arXiv subjects

Ruihan Liu

Publications and source records attributed to Ruihan Liu.

6 recordsLinked to original sources

arXiv2026

Equivariant Covariance Tensors: Guaranteed SPD Uncertainty for Tensor-Valued Geometric Learning

Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. While E(3)-equivariant neural networks excel at point estimates, they lack rigorous confidence measures. We focus on symmetric rank-2 tensor prediction, where the target has six Kelvin--Mandel coordinates and full uncertainty is represented by a $6\times6$ covariance matrix. We introduce a framework for E(3)-equivariant UQ, modeling the full predictive distribution where both mean and covariance preserve rotational symmetry. Our approach decomposes the covariance into irreducible representations $\mathrm{Sym}^2(\rho_c) \cong 2\times(l=0) \oplus 2\times(l=2) \oplus 1\times(l=4)$. By mapping from the flat Lie algebra $\mathfrak{sym}(6)$ to the curved SPD manifold via matrix exponentiation, we strictly ensure positive-definite covariances while maintaining exact equivariance. Furthermore, we formulate a Log-Euclidean Equivariant Scoring Objective (LE-ESO)---a robust surrogate loss based on the Multivariate Laplace distribution---providing robustness to heavy-tailed errors and stable optimization. Validation on ModelNet40 inertia tensors and Materials Project dielectric tensors demonstrates that our method achieves competitive performance and provides physically consistent, symmetry-preserving uncertainty estimates with useful risk and OOD sensitivity.

cs.LG↗

arXiv2026

Deviation Tests for a High-dimensional Mean

This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbol{\mu}$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbol{\mu} = \boldsymbol{\mu}_0$ versus $H_1^\texttt{e} : \boldsymbol{\mu} \neq \boldsymbol{\mu}_0$, we focus on testing the deviation $H_0 : \|\boldsymbol{\mu} - \boldsymbol{\mu}_0\|_2 \ge d_0$ versus $H_1 : \|\boldsymbol{\mu} - \boldsymbol{\mu}_0\|_2 < d_0$ for a prespecified length $d_0 > 0$. Constructing a valid test statistic for this problem is technically nontrivial. By applying the concept of positive and negative feedback processes from control theory, we propose a test statistic based on a two-armed bandit (TAB) process. The deviation test is also extended to the two-sample setting. Simulation experiments confirm a good performance of the tests in finite samples. Finally, a real data analysis demonstrates the practical significance of the proposed deviation tests.

stat.ME↗

arXiv2026

Task-Aware Exploration via a Predictive Bisimulation Metric

Accelerating exploration in visual reinforcement learning under sparse rewards remains challenging due to the substantial task-irrelevant variations. Despite advances in intrinsic exploration, many methods either assume access to low-dimensional states or lack task-aware exploration strategies, thereby rendering them fragile in visual domains. To bridge this gap, we present TEB, a Task-aware Exploration approach that tightly couples task-relevant representations with exploration through a predictive Bisimulation metric. Specifically, TEB leverages the metric not only to learn behaviorally grounded task representations but also to measure behaviorally intrinsic novelty over the learned latent space. To realize this, we first theoretically mitigate the representation collapse of degenerate bisimulation metrics under sparse rewards by internally introducing a simple but effective predicted reward differential. Building on this robust metric, we design potential-based exploration bonuses, which measure the relative novelty of adjacent observations over the latent space. Extensive experiments on MetaWorld and Maze2D show that TEB achieves superior exploration ability and outperforms recent baselines.

cs.AI↗

arXiv2025

4D-ROLLS: 4D Radar Occupancy Learning via LiDAR Supervision

A comprehensive understanding of 3D scenes is essential for autonomous vehicles (AVs), and among various perception tasks, occupancy estimation plays a central role by providing a general representation of drivable and occupied space. However, most existing occupancy estimation methods rely on LiDAR or cameras, which perform poorly in degraded environments such as smoke, rain, snow, and fog. In this paper, we propose 4D-ROLLS, the first weakly supervised occupancy estimation method for 4D radar using the LiDAR point cloud as the supervisory signal. Specifically, we introduce a method for generating pseudo-LiDAR labels, including occupancy queries and LiDAR height maps, as multi-stage supervision to train the 4D radar occupancy estimation model. Then the model is aligned with the occupancy map produced by LiDAR, fine-tuning its accuracy in occupancy estimation. Extensive comparative experiments validate the exceptional performance of 4D-ROLLS. Its robustness in degraded environments and effectiveness in cross-dataset training are qualitatively demonstrated. The model is also seamlessly transferred to downstream tasks BEV segmentation and point cloud occupancy prediction, highlighting its potential for broader applications. The lightweight network enables 4D-ROLLS model to achieve fast inference speeds at about 30 Hz on a 4060 GPU. The code of 4D-ROLLS will be made available at https://github.com/CLASS-Lab/4D-ROLLS.

cs.CV↗

arXiv2024

Alignment and matching tests for high-dimensional tensor signals via tensor contraction

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit long-range dependence, which makes the analysis of the matrix challenging, involved, and distinct from standard random matrix theory. Our approach provides a novel framework for addressing hypothesis testing problems in the context of high-dimensional tensor signals.

stat.ME↗

arXiv2023

Testing High-dimensional Nonstationary Time Series

In this article, we first establish the joint central limit theorem (CLT) for the extreme eigenvalues of the sample correlation matrix of high-dimensional random walks with cross-sectional dependence. We further investigate the asymptotic spectral properties of the sample correlation matrix of high-dimensional autoregressive processes. To apply our theoretical results, we propose a novel high-dimensional unit root test and develop a forward sequential test to determine the number of unit roots in high-dimensional time series data. Finally, we conduct an empirical study of the purchasing power parity (PPP) hypothesis in high-dimensional settings.

stat.ME↗