Ziyuan Tang

Huan He, Shifan Zhao, Ziyuan Tang et al.

Nonlinear acceleration methods are powerful techniques to speed up fixed-point iterations. However, many acceleration methods require storing a large number of previous iterates and this can become impractical if computational resources are limited. In this paper, we propose a nonlinear Truncated Generalized Conjugate Residual method (nlTGCR) whose goal is to exploit the symmetry of the Hessian to reduce memory usage. The proposed method can be interpreted as either an inexact Newton or a quasi-Newton method. We show that, with the help of global strategies like residual check techniques, nlTGCR can converge globally for general nonlinear problems and that under mild conditions, nlTGCR is able to achieve superlinear convergence. We further analyze the convergence of nlTGCR in a stochastic setting. Numerical results demonstrate the superiority of nlTGCR when compared with several other competitive baseline approaches on a few problems. Our code will be available in the future.

Ziyuan Tang, Yitian Guo, Chenxi Xiao

Recent advancements in virtual reality and robotic teleoperation have greatly increased the variety of haptic information that must be conveyed to users. While existing haptic devices typically provide unimodal feedback to enhance situational awareness, a gap remains in their ability to deliver rich, multimodal sensory feedback encompassing force, pressure, and thermal sensations. To address this limitation, we present the Multimodal Feedback Exoskeleton (MFE), a hand exoskeleton designed to deliver hybrid haptic feedback. The MFE features 20 degrees of freedom for capturing hand pose. For force feedback, it employs an active mechanism capable of generating 3.5-8.1 N of pushing and pulling forces at the fingers' resting pose, enabling realistic interaction with deformable objects. The fingertips are equipped with flat actuators based on the electro-osmotic principle, providing pressure and vibration stimuli and achieving up to 2.47 kPa of contact pressure to render tactile sensations. For thermal feedback, the MFE integrates thermoelectric heat pumps capable of rendering temperatures from 10 to 55 degrees Celsius. We validated the MFE by integrating it into a robotic teleoperation system using the X-Arm 6 and Inspire Hand manipulator. In user studies, participants successfully recognized and manipulated deformable objects and differentiated remote objects with varying temperatures. These results demonstrate that the MFE enhances situational awareness, as well as the usability and transparency of robotic teleoperation systems.

Mitchell Scott, Tianshi Xu, Ziyuan Tang et al.

Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise. We analyze preconditioned SGD in the geometry induced by a symmetric positive definite matrix $\mathbf{M}$, deriving bounds in which both the convergence rate and the stochastic noise floor are governed by $\mathbf{M}$-dependent quantities: the rate through an effective condition number in the $\mathbf{M}$-metric, and the floor through the product of that condition number and the preconditioned noise level. For nonconvex objectives, we establish a preconditioner-dependent basin-stability guarantee: when smoothness and basin size are measured in the $\mathbf{M}$-norm, the probability that the iterates remain in a well-behaved local region admits an explicit lower bound. This perspective is particularly relevant in Scientific Machine Learning (SciML), where achieving small training loss under stochastic updates is closely tied to physical fidelity, numerical stability, and constraint satisfaction. The framework applies to both diagonal/adaptive and curvature-aware preconditioners and yields a simple design principle: choose $\mathbf{M}$ to improve local conditioning while attenuating noise. Experiments on a quadratic diagnostic and three SciML benchmarks validate the predicted rate-floor behavior.

Ziyuan Tang, Jie Chen

A foundation model like GPT elicits many emergent abilities, owing to the pre-training with broad inclusion of data and the use of the powerful Transformer architecture. While foundation models in natural languages are prevalent, can we build similar models for graphs? This paper describes an approach toward a graph foundation model that is pre-trained with diverse graph datasets by adapting the Transformer backbone. A central challenge toward this end is how a sequence model encodes graphs of varying sizes and from different domains. We propose representing a node as multiple random walks, such that the Transformer can extract node representations from sequences, which in turn form edge and graph representations. We develop a novel context prediction loss for these random walks and theoretically analyze their expressive power in distinguishing neighborhoods and graphs. We also demonstrate the pre-training of our model and its adaptation to downstream tasks, showcasing its potential as a foundation for processing and reasoning with graph-structured data.