arXiv subjects

Zhijian He

Publications and source records attributed to Zhijian He.

At least 19 recordsLinked to original sources

arXiv2026

Respect Your Zero-Shot Uncertainty: Conservative Calibration for Test-Time-Adapted Vision-Language Models

Test-time adaptation (TTA) can improve the recognition accuracy of vision-language models under distribution shift, but often degrades calibration, making predictive confidence unreliable for downstream decision-making. Many existing label-free calibration approaches are either coupled to prompt optimization or rely on logit-range statistics that provide only a coarse characterization of the predictive distribution. We show that TTA can increase confidence and reduce entropy even when the top-1 prediction and its correctness remain unchanged, a failure mode we term prediction-preserving sharpening. Across diverse TTA methods and benchmarks, larger entropy reductions relative to paired zero-shot predictions are associated with greater increases in Expected Calibration Error (ECE). On entropy-reduced samples, confidence gains also tend to exceed accuracy gains. Based on these findings, we propose Zero-Shot-Anchored Entropy Calibration (ZAEC), a label-free post-hoc method that uses zero-shot entropy as a sample-specific uncertainty reference. ZAEC selectively restores the zero-shot entropy of sharpened predictions through minimal temperature scaling while leaving all other predictions unchanged. It requires no labeled calibration data or learned parameters and preserves class rankings and classification accuracy. Across five TTA methods and 15 datasets, ZAEC achieves the lowest post-hoc macro-average ECE on ViT-B/16, with consistent gains on RN50.

cs.CV↗

arXiv2026

The $L_p$-error rate for randomized quasi-Monte Carlo self-normalized importance sampling of unbounded integrands

Self-normalized importance sampling (SNIS) is a fundamental tool in Bayesian inference when the posterior distribution involves an unknown normalizing constant. In many applications, both the test function of interest and the underlying state space are unbounded, making direct $L_1$-error (mean absolute error) and $L_2$-error (root mean square error) estimates challenging for SNIS under randomized quasi-Monte Carlo (RQMC) sampling. In this work, we derive the $L_p$-error rate $(p\ge1)$ for RQMC-based SNIS (RQMC-SNIS) estimators with unbounded integrands on unbounded domains. A key step in our analysis is to first establish the $L_p$-error rate for plain RQMC integration. Our results allow for a broader class of transport maps used to generate samples from RQMC points. Under mild function boundary growth conditions, we further establish the $L_p$-error rate of order $\mathcal{O}(N^{-β+ ε})$ for RQMC-SNIS estimators, where $ε>0$ is arbitrarily small, $N$ is the sample size, and $β\in (0,1]$ depends on the boundary growth rate of the resulting integrand. Numerical experiments validate the theoretical results.

math.NA↗

arXiv2026

Quasi-Monte Carlo for SDE Simulation: Error Analysis and Dimensionality Reduction

We investigate the numerical simulation of general stochastic differential equations (SDEs) using Quasi-Monte Carlo (QMC) methods. First, we provide a rigorous theoretical analysis of the QMC method applied to the Euler-Maruyama (EM) scheme, establishing that it significantly accelerates the decay of the sampling error and achieves an asymptotically superior convergence rate over the classical Monte Carlo method. Second, the traditional EM scheme exhibits a slow polynomial decay of the discretization error, which necessitates a large number of time steps and leads to a significantly high integration dimension. To address this issue, we propose a Multilevel Stochastic Time Grid (MSTG) method based on Exact Simulation techniques, and we rigorously establish its convergence rate under randomized QMC sampling, proving that it preserves the high-order convergence of the sampling error. In terms of the overall error, the truncation error of the proposed MSTG method exhibits a remarkably fast super-exponential decay. Consequently, to achieve a given accuracy level, our approach requires significantly fewer discretization steps than the EM scheme, thereby drastically reducing the actual integration dimension of the QMC method. This substantial dimensionality reduction strategy greatly enhances the practical efficiency of the QMC algorithm. Numerical experiments fully corroborate the superiority of the proposed approach.

math.NA↗

arXiv2026

Beyond First-Order: Learning Riemannian Geometries for Invariant Visual Place Recognition

Visual Place Recognition (VPR) demands representations robust to drastic environmental and viewpoint shifts. Existing aggregation paradigms either depend on extensive supervised training or rely on first-order pooling, often struggling to preserve structural correlations under extreme shifts or incurring high adaptation costs. In this work, we propose Riemannian Invariant Aggregation (RIA), a unified geometric framework that explicitly models second-order scene structure on the Symmetric Positive Definite (SPD) manifold. By treating perturbations as tractable congruence transformations, RIA leverages geometry-aware Riemannian mappings to project covariance descriptors into a linearized Euclidean space, effectively preserving invariant structural components while suppressing noise. Extensive evaluations demonstrate that RIA achieves zero-shot performance comparable to supervised methods, and establishes state-of-the-art accuracy with simple fine-tuning, particularly in unstructured environments. The source code will be released.

cs.CV↗

arXiv2026

Uncertainty quantification using importance-sampled quasi-Monte Carlo with dimension-independent convergence rates

Quasi-Monte Carlo (QMC) integration over unbounded domains $\mathbb{R}^s$ remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification (UQ), the dimension $s$ can reach hundreds or even thousands. To restore the efficiency of quadrature rules in high dimensions, constructive QMC methods like lattice rules have been successfully developed within the framework of weighted function spaces. In contrast to designing problem-specific quadrature points, this paper proposes transforming the underlying integrand to accommodate the off-the-shelf scrambled nets (a construction-free randomized QMC method) via the boundary-damping importance sampling (BDIS) proposed by Pan et al. (2025). We provide a rigorous analysis of the dimension-independent convergence rate of BDIS-based scrambled nets while covering a broader class of unbounded functions than that in Pan et al. (2025). By exploiting the dimension structure of the parametric input random field, the proposed $n$-point quadrature rule achieves a dimension-independent mean squared error rate of $O(n^{-1-α^*+\varepsilon})$ on standard UQ problems in elliptic partial differential equations (PDEs), where $\varepsilon>0$ is arbitrarily small and $α^*\in (0,1)$ reflects the regularity with respect to the parametric variables. Numerical experiments on elliptic PDEs with high-dimensional parameters further demonstrate the effectiveness of the method.

math.NA↗

arXiv2025

Density estimation via periodic scaled Korobov kernel method with exponential decay condition

We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge regression in scaled Korobov spaces, we extend the kernel approach proposed by Kazashi and Nobile (SIAM J. Numer. Anal., 2023) and eliminate its requirement for inherent periodicity of the density function. This key modification enables effective estimation of densities defined on unbounded domains. We establish rigorous mean integrated squared error (MISE) bounds, proving that for densities with smoothness of order $α$ and exponential decay, our PSKK method achieves an $\mathcal{O}(M^{-1/(1+1/(2α)+ε)})$ MISE convergence rate with an arbitrarily small $ε>0$. While matching the convergence rate of the previous kernel approach, our method applies to non-periodic distributions at the cost of stronger differentiability and exponential decay assumptions. Numerical experiments confirm the theoretical results and demonstrate a significant improvement over traditional kernel density estimation in large-sample regimes.

math.ST↗

arXiv2025

Diffusion-Based Restoration for Multi-Modal 3D Object Detection in Adverse Weather

Multi-modal 3D object detection is important for reliable perception in robotics and autonomous driving. However, its effectiveness remains limited under adverse weather conditions due to weather-induced distortions and misalignment between different data modalities. In this work, we propose DiffFusion, a novel framework designed to enhance robustness in challenging weather through diffusion-based restoration and adaptive cross-modal fusion. Our key insight is that diffusion models possess strong capabilities for denoising and generating data that can adapt to various weather conditions. Building on this, DiffFusion introduces Diffusion-IR restoring images degraded by weather effects and Point Cloud Restoration (PCR) compensating for corrupted LiDAR data using image object cues. To tackle misalignments between two modalities, we develop Bidirectional Adaptive Fusion and Alignment Module (BAFAM). It enables dynamic multi-modal fusion and bidirectional bird's-eye view (BEV) alignment to maintain consistent spatial correspondence. Extensive experiments on three public datasets show that DiffFusion achieves state-of-the-art robustness under adverse weather while preserving strong clean-data performance. Zero-shot results on the real-world DENSE dataset further validate its generalization. The implementation of our DiffFusion will be released as open-source.

cs.CV↗

arXiv2025

Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoods

There is a growing interest in studying sequential neural posterior estimation (SNPE) techniques due to their advantages for simulation-based models with intractable likelihoods. The methods aim to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators. As an SNPE technique, the automatic posterior transformation (APT) method proposed by Greenberg et al. (2019) performs well and scales to high-dimensional data. However, the APT method requires computing the expectation of the logarithm of an intractable normalizing constant, i.e., a nested expectation. Although atomic proposals were used to render an analytical normalizing constant, it remains challenging to analyze the convergence of learning. In this paper, we reformulate APT as a nested estimation problem. Building on this, we construct several multilevel Monte Carlo (MLMC) estimators for the loss function and its gradients to accommodate different scenarios, including two unbiased estimators, and a biased estimator that trades a small bias for reduced variance and controlled runtime and memory usage. We also provide convergence results of stochastic gradient descent to quantify the interaction of the bias and variance of the gradient estimator. Numerical experiments for approximating complex posteriors with multimodality in moderate dimensions are provided to examine the effectiveness of the proposed methods.

stat.CO↗

arXiv2025

Beyond ADE and FDE: A Comprehensive Evaluation Framework for Safety-Critical Prediction in Multi-Agent Autonomous Driving Scenarios

Current evaluation methods for autonomous driving prediction models rely heavily on simplistic metrics such as Average Displacement Error (ADE) and Final Displacement Error (FDE). While these metrics offer basic performance assessments, they fail to capture the nuanced behavior of prediction modules under complex, interactive, and safety-critical driving scenarios. For instance, existing benchmarks do not distinguish the influence of nearby versus distant agents, nor systematically test model robustness across varying multi-agent interactions. This paper addresses this critical gap by proposing a novel testing framework that evaluates prediction performance under diverse scene structures, saying, map context, agent density and spatial distribution. Through extensive empirical analysis, we quantify the differential impact of agent proximity on target trajectory prediction and identify scenario-specific failure cases that are not exposed by traditional metrics. Our findings highlight key vulnerabilities in current state-of-the-art prediction models and demonstrate the importance of scenario-aware evaluation. The proposed framework lays the groundwork for rigorous, safety-driven prediction validation, contributing significantly to the identification of failure-prone corner cases and the development of robust, certifiable prediction systems for autonomous vehicles.

cs.RO↗

arXiv2025

Quasi-Monte Carlo integration over $\mathbb{R}^s$ with boundary-damping importance sampling

This paper proposes a new importance sampling (IS) that is tailored to quasi-Monte Carlo (QMC) integration over $\mathbb{R}^s$. IS introduces a multiplicative adjustment to the integrand by compensating the sampling from the proposal instead of the target distribution. Improper proposals result in severe adjustment factor for QMC. Our strategy is to first design a adjustment factor to meet desired regularities and then determine a tractable transport map from the standard uniforms to the proposal for using QMC quadrature points as inputs. The transport map has the effect of damping the boundary growth of the resulting integrand so that the effectiveness of QMC can be reclaimed. Under certain conditions on the original integrand, our proposed IS enjoys a fast convergence rate independently of the dimension $s$, making it amenable to high-dimensional problems.

math.NA↗

arXiv2025

Scale, Don't Fine-tune: Guiding Multimodal LLMs for Efficient Visual Place Recognition at Test-Time

Visual Place Recognition (VPR) has evolved from handcrafted descriptors to deep learning approaches, yet significant challenges remain. Current approaches, including Vision Foundation Models (VFMs) and Multimodal Large Language Models (MLLMs), enhance semantic understanding but suffer from high computational overhead and limited cross-domain transferability when fine-tuned. To address these limitations, we propose a novel zero-shot framework employing Test-Time Scaling (TTS) that leverages MLLMs' vision-language alignment capabilities through Guidance-based methods for direct similarity scoring. Our approach eliminates two-stage processing by employing structured prompts that generate length-controllable JSON outputs. The TTS framework with Uncertainty-Aware Self-Consistency (UASC) enables real-time adaptation without additional training costs, achieving superior generalization across diverse environments. Experimental results demonstrate significant improvements in cross-domain VPR performance with up to 210$\times$ computational efficiency gains.

cs.LG↗

arXiv2025

KDMOS:Knowledge Distillation for Motion Segmentation

Motion Object Segmentation (MOS) is crucial for autonomous driving, as it enhances localization, path planning, map construction, scene flow estimation, and future state prediction. While existing methods achieve strong performance, balancing accuracy and real-time inference remains a challenge. To address this, we propose a logits-based knowledge distillation framework for MOS, aiming to improve accuracy while maintaining real-time efficiency. Specifically, we adopt a Bird's Eye View (BEV) projection-based model as the student and a non-projection model as the teacher. To handle the severe imbalance between moving and non-moving classes, we decouple them and apply tailored distillation strategies, allowing the teacher model to better learn key motion-related features. This approach significantly reduces false positives and false negatives. Additionally, we introduce dynamic upsampling, optimize the network architecture, and achieve a 7.69% reduction in parameter count, mitigating overfitting. Our method achieves a notable IoU of 78.8% on the hidden test set of the SemanticKITTI-MOS dataset and delivers competitive results on the Apollo dataset. The KDMOS implementation is available at https://github.com/SCNU-RISLAB/KDMOS.

cs.CV↗

arXiv2025

Enhanced convergence rates of Adaptive Importance Sampling with recycling schemes via quasi-Monte Carlo methods

This article investigates the integration of quasi-Monte Carlo (QMC) methods using the Adaptive Multiple Importance Sampling (AMIS). Traditional Importance Sampling (IS) often suffers from poor performance since it heavily relies on the choice of the proposal distributions. The AMIS and the Modified version of AMIS (MAMIS) address this by iteratively refining proposal distributions and reusing all past samples through a recycling strategy. We introduce the RQMC methods into the MAMIS, achieving higher convergence rates compared to the Monte Carlo (MC) methods. Our main contributions include a detailed convergence analysis of the MAMIS estimator under randomized QMC (RQMC) sampling. Specifically, we establish the $L^q$ $(q \geq 2)$ error bound for the RQMC-based estimator using a smoothed projection method, which enables us to apply the Hölder's inequality in the error analysis of the RQMC-based MAMIS estimator. As a result, we prove that the root mean square error of the RQMC-based MAMIS estimator converges at a rate of $\mathcal{O}(\bar{N}_T^{-1+ε})$, where $\bar{N}_T$ is the average number of samples used in each step over $T$ iterations, and $ε> 0$ is arbitrarily small. Numerical experiments validate the effectiveness of our method, including mixtures of Gaussians, a banana-shaped model, and Bayesian Logistic regression.

math.NA↗

arXiv2025

An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments. We also managed to demonstrate the superiority of the proposed method for a high-dimensional model with a real-world dataset.

stat.ML↗

arXiv2024

Unbiased Markov chain quasi-Monte Carlo for Gibbs samplers

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased after a fixed number of iterations. Unbiased MCMC, an advancement achieved through coupling techniques, addresses this bias issue in MCMC. It allows us to run many short chains in parallel. Quasi-Monte Carlo (QMC), known for its high order of convergence, is an alternative of MC. By incorporating the idea of QMC into MCMC, Markov chain quasi-Monte Carlo (MCQMC) effectively reduces the variance of MCMC, especially in Gibbs samplers. This work presents a novel approach that integrates unbiased MCMC with MCQMC, called as an unbiased MCQMC method. This method renders unbiased estimators while improving the rate of convergence significantly. Numerical experiments demonstrate that for Gibbs sampling, unbiased MCQMC with a sample size of $N$ yields a faster root mean square error (RMSE) rate than the $O(N^{-1/2})$ rate of unbiased MCMC, toward an RMSE rate of $O(N^{-1})$ for low-dimensional problems. Surprisingly, in a challenging problem of 1049-dimensional Pólya Gamma Gibbs sampler, the RMSE can still be reduced by several times for moderate sample sizes. In the setting of parallelization, unbiased MCQMC also performs better than unbiased MCMC, even running with short chains.

math.NA↗

arXiv2024

Quasi-Monte Carlo and importance sampling methods for Bayesian inverse problems

Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC with low discrepancy points and has the potential to substantially enhance error rates. In this paper, we integrate IS with a randomly shifted rank-1 lattice rule, a widely used QMC method, to approximate posterior expectations arising from Bayesian Inverse Problems (BIPs) where the posterior density tends to concentrate as the intensity of noise diminishes. Within the framework of weighted Hilbert spaces, we first establish the convergence rate of the lattice rule for a large class of unbounded integrands. This method extends to the analysis of QMC combined with IS in BIPs. Furthermore, we explore the robustness of the IS-based randomly shifted rank-1 lattice rule by determining the quadrature error rate with respect to the noise level. The effects of using Gaussian distributions and $t$-distributions as the proposal distributions on the error rate of QMC are comprehensively investigated. We find that the error rate may deteriorate at low intensity of noise when using improper proposals, such as the prior distribution. To reclaim the effectiveness of QMC, we propose a new IS method such that the lattice rule with $N$ quadrature points achieves an optimal error rate close to $O(N^{-1})$, which is insensitive to the noise level. Numerical experiments are conducted to support the theoretical results.

math.NA↗

arXiv2023

Quasi-Monte Carlo for unbounded integrands with importance sampling

We consider the problem of estimating an expectation $ \mathbb{E}\left[ h(W)\right]$ by quasi-Monte Carlo (QMC) methods, where $ h $ is an unbounded smooth function on $ \mathbb{R}^d $ and $ W$ is a standard normal distributed random variable. To study rates of convergence for QMC on unbounded integrands, we use a smoothed projection operator to project the output of $W$ to a bounded region, which differs from the strategy of avoiding the singularities along the boundary of the unit cube $ [0,1]^d $ in 10.1137/S0036144504441573. The error is then bounded by the quadrature error of the transformed integrand and the projection error. If the function $h(\boldsymbol{x})$ and its mixed partial derivatives do not grow too fast as the Euclidean norm $|\boldsymbol{x}|$ goes to infinity, we obtain an error rate of $O(n^{-1+ε})$ for QMC and randomized QMC (RQMC) with a sample size $n$ and an arbitrarily small $ε>0$. However, the rate turns out to be $O(n^{-1+2M+ε})$ if the functions grow exponentially with a rate of $O(\exp\{M|\boldsymbol{x}|^2\})$ for a constant $M\in(0,1/2)$. Superisingly, we find that using importance sampling with t distribution as the proposal can improve the root mean squared error of RQMC from $O(n^{-1+2M+ε})$ to $O( n^{-3/2+ε})$ for any $M\in(0,1/2)$.

math.NA↗

arXiv2022

FusionPortable: A Multi-Sensor Campus-Scene Dataset for Evaluation of Localization and Mapping Accuracy on Diverse Platforms

Combining multiple sensors enables a robot to maximize its perceptual awareness of environments and enhance its robustness to external disturbance, crucial to robotic navigation. This paper proposes the FusionPortable benchmark, a complete multi-sensor dataset with a diverse set of sequences for mobile robots. This paper presents three contributions. We first advance a portable and versatile multi-sensor suite that offers rich sensory measurements: 10Hz LiDAR point clouds, 20Hz stereo frame images, high-rate and asynchronous events from stereo event cameras, 200Hz inertial readings from an IMU, and 10Hz GPS signal. Sensors are already temporally synchronized in hardware. This device is lightweight, self-contained, and has plug-and-play support for mobile robots. Second, we construct a dataset by collecting 17 sequences that cover a variety of environments on the campus by exploiting multiple robot platforms for data collection. Some sequences are challenging to existing SLAM algorithms. Third, we provide ground truth for the decouple localization and mapping performance evaluation. We additionally evaluate state-of-the-art SLAM approaches and identify their limitations. The dataset, consisting of raw sensor easurements, ground truth, calibration data, and evaluated algorithms, will be released: https://ram-lab.com/file/site/multi-sensor-dataset.

cs.RO↗