arXiv subjects

Jiahang Liu

Publications and source records attributed to Jiahang Liu.

16 recordsLinked to original sources

arXiv2026

Root-of-unity weighted trigonometric power sums: a constant term approach

We present a unified method for evaluating finite sums of powers of cotangent, tangent, cosecant and secant weighted by primitive $k$th roots of unity. The approach relies on constant term extraction for iterated Laurent series, combined with generating functions and partial fraction decomposition. We obtain explicit closed-form expressions for all even-power sums of the four functions, as well as for odd-power cotangent and tangent sums. The formulas are given in terms of Bernoulli polynomials, Euler polynomials, and universal coefficients $r_{n,t}$. As applications, we recover numerous classical identities---including the ordinary and alternating cotangent power sums and Acton's alternating tangent sum---in a systematic and elementary way.

math.CO↗

arXiv2026

AllDayNav: Lifelong Navigation via Real-World Reinforcement Learning

Lifelong embodied navigation in dynamic environments requires robots to form persistent scene understanding from fragmentary observations, which remains difficult for existing methods that rely on explicit maps or scene graphs and struggle to generalize beyond structured settings. We propose AllDayNav, a lifelong self-learning navigation framework that implicitly encodes scene dynamics into the billion-scale parameters of a large model via reinforcement learning, powered by a self-evolving multimodal memory that maintains and updates visual keyframes, semantic descriptions, and temporal context while autonomously generating open-vocabulary instructions, image goals, and structured rewards. Experiments in both synthetic and real-world environments across cross-room, cross-episode, and cross-task scenarios show that AllDayNav achieves success rates approaching $100\%$ and consistently surpasses strong map-based, VLM, and RL baselines in path efficiency and robustness, demonstrating implicit, memory-driven reinforcement learning as a scalable alternative to explicit mapping for reliable lifelong navigation.

cs.RO↗

arXiv2026

MesonGS++: Post-training Compression of 3D Gaussian Splatting with Hyperparameter Searching

3D Gaussian Splatting (3DGS) achieves high-quality novel view synthesis with real-time rendering, but its storage cost remains prohibitive for practical deployment. Existing post-training compression methods still rely on many coupled hyperparameters across pruning, transformation, quantization, and entropy coding, making it difficult to control the final compressed size and fully exploit the rate-distortion trade-off. We propose MesonGS++, a size-aware post-training codec for 3D Gaussian compression. On the codec side, MesonGS++ combines joint importance-based pruning, octree geometry coding, attribute transformation, selective vector quantization for higher-degree spherical harmonics, and group-wise mixed-precision quantization with entropy coding. On the configuration side, it treats the reserve ratio and bit-width allocation as the dominant rate-distortion knobs and jointly optimizes them under a target storage budget via discrete sampling and 0--1 integer linear programming. We further propose a linear size estimator and a CUDA parallel quantization operator to accelerate the hyperparameter searching process. Extensive experiments show that MesonGS++ achieves over 34$\times$ compression while preserving rendering fidelity, outperforming state-of-the-art post-training methods and accurately meeting target size budgets. Remarkably, without any training, MesonGS++ can even surpass the PSNR of vanilla 3DGS at a 20$\times$ compression rate on the Stump scene. Our code is available at https://github.com/mmlab-sigs/mesongs_plus

cs.CV↗

arXiv2026

Seed3D 2.0: Advancing High-Fidelity Simulation-Ready 3D Content Generation

We present Seed3D 2.0, an advanced 3D content generation system built on Seed3D 1.0, with substantial improvements across generation fidelity, simulation-ready capabilities, and application coverage. For geometry, a coarse-to-fine two-stage pipeline decouples global structure learning from high-frequency detail recovery, while a locality-aware VAE achieves higher spatial compression and more efficient decoding. For texture and material generation, we replace the cascaded pipeline of Seed3D 1.0 with a unified PBR model that directly generates multi-view albedo and metallic-roughness maps, enhanced by Mixture-of-Experts scaling and VLM-based semantic conditioning for improved material precision and visual fidelity. Beyond single-object generation, Seed3D 2.0 introduces a simulation-ready model suite comprising scene layout planning, part-aware decomposition, and training-free articulation generation, enabling coherent scene construction and part-level physical interaction across physics and graphics engines. A large-scale human preference study against five recent commercial models shows that Seed3D 2.0 achieves consistent win rates of 69.0% to 89.9% in textured 3D asset generation. Seed3D 2.0 is available on https://exp.volcengine.com/ark/vision?_vtm_=0.0.c70961.d701978.0&mode=vision&modelId=doubao-seed3d-2-0-260328&tab=Gen3D

cs.GR↗

arXiv2026

TopoMesh: High-Fidelity Mesh Autoencoding via Topological Unification

The dominant paradigm for high-fidelity 3D generation relies on a VAE-Diffusion pipeline, where the VAE's reconstruction capability sets a firm upper bound on generation quality. A fundamental challenge limiting existing VAEs is the representation mismatch between ground-truth meshes and network predictions: GT meshes have arbitrary, variable topology, while VAEs typically predict fixed-structure implicit fields (\eg, SDF on regular grids). This inherent misalignment prevents establishing explicit mesh-level correspondences, forcing prior work to rely on indirect supervision signals such as SDF or rendering losses. Consequently, fine geometric details, particularly sharp features, are poorly preserved during reconstruction. To address this, we introduce TopoMesh, a sparse voxel-based VAE that unifies both GT and predicted meshes under a shared Dual Marching Cubes (DMC) topological framework. Specifically, we convert arbitrary input meshes into DMC-compliant representations via a remeshing algorithm that preserves sharp edges using an L$\infty$ distance metric. Our decoder outputs meshes in the same DMC format, ensuring that both predicted and target meshes share identical topological structures. This establishes explicit correspondences at the vertex and face level, allowing us to derive explicit mesh-level supervision signals for topology, vertex positions, and face orientations with clear gradients. Our sparse VAE architecture employs this unified framework and is trained with Teacher Forcing and progressive resolution training for stable and efficient convergence. Extensive experiments demonstrate that TopoMesh significantly outperforms existing VAEs in reconstruction fidelity, achieving superior preservation of sharp features and geometric details.

cs.CV↗

arXiv2026

NavGSim: High-Fidelity Gaussian Splatting Simulator for Large-Scale Navigation

Simulating realistic environments for robots is widely recognized as a critical challenge in robot learning, particularly in terms of rendering and physical simulation. This challenge becomes even more pronounced in navigation tasks, where trajectories often extend across multiple rooms or entire floors. In this work, we present NavGSim, a Gaussian Splatting-based simulator designed to generate high-fidelity, large-scale navigation environments. Built upon a hierarchical 3D Gaussian Splatting framework, NavGSim enables photorealistic rendering in expansive scenes spanning hundreds of square meters. To simulate navigation collisions, we introduce a Gaussian Splatting-based slice technique that directly extracts navigable areas from reconstructed Gaussians. Additionally, for ease of use, we provide comprehensive NavGSim APIs supporting multi-GPU development, including tools for custom scene reconstruction, robot configuration, policy training, and evaluation. To evaluate NavGSim's effectiveness, we train a Vision-Language-Action (VLA) model using trajectories collected from NavGSim and assess its performance in both simulated and real-world environments. Our results demonstrate that NavGSim significantly enhances the VLA model's scene understanding, enabling the policy to handle diverse navigation queries effectively.

cs.RO↗

arXiv2026

SPAN-Nav: Generalized Spatial Awareness for Versatile Vision-Language Navigation

Recent embodied navigation approaches leveraging Vision-Language Models (VLMs) demonstrate strong generalization in versatile Vision-Language Navigation (VLN). However, reliable path planning in complex environments remains challenging due to insufficient spatial awareness. In this work, we introduce SPAN-Nav, an end-to-end foundation model designed to infuse embodied navigation with universal 3D spatial awareness using RGB video streams. SPAN-Nav extracts spatial priors across diverse scenes through an occupancy prediction task on extensive indoor and outdoor environments. To mitigate the computational burden, we introduce a compact representation for spatial priors, finding that a single token is sufficient to encapsulate the coarse-grained cues essential for navigation tasks. Furthermore, inspired by the Chain-of-Thought (CoT) mechanism, SPAN-Nav utilizes this single spatial token to explicitly inject spatial cues into action reasoning through an end-to end framework. Leveraging multi-task co-training, SPAN-Nav captures task-adaptive cues from generalized spatial priors, enabling robust spatial awareness to generalize even to the task lacking explicit spatial supervision. To support comprehensive spatial learning, we present a massive dataset of 4.2 million occupancy annotations that covers both indoor and outdoor scenes across multi-type navigation tasks. SPAN-Nav achieves state-of-the-art performance across three benchmarks spanning diverse scenarios and varied navigation tasks. Finally, real-world experiments validate the robust generalization and practical reliability of our approach across complex physical scenarios.

cs.RO↗

arXiv2026

Proof of a Conjecture on Young Tableaux with Walls

Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Together with the work of Chang, Fuchs, Liu, Wallner, and Yu, our result verifies a conjecture of Pons and Batle on tree-child networks. This conjecture had been regarded as a specific and challenging problem in the phylogenetics community until its resolution in the present work.

math.CO↗

arXiv2025

Seed3D 1.0: From Images to High-Fidelity Simulation-Ready 3D Assets

Developing embodied AI agents requires scalable training environments that balance content diversity with physics accuracy. World simulators provide such environments but face distinct limitations: video-based methods generate diverse content but lack real-time physics feedback for interactive learning, while physics-based engines provide accurate dynamics but face scalability limitations from costly manual asset creation. We present Seed3D 1.0, a foundation model that generates simulation-ready 3D assets from single images, addressing the scalability challenge while maintaining physics rigor. Unlike existing 3D generation models, our system produces assets with accurate geometry, well-aligned textures, and realistic physically-based materials. These assets can be directly integrated into physics engines with minimal configuration, enabling deployment in robotic manipulation and simulation training. Beyond individual objects, the system scales to complete scene generation through assembling objects into coherent environments. By enabling scalable simulation-ready content creation, Seed3D 1.0 provides a foundation for advancing physics-based world simulators. Seed3D 1.0 is now available on https://console.volcengine.com/ark/region:ark+cn-beijing/experience/vision?modelId=doubao-seed3d-1-0-250928&tab=Gen3D

eess.IV↗

arXiv2025

TrackVLA++: Unleashing Reasoning and Memory Capabilities in VLA Models for Embodied Visual Tracking

Embodied Visual Tracking (EVT) is a fundamental ability that underpins practical applications, such as companion robots, guidance robots and service assistants, where continuously following moving targets is essential. Recent advances have enabled language-guided tracking in complex and unstructured scenes. However, existing approaches lack explicit spatial reasoning and effective temporal memory, causing failures under severe occlusions or in the presence of similar-looking distractors. To address these challenges, we present TrackVLA++, a novel Vision-Language-Action (VLA) model that enhances embodied visual tracking with two key modules, a spatial reasoning mechanism and a Target Identification Memory (TIM). The reasoning module introduces a Chain-of-Thought paradigm, termed Polar-CoT, which infers the target's relative position and encodes it as a compact polar-coordinate token for action prediction. Guided by these spatial priors, the TIM employs a gated update strategy to preserve long-horizon target memory, ensuring spatiotemporal consistency and mitigating target loss during extended occlusions. Extensive experiments show that TrackVLA++ achieves state-of-the-art performance on public benchmarks across both egocentric and multi-camera settings. On the challenging EVT-Bench DT split, TrackVLA++ surpasses the previous leading approach by 5.1 and 12, respectively. Furthermore, TrackVLA++ exhibits strong zero-shot generalization, enabling robust real-world tracking in dynamic and occluded scenarios.

cs.RO↗

arXiv2025

Embodied Navigation Foundation Model

Navigation is a fundamental capability in embodied AI, representing the intelligence required to perceive and interact within physical environments following language instructions. Despite significant progress in large Vision-Language Models (VLMs), which exhibit remarkable zero-shot performance on general vision-language tasks, their generalization ability in embodied navigation remains largely confined to narrow task settings and embodiment-specific architectures. In this work, we introduce a cross-embodiment and cross-task Navigation Foundation Model (NavFoM), trained on eight million navigation samples that encompass quadrupeds, drones, wheeled robots, and vehicles, and spanning diverse tasks such as vision-and-language navigation, object searching, target tracking, and autonomous driving. NavFoM employs a unified architecture that processes multimodal navigation inputs from varying camera configurations and navigation horizons. To accommodate diverse camera setups and temporal horizons, NavFoM incorporates identifier tokens that embed camera view information of embodiments and the temporal context of tasks. Furthermore, to meet the demands of real-world deployment, NavFoM controls all observation tokens using a dynamically adjusted sampling strategy under a limited token length budget. Extensive evaluations on public benchmarks demonstrate that our model achieves state-of-the-art or highly competitive performance across multiple navigation tasks and embodiments without requiring task-specific fine-tuning. Additional real-world experiments further confirm the strong generalization capability and practical applicability of our approach.

cs.RO↗

arXiv2025

TrackVLA: Embodied Visual Tracking in the Wild

Embodied visual tracking is a fundamental skill in Embodied AI, enabling an agent to follow a specific target in dynamic environments using only egocentric vision. This task is inherently challenging as it requires both accurate target recognition and effective trajectory planning under conditions of severe occlusion and high scene dynamics. Existing approaches typically address this challenge through a modular separation of recognition and planning. In this work, we propose TrackVLA, a Vision-Language-Action (VLA) model that learns the synergy between object recognition and trajectory planning. Leveraging a shared LLM backbone, we employ a language modeling head for recognition and an anchor-based diffusion model for trajectory planning. To train TrackVLA, we construct an Embodied Visual Tracking Benchmark (EVT-Bench) and collect diverse difficulty levels of recognition samples, resulting in a dataset of 1.7 million samples. Through extensive experiments in both synthetic and real-world environments, TrackVLA demonstrates SOTA performance and strong generalizability. It significantly outperforms existing methods on public benchmarks in a zero-shot manner while remaining robust to high dynamics and occlusion in real-world scenarios at 10 FPS inference speed. Our project page is: https://pku-epic.github.io/TrackVLA-web.

cs.RO↗

arXiv2024

SizeGS: Size-aware Compression of 3D Gaussian Splatting via Mixed Integer Programming

Recent advances in 3D Gaussian Splatting (3DGS) have greatly improved 3D reconstruction. However, its substantial data size poses a significant challenge for transmission and storage. While many compression techniques have been proposed, they fail to efficiently adapt to fluctuating network bandwidth, leading to resource wastage. We address this issue from the perspective of size-aware compression, where we aim to compress 3DGS to a desired size by quickly searching for suitable hyperparameters. Through a measurement study, we identify key hyperparameters that affect the size -- namely, the reserve ratio of Gaussians and bit-width settings for Gaussian attributes. Then, we formulate this hyperparameter optimization problem as a mixed-integer nonlinear programming (MINLP) problem, with the goal of maximizing visual quality while respecting the size budget constraint. To solve the MINLP, we decouple this problem into two parts: discretely sampling the reserve ratio and determining the bit-width settings using integer linear programming (ILP). To solve the ILP more quickly and accurately, we design a quality loss estimator and a calibrated size estimator, as well as implement a CUDA kernel. Extensive experiments on multiple 3DGS variants demonstrate that our method achieves state-of-the-art performance in post-training compression. Furthermore, our method can achieve comparable quality to leading training-required methods after fine-tuning.

cs.CV↗

arXiv2023

Robot Learning in the Era of Foundation Models: A Survey

The proliferation of Large Language Models (LLMs) has s fueled a shift in robot learning from automation towards general embodied Artificial Intelligence (AI). Adopting foundation models together with traditional learning methods to robot learning has increasingly gained recent interest research community and showed potential for real-life application. However, there are few literatures comprehensively reviewing the relatively new technologies combined with robotics. The purpose of this review is to systematically assess the state-of-the-art foundation model techniques in the robot learning and to identify future potential areas. Specifically, we first summarized the technical evolution of robot learning and identified the necessary preliminary preparations for foundation models including the simulators, datasets, foundation model framework. In addition, we focused on the following four mainstream areas of robot learning including manipulation, navigation, planning, and reasoning and demonstrated how the foundation model techniques can be adopted in the above scenarios. Furthermore, critical issues which are neglected in the current literatures including robot hardware and software decoupling, dynamic data, generalization performance with the presence of human, etc. were discussed. This review highlights the state-of-the-art progress of foundation models in robot learning and future research should focus on multimodal interaction especially dynamics data, exclusive foundation models for robots, and AI alignment, etc.

cs.RO↗

arXiv2022

Robust Learning-based Predictive Control for Discrete-time Nonlinear Systems with Unknown Dynamics and State Constraints

Robust model predictive control (MPC) is a well-known control technique for model-based control with constraints and uncertainties. In classic robust tube-based MPC approaches, an open-loop control sequence is computed via periodically solving an online nominal MPC problem, which requires prior model information and frequent access to onboard computational resources. In this paper, we propose an efficient robust MPC solution based on receding horizon reinforcement learning, called r-LPC, for unknown nonlinear systems with state constraints and disturbances. The proposed r-LPC utilizes a Koopman operator-based prediction model obtained off-line from pre-collected input-output datasets. Unlike classic tube-based MPC, in each prediction time interval of r-LPC, we use an actor-critic structure to learn a near-optimal feedback control policy rather than a control sequence. The resulting closed-loop control policy can be learned off-line and deployed online or learned online in an asynchronous way. In the latter case, online learning can be activated whenever necessary; for instance, the safety constraint is violated with the deployed policy. The closed-loop recursive feasibility, robustness, and asymptotic stability are proven under function approximation errors of the actor-critic networks. Simulation and experimental results on two nonlinear systems with unknown dynamics and disturbances have demonstrated that our approach has better or comparable performance when compared with tube-based MPC and LQR, and outperforms a recently developed actor-critic learning approach.

eess.SY↗

arXiv2021

Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in vehicle dynamics. Recent efforts have resorted to machine learning techniques for building vehicle dynamical models, but the generalization ability and interpretability of existing methods still need to be improved. In this paper, we propose a data-driven vehicle modeling approach based on deep neural networks with an interpretable Koopman operator. The main advantage of using the Koopman operator is to represent the nonlinear dynamics in a linear lifted feature space. In the proposed approach, a deep learning-based extended dynamic mode decomposition algorithm is presented to learn a finite-dimensional approximation of the Koopman operator. Furthermore, a data-driven model predictive controller with the learned Koopman model is designed for path tracking control of autonomous vehicles. Simulation results in a high-fidelity CarSim environment show that our approach exhibit a high modeling precision at a wide operating range and outperforms previously developed methods in terms of modeling performance. Path tracking tests of the autonomous vehicle are also performed in the CarSim environment and the results show the effectiveness of the proposed approach.

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