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Runsheng Liu

Publications and source records attributed to Runsheng Liu.

15 recordsLinked to original sources
arXiv2026

Local scaling limit of the four-dimensional uniform spanning tree

In this paper, we prove that the uniform spanning tree of $\mathbb Z^4$, seen from the origin, converges locally to an infinite spatial Brownian Kesten tree: a Brownian spine onto which independent spatial Brownian trees are grafted at a constant rate. The convergence holds jointly for the intrinsic metric, the volume measure and the Euclidean positions of the vertices, after rescaling these quantities by suitable constant multiples of $n^{-1}$, $n^{-2}(\log n)^{1/3}$ and $n^{-1/2}(\log n)^{-1/6}$, respectively, under the local rooted spatial Gromov-weak topology. The rescaled space-time occupation measure converges to that of infinite canonical super-Brownian motion. We also identify the limiting law of the rescaled intrinsic-ball volume and obtain sharp first-moment asymptotics.

math.PR↗
arXiv2026

One Tile, Multiple Instances: Rethinking MIL for Sparse Diagnostic Evidence

In weakly supervised Whole Slide Image (WSI) classification, feature extractors typically compress each image tile into a single global embedding. Consequently, slide-level aggregators are restricted to this coarse tile scale, concealing fine-grained sub-tile evidence from the attention mechanism. We introduce DI-MIL, a framework that decouples encoding context from instance granularity through decomposed instances. By clustering dense spatial tokens from a frozen foundation model within each tile, DI-MIL converts a single tile into multiple independently weighted instance embeddings. As a training-free post-encoding module, DI-MIL integrates seamlessly into existing pipelines without requiring re-encoding or downstream architectural modifications. We evaluate DI-MIL on cytopathology, a challenging testbed where sparse diagnostic signals are easily diluted within standard tiles. Across four datasets, three frozen foundation models, and two attention-based aggregators, DI-MIL demonstrates consistent efficacy, improving 67 of 72 metric-level comparisons, with the largest mean gains reaching 3.64 points under cytopathology-specific backbones. In a broader comparison against seven representative MIL baselines, DI-MIL paired with ACMIL achieves highest mean performance in 33 of 36 backbone-dataset-metric comparisons. Ablations show that direct smaller tiling inflates the extracted tile count by up to 43.3$\times$ with non-monotonic performance, whereas DI-MIL incurs zero additional image-extraction overhead while achieving the strongest overall results. These results establish instance construction as an orthogonal design dimension in MIL, supporting DI-MIL as a cost-efficient solution under sparse diagnostic evidence.

cs.CV↗
arXiv2026

Intersection Exponents of Simple Random Walks in Two and Three Dimensions

The probability that several independent random walks avoid one another decays algebraically with the number of steps $N\to\infty$ in two and three dimensions, $P_N\sim N^{-ξ/2}$, where the intersection exponent $ξ$ depends on the number of random walks. More generally, one may consider several groups of independent random walks, with intersections allowed within each group and forbidden between different groups. We first study intersection exponents in two dimensions, where our results agree with the known exact formulas and test the numerical approach. In three dimensions, where no general exact expression is known, we determine $ξ$ for a range of cases. For two groups containing $k$ and $m$ random walks, respectively, we obtain the exponents $ξ(k,m)$ for $k=1,2$ and $m=1,2,\ldots,7$. We further extend $m$ to a continuous parameter $λ$, allowing us to obtain numerical values for $ξ(k,λ)$ for $k=1,2,3$ and $0.25\leqλ\leq3$. Away from the smallest moment orders, these functions increase with $λ$ with decreasing slopes, as expected from the strict concavity of Brownian intersection exponents. We also investigate three-group configurations for several representative cases. The resulting integer and continuous exponents supply numerical values for analytical studies of non-intersecting random paths.

cond-mat.stat-mech↗
arXiv2026

Tail exponents of the three-dimensional uniform spanning tree and Abelian sandpile

We study the local geometry of the three-dimensional uniform spanning tree and its connection with the Abelian sandpile model. We obtain sharp tail exponents, up to subpolynomial errors, for the past of the origin in the three-dimensional UST and for the $0$-tree of the $0$-wired uniform spanning forest. As a principal application, we prove the corresponding three-dimensional Abelian sandpile avalanche exponents: the avalanche-cluster radius has tail exponent $1$, while both the avalanche-cluster size and the total number of topplings have tail exponent $1/3$. These results identify the leading power-law behaviour of three-dimensional sandpile avalanches and improve previously known bounds.

math.PR↗
arXiv2026

Non-existence of several random fractals in Brownian motion and Brownian loop soup

We develop a unified approach to establish the non-existence of three types of random fractals: (1) the pioneer triple points of the planar Brownian motion, answering an open question in [7], (2) the pioneer double cut points of the planar and three-dimensional Brownian motions, and (3) the double points on the boundaries of the clusters of the planar Brownian loop soup at the critical intensity, answering an open question in [39]. These fractals have the common feature that they are associated with an intersection or disconnection exponent which yields a Hausdorff dimension ``exactly zero''.

math.PR↗
arXiv2025

The intermediate level-sets of the four-dimensional membrane model

In this paper, we consider the discrete membrane model in four dimensions. We confirm the existence of the scaling limit of the intermediate (i.e., a multiple of the expected maximum) level-sets of the model, and show that it is equal in law to the sub-critical Gaussian multiplicative chaos (GMC) measure of the continuum membrane model.

math.PR↗
arXiv2025

Generalizable Cervical Cancer Screening via Large-scale Pretraining and Test-Time Adaptation

Cervical cancer is a leading malignancy in female reproductive system. While AI-assisted cytology offers a cost-effective and non-invasive screening solution, current systems struggle with generalizability in complex clinical scenarios. To address this issue, we introduced Smart-CCS, a generalizable Cervical Cancer Screening paradigm based on pretraining and adaptation to create robust and generalizable screening systems. To develop and validate Smart-CCS, we first curated a large-scale, multi-center dataset named CCS-127K, which comprises a total of 127,471 cervical cytology whole-slide images collected from 48 medical centers. By leveraging large-scale self-supervised pretraining, our CCS models are equipped with strong generalization capability, potentially generalizing across diverse scenarios. Then, we incorporated test-time adaptation to specifically optimize the trained CCS model for complex clinical settings, which adapts and refines predictions, improving real-world applicability. We conducted large-scale system evaluation among various cohorts. In retrospective cohorts, Smart-CCS achieved an overall area under the curve (AUC) value of 0.965 and sensitivity of 0.913 for cancer screening on 11 internal test datasets. In external testing, system performance maintained high at 0.950 AUC across 6 independent test datasets. In prospective cohorts, our Smart-CCS achieved AUCs of 0.947, 0.924, and 0.986 in three prospective centers, respectively. Moreover, the system demonstrated superior sensitivity in diagnosing cervical cancer, confirming the accuracy of our cancer screening results by using histology findings for validation. Interpretability analysis with cell and slide predictions further indicated that the system's decision-making aligns with clinical practice. Smart-CCS represents a significant advancement in cancer screening across diverse clinical contexts.

q-bio.QM↗
arXiv2024

Holistic and Historical Instance Comparison for Cervical Cell Detection

Cytology screening from Papanicolaou (Pap) smears is a common and effective tool for the preventive clinical management of cervical cancer, where abnormal cell detection from whole slide images serves as the foundation for reporting cervical cytology. However, cervical cell detection remains challenging due to 1) hazily-defined cell types (e.g., ASC-US) with subtle morphological discrepancies caused by the dynamic cancerization process, i.e., cell class ambiguity, and 2) imbalanced class distributions of clinical data may cause missed detection, especially for minor categories, i.e., cell class imbalance. To this end, we propose a holistic and historical instance comparison approach for cervical cell detection. Specifically, we first develop a holistic instance comparison scheme enforcing both RoI-level and class-level cell discrimination. This coarse-to-fine cell comparison encourages the model to learn foreground-distinguishable and class-wise representations. To emphatically improve the distinguishability of minor classes, we then introduce a historical instance comparison scheme with a confident sample selection-based memory bank, which involves comparing current embeddings with historical embeddings for better cell instance discrimination. Extensive experiments and analysis on two large-scale cytology datasets including 42,592 and 114,513 cervical cells demonstrate the effectiveness of our method. The code is available at https://github.com/hjiangaz/HERO.

cs.CV↗
arXiv2024

GAInS: Gradient Anomaly-aware Biomedical Instance Segmentation

Instance segmentation plays a vital role in the morphological quantification of biomedical entities such as tissues and cells, enabling precise identification and delineation of different structures. Current methods often address the challenges of touching, overlapping or crossing instances through individual modeling, while neglecting the intrinsic interrelation between these conditions. In this work, we propose a Gradient Anomaly-aware Biomedical Instance Segmentation approach (GAInS), which leverages instance gradient information to perceive local gradient anomaly regions, thus modeling the spatial relationship between instances and refining local region segmentation. Specifically, GAInS is firstly built on a Gradient Anomaly Mapping Module (GAMM), which encodes the radial fields of instances through window sliding to obtain instance gradient anomaly maps. To efficiently refine boundaries and regions with gradient anomaly attention, we propose an Adaptive Local Refinement Module (ALRM) with a gradient anomaly-aware loss function. Extensive comparisons and ablation experiments in three biomedical scenarios demonstrate that our proposed GAInS outperforms other state-of-the-art (SOTA) instance segmentation methods. The code is available at https://github.com/DeepGAInS/GAInS.

cs.CV↗
arXiv2023

Collective flow and the fluid behavior in p/d/$^3$He+Au collisions at $\sqrt{s_{NN}} = 200$ GeV

By varying the intrinsic initial geometry, the p/d/$^3$He+Au collisions at the Relativistic Heavy Ion Collider (RHIC) provide a unique opportunity to understand the collective behavior and probe the possible sub-nucleon fluctuations in small systems. In this paper, we employ the hybrid model iEBE-VISHNU with Trento initial conditions to study the collective flow and the fluid behavior in p/d/$^3$He+Au collisions. With fine-tuned parameters, iEBE-VISHNU can describe the $v_2(p_T)$ and $v_3(p_T)$ data from the PHENIX and STAR collaborations. However, for some certain parameter sets with initial sub-nucleon fluctuation, the hydrodynamic simulations have already beyond their limits with the average Knudsen number $\langle K_n \rangle$ obviously larger than one. Our calculations demonstrate that, for a meaningful evaluation of the fluid behavior in the small systems, model simulations should also pay attention to the validity range of hydrodynamics.

nucl-th↗
arXiv2019

Frank-Wolfe Network: An Interpretable Deep Structure for Non-Sparse Coding

The problem of $L_p$-norm constrained coding is to convert signal into code that lies inside an $L_p$-ball and most faithfully reconstructs the signal. Previous works under the name of sparse coding considered the cases of $L_0$ and $L_1$ norms. The cases with $p>1$ values, i.e. non-sparse coding studied in this paper, remain a difficulty. We propose an interpretable deep structure namely Frank-Wolfe Network (F-W Net), whose architecture is inspired by unrolling and truncating the Frank-Wolfe algorithm for solving an $L_p$-norm constrained problem with $p\geq 1$. We show that the Frank-Wolfe solver for the $L_p$-norm constraint leads to a novel closed-form nonlinear unit, which is parameterized by $p$ and termed $pool_p$. The $pool_p$ unit links the conventional pooling, activation, and normalization operations, making F-W Net distinct from existing deep networks either heuristically designed or converted from projected gradient descent algorithms. We further show that the hyper-parameter $p$ can be made learnable instead of pre-chosen in F-W Net, which gracefully solves the non-sparse coding problem even with unknown $p$. We evaluate the performance of F-W Net on an extensive range of simulations as well as the task of handwritten digit recognition, where F-W Net exhibits strong learning capability. We then propose a convolutional version of F-W Net, and apply the convolutional F-W Net into image denoising and super-resolution tasks, where F-W Net all demonstrates impressive effectiveness, flexibility, and robustness.

cs.CV↗
arXiv2013

A Three-class ROC for Evaluating Doubletalk Detectors in Acoustic Echo Cancellation

Doubletalk detector (DTD) is essential to keep adaptive filter from diverging in the presence of near-end speech in acoustic echo cancellation (AEC), and there was a receiver operating characteristic (ROC) to characterize DTD performance. However, the traditional ROC for evaluating DTD used a static time-invariant room acoustic impulse response and could not evaluate DTDs which distinguish echo path change from doubletalk. We solve these problems by extending the traditional binary detection ROC to three class, and simulations show the efficiency of the proposed method.

cs.IT↗