Zhijian He

Zhijian He, Lingjiong Zhu

Recently, He and Owen (2016) proposed the use of Hilbert's space filling curve (HSFC) in numerical integration as a way of reducing the dimension from $d>1$ to $d=1$. This paper studies the asymptotic normality of the HSFC-based estimate when using scrambled van der Corput sequence as input. We show that the estimate has an asymptotic normal distribution for functions in $C^1([0,1]^d)$, excluding the trivial case of constant functions. The asymptotic normality also holds for discontinuous functions under mild conditions. It was previously known only that scrambled $(0,m,d)$-net quadratures enjoy the asymptotic normality for smooth enough functions, whose mixed partial gradients satisfy a Hölder condition. As a by-product, we find lower bounds for the variance of the HSFC-based estimate. Particularly, for nontrivial functions in $C^1([0,1]^d)$, the low bound is of order $n^{-1-2/d}$, which matches the rate of the upper bound established in He and Owen (2016).

Zhijian He, Xiaoqun Wang

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is asymptotically better than Monte Carlo in the numerical integration. We first prove the convergence of QMC-based quantile estimates under very mild conditions, and then establish a deterministic error bound of $O(N^{-1/d})$ for the quantile estimates, where $d$ is the dimension of the QMC point sets used in the simulation and $N$ is the sample size. Under certain conditions, we show that the mean squared error (MSE) of the randomized QMC estimate for expected shortfall is $o(N^{-1})$. Moreover, under stronger conditions the MSE can be improved to $O(N^{-1-1/(2d-1)+ε})$ for arbitrarily small $ε>0$.

Zhijian He

This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $R^d$, which can be unbounded. Under suitable conditions, we show that conditional QMC not only has the smoothing effect (up to infinitely times differentiable), but also can bring orders of magnitude reduction in integration error compared to plain QMC. Particularly, for some typical problems in options pricing and Greeks estimation, conditional randomized QMC that uses $n$ samples yields a mean error of $O(n^{-1+ε})$ for arbitrarily small $ε>0$. As a by-product, we find that this rate also applies to randomized QMC integration with all terms of the ANOVA decomposition of the discontinuous integrand, except the one of highest order.

Zhijian He, Xiaoqun Wang

Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the performance of the QMC method. This paper develops an integrated method that overcomes the challenges of the high dimensionality and discontinuities concurrently. For this purpose, a smoothing method is proposed to remove the discontinuities for some typical functions arising from financial engineering. To make the smoothing method applicable for more general functions, a new path generation method is designed for simulating the paths of the underlying assets such that the resulting function has the required form. The new path generation method has an additional power to reduce the effective dimension of the target function. Our proposed method caters for a large variety of model specifications, including the Black-Scholes, exponential normal inverse Gaussian Lévy, and Heston models. Numerical experiments dealing with these models show that in the QMC setting the proposed smoothing method in combination with the new path generation method can lead to a dramatic variance reduction for pricing exotic options with discontinuous payoffs and for calculating options' Greeks. The investigation on the effective dimension and the related characteristics explains the significant enhancement of the combined procedure.

Jintao Cheng, Weibin Li, Zhijian He et al.

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.

Zhijian He, Feifei Liu, Yuwei Li et al.

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.

Chunyu Cao, Jintao Cheng, Zeyu Chen et al.

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.

Jianhao Jiao, Huaiyang Huang, Liang Li et al.

This paper investigates two typical image-type representations for event camera-based tracking: time surface (TS) and event map (EM). Based on the original TS-based tracker, we make use of these two representations' complementary strengths to develop an enhanced version. The proposed tracker consists of a general strategy to evaluate the optimization problem's degeneracy online and then switch proper representations. Both TS and EM are motion- and scene-dependent, and thus it is important to figure out their limitations in tracking. We develop six tracker variations and conduct a thorough comparison of them on sequences covering various scenarios and motion complexities. We release our implementations and detailed results to benefit the research community on event cameras: https: //github.com/gogojjh/ESVO_extension.

Yifei Xiong, Xiliang Yang, Sanguo Zhang et al.

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.

Jintao Cheng, Weibin Li, Jiehao Luo et al.

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.

Xiliang Yang, Yifei Xiong, Zhijian He

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.

Zhijian He

This paper studies randomized quasi-Monte Carlo (QMC) sampling for discontinuous integrands having singularities along the boundary of the unit cube $[0,1]^d$. Both discontinuities and singularities are extremely common in the pricing and hedging of financial derivatives and have a tremendous impact on the accuracy of QMC. It was previously known that the root mean square error of randomized QMC is only $o(n^{-1/2})$ for discontinuous functions with singularities. We find that under some mild conditions, randomized QMC yields an expected error of $O(n^{-1/2-1/(4d-2)+ε})$ for arbitrarily small $ε>0$. Moreover, one can get a better rate if the boundary of discontinuities is parallel to some coordinate axes. As a by-product, we find that the expected error rate attains $O(n^{-1+ε})$ if the discontinuities are QMC-friendly, in the sense that all the discontinuity boundaries are parallel to coordinate axes. The results can be used to assess the QMC accuracy for some typical problems from financial engineering.