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Zhe Zhang

Publications and source records attributed to Zhe Zhang.

At least 19 recordsLinked to original sources
arXiv2026

A Product on Lorenz Hulls, Zonoids, and Vector Measure Ranges

A Lorenz skeleton and Lorenz hull are the range and the convex hull of the range of an $\mathbb{R}^n$-valued measure, respectively. A Lorenz hull is also known as a zonoid. We extend the tensor product of centered zonoids introduced by Aubrun and Lancien and developed by Breiding et al. to Lorenz hulls without a centering restriction, and further to Lorenz skeletons. We show that this product admits a direct interpretation in terms of the elementary notion of a product measure. Inclusion preservation and Hausdorff continuity, shown by Aubrun and Lancien and Breiding et al., respectively, for centered zonoids, hold in this more general setting as well.

math.DS↗
arXiv2026

Two-colour crossing minimization in complete geometric graphs is NP-hard

Given a fixed straight-line drawing of a complete graph, we seek a two-colouring of its edges that minimizes monochromatic crossing pairs. We prove that the threshold decision problem is NP-complete, even for points in general position with integer coordinates. Thus exact minimization is NP-hard, resolving the complexity question posed at the Crossing Number Workshop in 2019. We reduce from MaxCut on permutation graphs by representing source vertices with classes of geometric edges, whose crossings encode source adjacencies. The complete target also contains every other edge between its points, and their freely chosen colours can affect the encoded cost. To control these interactions, we construct a large comparison grid with two stable colour phases and use program points to turn this reference into colour preferences on other edges. The optimum differs from a computable baseline plus the amplified minimum number of uncut source edges by an error small enough to distinguish consecutive source values. The reduction is deterministic, with polynomially many points and polynomial coordinate bit length.

cs.CC↗
arXiv2026

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients?

Training instabilities such as loss spikes are frequently the result of stochastic gradient noise. Because of rare expressions in language training data, and multiple layer composition, the noise impact is heavy-tailed and survives mini-batch averaging. Existing remedies trade off structure against cost: vector-norm clipping ignores the matrix structure of weight updates, while spectral normalization (e.g., Muon (Jordan et al., 2024)) respects it at additional cost. We show that this trade-off can be balanced. Real gradient noise appears to be similar to entry-wise heavy-tailed contamination, and a first-order perturbation analysis reveals a localization property of such noise, under which a simple entry-wise method achieves spectral control. Exploiting this, we derive a tractable surrogate for the Bayes-optimal entry-wise estimator under a Gaussian signal prior. We establish $O(\varepsilon^{-4})$ convergence guarantee under Cauchy-contaminated noise. Empirically, we find that smooth shrinkage improves Adam on NanoGPT pretraining, saving ${\sim}7\%$ of training tokens. We further find that applying the entry-wise clipping before spectral normalization yields a ${\sim}2\%$ token saving on top of Muon.

cs.LG↗
arXiv2026

Adaptive Dual-Teacher Distillation with Subnetwork Rectification for Bridging Semantic Gaps in Black-Box Domain Adaptation

Assuming that neither source data nor source model parameters are accessible, black-box domain adaptation (BBDA) represents a highly practical yet challenging setting, where transferable knowledge is limited to the predictions of a black-box source model. Existing approaches exploit such knowledge via pseudo-label refinement or by leveraging vision-language models (ViLs), but they often fail to reconcile the inherent discrepancy between task-specific knowledge from black-box models and language-aligned semantic priors of ViLs, resulting in suboptimal integration and degraded adaptation performance. To address this challenge, we propose adaptive Dual-Teacher Distillation with Subnetwork Rectification (DDSR), a framework that explicitly reconciles these complementary yet inconsistent knowledge sources. DDSR employs an adaptive prediction fusion strategy to integrate predictions from the black-box source model and a ViL, generating reliable pseudo-labels for the target domain. A subnetwork-based regularization mechanism mitigates overfitting to noisy supervision by enforcing output consistency and gradient divergency. Furthermore, progressively improved target predictions iteratively refine both pseudo-labels and ViL prompts, enhancing semantic alignment. Finally, class-wise prototypes are used to further optimize target predictions via self-training. Extensive experiments on multiple benchmark datasets demonstrate that DDSR consistently outperforms state-of-the-art methods, including those with access to source data or source model parameters.

cs.CV↗
arXiv2026

A counterexample to the local existence of conformal normal metrics

For every dimension $n\ge3$, we construct a smooth Riemannian metric whose entire Taylor series at a point agrees with the Euclidean metric and whose conformal class contains no smooth conformal normal metric near that point. For the metric used in the construction, parametrized by a smooth angular function, we prove that conformal normalization forces a dimension-dependent exponential decay rate for the spherical harmonic components of that function. This gives counterexamples whenever the angular coefficients decay too slowly. In particular, every nonanalytic angular function yields a counterexample. The proof combines a weighted cylinder estimate with an integral identity relating the angular spectral coefficients of the background volume defect to the nonlinear remainder. We also give a direct counterexample to the linear right inverse used in Cao's smooth existence argument and identify the failure of angular summability in that construction.

math.DG↗
arXiv2026

Linearly Convergent Algorithms for Nonsmooth Problems with Unknown Smooth Regions

We develop efficient algorithms for optimizing piecewise smooth (PWS) functions when their smooth regions are \emph{unknown} to the algorithm. For convex PWS functions satisfying a quadratic growth (QG) condition, we demonstrate that the bundle-level (BL)-type method~\cite{lemarechal1995new} achieves global linear convergence---to our knowledge, the first such result for any algorithm for this problem class. We extend the method to solve weakly convex PWS problems, achieving the same order of complexity as in smooth non-convex optimization. Furthermore, we introduce a verifiable and accurate termination criterion for PWS optimization. Like the gradient norm in smooth optimization, this certificate tightly characterizes the optimality gap under the QG condition and can be evaluated without knowledge of any problem parameters. We develop a search subroutine for this certificate and embed it within a guess-and-check framework, resulting in almost parameter-free algorithms for both convex QG and weakly convex PWS problems.

math.OC↗
arXiv2026

Extended-range percolation on lattices with cubic and non-compact neighborhoods in three dimensions

Using MC simulations based on an efficient single-cluster growth algorithm, we investigate two types of three-dimensional extended-range percolation models, namely cubic and complex (non-compact) neighborhoods. We obtain high-precision percolation thresholds $p_c$ for approximately 100 distinct structures and further explore the relationship between these thresholds and the topology of the lattices, which includes the total coordination number $z$, the number of sites $z_i$ and these sites' distance to the central site $r_i$ of the given neighborhood in the $i$th coordination zone. Both bond and site percolation are analyzed for cubic neighborhoods on the SC lattice. For bond percolation, the asymptotic value of $zp_c$ tends to Bethe-lattice behavior ($zp_c\sim1$), and finite-$z$ correction is found to be consistent with $zp_{c}-1\sim a_{1}z^{-x}$, where $x=(d-1)/d$. For site percolation, the value of $zp_c$ varies non-monotonically, exhibiting an initial increase followed by a decrease with the coordination number $z$. Linear fitting leads to $zp_c\sim2.5987(1)$ for large $z$, predicting a value of continuum percolation threshold of aligned cubes $η_c=0.324838(12)$ using $zp_c=2^{d}η_c$. We then examine site percolation for non-compact neighborhoods extending to the fifth coordination zone on SC, FCC, and BCC lattices. Through a comparison of the three indices of $z$, $ξ=\sum_iz_ir_i^2/i$, and $ζ=\sum_iz_ir_i$, we find that $ζ$ is effective in removing the degeneracy. The results obtained show power-law dependence $p_c\propto(ζ/K)^{-γ}$ with $γ_{\mathrm{SC}}^ζ=0.703(12)$, $γ_{\mathrm{FCC}}^ζ=0.728(10)$, and $γ_{\mathrm{BCC}}^ζ=0.699(12)$ for SC, FCC, and BCC lattices, and $p_c\proptoζ^{-γ}$ with $γ^ζ=0.719(9)$ independent of the underlying lattice. The number $K$ indicates lattice connectivity.

cond-mat.stat-mech↗
arXiv2026

An LLM-powered Agentic Recommendation System for Connected TV Content Discovery

Recommendation systems, from traditional multi-stage to recent unified generative architectures, face challenges in incorporating diverse contextual signals, such as trending topics, breaking news, cultural events, and cross-surface user activities, into their ranking pipelines. These systems are designed to consume structured behavioral signals with consistent schemas, and lack the reasoning capability to naturally process unstructured or heterogeneously formatted contextual information. Incorporating such signals typically requires feature engineering, bespoke data pipelines, and carefully tuned heuristics. In this paper, we present an LLM-powered agentic recommendation system designed for Connected TV (CTV) content discovery that addresses these limitations. Our system leverages the reasoning capabilities of large language models to naturally process and synthesize diverse signals across varying schemas and structures, eliminating much of the manual integration inherent in traditional ranking and retrieval systems. Recognizing that current LLM-based solutions still fall short of traditional machine learning models in several recommendation tasks, including retrieval efficiency, personalization precision, and scalability, we adopt an agentic architecture that orchestrates specialized components, allowing each sub-task to be handled by the most suitable method, whether LLM-based or traditional ML. The main contribution of this work is our engineering approach to successfully overcoming the practical limitations of enabling LLM for recommendation, particularly inference latency. We share insights from our work and discuss the trade-offs and lessons learned in building a hybrid system that combines the flexibility of LLMs with the performance of established recommendation techniques.

cs.IR↗
arXiv2026

DIA: A Deep Reinforcement Learning-Based Interest-Aware ABR Scheme for Cloud Gaming

The continuous evolution of cloud gaming has enabled users to play high-quality cloud games on thin clients, such as smartphones and tablets. However, how to effectively transmit the gameplay frames with high resolution and low latency, especially over wireless networks, remains a significant challenge. To address this challenge, we propose a Deep Reinforcement Learning (DRL)-based Interest-Aware Adaptive Bitrate (ABR) scheme, called DIA, that guarantees the quality of perceptually key objects in each frame, while dynamically allocating lower resolutions for non-key objects to conserve bandwidth under constrained network conditions. By leveraging an off-the-shelf semantic segmentation model, the proposed DIA scheme can adjust the bitrate at the object-level. We also design a transformer-based feature extractor and an interest-aware reward function to enable the proposed DIA scheme to identify key objects and dynamically adjust their bitrates. This adaptation is guided by users' in-game movement speed, object features, and prevailing network conditions and operates without requiring additional hardware, such as gaze trackers. Extensive experiments show that the proposed DIA scheme outperforms existing ABR schemes in dynamic wireless network environments. Notably, DIA achieves at least a 20% higher normalized average Quality of Experience (QoE) than the State-Of-The-Art (SOTA) ABR algorithms in 5G scenarios.

cs.MM↗
arXiv2026

Generative-AI for XR Content Transmission in the Metaverse: Potential Approaches, Challenges, and a Generation-Driven Transmission Framework

How to efficiently transmit large volumes of Extended Reality (XR) content through current networks has been a major bottleneck in realizing the Metaverse. The recently emerging Generative Artificial Intelligence (GAI) has already revolutionized various technological fields and provides promising solutions to this challenge. In this article, we first demonstrate current networks' bottlenecks for supporting XR content transmission in the Metaverse. Then, we explore the potential approaches and challenges of utilizing GAI to overcome these bottlenecks. To address these challenges, we propose a GAI-based XR content transmission framework which leverages a cloud-edge collaboration architecture. The cloud servers are responsible for storing and rendering the original XR content, while edge servers utilize GAI models to generate essential parts of XR content (e.g., subsequent frames, selected objects, etc.) when network resources are insufficient to transmit them. A Deep Reinforcement Learning (DRL)-based decision module is proposed to solve the decision-making problems. Our case study demonstrates that the proposed GAI-based transmission framework achieves a 2.8-fold increase in normal frame ratio (percentage of frames that meet the quality and latency requirements for XR content transmission) over baseline approaches, underscoring the potential of GAI models to facilitate XR content transmission in the Metaverse.

cs.NI↗
arXiv2026

Conductivity-driven chirality in geometrically achiral plasmonic nanostructures and metasurfaces

Resonant nanostructures are powerful for chiral control of light, but widely assumed to require achiral geometry. Here we demonstrate that optical chirality can emerge in geometrically achiral nanostructures, through the misalignment of independent linear responses. By rotating the conductivity tensor of an anisotropic plasmonic medium relative to a geometrically symmetric nanostructure, we generate a spin-selective optical response that can be continuously tuned both in magnitude and handedness, including reversible switching between left- and right-handed behaviour. We experimentally realize this concept using an aligned plasmonic conducting polymer and by controlling the orientation of its polymer backbone relative to otherwise identical rectangular nanoantennas. This leads to strong planar chirality that can also be reversibly modulated by varying the carrier density of the polymer. Moreover, the rotation angle of rectangular meta-atoms made through this principle encodes no longer only the local geometric phase but simultaneously the local optical chirality. This enables a new design paradigm for phase-gradient metasurfaces , enabling simultaneous control of optical chirality and wavefronts through a single rotational degree of freedom.

physics.optics↗
arXiv2026

Traverse: Learning When to Remember, Reset, and Redirect for Long-Horizon Web Search

Long-horizon information-seeking agents often accumulate noisy or misleading context, causing early mistakes to persist and making recovery increasingly difficult. We introduce an autonomous search harness in which the agent manages its own search process through three states: Rubric, Answer, and Verify. The agent first defines criteria for a valid answer, searches under these criteria, and then independently verifies the result before deciding whether to terminate or continue searching. It is further equipped with a Seal Memory tool that enables active context management. Training this behavior with reinforcement learning, however, can induce Seal Collapse, resulting in unstable training and preventing the agent from reliably learning when and how to use its memory tools. We solve this with a simple strategy that trains only the final segment after context management. Our 35B model achieves 72.83 on BrowseComp, outperforming comparable open-source systems, and consistently improves over the base model across BrowseComp-ZH, xbench, DeepSearchQA, WideSearch, financial investigation, and product search. Ablations show that autonomous compression outperforms automatic compaction and validate our RL design.

cs.CL↗
arXiv2026

Flow-Matching-Based Protein Structure Tokenizer Made Efficient and Easy

As the bridge between protein modality and discrete modeling, protein structure tokenization still largely relies on heavily engineered training objectives tailored to specific downstream tasks and large training datasets, which hinders its transfer to broader application scenarios. To address this issue, we propose ProFiT, a lightweight flow matching tokenizer. With simple training strategies that encourage healthy codebook utilization, ProFiT can be trained efficiently and naturally learns semantically meaningful representations without any manual semantic alignment, while achieving reconstruction quality and generalization that match or surpass those of substantially larger tokenizers. We conduct extensive evaluations across a wide range of settings and demonstrate that ProFiT is a plug-and-play tokenizer adaptable to diverse downstream tasks. This study further reveals the significant potential of the flow matching tokenizer paradigm. Our code is publicly available at https://github.com/QDKStorm/ProFiT.

cs.LG↗
arXiv2026

DCFold: Efficient Protein Structure Generation with Single Forward Pass

AlphaFold3 introduces a diffusion-based architecture that elevates protein structure prediction to all-atom resolution with improved accuracy. This state-of-the-art performance has established AlphaFold3 as a foundation model for diverse generation and design tasks. However, its iterative design substantially increases inference time, limiting practical deployment in downstream settings such as virtual screening and protein design. We propose DCFold, a single-step generative model that attains AlphaFold3-level accuracy. Our Dual Consistency training framework, which incorporates a novel Temporal Geodesic Matching (TGM) scheduler, enables DCFold to achieve a 15x acceleration in inference while maintaining predictive fidelity. We validate its effectiveness across both structure prediction and binder design benchmarks.

cs.LG↗
arXiv2026

Harmonic Map Heat Flow Coupled to a Green-Potential

We introduce a Green--potential heat flow for maps from a closed Riemannian surface. Inspired by Parker--Wolfson renormalization~\cite{ParkerWolfson1993,Parker1996}, the conformal factor is reconstructed at each time from an energy-based source determined by the current map. The resulting parabolic--elliptic system incorporates renormalization into the evolution while leaving the Dirichlet energy functional and its harmonic critical points unchanged. We establish local well-posedness for $H^3$ initial data and a continuation criterion in terms of energy concentration. For sufficiently large coupling, we exclude finite-time bubbling and obtain global solutions. At infinite time, the energy identity provides only weighted $L^2$ control of the tension field. Localizing to regular regions of concentration charts yields harmonic profiles along subsequences of prescribed times. We represent these profiles in the flow's packet charts, organize them into a finite bubble tree, and decompose the limiting energy into harmonic component energies and neck energies. A critically normalized radial example illustrates how the modified flow can prevent finite-time blow-up and produce harmonic bubbles with no-neck property.

math.AP↗
arXiv2026

A Training-Free Proactive Defense Against Partial Speech Manipulation via Self-Embedding Steganography

Partial deepfake speech, where only limited segments of an utterance are synthesized or manipulated, poses a significant challenge to existing deepfake detection systems. As the proportion of spoofed regions decreases, passive detectors become increasingly unreliable, and accurate detection and restoration remain challenging. In this paper, we revisit audio steganography from a new perspective and propose its use as a proactive defense against partially deepfaked audio. In particular, we consider a self-embedding strategy in which a clean speech signal embeds a compressed representation of itself, enabling post-hoc extraction of reference content. We demonstrate how existing audio steganography methods can be repurposed to support detection of partial deepfakes through codec-based restoration. Experiments on a benchmark dataset show that the proposed approach complements passive defenses. Remarkably, the proposed method operates without any training, providing a robust and data-efficient alternative for partial deepfake detection.

cs.SD↗
arXiv2026

VoxTubeS: Distributable Speaker-Anonymized Synthetic Speech Corpora and Their Analysis

Large speech corpora support research, but recordings can expose speaker identity because voice remains a recognizable biometric. Meanwhile, speech data derived from media can be difficult to redistribute reliably. We present \emph{VoxTubeS}, a family of speaker-anonymized synthetic speech corpora designed for redistribution, comprising three method families and seven variants derived from the VoxTube corpus, which is distributed under CC BY-NC-SA 4.0, using 1.29M quality-filtered English utterances from 1,511 speakers. The synthesis methods span voice conversion, latent-space anonymization, and controllable text-to-speech. We evaluate VoxTubeS using utterance-level unlinkability, conversation-level linkability and singling-out, downstream speaker verification, linguistic consistency, speaker diversity, and fairness metrics for gender and accents. Our comprehensive analysis exposes a complex trade-off: stronger identity suppression often reduces linkability but sacrifices utility and population diversity, whereas speaker consistency training improves both utterance- and conversation-level privacy while retaining comparable utility and a broader speaker space. Fairness varies independently of aggregate performance. No method dominates; VoxTubeS therefore treats corpus construction as a choice among operating points that balances privacy, utility, diversity, fairness, and responsible redistribution under the source license.

eess.AS↗
arXiv2026

Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth

We study why the proximal bundle method (PBM) can perform better in practice when it retains more cutting planes. We consider convex objectives with quadratic growth and an unknown piecewise-smooth structure. Our key observation is that retaining sufficiently many cutting planes allows PBM to exploit the objective's piecewise-smooth structure and behave as if it were optimizing a smooth function. We provide a theoretical explanation for the observed linear convergence of PBM on piecewise-smooth objectives when it retains sufficiently many cutting planes.

math.OC↗