arXiv subjects

Zhenyuan Zhang

Publications and source records attributed to Zhenyuan Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2026

Viral Quasispecies Evolution as a Branching Random Walk on the Hypercube

We study a continuous-time nearest-neighbor branching random walk on the $d$-dimensional $b$-ary hypercube $\{0,1,\dots,b-1\}^d$ as a model for viral quasispecies evolution under mutation and replication. Motivated by mutagenic antiviral treatments and evolutionary-safety questions, we analyze the first passage time to a fixed target genotype at Hamming distance $m$, corresponding to the first appearance of a prescribed collection of mutations. We derive sharp asymptotics for these first passage times, uniformly for $m\le d/L$ as $d\to\infty$ (where $L>0$ is a large constant), and identify a phase transition in first-passage scaling at $ρ=e$, where $ρ$ denotes the effective growth parameter. In the slow-branching regime $ρ\in(1,e)$ relevant to mutagenic treatment scenarios, the first passage time is asymptotically affine in the genome length $d$ and the target distance $m$. In particular, when replication is fixed and mutation exceeds branching, increasing the mutation rate can delay the first appearance of a prescribed genotype by order $d$, providing a quantitative perspective on evolutionary safety.

math.PR↗

arXiv2026

Boundedness of discounted branching random walks via generic chaining

Consider a discrete-time supercritical discounted branching random walk, in which increments at depth $k$ are independent and identically distributed with the same law as $m^{-kH}Y$, where $Y$ has a fixed law, $H>0$, and $m>1$ is the expected number of offspring at depth one. We provide a clean characterization of the boundedness of the discounted branching random walk: under mild conditions on the offspring distribution, the process is almost surely bounded if and only if $\mathbb{E}[|Y|^{1/H}]<\infty$. This extends results of Athreya (1985) and Aïdékon--Hu--Shi (2024), and provides a partial answer to Open Problem 31 of Aldous--Bandyopadhyay (2005).

math.PR↗

arXiv2026

On the First Passage Times of Branching Random Walks in $\mathbb R^d$

We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage times to a ball of radius one with a distance $x$ from the origin, conditioned upon survival. We provide explicitly the linear dominating term and the logarithmic correction term as a function of $x$. The asymptotics are precise up to an order of $o_{\mathbb P}(\log x)$ for general jump distributions and up to $O_{\mathbb P}(\log\log x)$ for spherically symmetric jumps. A crucial ingredient of both results is the tightness of first passage times. We also discuss an extension of the first passage time analysis to a modified branching random walk model that has been proven to successfully capture shortest path statistics in polymer networks.

math.PR↗

arXiv2025

Motion-R1: Enhancing Motion Generation with Decomposed Chain-of-Thought and RL Binding

Text-to-Motion generation has become a fundamental task in human-machine interaction, enabling the synthesis of realistic human motions from natural language descriptions. Although recent advances in large language models and reinforcement learning have contributed to high-quality motion generation, two major challenges remain. Existing approaches often fail to capture the temporal and causal complexities inherent in natural language, leading to oversimplified or incoherent motions. Additionally, RL-based methods are frequently overly complex, hindering their scalability and adaptability across various motion generation tasks. To address these challenges, we propose Motion-R1, a novel framework that combines decomposed Chain-of-Thought reasoning with reinforcement learning to enhance both the quality and interpretability of generated motions. Specifically, we introduce the Decomposed CoT Data Engine, which leverages an automated pipeline to synthesize high-quality reasoning data, allowing the model to better capture the temporal dependencies and causal relationships of human motion. We also propose RL Binding, a reinforcement learning strategy that incorporates multi-modal text-motion alignment into the RL reward function, guiding the model to produce motions that are both semantically accurate and motionally realistic. Extensive experiments across benchmark datasets demonstrate that Motion-R1 achieves state-of-the-art performance, with a 3.5% improvement in MM-Dist on HumanML3D and improvements in R-Precision and FID on KIT-ML and BABEL, surpassing existing methods across key metrics and highlighting its superior capability in handling complex motion generation tasks. Project page: https://motion-r1.github.io/.

cs.CV↗

arXiv2025

Empirical martingale projections via the adapted Wasserstein distance

Given a collection of multidimensional pairs $\{(X_i,Y_i):1 \leq i\leq n\}$, we study the problem of projecting the associated suitably smoothed empirical measure onto the space of martingale couplings (i.e. distributions satisfying $\mathbb{E}[Y|X]=X$) using the adapted Wasserstein distance. We call the resulting distance the smoothed empirical martingale projection distance (SE-MPD), for which we obtain an explicit characterization. We also show that the space of martingale couplings remains invariant under the smoothing operation. We study the asymptotic limit of the SE-MPD, which converges at a parametric rate as the sample size increases if the pairs are either i.i.d. or satisfy appropriate mixing assumptions. Additional finite-sample results are also investigated. Using these results, we introduce a novel consistent martingale coupling hypothesis test, which we apply to test the existence of arbitrage opportunities in recently introduced neural network-based generative models for asset pricing calibration.

math.PR↗

arXiv2025

Large Deviations of First Passage Times of Branching Random Walks in $\mathbb{R}^d$: Asymptotics and Algorithms

We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in $\mathbb{R}^d$ where $d\geq 1$. The FPT refers to the first time the BRW enters a ball of radius one with a distance $x$ from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers.

math.PR↗

arXiv2025

IR3D-Bench: Evaluating Vision-Language Model Scene Understanding as Agentic Inverse Rendering

Vision-language models (VLMs) excel at descriptive tasks, but whether they truly understand scenes from visual observations remains uncertain. We introduce IR3D-Bench, a benchmark challenging VLMs to demonstrate understanding through active creation rather than passive recognition. Grounded in the analysis-by-synthesis paradigm, IR3D-Bench tasks Vision-Language Agents (VLAs) with actively using programming and rendering tools to recreate the underlying 3D structure of an input image, achieving agentic inverse rendering through tool use. This "understanding-by-creating" approach probes the tool-using generative capacity of VLAs, moving beyond the descriptive or conversational capacity measured by traditional scene understanding benchmarks. We provide a comprehensive suite of metrics to evaluate geometric accuracy, spatial relations, appearance attributes, and overall plausibility. Initial experiments on agentic inverse rendering powered by various state-of-the-art VLMs highlight current limitations, particularly in visual precision rather than basic tool usage. IR3D-Bench, including data and evaluation protocols, is released to facilitate systematic study and development of tool-using VLAs towards genuine scene understanding by creating.

cs.CV↗

arXiv2025

FedDTG:Federated Data-Free Knowledge Distillation via Three-Player Generative Adversarial Networks

While existing federated learning approaches primarily focus on aggregating local models to construct a global model, in realistic settings, some clients may be reluctant to share their private models due to the inclusion of privacy-sensitive information. Knowledge distillation, which can extract model knowledge without accessing model parameters, is well-suited for this federated scenario. However, most distillation methods in federated learning (federated distillation) require a proxy dataset, which is difficult to obtain in the real world. Therefore, in this paper, we introduce a distributed three-player Generative Adversarial Network (GAN) to implement data-free mutual distillation and propose an effective method called FedDTG. We confirmed that the fake samples generated by GAN can make federated distillation more efficient and robust. Additionally, the distillation process between clients can deliver good individual client performance while simultaneously acquiring global knowledge and protecting data privacy. Our extensive experiments on benchmark vision datasets demonstrate that our method outperforms other federated distillation algorithms in terms of generalization.

cs.LG↗

arXiv2025

Universality and Phase Transitions in Low Moments of Secular Coefficients of Critical Holomorphic Multiplicative Chaos

We investigate the low moments $\mathbb{E}[|A_N|^{2q}], 0 2q$. As a consequence, we establish the universality for the tightness of the normalized secular coefficients $A_N(\log(1+N))^{1/4}$, generalizing a result of Najnudel, Paquette, and Simm. Another corollary is the almost sure regularity of some critical non-Gaussian holomorphic chaos in appropriate Sobolev spaces. Moreover, we characterize the asymptotics of $\mathbb{E}[|A_N|^{2q}]$ for $|X_k|$ following a stretched exponential distribution with an arbitrary scale parameter, which exhibits a completely different behavior and underlying mechanism from the Gaussian universality regime. As a result, we unveil a double-layer phase transition around the critical case of exponential tails. Our proofs combine Harper's robust approach with a careful analysis of the (possibly random) leading terms in the monomial decomposition of $A_N$.

math.PR↗

arXiv2025

Composite Sorting

This paper introduces an assignment model with concave costs of skill gaps, which arise generally when firms mitigate costs of mismatch as in Stigler (1939) and Laffont and Tirole (1986, 1991). Concave costs of skill gaps imply that the output function is neither supermodular nor submodular. We thus introduce a tractable model that interpolates between the polar canonical cases of supermodularity and submodularity. We characterize sorting, wages, and comparative statics and show these substantively differ from traditional assignment models. Under composite sorting: (1) distinct worker types work in the same occupation, and (2) worker types are simultaneously part of both positive and negative sorting. Quantitatively, our model can generate and help explain earnings dispersion between and within occupations.

econ.GN↗

arXiv2025

AS-FIBA: Adaptive Selective Frequency-Injection for Backdoor Attack on Deep Face Restoration

Deep learning-based face restoration models, increasingly prevalent in smart devices, have become targets for sophisticated backdoor attacks. These attacks, through subtle trigger injection into input face images, can lead to unexpected restoration outcomes. Unlike conventional methods focused on classification tasks, our approach introduces a unique degradation objective tailored for attacking restoration models. Moreover, we propose the Adaptive Selective Frequency Injection Backdoor Attack (AS-FIBA) framework, employing a neural network for input-specific trigger generation in the frequency domain, seamlessly blending triggers with benign images. This results in imperceptible yet effective attacks, guiding restoration predictions towards subtly degraded outputs rather than conspicuous targets. Extensive experiments demonstrate the efficacy of the degradation objective on state-of-the-art face restoration models. Additionally, it is notable that AS-FIBA can insert effective backdoors that are more imperceptible than existing backdoor attack methods, including WaNet, ISSBA, and FIBA.

cs.CV↗

arXiv2025

Heavy fermions, mass renormalization and local moments in magic-angle twisted bilayer graphene via planar tunneling spectroscopy

Topological heavy fermion models[1-5] describe the flat bands in magic-angle twisted bilayer graphene (MATBG) as arising from the hybridization between localized flat-band orbitals (f-electrons) and nearly-free conduction bands (c-electrons). The interplay between these f-electrons and c-electrons is theorized to give rise to emergent phenomena, including unconventional superconductivity[6-8], non-Fermi liquid behavior[9-11], and topologically nontrivial phases[12-14]. However, the fundamental properties of f- and c-electrons, such as their respective heavy and light effective mass and their properties under strain, need experimental verification. Here we report on the electronic inverse compressibility, effective mass, and entropy of MATBG, obtained from planar tunneling spectroscopy. Our results include the observation of electron mass renormalization, found to be consistent with the topological heavy fermion model prediction of heavy charge-one excitations away from integer fillings. Importantly, we present entropic evidence for 4-fold and 8-fold degenerate isospin local moment states emerging at temperatures of 10K and 20K, respectively, consistent with the entropy of 8 heavy-fermions flavors energetically split by the sample strain.

cond-mat.mes-hall↗

arXiv2024

Simultaneous Optimal Transport

We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously, i.e., in single trips, from specified origins to destinations; similarly, in economic matching, one needs to couple two groups, e.g., buyers and sellers, by equating supplies and demands of different goods at the same time. The mathematical structure of simultaneous transport is very different from the classic setting of optimal transport, leading to many new challenges. The Monge and Kantorovich formulations are contrasted and connected. Existence conditions and duality formulas are established. More interestingly, by connecting SOT to a natural relaxation of martingale optimal transport (MOT), we introduce the MOT-SOT parity, which allows for explicit solutions of SOT in many interesting cases.

econ.TH↗

arXiv2024

On the existence of powerful p-values and e-values for composite hypotheses

Given a composite null $ \mathcal P$ and composite alternative $ \mathcal Q$, when and how can we construct a p-value whose distribution is exactly uniform under the null, and stochastically smaller than uniform under the alternative? Similarly, when and how can we construct an e-value whose expectation exactly equals one under the null, but its expected logarithm under the alternative is positive? We answer these basic questions, and other related ones, when $ \mathcal P$ and $ \mathcal Q$ are convex polytopes (in the space of probability measures). We prove that such constructions are possible if and only if $ \mathcal Q$ does not intersect the span of $ \mathcal P$. If the p-value is allowed to be stochastically larger than uniform under $P\in \mathcal P$, and the e-value can have expectation at most one under $P\in \mathcal P$, then it is achievable whenever $ \mathcal P$ and $ \mathcal Q$ are disjoint. More generally, even when $ \mathcal P$ and $ \mathcal Q$ are not polytopes, we characterize the existence of a bounded nontrivial e-variable whose expectation exactly equals one under any $P \in \mathcal P$. The proofs utilize recently developed techniques in simultaneous optimal transport. A key role is played by coarsening the filtration: sometimes, no such p-value or e-value exists in the richest data filtration, but it does exist in some reduced filtration, and our work provides the first general characterization of this phenomenon. We also provide an iterative construction that explicitly constructs such processes, and under certain conditions it finds the one that grows fastest under a specific alternative $Q$. We discuss implications for the construction of composite nonnegative (super)martingales, and end with some conjectures and open problems.

math.ST↗

arXiv2024

Benchmarking Ultra-High-Definition Image Reflection Removal

Deep learning based methods have achieved significant success in the task of single image reflection removal (SIRR). However, the majority of these methods are focused on High-Definition/Standard-Definition (HD/SD) images, while ignoring higher resolution images such as Ultra-High-Definition (UHD) images. With the increasing prevalence of UHD images captured by modern devices, in this paper, we aim to address the problem of UHD SIRR. Specifically, we first synthesize two large-scale UHD datasets, UHDRR4K and UHDRR8K. The UHDRR4K dataset consists of $2,999$ and $168$ quadruplets of images for training and testing respectively, and the UHDRR8K dataset contains $1,014$ and $105$ quadruplets. To the best of our knowledge, these two datasets are the first largest-scale UHD datasets for SIRR. Then, we conduct a comprehensive evaluation of six state-of-the-art SIRR methods using the proposed datasets. Based on the results, we provide detailed discussions regarding the strengths and limitations of these methods when applied to UHD images. Finally, we present a transformer-based architecture named RRFormer for reflection removal. RRFormer comprises three modules, namely the Prepossessing Embedding Module, Self-attention Feature Extraction Module, and Multi-scale Spatial Feature Extraction Module. These modules extract hypercolumn features, global and partial attention features, and multi-scale spatial features, respectively. To ensure effective training, we utilize three terms in our loss function: pixel loss, feature loss, and adversarial loss. We demonstrate through experimental results that RRFormer achieves state-of-the-art performance on both the non-UHD dataset and our proposed UHDRR datasets. The code and datasets are publicly available at https://github.com/Liar-zzy/Benchmarking-Ultra-High-Definition-Single-Image-Reflection-Removal.

cs.CV↗

arXiv2024

Sample Path Properties of the Fractional Wiener--Weierstrass Bridge

Fractional Wiener--Weierstrass bridges are a class of Gaussian processes that arise from replacing the trigonometric function in the construction of classical Weierstrass functions by a fractional Brownian bridge. We investigate the sample path properties of such processes, including local and uniform moduli of continuity, $Φ$-variation, Hausdorff dimension, and location of the maximum. Our analysis relies heavily on upper and lower bounds of fractional integrals, where we establish a novel improvement of the classical Hardy--Littlewood inequality for fractional integrals of a special class of step functions.

math.PR↗

arXiv2024

Adversarial Purification and Fine-tuning for Robust UDC Image Restoration

This study delves into the enhancement of Under-Display Camera (UDC) image restoration models, focusing on their robustness against adversarial attacks. Despite its innovative approach to seamless display integration, UDC technology faces unique image degradation challenges exacerbated by the susceptibility to adversarial perturbations. Our research initially conducts an in-depth robustness evaluation of deep-learning-based UDC image restoration models by employing several white-box and black-box attacking methods. This evaluation is pivotal in understanding the vulnerabilities of current UDC image restoration techniques. Following the assessment, we introduce a defense framework integrating adversarial purification with subsequent fine-tuning processes. First, our approach employs diffusion-based adversarial purification, effectively neutralizing adversarial perturbations. Then, we apply the fine-tuning methodologies to refine the image restoration models further, ensuring that the quality and fidelity of the restored images are maintained. The effectiveness of our proposed approach is validated through extensive experiments, showing marked improvements in resilience against typical adversarial attacks.

eess.IV↗

arXiv2024

Martingale Transports and Monge Maps

It is well known that martingale transport plans between marginals $μ\neqν$ are never given by Monge maps -- with the understanding that the map is over the first marginal $μ$, or forward in time. Here, we change the perspective, with surprising results. We show that any distributions $μ,ν$ in convex order with $ν$ atomless admit a martingale coupling given by a Monge map over the second marginal $ν$. Namely, we construct a particular coupling called the barcode transport. Much more generally, we prove that such ``backward Monge'' martingale transports are dense in the set of all martingale couplings, paralleling the classical denseness result for Monge transports in the Kantorovich formulation of optimal transport. Various properties and applications are presented, including a refined version of Strassen's theorem and a mimicking theorem where the marginals of a given martingale are reproduced by a ``backward deterministic'' martingale, a remarkable type of process whose current state encodes its whole history.

math.PR↗