arXiv subjects

Wei Qian

Publications and source records attributed to Wei Qian.

At least 37 records · Page 2Linked to original sources

arXiv2025

Multiple points on the boundaries of Brownian loop-soup clusters

For a Brownian loop soup with intensity $c\in(0,1]$ in the unit disk, we show that almost surely, the set of simple (resp. double) points on any portion of boundary of any of its clusters has Hausdorff dimension $2-ξ_c(2)$ (resp. $2-ξ_c(4)$), where $ξ_c(k)$ is the generalized disconnection exponent computed in arxiv:1901.05436. As a consequence, when the dimension is positive, such points are a.s. dense on every boundary of every cluster. There are a.s. no triple points on the cluster boundaries. As an intermediate result, we establish a separation lemma for Brownian loop soups, which is a powerful tool for obtaining sharp estimates on non-intersection and non-disconnection probabilities in the setting of loop soups. In particular, it allows us to define a family of generalized intersection exponents $ξ_c(k, λ)$, and show that $ξ_c(k)$ is the limit as $λ\searrow 0$ of $ξ_c(k, λ)$.

math.PR↗

arXiv2025

Up-to-constants estimates on four-arm events for simple conformal loop ensemble

We prove up-to-constants estimates for a general class of four-arm events in simple conformal loop ensembles, i.e. CLE$_κ$ for $κ\in (8/3,4]$. The four-arm events that we consider can be created by either one or two loops, with no constraint on the topology of the crossings. Our result is a key input in our series of works arxiv:2409.16230 and arxiv:2409.16273 on percolation of the two-sided level sets in the discrete Gaussian free field (and level sets in the occupation field of the random walk loop soup). In order to get rid of all constraints on the topology of the crossings, we rely on the Brownian loop-soup representation of simple CLE [Ann. Math. 176 (2012) 1827-1917], and a "cluster version" of a separation lemma for the Brownian loop soup. As a corollary, we also obtain up-to-constants estimates for a general version of four-arm events for SLE$_κ$ for $κ\in (8/3,4]$. This fixes (in the case of four arms and $κ\in(8/3,4]$) an essential gap in [Ann. Probab. 46 (2018) 2863-2907] and improves some estimates therein.

math.PR↗

arXiv2025

Backbone exponent and annulus crossing probability for planar percolation

We report the recent derivation of the backbone exponent for 2D percolation. In contrast to previously known exactly solved percolation exponents, the backbone exponent is a transcendental number, which is a root of an elementary equation. We also report an exact formula for the probability that there are two disjoint paths of the same color crossing an annulus. The backbone exponent captures the leading asymptotic, while the other roots of the elementary equation capture the asymptotic of the remaining terms. This suggests that the backbone exponent is part of a conformal field theory (CFT) whose bulk spectrum contains this set of roots. Our approach is based on the coupling between SLE curves and Liouville quantum gravity (LQG), and the integrability of Liouville CFT that governs the LQG surfaces.

cond-mat.stat-mech↗

arXiv2025

Conformal invariance of double random currents I: identification of the limit

This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the convergence of loop ensembles obtained by taking the cluster boundaries in the sum of two independent currents with free and wired boundary conditions. The strategy is first to prove convergence of the associated height function to the continuum Gaussian free field, and then to characterize the scaling limit of the loop ensembles as certain local sets of this Gaussian Free Field. In this paper, we identify uniquely the possible subsequential limits of the loop ensembles. Combined with the second paper, this completes the proof of conformal invariance.

math.PR↗

arXiv2024

Dense Audio-Visual Event Localization under Cross-Modal Consistency and Multi-Temporal Granularity Collaboration

In the field of audio-visual learning, most research tasks focus exclusively on short videos. This paper focuses on the more practical Dense Audio-Visual Event Localization (DAVEL) task, advancing audio-visual scene understanding for longer, untrimmed videos. This task seeks to identify and temporally pinpoint all events simultaneously occurring in both audio and visual streams. Typically, each video encompasses dense events of multiple classes, which may overlap on the timeline, each exhibiting varied durations. Given these challenges, effectively exploiting the audio-visual relations and the temporal features encoded at various granularities becomes crucial. To address these challenges, we introduce a novel CCNet, comprising two core modules: the Cross-Modal Consistency Collaboration (CMCC) and the Multi-Temporal Granularity Collaboration (MTGC). Specifically, the CMCC module contains two branches: a cross-modal interaction branch and a temporal consistency-gated branch. The former branch facilitates the aggregation of consistent event semantics across modalities through the encoding of audio-visual relations, while the latter branch guides one modality's focus to pivotal event-relevant temporal areas as discerned in the other modality. The MTGC module includes a coarse-to-fine collaboration block and a fine-to-coarse collaboration block, providing bidirectional support among coarse- and fine-grained temporal features. Extensive experiments on the UnAV-100 dataset validate our module design, resulting in a new state-of-the-art performance in dense audio-visual event localization. The code is available at https://github.com/zzhhfut/CCNet-AAAI2025.

cs.CV↗

arXiv2024

Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra

We use the SLE$_κ$ loop measure to construct a natural representation of the Virasoro algebra of central charge $c = c(κ) \le 1$. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure.

math.PR↗

arXiv2024

Percolation of discrete GFF in dimension two I. Arm events in the random walk loop soup

In this work, which is the first part of a series of two papers, we study the random walk loop soup in dimension two. More specifically, we estimate the probability that two large connected components of loops come close to each other, in the subcritical and critical regimes. The associated four-arm event can be estimated in terms of exponents computed in the Brownian loop soup, relying on the connection between this continuous process and conformal loop ensembles (with parameter $κ\in (8/3,4]$). Along the way, we need to develop several useful tools for the loop soup, based on separation for random walks and surgery for loops, such as a "locality" property and quasi-multiplicativity. The results established here then play a key role in a second paper, in particular to study the connectivity properties of level sets in the random walk loop soup and in the discrete Gaussian free field.

math.PR↗

arXiv2024

MCICSAM: Monte Carlo-guided Interpolation Consistency Segment Anything Model for Semi-Supervised Prostate Zone Segmentation

Accurate segmentation of various regions within the prostate is pivotal for diagnosing and treating prostate-related diseases. However, the scarcity of labeled data, particularly in specialized medical fields like prostate imaging, poses a significant challenge. Segment Anything Model (SAM) is a new large model for natural image segmentation, but there are some challenges in medical imaging. In order to better utilize the powerful feature extraction capability of SAM as well as to address the problem of low data volume for medical image annotation, we use Low-Rank Adaptation (LoRA) and semi-supervised learning methods of Monte Carlo guided interpolation consistency (MCIC) to enhance the fine-tuned SAM. We propose Monte Carlo-guided Interpolation Consistency Segment Anything Model (MCICSAM) for application to semi-supervised learning based prostate region segmentation. In the unlabeled data section, MCIC performs two different interpolation transformations on the input data and incorporates Monte Carlo uncertainty analysis in the output, forcing the model to be consistent in its predictions. The consistency constraints imposed on these interpolated samples allow the model to fit the distribution of unlabeled data better, ultimately improving its performance in semi-supervised scenarios. We use Dice and Hausdorff Distance at 95th percentile (HD95) to validate model performance. MCICSAM yieldes Dice with 79.38% and 89.95%, along with improves HD95 values of 3.12 and 2.27 for transition zone and transition zone. At the same time MCICSAM demonstrates strong generalizability. This method is expected to bring new possibilities in the field of prostate image segmentation.

eess.IV↗

arXiv2024

Joint Spatial-Temporal Modeling and Contrastive Learning for Self-supervised Heart Rate Measurement

This paper briefly introduces the solutions developed by our team, HFUT-VUT, for Track 1 of self-supervised heart rate measurement in the 3rd Vision-based Remote Physiological Signal Sensing (RePSS) Challenge hosted at IJCAI 2024. The goal is to develop a self-supervised learning algorithm for heart rate (HR) estimation using unlabeled facial videos. To tackle this task, we present two self-supervised HR estimation solutions that integrate spatial-temporal modeling and contrastive learning, respectively. Specifically, we first propose a non-end-to-end self-supervised HR measurement framework based on spatial-temporal modeling, which can effectively capture subtle rPPG clues and leverage the inherent bandwidth and periodicity characteristics of rPPG to constrain the model. Meanwhile, we employ an excellent end-to-end solution based on contrastive learning, aiming to generalize across different scenarios from complementary perspectives. Finally, we combine the strengths of the above solutions through an ensemble strategy to generate the final predictions, leading to a more accurate HR estimation. As a result, our solutions achieved a remarkable RMSE score of 8.85277 on the test dataset, securing \textbf{2nd place} in Track 1 of the challenge.

cs.CV↗

arXiv2024

Exploring Fairness in Educational Data Mining in the Context of the Right to be Forgotten

In education data mining (EDM) communities, machine learning has achieved remarkable success in discovering patterns and structures to tackle educational challenges. Notably, fairness and algorithmic bias have gained attention in learning analytics of EDM. With the increasing demand for the right to be forgotten, there is a growing need for machine learning models to forget sensitive data and its impact, particularly within the realm of EDM. The paradigm of selective forgetting, also known as machine unlearning, has been extensively studied to address this need by eliminating the influence of specific data from a pre-trained model without complete retraining. However, existing research assumes that interactive data removal operations are conducted in secure and reliable environments, neglecting potential malicious unlearning requests to undermine the fairness of machine learning systems. In this paper, we introduce a novel class of selective forgetting attacks designed to compromise the fairness of learning models while maintaining their predictive accuracy, thereby preventing the model owner from detecting the degradation in model performance. Additionally, we propose an innovative optimization framework for selective forgetting attacks, capable of generating malicious unlearning requests across various attack scenarios. We validate the effectiveness of our proposed selective forgetting attacks on fairness through extensive experiments using diverse EDM datasets.

cs.LG↗

arXiv2024

Backbone exponent for two-dimensional percolation

We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. Contrary to previously known arm exponents for this model, which are all rational, it has a transcendental value. Our derivation relies on the connection to the SLE$_κ$ bubble measure, the coupling between SLE and Liouville quantum gravity, and the integrability of Liouville conformal field theory. Along the way, we derive a formula not only for $κ=6$ (corresponding to percolation), but for all $κ\in (4,8)$.

math.PR↗

arXiv2024

Towards Modeling Uncertainties of Self-explaining Neural Networks via Conformal Prediction

Despite the recent progress in deep neural networks (DNNs), it remains challenging to explain the predictions made by DNNs. Existing explanation methods for DNNs mainly focus on post-hoc explanations where another explanatory model is employed to provide explanations. The fact that post-hoc methods can fail to reveal the actual original reasoning process of DNNs raises the need to build DNNs with built-in interpretability. Motivated by this, many self-explaining neural networks have been proposed to generate not only accurate predictions but also clear and intuitive insights into why a particular decision was made. However, existing self-explaining networks are limited in providing distribution-free uncertainty quantification for the two simultaneously generated prediction outcomes (i.e., a sample's final prediction and its corresponding explanations for interpreting that prediction). Importantly, they also fail to establish a connection between the confidence values assigned to the generated explanations in the interpretation layer and those allocated to the final predictions in the ultimate prediction layer. To tackle the aforementioned challenges, in this paper, we design a novel uncertainty modeling framework for self-explaining networks, which not only demonstrates strong distribution-free uncertainty modeling performance for the generated explanations in the interpretation layer but also excels in producing efficient and effective prediction sets for the final predictions based on the informative high-level basis explanations. We perform the theoretical analysis for the proposed framework. Extensive experimental evaluation demonstrates the effectiveness of the proposed uncertainty framework.

cs.LG↗

arXiv2023

Regulating Intermediate 3D Features for Vision-Centric Autonomous Driving

Multi-camera perception tasks have gained significant attention in the field of autonomous driving. However, existing frameworks based on Lift-Splat-Shoot (LSS) in the multi-camera setting cannot produce suitable dense 3D features due to the projection nature and uncontrollable densification process. To resolve this problem, we propose to regulate intermediate dense 3D features with the help of volume rendering. Specifically, we employ volume rendering to process the dense 3D features to obtain corresponding 2D features (e.g., depth maps, semantic maps), which are supervised by associated labels in the training. This manner regulates the generation of dense 3D features on the feature level, providing appropriate dense and unified features for multiple perception tasks. Therefore, our approach is termed Vampire, stands for "Volume rendering As Multi-camera Perception Intermediate feature REgulator". Experimental results on the Occ3D and nuScenes datasets demonstrate that Vampire facilitates fine-grained and appropriate extraction of dense 3D features, and is competitive with existing SOTA methods across diverse downstream perception tasks like 3D occupancy prediction, LiDAR segmentation and 3D objection detection, while utilizing moderate GPU resources. We provide a video demonstration in the supplementary materials and Codes are available at github.com/cskkxjk/Vampire.

cs.CV↗

arXiv2023

An attention-based deep learning network for predicting Platinum resistance in ovarian cancer

Background: Ovarian cancer is among the three most frequent gynecologic cancers globally. High-grade serous ovarian cancer (HGSOC) is the most common and aggressive histological type. Guided treatment for HGSOC typically involves platinum-based combination chemotherapy, necessitating an assessment of whether the patient is platinum-resistant. The purpose of this study is to propose a deep learning-based method to determine whether a patient is platinum-resistant using multimodal positron emission tomography/computed tomography (PET/CT) images. Methods: 289 patients with HGSOC were included in this study. An end-to-end SE-SPP-DenseNet model was built by adding Squeeze-Excitation Block (SE Block) and Spatial Pyramid Pooling Layer (SPPLayer) to Dense Convolutional Network (DenseNet). Multimodal data from PET/CT images of the regions of interest (ROI) were used to predict platinum resistance in patients. Results: Through five-fold cross-validation, SE-SPP-DenseNet achieved a high accuracy rate and an area under the curve (AUC) in predicting platinum resistance in patients, which were 92.6% and 0.93, respectively. The importance of incorporating SE Block and SPPLayer into the deep learning model, and considering multimodal data was substantiated by carrying out ablation studies and experiments with single modality data. Conclusions: The obtained classification results indicate that our proposed deep learning framework performs better in predicting platinum resistance in patients, which can help gynecologists make better treatment decisions. Keywords: PET/CT, CNN, SE Block, SPP Layer, Platinum resistance, Ovarian cancer

eess.IV↗

arXiv2023

Automated Natural Language Explanation of Deep Visual Neurons with Large Models

Deep neural networks have exhibited remarkable performance across a wide range of real-world tasks. However, comprehending the underlying reasons for their effectiveness remains a challenging problem. Interpreting deep neural networks through examining neurons offers distinct advantages when it comes to exploring the inner workings of neural networks. Previous research has indicated that specific neurons within deep vision networks possess semantic meaning and play pivotal roles in model performance. Nonetheless, the current methods for generating neuron semantics heavily rely on human intervention, which hampers their scalability and applicability. To address this limitation, this paper proposes a novel post-hoc framework for generating semantic explanations of neurons with large foundation models, without requiring human intervention or prior knowledge. Our framework is designed to be compatible with various model architectures and datasets, facilitating automated and scalable neuron interpretation. Experiments are conducted with both qualitative and quantitative analysis to verify the effectiveness of our proposed approach.

cs.CV↗

arXiv2023

Conformally invariant fields out of Brownian loop soups

Consider a Brownian loop soup $\mathcal{L}_D^θ$ with subcritical intensity $θ\in (0,1/2]$ in some 2D bounded simply connected domain. We define and study the properties of a conformally invariant field $h_θ$ naturally associated to $\mathcal{L}_D^θ$. Informally, this field is a signed version of the local time of $\mathcal{L}_D^θ$ to the power $1-θ$. When $θ=1/2$, $h_θ$ is a Gaussian free field (GFF) in $D$. Our construction of $h_θ$ relies on the multiplicative chaos $\mathcal{M}_γ$ associated with $\mathcal{L}_D^θ$, as introduced in [ABJL23]. Assigning independent symmetric signs to each cluster, we restrict $\mathcal{M}_γ$ to positive clusters. We prove that, when $θ=1/2$, the resulting measure $\mathcal{M}_γ^+$ corresponds to the exponential of $γ$ times a GFF. At this intensity, the GFF can be recovered by differentiating at $γ=0$ the measure $\mathcal{M}_γ^+$. When $θ<1/2$, we show that $\mathcal{M}_γ^+$ has a nondegenerate fractional derivative at $γ=0$ defining a random generalised function $h_θ$. We establish a result which is analoguous to the recent work [ALS23] in the GFF case ($θ=1/2$), but for $h_θ$ with $θ\in (0,1/2]$. Relying on the companion article [JLQ23], we prove that each cluster of $\mathcal{L}_D^θ$ possesses a nondegenerate Minkowski content in some non-explicit gauge function $r \mapsto r^2 |\log r|^{1-θ+o(1)}$. We then prove that $h_θ$ agrees a.s. with the sum of the Minkowski content of each cluster multiplied by its sign. We further extend the couplings between CLE$_4$, SLE$_4$ and the GFF to $h_θ$ for $θ\in(0,1/2]$. We show that the (non-nested) CLE$_κ$ loops form level lines for $h_θ$ and that there exists a constant height gap between the values of the field on either side of the CLE loops.

math.PR↗

arXiv2023

MonoNeRD: NeRF-like Representations for Monocular 3D Object Detection

In the field of monocular 3D detection, it is common practice to utilize scene geometric clues to enhance the detector's performance. However, many existing works adopt these clues explicitly such as estimating a depth map and back-projecting it into 3D space. This explicit methodology induces sparsity in 3D representations due to the increased dimensionality from 2D to 3D, and leads to substantial information loss, especially for distant and occluded objects. To alleviate this issue, we propose MonoNeRD, a novel detection framework that can infer dense 3D geometry and occupancy. Specifically, we model scenes with Signed Distance Functions (SDF), facilitating the production of dense 3D representations. We treat these representations as Neural Radiance Fields (NeRF) and then employ volume rendering to recover RGB images and depth maps. To the best of our knowledge, this work is the first to introduce volume rendering for M3D, and demonstrates the potential of implicit reconstruction for image-based 3D perception. Extensive experiments conducted on the KITTI-3D benchmark and Waymo Open Dataset demonstrate the effectiveness of MonoNeRD. Codes are available at https://github.com/cskkxjk/MonoNeRD.

cs.CV↗

arXiv2023

A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising

Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel HyperGNNs from a HyperGSD perspective, and vice versa. In particular, the tensor-hypergraph convolutional network (T-HGCN) has emerged as a powerful architecture for preserving higher-order interactions on hypergraphs, and this work shows an equivalence relation between a HyperGSD problem and the T-HGCN. Inspired by this intriguing result, we further design a tensor-hypergraph iterative network (T-HGIN) based on the HyperGSD problem, which takes advantage of a multi-step updating scheme in every single layer. Numerical experiments are conducted to show the promising applications of the proposed T-HGIN approach.

cs.LG↗