arXiv subjects

Jin Cheng

Publications and source records attributed to Jin Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Explicit Runge approximation for Helmholtz equation with cylindrical harmonics

Originating from the complex approximation of holomorphic functions, the Runge approximation for elliptic equations has evolved into a fundamental tool for inverse problems and even learning-based numerical methods since its proposition by Lax, Malgrange, with quantitative characterizations further established by R\"uland and Salo. It should be remarked here that Runge approximation is ill-posed. In numerical analysis, explicit quantitative estimates are required to characterize the dependence of the approximant's growth on the outward continuation distance of the original solution. This paper investigates the spatial dependent quantitative Runge approximation for the Helmholtz equation using cylindrical harmonics, considering both interior and exterior boundary value problems. We explicitly derive the relevant indices for the three-circle configuration and obtain asymptotic indices for general geometric settings. The derived results provide norm estimates for the expansion coefficients, which are crucial for the implementation of regularization methods. Furthermore, the established bounds enable the construction of spectrally accurate numerical approximations for solutions to the Helmholtz equation.

math.NA↗

arXiv2026

Adaptive Spiking Neurons for Vision and Language Modeling

Regarded as the third generation of neural networks, Spiking Neural Networks (SNNs) have garnered significant traction due to their biological plausibility and energy efficiency. Recent advancements in large models necessitate spiking neurons capable of high performance, adaptability, and training efficiency. In this work, we first propose a novel functional perspective that provides general guidance for designing the new generation of spiking neurons. Following the insightful guidelines, we propose the Adaptive Spiking Neuron (ASN), which incorporates trainable parameters to learn membrane potential dynamics and enable adaptive firing. ASN adopts an integer training and spike inference paradigm, facilitating efficient SNN training. To further enhance robustness, we propose a specialized variant of ASN, the Normalized Adaptive Spiking Neuron (NASN), which integrates normalization to stabilize training. We evaluate our neuron model on 19 datasets spanning five distinct tasks in both vision and language modalities, demonstrating the effectiveness and versatility of the ASN family. Our ASN family is expected to become the new generation of general-purpose spiking neurons.

cs.NE↗

arXiv2026

Inverse source problems with reduced interior data for a coupled reaction-diffusion system

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and $0<t<T$. In this system, called the Klausmeier-Gray-Scott model, we assume that an unknown source depends only on the spatial variable and appears in the reaction-diffusion equation for $u$. The main subject is the inverse source problem of determining a source term from limited data on $(u,v)$. We establish two kinds of stability estimates by means of Carleman estimates. First, a Carleman estimate with a singular weight yields a Lipschitz stability estimate for the inverse source problem from data consisting of a snapshot $u(\cdot,t_0)$ in $\Omega$ and $(u,v)$ in a subdomain $\omega$ over a time interval. Second, without assuming boundary data, we prove a H\"older stability estimate in any interior subdomain $\Omega_0$ satisfying $\overline{\Omega_0}\subset\Omega$. We further study how much the observation data can be reduced while preserving uniqueness and stability in the inverse problem under suitable additional conditions.

math.AP↗

arXiv2026

Maximum Entropy Behavior Exploration for Sim2Real Zero-Shot Reinforcement Learning

Zero-shot reinforcement learning (RL) algorithms aim to learn a family of policies from a reward-free dataset, and recover optimal policies for any reward function directly at test time. Naturally, the quality of the pretraining dataset determines the performance of the recovered policies across tasks. However, pre-collecting a relevant, diverse dataset without prior knowledge of the downstream tasks of interest remains a challenge. In this work, we study $\textit{online}$ zero-shot RL for quadrupedal control on real robotic systems, building upon the Forward-Backward (FB) algorithm. We observe that undirected exploration yields low-diversity data, leading to poor downstream performance and rendering policies impractical for direct hardware deployment. Therefore, we introduce FB-MEBE, an online zero-shot RL algorithm that combines an unsupervised behavior exploration strategy with a regularization critic. FB-MEBE promotes exploration by maximizing the entropy of the achieved behavior distribution. Additionally, a regularization critic shapes the recovered policies toward more natural and physically plausible behaviors. We empirically demonstrate that FB-MEBE achieves and improved performance compared to other exploration strategies in a range of simulated downstream tasks, and that it renders natural policies that can be seamlessly deployed to hardware without further finetuning. Videos and code available on our website.

cs.LG↗

arXiv2026

A Robust Learning-Based Method for the Helmholtz Equation in Dissipative Media and Complex Domains

To mitigate pollution effects in high-frequency Helmholtz problems, Learning-based Numerical Methods (LbNM) reconstruct solution operators using complete systems of exact solutions. However, the previously used fundamental-solution (FS) basis suffers from instability in dissipative media and requires sensitive geometric tuning. In this paper, we propose a robust alternative using a Bessel basis (BB). From a learning theory perspective, the BB forms a complete hypothesis space of standing waves, ensuring immunity to dissipation-induced signal loss. We establish a convergence result that depends on intrinsic regularity. Numerical experiments demonstrate that the proposed method achieves machine-precision accuracy in dissipative regimes where FS fails, significantly outperforms the Finite Element Method (FEM) in efficiency, and demonstrates the framework's geometric extensibility via a multi-center strategy.

math.NA↗

arXiv2026

Teaching Robots Like Dogs: Learning Agile Navigation from Luring, Gesture, and Speech

In this work, we aim to enable legged robots to learn how to interpret human social cues and produce appropriate behaviors through physical human guidance. However, learning through physical engagement can place a heavy burden on users when the process requires large amounts of human-provided data. To address this, we propose a human-in-the-loop framework that enables robots to acquire navigational behaviors in a data-efficient manner and to be controlled via multimodal natural human inputs, specifically gestural and verbal commands. We reconstruct interaction scenes using a physics-based simulation and aggregate data to mitigate distributional shifts arising from limited demonstration data. Our progressive goal cueing strategy adaptively feeds appropriate commands and navigation goals during training, leading to more accurate navigation and stronger alignment between human input and robot behavior. We evaluate our framework across six real-world agile navigation scenarios, including jumping over or avoiding obstacles. Our experimental results show that our proposed method succeeds in almost all trials across these scenarios, achieving a 97.15% task success rate with less than 1 hour of demonstration data in total.

cs.RO↗

arXiv2025

Whole-Body Inverse Dynamics MPC for Legged Loco-Manipulation

Loco-manipulation demands coordinated whole-body motion to manipulate objects effectively while maintaining locomotion stability, presenting significant challenges for both planning and control. In this work, we propose a whole-body model predictive control (MPC) framework that directly optimizes joint torques through full-order inverse dynamics, enabling unified motion and force planning and execution within a single predictive layer. This approach allows emergent, physically consistent whole-body behaviors that account for the system's dynamics and physical constraints. We implement our MPC formulation using open software frameworks (Pinocchio and CasADi), along with the state-of-the-art interior-point solver Fatrop. In real-world experiments on a Unitree B2 quadruped equipped with a Unitree Z1 manipulator arm, our MPC formulation achieves real-time performance at 80 Hz. We demonstrate loco-manipulation tasks that demand fine control over the end-effector's position and force to perform real-world interactions like pulling heavy loads, pushing boxes, and wiping whiteboards.

cs.RO↗

arXiv2025

Switch-JustDance: Benchmarking Whole Body Motion Tracking Controllers Using a Commercial Console Game

Recent advances in whole-body robot control have enabled humanoid and legged robots to perform increasingly agile and coordinated motions. However, standardized benchmarks for evaluating these capabilities in real-world settings, and in direct comparison to humans, remain scarce. Existing evaluations often rely on pre-collected human motion datasets or simulation-based experiments, which limit reproducibility, overlook hardware factors, and hinder fair human-robot comparisons. We present Switch-JustDance, a low-cost and reproducible benchmarking pipeline that leverages motion-sensing console games, Just Dance on the Nintendo Switch, to evaluate robot whole-body control. Using Just Dance on the Nintendo Switch as a representative platform, Switch-JustDance converts in-game choreography into robot-executable motions through streaming, motion reconstruction, and motion retargeting modules and enables users to evaluate controller performance through the game's built-in scoring system. We first validate the evaluation properties of Just Dance, analyzing its reliability, validity, sensitivity, and potential sources of bias. Our results show that the platform provides consistent and interpretable performance measures, making it a suitable tool for benchmarking embodied AI. Building on this foundation, we benchmark three state-of-the-art humanoid whole-body controllers on hardware and provide insights into their relative strengths and limitations.

cs.RO↗

arXiv2025

APEX: Action Priors Enable Efficient Exploration for Robust Motion Tracking on Legged Robots

Learning natural, animal-like locomotion from demonstrations has become a core paradigm in legged robotics. Despite the recent advancements in motion tracking, most existing methods demand extensive tuning and rely on reference data during deployment, limiting adaptability. We present APEX (Action Priors enable Efficient Exploration), a plug-and-play extension to state-of-the-art motion tracking algorithms that eliminates any dependence on reference data during deployment, improves sample efficiency, and reduces parameter tuning effort. APEX integrates expert demonstrations directly into reinforcement learning (RL) by incorporating decaying action priors, which initially bias exploration toward expert demonstrations but gradually allow the policy to explore independently. This is combined with a multi-critic framework that balances task performance with motion style. Moreover, APEX enables a single policy to learn diverse motions and transfer reference-like styles across different terrains and velocities, while remaining robust to variations in reward design. We validate the effectiveness of our method through extensive experiments in both simulation and on a Unitree Go2 robot. By leveraging demonstrations to guide exploration during RL training, without imposing explicit bias toward them, APEX enables legged robots to learn with greater stability, efficiency, and generalization. We believe this approach paves the way for guidance-driven RL to boost natural skill acquisition in a wide array of robotic tasks, from locomotion to manipulation. Website and code: https://marmotlab.github.io/APEX/.

cs.RO↗

arXiv2025

Trading Vector Data in Vector Databases

Vector data trading is essential for cross-domain learning with vector databases, yet it remains largely unexplored. We study this problem under online learning, where sellers face uncertain retrieval costs and buyers provide stochastic feedback to posted prices. Three main challenges arise: (1) heterogeneous and partial feedback in configuration learning, (2) variable and complex feedback in pricing learning, and (3) inherent coupling between configuration and pricing decisions. We propose a hierarchical bandit framework that jointly optimizes retrieval configurations and pricing. Stage I employs contextual clustering with confidence-based exploration to learn effective configurations with logarithmic regret. Stage II adopts interval-based price selection with local Taylor approximation to estimate buyer responses and achieve sublinear regret. We establish theoretical guarantees with polynomial time complexity and validate the framework on four real-world datasets, demonstrating consistent improvements in cumulative reward and regret reduction compared with existing methods.

cs.DB↗

arXiv2025

TARC: Time-Adaptive Robotic Control

Fixed-frequency control in robotics imposes a trade-off between the efficiency of low-frequency control and the robustness of high-frequency control, a limitation not seen in adaptable biological systems. We address this with a reinforcement learning approach in which policies jointly select control actions and their application durations, enabling robots to autonomously modulate their control frequency in response to situational demands. We validate our method with zero-shot sim-to-real experiments on two distinct hardware platforms: a high-speed RC car and a quadrupedal robot. Our method matches or outperforms fixed-frequency baselines in terms of rewards while significantly reducing the control frequency and exhibiting adaptive frequency control under real-world conditions.

cs.RO↗

arXiv2025

Walk Like Dogs: Learning Steerable Imitation Controllers for Legged Robots from Unlabeled Motion Data

We present an imitation learning framework that extracts distinctive legged locomotion behaviors and transitions between them from unlabeled real-world motion data. By automatically discovering behavioral modes and mapping user steering commands to them, the framework enables user-steerable and stylistically consistent motion imitation. Our approach first bridges the morphological and physical gap between the motion source and the robot by transforming raw data into a physically consistent, robot-compatible dataset using a kino-dynamic motion retargeting strategy. This data is used to train a steerable motion synthesis module that generates stylistic, multi-modal kinematic targets from high-level user commands. These targets serve as a reference for a reinforcement learning controller, which reliably executes them on the robot hardware. In our experiments, a controller trained on dog motion data demonstrated distinctive quadrupedal gait patterns and emergent gait transitions in response to varying velocity commands. These behaviors were achieved without manual labeling, predefined mode counts, or explicit switching rules, maintaining the stylistic coherence of the data.

cs.RO↗

arXiv2025

Tensor product modules over the planar Galilean conformal algebra from free modules of rank one

In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra $\mathcal{G}$ named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in $(2+1)$ dimensional space-time. We give the necessary and sufficient conditions for the tensor product modules of any two of $\mathcal{U}(\mathfrak{h})$-free modules of rank one over $\mathcal{G}$ to be irreducible, where $\mathfrak{h}$ is the Cartan subalgebra of $\mathcal{G}$.Furthermore, the isomorphism classes of these irreducible tensor product modules are determined. As an application, we obtain the necessary conditions for the tensor product modules of any two of $\mathcal{U}(\mathbb{C} L_0)$-free modules of rank one over Witt algebra and Heisenberg-Virasoro algebra to be irreducible.

math.RT↗

arXiv2025

APEX: Action Priors Enable Efficient Exploration for Robust Motion Tracking on Legged Robots

Learning natural, animal-like locomotion from demonstrations has become a core paradigm in legged robotics. While motion tracking can reproduce reference gaits, many approaches still require substantial tuning and depend on reference motion inputs at deployment, which can limit responsiveness to task objectives and reduce adaptability. We present APEX (Action Priors enable Efficient eXploration), a motion-tracking reinforcement learning (RL) framework that removes deployment-time dependence on reference motion inputs, improves sample efficiency, and reduces tuning effort. APEX integrates demonstrations into RL via decaying action priors, which guide early exploration toward demonstration-consistent actions and then fade to zero, yielding a pure RL policy at deployment. This is combined with a multi-critic framework that separates style and task + regularization learning signals. Moreover, APEX enables a single policy to learn diverse motions and transfer reference-like styles across different terrains and velocities, while remaining robust to variations in training parameters. We validate our method in simulation on both humanoid and quadruped robots, and with zero-shot deployment on a Unitree Go2 robot. Website and code: https://marmotlab.github.io/APEX/.

cs.RO↗

arXiv2025

RAMBO: RL-Augmented Model-Based Whole-Body Control for Loco-Manipulation

Loco-manipulation, physical interaction of various objects that is concurrently coordinated with locomotion, remains a major challenge for legged robots due to the need for both precise end-effector control and robustness to unmodeled dynamics. While model-based controllers provide precise planning via online optimization, they are limited by model inaccuracies. In contrast, learning-based methods offer robustness, but they struggle with precise modulation of interaction forces. We introduce RAMBO, a hybrid framework that integrates model-based whole-body control within a feedback policy trained with reinforcement learning. The model-based module generates feedforward torques by solving a quadratic program, while the policy provides feedback corrective terms to enhance robustness. We validate our framework on a quadruped robot across a diverse set of real-world loco-manipulation tasks, such as pushing a shopping cart, balancing a plate, and holding soft objects, in both quadrupedal and bipedal walking. Our experiments demonstrate that RAMBO enables precise manipulation capabilities while achieving robust and dynamic locomotion.

cs.RO↗

arXiv2025

SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learning

Despite recent advances in learning-based controllers for legged robots, deployments in human-centric environments remain limited by safety concerns. Most of these approaches use position-based control, where policies output target joint angles that must be processed by a low-level controller (e.g., PD or impedance controllers) to compute joint torques. Although impressive results have been achieved in controlled real-world scenarios, these methods often struggle with compliance and adaptability when encountering environments or disturbances unseen during training, potentially resulting in extreme or unsafe behaviors. Inspired by how animals achieve smooth and adaptive movements by controlling muscle extension and contraction, torque-based policies offer a promising alternative by enabling precise and direct control of the actuators in torque space. In principle, this approach facilitates more effective interactions with the environment, resulting in safer and more adaptable behaviors. However, challenges such as a highly nonlinear state space and inefficient exploration during training have hindered their broader adoption. To address these limitations, we propose SATA, a bio-inspired framework that mimics key biomechanical principles and adaptive learning mechanisms observed in animal locomotion. Our approach effectively addresses the inherent challenges of learning torque-based policies by significantly improving early-stage exploration, leading to high-performance final policies. Remarkably, our method achieves zero-shot sim-to-real transfer. Our experimental results indicate that SATA demonstrates remarkable compliance and safety, even in challenging environments such as soft/slippery terrain or narrow passages, and under significant external disturbances, highlighting its potential for practical deployments in human-centric and safety-critical scenarios.

cs.RO↗

arXiv2025

CAIMAN: Causal Action Influence Detection for Sample-efficient Loco-manipulation

Enabling legged robots to perform non-prehensile loco-manipulation is crucial for enhancing their versatility. Learning behaviors such as whole-body object pushing often requires sophisticated planning strategies or extensive task-specific reward shaping, especially in unstructured environments. In this work, we present CAIMAN, a practical reinforcement learning framework that encourages the agent to gain control over other entities in the environment. CAIMAN leverages causal action influence as an intrinsic motivation objective, allowing legged robots to efficiently acquire object pushing skills even under sparse task rewards. We employ a hierarchical control strategy, combining a low-level locomotion module with a high-level policy that generates task-relevant velocity commands and is trained to maximize the intrinsic reward. To estimate causal action influence, we learn the dynamics of the environment by integrating a kinematic prior with data collected during training. We empirically demonstrate CAIMAN's superior sample efficiency and adaptability to diverse scenarios in simulation, as well as its successful transfer to real-world systems without further fine-tuning. A video demo is available at https://www.youtube.com/watch?v=dNyvT04Cqaw.

cs.RO↗

arXiv2025

Learning More With Less: Sample Efficient Model-Based RL for Loco-Manipulation

By combining the agility of legged locomotion with the capabilities of manipulation, loco-manipulation platforms have the potential to perform complex tasks in real-world applications. To this end, state-of-the-art quadrupeds with manipulators, such as the Boston Dynamics Spot, have emerged to provide a capable and robust platform. However, the complexity of loco-manipulation control, as well as the black-box nature of commercial platforms, pose challenges for deriving accurate dynamics models and robust control policies. To address these challenges, we turn to model-based reinforcement learning (RL). We develop a hand-crafted kinematic model of a quadruped-with-arm platform which - employing recent advances in Bayesian Neural Network (BNN)-based learning - we use as a physical prior to efficiently learn an accurate dynamics model from limited data. We then leverage our learned model to derive control policies for loco-manipulation via RL. We demonstrate the effectiveness of our approach on state-of-the-art hardware using the Boston Dynamics Spot, accurately performing dynamic end-effector trajectory tracking even in low data regimes. Project website and videos: https://sites.google.com/view/learning-more-with-less.

cs.RO↗