arXiv subjects

Yichun Yang

Publications and source records attributed to Yichun Yang.

11 recordsLinked to original sources

arXiv2026

Improved algorithm for counting spanning trees by $\ell_1$-regularized resistance

We study the basic problem of approximating the number of spanning trees of a graph. We propose an algorithm that approximates the number of spanning trees in $\widetilde O(m+n^{7/4}\eps^{-3/2})$ time on a graph with $n$ vertices and $m$ edges. Our algorithm improves upon the previously best known $\widetilde O(m+n^{15/8}\eps^{-7/4})$ time algorithm by Chu, Gao, Peng, Sachdeva, Sawlani, and Wang [FOCS 2018] and the $\widetilde O(m^{1.5}\eps^{-1})$ time algorithm by Liu, Peng and Yang [FOCS 2026] when $m\ge n^{7/6}$. Notably, our algorithm is based on the novel concept of $\ell_1$-regularized resistance. We propose simple and efficient algorithms for computing $\ell_1$-regularized resistance and we show that they can be used to approximate the number of spanning trees by combining with the determinant sparsifier framework of Durfee, Peebles, Peng, and Rao [FOCS 2017].

cs.DS↗

arXiv2026

Classical and quantum spectral density estimation under local graph access

We study spectral density estimation for the normalized adjacency matrix of an unweighted graph under local access model. Previously, Cohen-Steiner et al. [KDD 2018] proposed an algorithm for $\varepsilon$-approximate spectral density estimation in the Wasserstein-1 distance, using $2^{O(1/\varepsilon)}$ local queries to the graph. In this paper, we prove that every constant-success estimator with Wasserstein--$1$ error at most $\eps$ requires $2^{\Omega(1/\eps)}$ queries, showing that the Cohen-Steiner algorithm is optimal up to constant in the exponent. This resolves the open problem left by previous researches Jin et al. [COLT 2023] and Peng et al. [COLT 2026]. We then turn to quantum local access model. We give an $\widetilde O(\eps^{-3})$-query algorithm estimating the spectral density with Wasserstein-1 error at most $\eps$. Finally, we prove a $\widetilde\Omega(\eps^{-4/3})$ quantum lower bound when the graph is sufficiently large. As a result, quantum local access model changes the dependence on $\eps$ from exponential to polynomial.

quant-ph↗

arXiv2026

PercepCap: Video Captioner with Structured Spatio-Temporal Perception

Video captioning requires fine-grained spatio-temporal understanding of videos, including spatial perception of where objects are located and temporal perception of when events occur. Existing MLLMs usually generate captions directly from video inputs without exposing the perceptual evidence behind descriptions. As a result, mistakes in spatiotemporal perception are only observed in the final caption, making it difficult to identify the underlying perceptual errors directly. To address these issues, we present PercepCap, a perception-aware video captioning framework that makes perceptual evidence explicit before producing the final caption. Specifically, PercepCap follows a perceive-describe generation chain, where the model first produces a spatiotemporal perception trace comprising object trajectories and temporal events, and then generates the final caption conditioned on the perceived evidence. To support this, we design a two-stage training strategy. Perceive-then-Describe Supervised Fine-tuning adapts the model from caption-only generation to the proposed perceive-describe chain, while Perception-Grounded Reinforcement Learning optimizes perception trace and caption quality with joint rewards over perception chain and the final caption. To support our two-stage training, we introduce Caption-Anchored Perception Data Construction. This pipeline builds the SFT and RL training data by first generating a caption-only description, extracting the objects and events it mentions, and grounding them back in the video with boxes and timestamps. This yields caption-aligned perception data that provides solid training ground truth, ensuring that the explicit perception trace and final caption refer to the same objects and events. Across direct caption and caption-to-QA evaluation, PercepCap consistently improves upon the Qwen3-VL baseline and demonstrates leading caption quality.

cs.CV↗

arXiv2026

Fast counting and sampling for ferromagnetic two-spin systems

We introduce two new models equivalent to ferromagnetic two-spin systems: a weighted subgraph model and a random cluster type model. Using these new connections, we obtain an efficient sampling algorithm and a new randomised algorithm that efficiently approximates the partition function of ferromagnetic two-spin systems in certain parameter regimes. No efficient sampling algorithms are known before in this regime, and our new estimation algorithm runs in near-quadratic time for bounded degree graphs and in polynomial time for general graphs, improving upon the previous algorithm of Guo, Liu, and Lu (2020).

cs.DS↗

arXiv2026

An Exponential Lower Bound for Spectral Density Estimation on Unweighted Graphs

We study lower bounds for estimating the spectral density of the normalized adjacency matrix of a graph. Previously, Cohen-Steiner et al. [KDD 2018] proposed an algorithm for $\varepsilon$-approximate spectral density estimation in the Wasserstein-1 distance, using $2^{O(1/\varepsilon)}$ random walks initiated from uniformly random nodes in the graph. Later, Jin et al. [COLT 2023] established a nearly matching exponential lower bound for \emph{weighted} graphs, assuming the algorithm has access to samples from random walks started at random nodes. It was left open whether this lower bound could be extended to \emph{unweighted} graphs. In this paper, we answer this question in the affirmative by proving an exponential lower bound for unweighted graphs. Specifically, we show that no algorithm can compute an $\varepsilon$-approximation to the spectrum of a normalized graph adjacency matrix with constant success probability, even when given the full transcripts of $2^{\Omega(1/\varepsilon^{1/6})}$ random walks, each of length $2^{\Omega(1/\varepsilon^{1/6})}$, started from uniformly random nodes.

cs.DS↗

arXiv2026

Theoretically and Practically Efficient Resistance Distance Computation on Large Graphs

The computation of resistance distance is pivotal in a wide range of graph analysis applications, including graph clustering, link prediction, and graph neural networks. Despite its foundational importance, efficient algorithms for computing resistance distances on large graphs are still lacking. Existing state-of-the-art (SOTA) methods, including power iteration-based algorithms and random walk-based local approaches, often struggle with slow convergence rates, particularly when the condition number of the graph Laplacian matrix, denoted by $\kappa$, is large. To tackle this challenge, we propose two novel and efficient algorithms inspired by the classic Lanczos method: Lanczos Iteration and Lanczos Push, both designed to reduce dependence on $\kappa$. Among them, Lanczos Iteration is a near-linear time global algorithm, whereas Lanczos Push is a local algorithm with a time complexity independent of the size of the graph. More specifically, we prove that the time complexity of Lanczos Iteration is $\tilde{O}(\sqrt{\kappa} m)$ ($m$ is the number of edges of the graph and $\tilde{O}$ means the complexity omitting the $\log$ terms) which achieves a speedup of $\sqrt{\kappa}$ compared to previous power iteration-based global methods. For Lanczos Push, we demonstrate that its time complexity is $\tilde{O}(\kappa^{2.75})$ under certain mild and frequently established assumptions, which represents a significant improvement of $\kappa^{0.25}$ over the SOTA random walk-based local algorithms. We validate our algorithms through extensive experiments on eight real-world datasets of varying sizes and statistical properties, demonstrating that Lanczos Iteration and Lanczos Push significantly outperform SOTA methods in terms of both efficiency and accuracy.

cs.LG↗

arXiv2025

SAM 2++: Tracking Anything at Any Granularity

Due to the varying granularity of target states across different tasks, most existing trackers are tailored to a single task, which specificity limits their generalization, preventing them from effectively utilizing multi-task training data and leading to redundancy in both model design and parameters. Although recent unified vision models share partial architectures across tasks, they usually retain task-specific interfaces and overlook the common tracking principle behind different granularities, leaving a gap for truly unified video tracking. To unify video tracking tasks, we present SAM 2++, a unified framework that can handle target states at different granularities, including masks, boxes, and points, through an integrated design of prompt encoding, output decoding, and memory representation. First, to handle different target granularities, we design task-specific prompts that map diverse task inputs into general prompt embeddings, together with a Unified Decoder that produces task results in a common output form without redesigning the overall pipeline. Next, to satisfy memory matching, the core operation of tracking, we introduce a task-adaptive memory mechanism that unifies memory across different granularities while preserving their distinct state semantics, preventing full parameter sharing from causing interference across granularities. Finally, we introduce Tracking-Any-Granularity, the first large and diverse video tracking dataset with rich annotations at three granularities. It is constructed through a customized data engine with phased manual annotation and model-assisted completion, providing a comprehensive resource for training, benchmarking, and analyzing unified tracking models. Comprehensive experiments confirm that SAM 2++ sets a new state of the art across diverse tracking tasks at different granularities, establishing a unified and robust tracking framework.

cs.CV↗

arXiv2025

Improved Algorithms for Effective Resistance Computation on Graphs

Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges. First, we focus on local online-computation algorithms for ER approximation, aiming to improve the dependency on the approximation error parameter $\epsilon$. Specifically, for a given vertex pair $(s,t)$, we propose a local algorithm with a time complexity of $\tilde{O}(\sqrt{d}/\epsilon)$ to compute an $\epsilon$-approximation of the $s,t$-ER value for expander graphs, where $d=\min \{d_s,d_t\}$. This improves upon the previous state-of-the-art, including an $\tilde{O}(1/\epsilon^2)$ time algorithm based on random walk sampling by Andoni et al. (ITCS'19) and Peng et al. (KDD'21). Our method achieves this improvement by combining deterministic search with random walk sampling to reduce variance. Second, we establish a lower bound for ER approximation on expander graphs. We prove that for any $\epsilon\in (0,1)$, there exist an expander graph and a vertex pair $(s,t)$ such that any local algorithm requires at least $\Omega(1/\epsilon)$ time to compute the $\epsilon$-approximation of the $s,t$-ER value. Finally, we extend our techniques to index-based algorithms for ER computation. We propose an algorithm with $\tilde{O}(\min \{m+n/\epsilon^{1.5},\sqrt{nm}/\epsilon\})$ processing time, $\tilde{O}(n/\epsilon)$ space complexity and $O(1)$ query complexity, which returns an $\epsilon$-approximation of the $s,t$-ER value for any $s,t\in \mathcal{V}$ for expander graphs. Our approach improves upon the state-of-the-art $\tilde{O}(m/\epsilon)$ processing time by Dwaraknath et al. (NeurIPS'24) and the $\tilde{O}(m+n/\epsilon^2)$ processing time by Li and Sachdeva (SODA'23).

cs.DS↗

arXiv2024

CaReBench: A Fine-Grained Benchmark for Video Captioning and Retrieval

Video understanding, including video captioning and retrieval, is still a great challenge for video-language models (VLMs). The existing video retrieval and caption benchmarks only include short descriptions, limits their ability of detailed video understanding evaluation. To address this problem, we present CaReBench, a testing benchmark for fine-grained video captioning and retrieval with 1,000 high-quality pairs of videos and human-annotated detailed captions. Uniquely, it provides manually separated spatial annotations and temporal annotations for each video. Based on this design, we introduce two evaluation metrics, ReBias and CapST, specifically tailored for video retrieval and video captioning tasks, respectively. These metrics enable a comprehensive investigation into the spatial and temporal biases inherent in VLMs. In addition, to handle both video retrieval and video captioning tasks in a unified framework, we develop a simple baseline based on a Multimodal Language Model (MLLM). By implementing a two-stage Supervised Fine-Tuning (SFT), we fully unlock the potential of MLLM, enabling it not only to generate detailed video descriptions but also to extract video features. Surprisingly, experimental results demonstrate that, compared to the CLIP-based models designed for retrieval and the popular MLLMs skilled in video captioning, our baseline shows competitive performance in both fine-grained video retrieval and video detailed captioning.

cs.CV↗

arXiv2024

Scaling Up Graph Propagation Computation on Large Graphs: A Local Chebyshev Approximation Approach

Graph propagation (GP) computation plays a crucial role in graph data analysis, supporting various applications such as graph node similarity queries, graph node ranking, graph clustering, and graph neural networks. Existing methods, mainly relying on power iteration or push computation frameworks, often face challenges with slow convergence rates when applied to large-scale graphs. To address this issue, we propose a novel and powerful approach that accelerates power iteration and push methods using Chebyshev polynomials. Specifically, we first present a novel Chebyshev expansion formula for general GP functions, offering a new perspective on GP computation and achieving accelerated convergence. Building on these theoretical insights, we develop a novel Chebyshev power iteration method (\ltwocheb) and a novel Chebyshev push method (\chebpush). Our \ltwocheb method demonstrates an approximate acceleration of $O(\sqrt{N})$ compared to existing power iteration techniques for both personalized PageRank and heat kernel PageRank computations, which are well-studied GP problems. For \chebpush, we propose an innovative subset Chebyshev recurrence technique, enabling the design of a push-style local algorithm with provable error guarantee and reduced time complexity compared to existing push methods. We conduct extensive experiments using 5 large real-world datasets to evaluate our proposed algorithms, demonstrating their superior efficiency compared to state-of-the-art approaches.

cs.LG↗

arXiv2023

SportsMOT: A Large Multi-Object Tracking Dataset in Multiple Sports Scenes

Multi-object tracking in sports scenes plays a critical role in gathering players statistics, supporting further analysis, such as automatic tactical analysis. Yet existing MOT benchmarks cast little attention on the domain, limiting its development. In this work, we present a new large-scale multi-object tracking dataset in diverse sports scenes, coined as \emph{SportsMOT}, where all players on the court are supposed to be tracked. It consists of 240 video sequences, over 150K frames (almost 15\times MOT17) and over 1.6M bounding boxes (3\times MOT17) collected from 3 sports categories, including basketball, volleyball and football. Our dataset is characterized with two key properties: 1) fast and variable-speed motion and 2) similar yet distinguishable appearance. We expect SportsMOT to encourage the MOT trackers to promote in both motion-based association and appearance-based association. We benchmark several state-of-the-art trackers and reveal the key challenge of SportsMOT lies in object association. To alleviate the issue, we further propose a new multi-object tracking framework, termed as \emph{MixSort}, introducing a MixFormer-like structure as an auxiliary association model to prevailing tracking-by-detection trackers. By integrating the customized appearance-based association with the original motion-based association, MixSort achieves state-of-the-art performance on SportsMOT and MOT17. Based on MixSort, we give an in-depth analysis and provide some profound insights into SportsMOT. The dataset and code will be available at https://deeperaction.github.io/datasets/sportsmot.html.

cs.CV↗