Ziming Liu

Ziming Liu, Andrew M. Stuart, Yixuan Wang

We propose a sampling method based on an ensemble approximation of second order Langevin dynamics. The log target density is appended with a quadratic term in an auxiliary momentum variable and damped-driven Hamiltonian dynamics introduced; the resulting stochastic differential equation is invariant to the Gibbs measure, with marginal on the position coordinates given by the target. A preconditioner based on covariance under the law of the dynamics does not change this invariance property, and is introduced to accelerate convergence to the Gibbs measure. The resulting mean-field dynamics may be approximated by an ensemble method; this results in a gradient-free and affine-invariant stochastic dynamical system. Numerical results demonstrate its potential as the basis for a numerical sampler in Bayesian inverse problems.

Yang Li, Zongzheng Zhang, Xuchong Qiu et al. · tsinghua

Understanding lane toplogy relationships accurately is critical for safe autonomous driving. However, existing two-stage methods suffer from inefficiencies due to error propagations and increased computational overheads. To address these challenges, we propose a one-stage architecture that simultaneously predicts traffic elements, lane centerlines and topology relationship, improving both the accuracy and inference speed of lane topology understanding for autonomous driving. Our key innovation lies in reusing intermediate attention resources within distinct transformer decoders. This approach effectively leverages the inherent relational knowledge within the element detection module to enable the modeling of topology relationships among traffic elements and lanes without requiring additional computationally expensive graph networks. Furthermore, we are the first to demonstrate that knowledge can be distilled from models that utilize standard definition (SD) maps to those operates without using SD maps, enabling superior performance even in the absence of SD maps. Extensive experiments on the OpenLane-V2 dataset show that our approach outperforms baseline methods in both accuracy and efficiency, achieving superior results in lane detection, traffic element identification, and topology reasoning. Our code is available at https://github.com/Yang-Li-2000/one-stage.git.

Ziming Liu, Bryan Liu, Alvaro Valcarce et al.

Integrating Large AI Models (LAMs) into 6G mobile networks is a key enabler of the AI-Native Air Interface (AI-AI), where protocol intelligence must scale beyond handcrafted logic. This paper presents, to our knowledge, the first standards-compliant emulation of the Radio Resource Control (RRC) layer using a decoder-only LAM (LLAMA-class) fine-tuned with Low-Rank Adaptation (LoRA) on a multi-vendor corpus of real-world traces spanning both 5G and 4G systems. We treat RRC as a domain-specific language and construct a segmentation-safe, question--answer (Question-and-Answer (QA)) dataset that preserves Abstract Syntax Notation (ASN.1) structure through linearization prior to Byte Pair Encoding (BPE) tokenization. The proposed approach combines parameter-efficient adaptation with schema-bounded prompting to ensure syntactic and procedural fidelity. Evaluation introduces a standards-aware triad -- ASN.1 conformance, field-level coverage analysis, and uplink-to-downlink state-machine checks -- alongside semantic similarity and latency profiling across 120 configurations. On 30k 5G request--response pairs plus an additional 4.8k QA turns from 4G sessions, our 8B model achieves a median cosine similarity of 0.97, a 61% relative gain over a zero-shot baseline, while sustaining high conformance rates. These results demonstrate that LAMs, when augmented with protocol-aware reasoning, can directly orchestrate control-plane procedures, laying the foundation for the future Artificial Intelligence (AI)-native Radio Access Network (RAN).

Yixuan Wang, Ziming Liu, Zongyi Li et al.

We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs. We propose a modularized approach and study the choices of neural network ansatz, sampling strategy, and optimization algorithm. When combined with rigorous computer-assisted proofs and PDE analysis, the numerical solutions identified by PINNs, provided they are of high precision, can serve as a powerful tool for studying singularities in PDEs. For 1D Burgers equation, our framework can lead to a solution with very high precision, and for the 2D Boussinesq equation, which is directly related to the singularity formulation in 3D Euler and Navier-Stokes equations, we obtain a solution whose loss is $4$ digits smaller than that obtained in \cite{wang2023asymptotic} with fewer training steps. We also discuss potential directions for pushing towards machine precision for higher-dimensional problems.

Ziming Liu, Zheng Zhang

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the energy-time uncertainty relation from quantum mechanics, we propose a Quantum-Inspired Hamiltonian Monte Carlo algorithm (QHMC). This algorithm allows a particle to have a random mass matrix with a probability distribution rather than a fixed mass. We prove the convergence property of QHMC and further show why such a random mass can improve the performance when we sample a broad class of distributions. In order to handle the big training data sets in large-scale machine learning, we develop a stochastic gradient version of QHMC using Nos{é}-Hoover thermostat called QSGNHT, and we also provide theoretical justifications about its steady-state distributions. Finally in the experiments, we demonstrate the effectiveness of QHMC and QSGNHT on synthetic examples, bridge regression, image denoising and neural network pruning. The proposed QHMC and QSGNHT can indeed achieve much more stable and accurate sampling results on the test cases.