameter region and prove existence and uniqueness in a positive-parameter region. We also prove Conjecture~2.1 in [J. Math. Anal. Appl., 2025]. Examples attain the two-cycle bound.

math.DS↗

arXiv2026

Global Dynamics and Periodic-Annulus Bifurcations in a Reversible Quintic Liénard System

We study the global dynamics and bifurcations of the reversible quintic Liénard system $\dot{x}=y$, $\dot{y}=a_0x+a_1x^3+a_2x^5+y(b_0x+b_1x^3)$, with $a_2\ne0$. In the original five-parameter space we treat both signs of $a_2$ and determine all global phase-portrait types on the Poincaré disc with one, three, or five finite equilibria. The analysis covers generic and generalized pitchfork, saddle-node, Bogdanov--Takens, and Hopf bifurcations; nilpotent and Hamiltonian degeneracies; bifurcations at infinity; and homoclinic, heteroclinic, limit-cycle-breaking, and periodic-annulus-breaking transitions. For a parameterized class of generalized polynomial Liénard systems whose unique finite equilibrium is the nilpotent origin with exactly one elliptic and one hyperbolic sector we establish a unique critical value of the higher-order damping parameter in the intermediate-degree range, nonexistence of a large-scale periodic annulus in the critical-degree case, and its persistence when the restoring degree dominates. Here large-scale means that the annulus closure meets the boundary of the Poincaré disc. In the degree range relevant to the quintic system the critical value gives a large-scale periodic-annulus--homoclinic-orbit-family bifurcation marked by a unique separatrix connection to infinity. For the quintic system with multiple finite equilibria periodic-annulus-breaking bifurcations arise from finite separatrix connections or separatrices reaching equilibria at infinity. Using Poincaré compactification, local normal forms, rotated vector fields, and separatrix arguments we describe bifurcation sets algebraically or by uniquely characterized critical functions. We obtain complete fixed-coefficient parameter partitions outside $Ω_{14}$ and determine the admissible critical-surface configurations and their phase portraits inside it.

math.DS↗

arXiv2026

Complete solution to the weak persistent center and isochronous center problems of cubic polynomial systems

In this paper, we investigate weakly persistent centers for several classes of planar cubic differential systems, including systems with a nondegenerate linear center and systems with a nilpotent center. Necessary parameter relations are obtained by computing singular point quantities or quasi-Lyapunov constants, while their sufficiency is established by suitable analytic constructions. For the general complex cubic system, we obtain necessary and sufficient conditions for the origin to be a weakly persistent center, and the corresponding result for the associated general real cubic system follows by imposing the conjugacy relations between the complex coefficients. We further characterize the weakly persistent isochronous centers of the general complex cubic system by combining the weakly persistent center conditions with the vanishing of the linearization quantities and constructing time-preserving analytic linearizations.

math.DS↗

arXiv2026

Herschel: Continuous Optimization of Production LLM Inference through On-Demand Profiling

Model-as-a-service platforms call for continuous optimization as complex serving conditions expose inefficiencies missed before deployment. Detailed always-on profiling can incur substantial overhead, while lightweight collection omits information needed for diagnosis. We present Herschel, a continuous optimization system for production large language model (LLM) inference. Our key insight is that adaptive, on-demand profiling can provide rich full-stack evidence without continuous collection. Herschel safely attaches to and detaches from selected running processes without engine changes or restarts, and adapts coverage as investigations reveal missing evidence. Herschel reconstructs operator executions and cross-process dependencies to identify inefficiency mechanisms and suggest solutions using applicable reference fixes. AI agents implement and test engine and kernel changes under controlled conditions that preserve the triggering workload and dependencies, with expert review before deployment. Controlled tests show active-collection overhead below 0.5% for time to first token and 7% for time per output token. Bounded windows, typically 30 s, avoid the continuous cost of always-on tracing. Over six months, Herschel collected approximately 17,000 traces across over 120 model variants and more than 10 accelerator types, identifying inefficiency patterns in 23% of the traces. Representative findings guide widely deployed optimizations, including restructured synchronization, removal of unused computation, and improved operator implementations.

cs.OS↗

arXiv2026

LUNA: Learning Universal 3D Human Animation Beyond Skinning

Creating photorealistic, animatable 3D human avatars from monocular images still largely depends on Linear Blend Skinning (LBS) and parametric body models, which constrain expressivity and often introduce artifacts due to imperfect fitting. We propose LUNA, an LBS-free universal neural animation model that directly maps multiple 2D controls like images, keypoints, sketches, and unseen characters into 3D Gaussian deformations, bypassing explicit body fitting. At its core, a transformer-based motion regressor disentangles global rigid motion from fine-grained local dynamics to capture both coherent movement and subtle non-rigid effects. To resolve the inherent ambiguity of 2D-to-3D lifting while scaling beyond fitted datasets, we introduce hybrid supervision that distills soft structural priors from an LBS teacher and a loss that supports training on both limited fitted data and large in-the-wild unlabeled videos. Extensive experiments show LUNA achieves competitive visual fidelity compared to LBS-based approaches, while delivering realistic human motion and zero-shot cross-identity generalization across diverse driving modalities. To the best of our knowledge, LUNA is the first end-to-end 3D animatable model that supports implicit 2D driving.

cs.CV↗

arXiv2026

FiCA: Feed-forward instant Gaussian Codec Avatars from a Single Portrait Image

We introduce FiCA, a Feed-forward, instant Gaussian Codec Avatar generation pipeline that creates lifelike avatars from a single portrait image. Generating a photorealistic and drivable avatar from just a single image is significantly challenging due to the limited visual information available to accurately infer the 3D appearance and geometry of human heads. To address this, we develop a novel system that combines human-centric vision foundation models with a diffusion model. This system is designed to fully exploit partial visual observations to generate lifelike human avatars. Our proposed diffusion model learns a generative mapping from these partial observations to complete and authentic 3D mesh reconstruction. Additionally, we introduce a feed-forward mesh refinement network that enhances the fidelity and identity preservation of the generated avatars, eliminating the need for person-specific test-time optimization. By leveraging a universal prior model that decodes a generated mesh into a set of 3D Gaussians, we generate a photorealistic 3D Gaussian avatar, capable of being driven with novel expressions in real-time. Our experiments demonstrate that the avatars generated by our feed-forward approach faithfully represent diverse identities and surpass the visual quality of avatars produced by recent competing methods.

cs.CV↗

arXiv2026

SAM3D-Guided Object-Centric Representation Alignment for Vision-Language-Action Models

Vision-Language-Action (VLA) models have shown strong potential for general robot manipulation, but most existing models rely on 2D visual-language backbones and lack fine-grained 3D understanding of target objects, especially under occlusion, pose variation, scale changes, and precise spatial interaction. We propose an object-centric 3D representation alignment framework built upon $π_0$, using SAM3D as a frozen 3D teacher to provide target-object 3D priors during training. Specifically, we localize task-relevant objects with object recognition models, generate corresponding object masks, and use SAM3D to extract dense object-level 3D representations, which are aligned with intermediate visual features of $π_0$. This enables the policy to internalize target-object 3D information while preserving the original RGB-language-to-action inference pipeline without requiring depth, point clouds, masks, SAM3D, or additional 3D modules at test time. Simulation experiments show consistent improvements, achieving 99.1\% on LIBERO and an average length of 4.11 on CALVIN. Real-world experiments further demonstrate that our method is particularly effective in long-horizon manipulation scenarios where the robot must focus on different target objects across multiple subtasks.

cs.RO↗

arXiv2026

HiMem-WAM: Hierarchical Memory-Gated World Action Models for Robotic Manipulation

World Action Models (WAMs) have emerged as a new powerful paradigm for embodied intelligence, learning action-relevant visual dynamics that significantly enhance generalization and robustness. However, existing WAMs still struggle with task-relevant memory in long-horizon robotic manipulation. To address this, we present HiMem-WAM, a Hierarchical Memory-Gated WAM that integrates motion-centric latent actions, high-level skill latents, and boundary-triggered memory updates. Specifically, we develop a hierarchical latent action framework that jointly learns low-level motion and high-level skill latents, providing structured temporal abstraction. Meanwhile, a boundary-aware memory gate writes compact task states at predicted skill transitions, enabling causal inference without test-time generation of future video or optical flow estimation. Evaluated on LIBERO, LIBERO-PLUS, RMBench and real-world tasks, HiMem-WAM shows that hierarchical latents improve robustness under deployment perturbations, and the memory module substantially benefits memory-dependent long-horizon manipulation.

cs.RO↗

arXiv2026

GeoRelight: Learning Joint Geometrical Relighting and Reconstruction with Flexible Multi-Modal Diffusion Transformers

Relighting a person from a single photo is an attractive but ill-posed task, as a 2D image ambiguously entangles 3D geometry, intrinsic appearance, and illumination. Current methods either use sequential pipelines that suffer from error accumulation, or they do not explicitly leverage 3D geometry during relighting, which limits physical consistency. Since relighting and estimation of 3D geometry are mutually beneficial tasks, we propose a unified Multi-Modal Diffusion Transformer (DiT) that jointly solves for both: GeoRelight. We make this possible through two key technical contributions: isotropic NDC-Orthographic Depth (iNOD), a distortion-free 3D representation compatible with latent diffusion models; and a strategic mixed-data training method that combines synthetic and auto-labeled real data. By solving geometry and relighting jointly, GeoRelight achieves better performance than both sequential models and previous systems that ignored geometry.

cs.CV↗

arXiv2026

AIM: Intent-Aware Unified world action Modeling with Spatial Value Maps

Pretrained video generation models provide strong priors for robot control, but existing unified world action models still struggle to decode reliable actions without substantial robot-specific training. We attribute this limitation to a structural mismatch: while video models capture how scenes evolve, action generation requires explicit reasoning about where to interact and the underlying manipulation intent. We introduce AIM, an intent-aware unified world action model that bridges this gap via an explicit spatial interface. Instead of decoding actions directly from future visual representations, AIM predicts an aligned spatial value map that encodes task-relevant interaction structure, enabling a control-oriented abstraction of future dynamics. Built on a pretrained video generation model, AIM jointly models future observations and value maps within a shared mixture-of-transformers architecture. It employs intent-causal attention to route future information to the action branch exclusively through the value representation. We further propose a self-distillation reinforcement learning stage that freezes the video and value branches and optimizes only the action head using dense rewards derived from projected value-map responses together with sparse task-level signals. To support training and evaluation, we construct a simulation dataset of 30K manipulation trajectories with synchronized multi-view observations, actions, and value-map annotations. Experiments on RoboTwin 2.0 benchmark show that AIM achieves a 94.0% average success rate, significantly outperforming prior unified world action baselines. Notably, the improvement is more pronounced in long-horizon and contact-sensitive manipulation tasks, demonstrating the effectiveness of explicit spatial-intent modeling as a bridge between visual world modeling and robot control.

cs.RO↗

arXiv2026

Large-scale Codec Avatars: The Unreasonable Effectiveness of Large-scale Avatar Pretraining

High-quality 3D avatar modeling faces a critical trade-off between fidelity and generalization. On the one hand, multi-view studio data enables high-fidelity modeling of humans with precise control over expressions and poses, but it struggles to generalize to real-world data due to limited scale and the domain gap between the studio environment and the real world. On the other hand, recent large-scale avatar models trained on millions of in-the-wild samples show promise for generalization across a wide range of identities, yet the resulting avatars are often of low-quality due to inherent 3D ambiguities. To address this, we present Large-Scale Codec Avatars (LCA), a high-fidelity, full-body 3D avatar model that generalizes to world-scale populations in a feedforward manner, enabling efficient inference. Inspired by the success of large language models and vision foundation models, we present, for the first time, a pre/post-training paradigm for 3D avatar modeling at scale: we pretrain on 1M in-the-wild videos to learn broad priors over appearance and geometry, then post-train on high-quality curated data to enhance expressivity and fidelity. LCA generalizes across hair styles, clothing, and demographics while providing precise, fine-grained facial expressions and finger-level articulation control, with strong identity preservation. Notably, we observe emergent generalization to relightability and loose garment support to unconstrained inputs, and zero-shot robustness to stylized imagery, despite the absence of direct supervision.

cs.CV↗

arXiv2026

AtomVLA: Scalable Post-Training for Robotic Manipulation via Predictive Latent World Models

Vision-Language-Action (VLA) models demonstrate remarkable potential for generalizable robotic manipulation. The execution of complex multi-step behaviors in VLA models can be improved by robust instruction grounding, a critical component for effective control. However, current paradigms predominantly rely on coarse, high-level task instructions during supervised fine-tuning. This instruction grounding gap leaves models without explicit intermediate guidance, leading to severe compounding errors in long-horizon tasks. Therefore, bridging this instruction gap and providing scalable post-training for VLA models is urgent. To tackle this problem, we propose \method, the first subtask-aware VLA framework integrated with a scalable offline post-training pipeline. Our framework leverages a large language model to decompose high-level demonstrations into fine-grained atomic subtasks. This approach utilizes a pretrained predictive world model to score candidate action chunks against subtask goals in the latent space, mitigating error accumulation while significantly improving long-horizon robustness. Furthermore, this approach enables highly efficient Group Relative Policy Optimization without the prohibitive expenses associated with online rollouts on physical robots. Extensive simulations validate that our AtomVLA maintains strong robustness under perturbations. When evaluated against fundamental baseline models, it achieves an average success rate of 97.0\% on the LIBERO benchmark and 48.0\% on the LIBERO-PRO benchmark. Finally, experiments conducted in the real world using the Galaxea R1 Lite platform confirm its broad applicability across diverse tasks, especially long-horizon tasks. All datasets, checkpoints, and code will be released to the public domain following the acceptance of this work for future research.

cs.RO↗

arXiv2025

3DGH: 3D Head Generation with Composable Hair and Face

We present 3DGH, an unconditional generative model for 3D human heads with composable hair and face components. Unlike previous work that entangles the modeling of hair and face, we propose to separate them using a novel data representation with template-based 3D Gaussian Splatting, in which deformable hair geometry is introduced to capture the geometric variations across different hairstyles. Based on this data representation, we design a 3D GAN-based architecture with dual generators and employ a cross-attention mechanism to model the inherent correlation between hair and face. The model is trained on synthetic renderings using carefully designed objectives to stabilize training and facilitate hair-face separation. We conduct extensive experiments to validate the design choice of 3DGH, and evaluate it both qualitatively and quantitatively by comparing with several state-of-the-art 3D GAN methods, demonstrating its effectiveness in unconditional full-head image synthesis and composable 3D hairstyle editing. More details will be available on our project page: https://c-he.github.io/projects/3dgh/.

cs.GR↗

arXiv2025

LUCAS: Layered Universal Codec Avatars

Photorealistic 3D head avatar reconstruction faces critical challenges in modeling dynamic face-hair interactions and achieving cross-identity generalization, particularly during expressions and head movements. We present LUCAS, a novel Universal Prior Model (UPM) for codec avatar modeling that disentangles face and hair through a layered representation. Unlike previous UPMs that treat hair as an integral part of the head, our approach separates the modeling of the hairless head and hair into distinct branches. LUCAS is the first to introduce a mesh-based UPM, facilitating real-time rendering on devices. Our layered representation also improves the anchor geometry for precise and visually appealing Gaussian renderings. Experimental results indicate that LUCAS outperforms existing single-mesh and Gaussian-based avatar models in both quantitative and qualitative assessments, including evaluations on held-out subjects in zero-shot driving scenarios. LUCAS demonstrates superior dynamic performance in managing head pose changes, expression transfer, and hairstyle variations, thereby advancing the state-of-the-art in 3D head avatar reconstruction.

cs.CV↗

arXiv2025

Vid2Avatar-Pro: Authentic Avatar from Videos in the Wild via Universal Prior

We present Vid2Avatar-Pro, a method to create photorealistic and animatable 3D human avatars from monocular in-the-wild videos. Building a high-quality avatar that supports animation with diverse poses from a monocular video is challenging because the observation of pose diversity and view points is inherently limited. The lack of pose variations typically leads to poor generalization to novel poses, and avatars can easily overfit to limited input view points, producing artifacts and distortions from other views. In this work, we address these limitations by leveraging a universal prior model (UPM) learned from a large corpus of multi-view clothed human performance capture data. We build our representation on top of expressive 3D Gaussians with canonical front and back maps shared across identities. Once the UPM is learned to accurately reproduce the large-scale multi-view human images, we fine-tune the model with an in-the-wild video via inverse rendering to obtain a personalized photorealistic human avatar that can be faithfully animated to novel human motions and rendered from novel views. The experiments show that our approach based on the learned universal prior sets a new state-of-the-art in monocular avatar reconstruction by substantially outperforming existing approaches relying only on heuristic regularization or a shape prior of minimally clothed bodies (e.g., SMPL) on publicly available datasets.

cs.CV↗

arXiv2024

URAvatar: Universal Relightable Gaussian Codec Avatars

We present a new approach to creating photorealistic and relightable head avatars from a phone scan with unknown illumination. The reconstructed avatars can be animated and relit in real time with the global illumination of diverse environments. Unlike existing approaches that estimate parametric reflectance parameters via inverse rendering, our approach directly models learnable radiance transfer that incorporates global light transport in an efficient manner for real-time rendering. However, learning such a complex light transport that can generalize across identities is non-trivial. A phone scan in a single environment lacks sufficient information to infer how the head would appear in general environments. To address this, we build a universal relightable avatar model represented by 3D Gaussians. We train on hundreds of high-quality multi-view human scans with controllable point lights. High-resolution geometric guidance further enhances the reconstruction accuracy and generalization. Once trained, we finetune the pretrained model on a phone scan using inverse rendering to obtain a personalized relightable avatar. Our experiments establish the efficacy of our design, outperforming existing approaches while retaining real-time rendering capability.

cs.CV↗

arXiv2024

A Systematic Review on Prompt Engineering in Large Language Models for K-12 STEM Education

Large language models (LLMs) have the potential to enhance K-12 STEM education by improving both teaching and learning processes. While previous studies have shown promising results, there is still a lack of comprehensive understanding regarding how LLMs are effectively applied, specifically through prompt engineering-the process of designing prompts to generate desired outputs. To address this gap, our study investigates empirical research published between 2021 and 2024 that explores the use of LLMs combined with prompt engineering in K-12 STEM education. Following the PRISMA protocol, we screened 2,654 papers and selected 30 studies for analysis. Our review identifies the prompting strategies employed, the types of LLMs used, methods of evaluating effectiveness, and limitations in prior work. Results indicate that while simple and zero-shot prompting are commonly used, more advanced techniques like few-shot and chain-of-thought prompting have demonstrated positive outcomes for various educational tasks. GPT-series models are predominantly used, but smaller and fine-tuned models (e.g., Blender 7B) paired with effective prompt engineering outperform prompting larger models (e.g., GPT-3) in specific contexts. Evaluation methods vary significantly, with limited empirical validation in real-world settings.

cs.CL↗

arXiv2024

Bridging the Gap: Studio-like Avatar Creation from a Monocular Phone Capture

Creating photorealistic avatars for individuals traditionally involves extensive capture sessions with complex and expensive studio devices like the LightStage system. While recent strides in neural representations have enabled the generation of photorealistic and animatable 3D avatars from quick phone scans, they have the capture-time lighting baked-in, lack facial details and have missing regions in areas such as the back of the ears. Thus, they lag in quality compared to studio-captured avatars. In this paper, we propose a method that bridges this gap by generating studio-like illuminated texture maps from short, monocular phone captures. We do this by parameterizing the phone texture maps using the $W^+$ space of a StyleGAN2, enabling near-perfect reconstruction. Then, we finetune a StyleGAN2 by sampling in the $W^+$ parameterized space using a very small set of studio-captured textures as an adversarial training signal. To further enhance the realism and accuracy of facial details, we super-resolve the output of the StyleGAN2 using carefully designed diffusion model that is guided by image gradients of the phone-captured texture map. Once trained, our method excels at producing studio-like facial texture maps from casual monocular smartphone videos. Demonstrating its capabilities, we showcase the generation of photorealistic, uniformly lit, complete avatars from monocular phone captures. The project page can be found at http://shahrukhathar.github.io/2024/07/22/Bridging.html

cs.CV↗