arXiv subjects

Yi Tian

Publications and source records attributed to Yi Tian.

At least 19 recordsLinked to original sources

arXiv2026

The conformally invariant metric on CLE$_4$ I: subsequential limits of the non-simple CLE graph metric

We consider the conformal loop ensemble (CLE) with the parameter $\kappa=4$, the critical value at or below which the loops are simple and do not intersect each other or the domain boundary. We show that the loops of a CLE$_4$ uniquely determine a conformally invariant, local, and geodesic metric so that the metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. This metric was previously constructed in unpublished work of Sheffield, Watson, and Wu. Our approach differs in that we show that the metric arises as the renormalized limit of the graph metric on CLE$_\kappa$ loops as $\kappa \downarrow 4$. In this first paper in a series of three, we prove that the subsequential limits exist and define a non-trivial conformally invariant metric on CLE$_4$ which is local and such that the metric ball growth from the boundary is given by the uniform exploration of Werner and Wu. In subsequent work, we will show that the subsequential limit exists as a true limit.

math.PR↗

arXiv2026

The conformally invariant metric on CLE$_4$ II: existence of geodesics

We continue our study of the conformal loop ensemble (CLE) with parameter $\kappa=4$, the critical threshold at or below which the loops are simple and disjoint, touching neither each other nor the domain boundary. This paper is the second in a series of three establishing that the loops of a CLE$_4$ uniquely determine a conformally invariant, local, and geodesic metric such that the metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. In this second paper, we prove the existence of geodesics, showing that any geodesic between two loops is supported on the CLE$_4$ loops (off a set of Hausdorff dimension zero) and does not intersect the domain boundary. Along the way, we establish sharp quantitative estimates for the CLE$_4$ metric geometry, including exponential tail bounds for rectangle distances and multi-scale four-arm SLE$_4$ non-intersection bounds for metric balls.

math.PR↗

arXiv2026

The conformally invariant metric on CLE$_4$ III: uniqueness

This paper is the third and final article in a series of papers constructing the canonical conformally invariant metric on the set of loops of the conformal loop ensemble (CLE) with critical parameter $\kappa=4$. The previous two articles construct, as a subsequential limit of the renormalized graph metric on the loops of CLE$_\kappa$ as $\kappa \downarrow 4$, a conformally invariant, local metric on the loops of a CLE$_4$ whose metric ball growth from the domain boundary coincides with the uniform exploration of Werner and Wu. In this paper, we establish that this metric is uniquely characterized by its properties, as are its geodesics, and that it is a measurable function of the CLE$_4$. In particular, we show that the renormalized CLE$_\kappa$ graph metric converges as $\kappa \downarrow 4$ without passing to a subsequence. A key step in the proof is to show that the metric is determined by the geodesics from each loop to the domain boundary, which are in turn determined by the uniform exploration; this representation will have important applications in future work.

math.PR↗

arXiv2026

Quasisymmetric rigidity of the Brownian sphere

The Brownian sphere, also known as the Brownian map, is a canonical random metric measure space homeomorphic to the two-dimensional sphere $\mathbf S^2$. It can be interpreted as the uniform measure on surfaces homeomorphic to $\mathbf S^2$, in the sense that it arises as the scaling limit of many natural models of random planar maps chosen uniformly from a given class. It is also equivalent to the $\sqrt{8/3}$-Liouville quantum gravity sphere. We prove that the Brownian sphere is quasisymmetrically rigid, meaning that, almost surely, it has no nontrivial quasisymmetric automorphisms. We also show that two independent Brownian spheres are almost surely not quasisymmetrically equivalent. Our argument also gives a new proof that the conformal structure of the Brownian sphere is almost surely determined by its metric structure.

math.PR↗

arXiv2026

The conformal dimension of the Brownian tree is one

The Brownian tree, also known as the continuum random tree, is a canonical random compact, geodesic $\mathbf R$-tree that arises as the universal scaling limit for numerous models of discrete random trees. A key quasisymmetric invariant of a metric space is its conformal dimension, defined as the infimum of the Hausdorff dimensions over all quasisymmetrically equivalent spaces. This value is always bounded below by the space's topological dimension and above by its Hausdorff dimension. In the present paper, we prove that the conformal dimension of the Brownian tree is $1$, matching its topological dimension.

math.PR↗

arXiv2026

See Through the Noise: Improving Domain Generalization in Gaze Estimation

Generalizable gaze estimation methods have garnered increasing attention due to their critical importance in real-world applications and have achieved significant progress. However, they often overlook the effect of label noise, arising from the inherent difficulty of acquiring precise gaze annotations, on model generalization performance. In this paper, we are the first to comprehensively investigate the negative effects of label noise on generalization in gaze estimation. Further, we propose a novel solution, called See-Through-Noise (SeeTN) framework, which improves generalization from a novel perspective of mitigating label noise. Specifically, we propose to construct a semantic embedding space via a prototype-based transformation to preserve a consistent topological structure between gaze features and continuous labels. We then measure feature-label affinity consistency to distinguish noisy from clean samples, and introduce a novel affinity regularization in the semantic manifold to transfer gaze-related information from clean to noisy samples. Our proposed SeeTN promotes semantic structure alignment and enforces domain-invariant gaze relationships, thereby enhancing robustness against label noise. Extensive experiments demonstrate that our SeeTN effectively mitigates the adverse impact of source-domain noise, leading to superior cross-domain generalization without compromising the source-domain accuracy, and highlight the importance of explicitly handling noise in generalized gaze estimation.

cs.CV↗

arXiv2026

The conformal dimension of the Brownian sphere is two

The conformal dimension of a metric space $(X, d)$ is equal to the infimum of the Hausdorff dimensions among all metric spaces quasisymmetric to $(X, d)$. It is an important quasisymmetric invariant which lies non-strictly between the topological and Hausdorff dimensions of $(X, d)$. We consider the conformal dimension of the Brownian sphere (a.k.a. the Brownian map), whose law can be thought of as the uniform measure on metric measure spaces homeomorphic to the standard sphere $\mathbf S^2$ with unit area. Since the Hausdorff dimension of the Brownian sphere is $4$, its conformal dimension lies in $[2, 4]$. Our main result is that its conformal dimension is equal to $2$, its topological dimension.

math.PR↗

arXiv2026

Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part II

We study the problem of state representation learning for control from partial and potentially high-dimensional observations. We approach this problem via cost-driven state representation learning, in which we learn a dynamical model in a latent state space by predicting cumulative costs. In particular, we establish finite-sample guarantees on finding a near-optimal representation function and a near-optimal controller using the learned latent model for infinite-horizon time-invariant Linear Quadratic Gaussian (LQG) control. We study two approaches to cost-driven representation learning, which differ in whether the transition function of the latent state is learned explicitly or implicitly. The first approach has also been investigated in Part I of this work, for finite-horizon time-varying LQG control. The second approach closely resembles MuZero, a recent breakthrough in empirical reinforcement learning, in that it learns latent dynamics implicitly by predicting cumulative costs. A key technical contribution of this Part II is to prove persistency of excitation for a new stochastic process that arises from the analysis of quadratic regression in our approach, and may be of independent interest.

cs.LG↗

arXiv2025

CellMamba: Adaptive Mamba for Accurate and Efficient Cell Detection

Cell detection in pathological images presents unique challenges due to densely packed objects, subtle inter-class differences, and severe background clutter. In this paper, we propose CellMamba, a lightweight and accurate one-stage detector tailored for fine-grained biomedical instance detection. Built upon a VSSD backbone, CellMamba integrates CellMamba Blocks, which couple either NC-Mamba or Multi-Head Self-Attention (MSA) with a novel Triple-Mapping Adaptive Coupling (TMAC) module. TMAC enhances spatial discriminability by splitting channels into two parallel branches, equipped with dual idiosyncratic and one consensus attention map, adaptively fused to preserve local sensitivity and global consistency. Furthermore, we design an Adaptive Mamba Head that fuses multi-scale features via learnable weights for robust detection under varying object sizes. Extensive experiments on two public datasets-CoNSeP and CytoDArk0-demonstrate that CellMamba outperforms both CNN-based, Transformer-based, and Mamba-based baselines in accuracy, while significantly reducing model size and inference latency. Our results validate CellMamba as an efficient and effective solution for high-resolution cell detection.

cs.CV↗

arXiv2025

Existence and uniqueness of the conformally covariant geodesic metric on simple conformal loop ensemble carpets

We prove that for each $\kappa \in (8/3, 4)$ there exists a geodesic metric on the carpet of a CLE$_\kappa$ which is canonical in the sense that it is characterized by a certain list of axioms. Our metric can be constructed explicitly as the scaling limit of Minkowski first passage percolation (MFPP), i.e., the metric obtained by taking the infimum of the Lebesgue measure of the $\varepsilon$-neighborhood of all paths connecting each pair of points. Earlier work by the first co-author showed that MFPP admits nontrivial subsequential limits. The present paper shows that this subsequential limit is unique and is characterized by our list of axioms. We conjecture that our metric describes the scaling limit of the chemical distance metric for discrete loop models that converge to CLE$_\kappa$ for $\kappa \in (8/3, 4)$ in the scaling limit, e.g., the critical Ising model for $\kappa=3$. Our argument is inspired by recent works of Gwynne and Miller and Ding and Gwynne on the uniqueness of Liouville quantum gravity metrics.

math.PR↗

arXiv2025

Enhancing Fault-Tolerant Surface Code Decoding with Iterative Lattice Reweighting

Efficient and realistic error decoding is crucial for fault-tolerant quantum computation (FTQC) on near-term devices. While decoding is a classical post-processing task, its effectiveness depends on accurately modeling quantum noise, which is hardware-dependent. In particular, correlated bit-flip ($X$) and phase-flip ($Z$) errors often arise under circuit-level noise. We introduce the Iterative Reweighting Minimum-Weight Perfect Matching (IRMWPM) decoder, which systematically incorporates such correlations to enhance quantum error correction. Our method leverages fault-detection patterns to guide reweighting: correlated $X$ and $Z$ detection events are identified, and their conditional probabilities update weights on the primal and dual lattices. This iterative procedure improves handling of realistic error propagation in a hardware-agnostic yet noise-aware manner. We prove that IRMWPM converges in finite time while preserving the distance guarantee of MWPM. Numerical results under circuit-level noise show substantial improvements. For distances $\geq 17$ and physical error rates $\leq 0.001$, IRMWPM reduces logical error rates by over 20x with only a few iterations. It also raises the accuracy threshold from 1% to 1.16%, making it practical for near-term real-time decoding. Extrapolated estimates suggest that to reach logical error rate $10^{-16}$, IRMWPM requires distance $d=31$, while standard MWPM needs $d=50$, implying a major reduction in qubit overhead.

quant-ph↗

arXiv2025

Advancing Cross-Organ Domain Generalization with Test-Time Style Transfer and Diversity Enhancement

Deep learning has made significant progress in addressing challenges in various fields including computational pathology (CPath). However, due to the complexity of the domain shift problem, the performance of existing models will degrade, especially when it comes to multi-domain or cross-domain tasks. In this paper, we propose a Test-time style transfer (T3s) that uses a bidirectional mapping mechanism to project the features of the source and target domains into a unified feature space, enhancing the generalization ability of the model. To further increase the style expression space, we introduce a Cross-domain style diversification module (CSDM) to ensure the orthogonality between style bases. In addition, data augmentation and low-rank adaptation techniques are used to improve feature alignment and sensitivity, enabling the model to adapt to multi-domain inputs effectively. Our method has demonstrated effectiveness on three unseen datasets.

cs.CV↗

arXiv2025

Differential Contrastive Training for Gaze Estimation

The complex application scenarios have raised critical requirements for precise and generalizable gaze estimation methods. Recently, the pre-trained CLIP has achieved remarkable performance on various vision tasks, but its potentials have not been fully exploited in gaze estimation. In this paper, we propose a novel Differential Contrastive Training strategy, which boosts gaze estimation performance with the help of the CLIP. Accordingly, a Differential Contrastive Gaze Estimation network (DCGaze) composed of a Visual Appearance-aware branch and a Semantic Differential-aware branch is introduced. The Visual Appearance-aware branch is essentially a primary gaze estimation network and it incorporates an Adaptive Feature-refinement Unit (AFU) and a Double-head Gaze Regressor (DGR), which both help the primary network to extract informative and gaze-related appearance features. Moreover, the Semantic Difference-aware branch is designed on the basis of the CLIP's text encoder to reveal the semantic difference of gazes. This branch could further empower the Visual Appearance-aware branch with the capability of characterizing the gaze-related semantic information. Extensive experimental results on four challenging datasets over within and cross-domain tasks demonstrate the effectiveness of our DCGaze.The code is available at https://github.com/LinZhang-bjtu/DCGaze.

cs.CV↗

arXiv2024

Cross-Dataset Gaze Estimation by Evidential Inter-intra Fusion

Achieving accurate and reliable gaze predictions in complex and diverse environments remains challenging. Fortunately, it is straightforward to access diverse gaze datasets in real-world applications. We discover that training these datasets jointly can significantly improve the generalization of gaze estimation, which is overlooked in previous works. However, due to the inherent distribution shift across different datasets, simply mixing multiple dataset decreases the performance in the original domain despite gaining better generalization abilities. To address the problem of ``cross-dataset gaze estimation'', we propose a novel Evidential Inter-intra Fusion EIF framework, for training a cross-dataset model that performs well across all source and unseen domains. Specifically, we build independent single-dataset branches for various datasets where the data space is partitioned into overlapping subspaces within each dataset for local regression, and further create a cross-dataset branch to integrate the generalizable features from single-dataset branches. Furthermore, evidential regressors based on the Normal and Inverse-Gamma (NIG) distribution are designed to additionally provide uncertainty estimation apart from predicting gaze. Building upon this foundation, our proposed framework achieves both intra-evidential fusion among multiple local regressors within each dataset and inter-evidential fusion among multiple branches by Mixture \textbfof Normal Inverse-Gamma (MoNIG distribution. Experiments demonstrate that our method consistently achieves notable improvements in both source domains and unseen domains.

cs.CV↗

arXiv2024

SDformerFlow: Spatiotemporal swin spikeformer for event-based optical flow estimation

Event cameras generate asynchronous and sparse event streams capturing changes in light intensity. They offer significant advantages over conventional frame-based cameras, such as a higher dynamic range and an extremely faster data rate, making them particularly useful in scenarios involving fast motion or challenging lighting conditions. Spiking neural networks (SNNs) share similar asynchronous and sparse characteristics and are well-suited for processing data from event cameras. Inspired by the potential of transformers and spike-driven transformers (spikeformers) in other computer vision tasks, we propose two solutions for fast and robust optical flow estimation for event cameras: STTFlowNet and SDformerFlow. STTFlowNet adopts a U-shaped artificial neural network (ANN) architecture with spatiotemporal shifted window self-attention (swin) transformer encoders, while SDformerFlow presents its fully spiking counterpart, incorporating swin spikeformer encoders. Furthermore, we present two variants of the spiking version with different neuron models. Our work is the first to make use of spikeformers for dense optical flow estimation. We conduct end-to-end training for all models using supervised learning. Our results yield state-of-the-art performance among SNN-based event optical flow methods on both the DSEC and MVSEC datasets, and show significant reduction in power consumption compared to the equivalent ANNs.

cs.CV↗

arXiv2023

Convex and Non-convex Optimization Under Generalized Smoothness

Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness condition with the Hessian norm bounded by an affine function of the gradient norm, and proved convergence in the non-convex setting via gradient clipping, assuming bounded noise. In this paper, we further generalize this non-uniform smoothness condition and develop a simple, yet powerful analysis technique that bounds the gradients along the trajectory, thereby leading to stronger results for both convex and non-convex optimization problems. In particular, we obtain the classical convergence rates for (stochastic) gradient descent and Nesterov's accelerated gradient method in the convex and/or non-convex setting under this general smoothness condition. The new analysis approach does not require gradient clipping and allows heavy-tailed noise with bounded variance in the stochastic setting.

math.OC↗

arXiv2023

Dynamic Game of the Dual-Channel Supply Chain Under a Carbon Subsidy Policy

This study investigates the dynamic game behaviors of dual-channel supply chains involving an oligopoly manufacturer selling low-carbon products to online and offline retailers. The price game models under government subsidy are discussed under three scenarios: (1) simultaneous decision, (2) manufacturer dominates the market, and (3) retailer dominates the market. The equilibrium strategies are compared under the government subsidy policy. Using numerical simulation,complex characteristics of the dual-channel supply chain under the carbon subsidy policy are investigated. The complexity of wholesale price and sales commission of each channel are analyzed by bifurcation, largest Lyapunov exponent and basin of attraction diagrams. Furthermore,parameter adjustment and delayed feedback control methods are proven to be effective approaches to chaos control.

math.NA↗

arXiv2022

Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I

We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system. We pursue a cost-driven approach, where a dynamic model in some latent state space is learned by predicting the costs without predicting the observations or actions. In particular, we focus on an intuitive cost-driven state representation learning method for solving Linear Quadratic Gaussian (LQG) control, one of the most fundamental partially observable control problems. As our main results, we establish finite-sample guarantees of finding a near-optimal state representation function and a near-optimal controller using the directly learned latent model, for finite-horizon time-varying LQG control problems. To the best of our knowledge, despite various empirical successes, finite-sample guarantees of such a cost-driven approach remain elusive. Our result underscores the value of predicting multi-step costs, an idea that is key to our theory, and notably also an idea that is known to be empirically valuable for learning state representations. A second part of this work, that is to appear as Part II, addresses the infinite-horizon linear time-invariant setting; it also extends the results to an approach that implicitly learns the latent dynamics, inspired by the recent empirical breakthrough of MuZero in model-based reinforcement learning.

cs.LG↗