arXiv subjects

Shuo Qin

Publications and source records attributed to Shuo Qin.

13 recordsLinked to original sources

arXiv2026

Survival probability in reactive gambling: monotonicity, singularity, and Hölder continuity

A gambler starts with fortune $x$ and unit bet, then aims to double the bet after every win and halve it after every loss, while the actual bet is capped by the current fortune. Each round is won independently with probability $p\in(0,1)$. We study $f(x,p)$, the probability that the gambler is never ruined. We prove that $f(x,p)>0$ exactly when $x>2$ and $p<1/2$. For fixed $x>2$, $f(x,\cdot)$ is strictly decreasing and real analytic on $(0,1/2)$, and vanishes on $[1/2,1)$: playing a more favourable game lowers the chance of surviving it. For fixed $p\in(0,1/2)$, $f(\cdot,p)$ is strictly increasing and singular continuous on $[2,\infty)$. An elementary two-step argument gives an explicit global Hölder exponent, with constant one, which is strictly larger than $\log_2(1+p)$ and tends to $\frac12\log_2(111/46)=0.635426\ldots$ as $p\uparrow1/2$; we place it in a hierarchy of computable exponents and show, by an exact finite computation, that the optimal exponent is strictly smaller than the pointwise exponent at $x=2$ once $p$ is close to $1/2$. We determine that boundary exponent, and give the complete phase diagram when wins and losses use unequal multipliers.

math.PR↗

arXiv2026

Cover times and ranges of elephant random walks

We study cover times on discrete tori and ranges on $\mathbb{Z}^d$ for elephant random walks with memory parameter $p\in[0,1)$. In dimension one there is a phase transition at $p=3/4$. Away from criticality we determine the exact first-order asymptotics of the mean cover time, while at $p=3/4$ the mean is of order $L^2/\sqrt{\log L}$, a factor $\sqrt{\log L}$ larger than the natural fluctuation scale $L^2/\log L$. We identify the limiting distribution under each of the three natural fluctuation normalizations. In dimensions $d\geq2$, for every fixed $p<1$, the cover time has the same order as for simple random walk, in expectation and with high probability. The leading constants also agree when $p<(2d+1)/(4d)$, and at equality when $d\geq3$. For the range on $\mathbb{Z}^d$, we prove $L^1$ convergence to the simple random walk asymptotics when $d=2$ and $p<5/8$, and for every $p<1$ when $d\geq3$. Finally, we give a cover-time upper bound for generalized step-reinforced random walks on finite groups in terms of a conditional $L^\infty$ mixing profile.

math.PR↗

arXiv2026

Mixing times of step-reinforced random walks

We study the mixing time of a non-Markovian process, the step-reinforced random walk (SRRW) on a finite group. This process differs from a classical random walk in that at each integer time, with probability $α$ the next step is chosen uniformly from the previous steps of the walk. We prove that the distribution of the SRRW converges to the uniform distribution exponentially fast if the walk is irreducible and aperiodic. When the step distribution is either symmetric, a class function, or has an atom at the identity, we relate the mixing time of the SRRW to the spectral gap and the mixing time of the underlying walk. For the reinforced (lazy) simple random walk on $L$-cycles, we show that the mixing time undergoes a phase transition at $α=1/2$ and the reinforcement reduces the mixing time to order $L^{1/α}$ for $α>1/2$. On the $d$-dimensional hypercube, the reinforcement slows down mixing, and the SRRW exhibits cutoff as $d\to\infty$ at time $d\log(d)/[F(α)(1-α)]$, with an $O(d)$ window for each fixed $α\in(0,1)$, where $F(\cdot)$ is a hypergeometric function.

math.PR↗

arXiv2026

Transition probabilities of step-reinforced random walks

The step-reinforced random walk (SRRW) either repeats a uniformly chosen past step or takes a fresh independent step. We consider a generalized SRRW on groups, where the selected past step is transformed by a random map. The transformations are independent of the fresh steps but may be dependent on one another. For every reinforcement parameter $α<1$, we obtain upper bounds on transition probabilities in terms of the geometry of the group. On $\mathbb{R}^d$, a non-singular step distribution yields bounds of order $n^{-d/2}$ for balls of any fixed radius, uniformly over their centers and without any moment assumption, and hence transience for $d\geq 3$. On finitely generated groups, we give bounds in terms of the isoperimetric profile. We also prove exponential decay for the elephant random walk on every nonamenable Cayley graph with a finite symmetric generating set and every memory parameter $p<1$. In particular, this answers a question of Mukherjee for Cayley trees.

math.PR↗

arXiv2025

How two elephants can learn from each other

We consider a two-elephant walking model in which the elephants interact dynamically. At each time step, each elephant determines its next move randomly based on its partner's past movements. We show that the asymptotic behavior of the elephants mainly depends on the sign and the absolute value of the product of their reinforcement parameters. In various regimes, we establish the law of large numbers and the central limit theorem. Our proofs are based on a connection to the random recursive trees and employ stochastic approximation techniques and martingale methods.

math.PR↗

arXiv2025

Step-reinforced random walks and one-half

Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions $d=1,2$, and that it is transient for all reinforcement parameters in dimensions $d\geq 3$, which solves a conjecture of Bertoin.

math.PR↗

arXiv2024

VividFace: A Diffusion-Based Hybrid Framework for High-Fidelity Video Face Swapping

Video face swapping is becoming increasingly popular across various applications, yet existing methods primarily focus on static images and struggle with video face swapping because of temporal consistency and complex scenarios. In this paper, we present the first diffusion-based framework specifically designed for video face swapping. Our approach introduces a novel image-video hybrid training framework that leverages both abundant static image data and temporal video sequences, addressing the inherent limitations of video-only training. The framework incorporates a specially designed diffusion model coupled with a VidFaceVAE that effectively processes both types of data to better maintain temporal coherence of the generated videos. To further disentangle identity and pose features, we construct the Attribute-Identity Disentanglement Triplet (AIDT) Dataset, where each triplet has three face images, with two images sharing the same pose and two sharing the same identity. Enhanced with a comprehensive occlusion augmentation, this dataset also improves robustness against occlusions. Additionally, we integrate 3D reconstruction techniques as input conditioning to our network for handling large pose variations. Extensive experiments demonstrate that our framework achieves superior performance in identity preservation, temporal consistency, and visual quality compared to existing methods, while requiring fewer inference steps. Our approach effectively mitigates key challenges in video face swapping, including temporal flickering, identity preservation, and robustness to occlusions and pose variations.

cs.CV↗

arXiv2024

Interacting urn models with strong reinforcement

For the interacting urn model with polynomial reinforcement, it has been conjectured that almost surely one color monopolizes all the urns if the interaction parameter $p>0$. We disprove the conjecture. For the case $p=1$, we give a sufficient condition for monopoly, which improves a previous result obtained by Launay.

math.PR↗

arXiv2023

Recurrence and transience of multidimensional elephant random walks

We prove a conjecture by Bertoin that the multi-dimensional elephant random walk on $\mathbb{Z}^d$($d\geq 3$) is transient and the expected number of zeros is finite. We also provide some estimates on the rate of escape. In dimensions $d= 1, 2$, we prove that phase transitions between recurrence and transience occur at $p=(2d+1)/(4d)$. Let $S$ be an elephant random walk with parameter $p$. For $p \leq 3/4$, we provide a Berry-Esseen type bound for properly normalized $S_n$. For $p>3/4$, the distribution of $\lim_{n\to \infty} S_n/n^{2p-1}$ will be studied.

math.PR↗

arXiv2023

Continuous-time vertex-reinforced random walks on complete-like graphs

We introduce the continuous-time vertex-reinforced random walk (cVRRW) as a continuous-time version of the vertex-reinforced random walk (VRRW), which might open a new perspective on the study of the VRRW. It has been proved by Limic and Volkov that for the VRRW on a complete-like graph $K_d \cup \partial K_d$, the asymptotic frequency of visits is uniform over the non-leaf vertices. We give short proofs of those results by establishing a stochastic approximation result for the cVRRW on complete-like graphs. We also prove that almost surely, the number of visits to each leaf up to time n divided by $n^{\frac{1}{d-1}}$ converges to a non-zero limit. We solve a conjecture by Limic and Volkov on the rate of convergence in the case of the complete graph.

math.PR↗

arXiv2022

INTERN: A New Learning Paradigm Towards General Vision

Enormous waves of technological innovations over the past several years, marked by the advances in AI technologies, are profoundly reshaping the industry and the society. However, down the road, a key challenge awaits us, that is, our capability of meeting rapidly-growing scenario-specific demands is severely limited by the cost of acquiring a commensurate amount of training data. This difficult situation is in essence due to limitations of the mainstream learning paradigm: we need to train a new model for each new scenario, based on a large quantity of well-annotated data and commonly from scratch. In tackling this fundamental problem, we move beyond and develop a new learning paradigm named INTERN. By learning with supervisory signals from multiple sources in multiple stages, the model being trained will develop strong generalizability. We evaluate our model on 26 well-known datasets that cover four categories of tasks in computer vision. In most cases, our models, adapted with only 10% of the training data in the target domain, outperform the counterparts trained with the full set of data, often by a significant margin. This is an important step towards a promising prospect where such a model with general vision capability can dramatically reduce our reliance on data, thus expediting the adoption of AI technologies. Furthermore, revolving around our new paradigm, we also introduce a new data system, a new architecture, and a new benchmark, which, together, form a general vision ecosystem to support its future development in an open and inclusive manner. See project website at https://opengvlab.shlab.org.cn .

cs.CV↗

arXiv2019

Beyond the Coverage of Information Spreading: Analytical and Empirical Evidence of Re-exposure in Large-scale Online Social Networks

Peer influence and social contagion are key denominators in the adoption and participation of information spreading, such as news propagation, word-of-mouth or viral marketing. In this study, we argue that it is biased to only focus on the scale and coverage of information spreading, and propose that the level of influence reinforcement, quantified by the re-exposure rate, i.e., the rate of individuals who are repeatedly exposed to the same information, should be considered together to measure the effectiveness of spreading. We show that local network structural characteristics significantly affects the probability of being exposed or re-exposed to the same information. After analyzing trending news on the super large-scale online network of Sina Weibo (China's Twitter) with 430 million connected users, we find a class of users with extremely low exposure rate, even they are following tens of thousands of others; and the re-exposure rate is substantially higher for news with more transmission waves and stronger secondary forwarding. While exposure and re-exposure rate typically grow together with the scale of spreading, we find exceptional cases where it is possible to achieve a high exposure rate while maintaining low re-exposure rate, or vice versa.

physics.soc-ph↗

arXiv2019

DuBox: No-Prior Box Objection Detection via Residual Dual Scale Detectors

Traditional neural objection detection methods use multi-scale features that allow multiple detectors to perform detecting tasks independently and in parallel. At the same time, with the handling of the prior box, the algorithm's ability to deal with scale invariance is enhanced. However, too many prior boxes and independent detectors will increase the computational redundancy of the detection algorithm. In this study, we introduce Dubox, a new one-stage approach that detects the objects without prior box. Working with multi-scale features, the designed dual scale residual unit makes dual scale detectors no longer run independently. The second scale detector learns the residual of the first. Dubox has enhanced the capacity of heuristic-guided that can further enable the first scale detector to maximize the detection of small targets and the second to detect objects that cannot be identified by the first one. Besides, for each scale detector, with the new classification-regression progressive strapped loss makes our process not based on prior boxes. Integrating these strategies, our detection algorithm has achieved excellent performance in terms of speed and accuracy. Extensive experiments on the VOC, COCO object detection benchmark have confirmed the effectiveness of this algorithm.

cs.CV↗