arXiv subjects

Zhiwei Zheng

Publications and source records attributed to Zhiwei Zheng.

At least 19 recordsLinked to original sources

arXiv2026

Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds

We study the full automorphism groups of smooth cubic fourfolds with prescribed symplectic automorphism group. Our starting point is the classification of symplectic automorphism groups by Laza and Zheng. We focus on the non-symplectic index, namely, the index of the symplectic automorphism group in the full automorphism group. We prove general restrictions on this index. We also compute bounds by group-theoretic and lattice-theoretic methods. In several cases, we determine all possible indices. For coinvariant lattices of rank 19, we classify all possible pairs consisting of the symplectic automorphism group and the full automorphism group.

math.AG↗

arXiv2026

Classification of Automorphism Groups of Smooth Cubic Threefolds and Fourfolds

We classify the automorphism groups of smooth cubic threefolds and fourfolds. We also show that there are $156$ (respectively, $40$) connected families of smooth cubic fourfolds (respectively, threefolds) with specified automorphism group action. For each family, the group action and defining equations are also given. The classification combines both representation theory (based on GAP) and lattice theory (based on SageMath).

math.AG↗

arXiv2026

Small-Subgroup Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces

In this paper, building on our previous Sylow criteria, we establish small-subgroup criteria of liftability and $F$-liftability for the linear automorphism group $G$ of smooth hypersurfaces $X$ over algebraically closed field of characteristic zero. When $\mathrm{dim} X = p-2$ for some odd prime $p$, we prove that ($F$-)liftability of any finite subgroup of $G$ can be tested on its $p$-subgroups of order at most $p^2$. When $X$ is a degree $p$ hypersurface of dimension $2p-2$, we prove that ($F$-)liftability of $G$ can be tested on all its $p$-subgroups of order at most $p^3$, which is sharp for $p\geq5$. When $p=3$, this bound improves to $9$, giving the corresponding criteria for smooth cubic fourfolds.

math.AG↗

arXiv2026

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements

It is an important problem to know whether the monodromy on the cohomology of Milnor fibers associated to hyperplane arrangements is a combinatorial invariant. In this paper, we obtain a combinatorial vanishing criterion for certain eigenspaces of this algebraic monodromy in line arrangements. Combining with Hirzebruch inequality, which is a consequence of Bogomolov--Miyaoka--Yau inequality, we prove that for essential complex line arrangements, the eigenvalues of the monodromy have orders at most five. This is a partial progress toward Papadima--Suciu conjecture and proves Salvetti--Serventi connectivity conjecture. For essential complexified real line arrangements, the monodromy order is improved to at most four thanks to Shnurnikov's inequality. This confirms Papadima--Suciu conjecture for real line arrangements and also Yoshinaga's sharp pair conjecture.

math.AG↗

arXiv2026

Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory

Laza and the second author have classified all possible symplectic automorphism groups of smooth cubic fourfolds. There are $34$ such groups, and by Koike, there are $48$ families of cubic fourfolds with speficied symplectic automorphism group. For $42$ among those families, we complete the classification of all possible automorphism groups. The approach of this paper is mainly lattice theoretic, starting from known results about the period map of cubic fourfolds by Voisin, Hassett, Looijenga and Laza. We use a lattice-enumeration algorithm implemented in OSCAR.

math.AG↗

arXiv2026

Optimal convergence rates of the Klein-Gordon-Schrödinger system in the nonrelativistic limit

In this paper, we study the Klein-Gordon-Schrödinger system in the nonrelativistic regime $ε\to 0$, where $ε$ is proportional to the inverse of the speed of light. We show that the Klein-Gordon-Schrödinger system converges to a system of decoupled linear Schrödinger equations over a long time interval of order $ε^{-1}$ with error estimates of the form $(1+t)ε^2$; in particular, the error estimate for the Schrödinger component is uniform in time of the form $ε^{2}$ The specific forms of the error estimates coincide with the numerical results shown by Bao et a.l., and the $O(ε^{2})$ convergence rates coincide with the order of initial error, and thus are optimal.

math.AP↗

arXiv2026

Vision-TL-Action: Neuro-Symbolic Trajectory Generation from Visual Observations and Temporal Logic

Temporal logic (TL) provides a compositional language for the formulation of long horizon robotic tasks, but existing TL-conditioned trajectory generators can sidestep perception-to-symbol binding by encoding exact object geometry in the task graph. We introduce \emph{Vision-TL-Action}, which generates action trajectories from multi-view images, a coordinate-free TL syntax graph, and the robot initial state. TL-node tokens and spatial visual tokens are fused through bidirectional cross-attention, and the resulting representation conditions a flow-matching trajectory generator. Visual tokens are augmented only with normalized image-plane locations and camera-view identifiers, while a training-only predicate-to-region objective encourages grounding to referenced objects. Consistent with prior work in this domain, we evaluate the model using Success@$K$, the fraction of tasks for which at least one of K sampled trajectories satisfies the TL specification. On Panda task, our model achieves 67.45% Success@1024, compared with 59.11% for the oracle-state baseline. On AntMaze task, it achieves 96.35% Success@256, comparable to the oracle result of 96.88%. Resolution and intervention studies show that spatial detail depends on semantic grounding and predicate identity affects both attention and performance. These results demonstrate a direct mapping from visual observations and structured TL goals to action trajectories without requiring object geometry at inference. Code is available at https://github.com/AricLau07/vision-tl-action.

cs.RO↗

arXiv2026

Sylow Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces

In this paper, we first establish Sylow criteria for liftability of finite subgroups of the projective linear groups over arbitrary field. We also obtain Sylow criteria for $F$-liftability: if $F$ is a nonsingular polynomial of degree $d$ in $N$ variables over a field of characteristic zero, then a finite subgroup $G$ of $\mathrm{Lin}(F)$ is $F$-liftable if and only if for every prime $p$ dividing $\gcd(|G|,N,d)$, there exists a Sylow $p$-subgroup of $G$ that is $F$-liftable. Our proof combines restriction and corestriction in group cohomology with the reduction-to-Klein method.

math.AG↗

arXiv2026

Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces

In this paper we mainly study Calabi--Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those families of Calabi--Yau varieties, the period maps factor through arithmetic quotients of complex hyperbolic balls. We give a classification of such examples. One of the families was previously studied by Voisin, Borcea and Rohde. For these ball-type cases, we will show arithmeticity of the monodromy groups. These ball quotients are all commensurable to ball quotients in Deligne--Mostow theory. As a byproduct, we prove some commensurability relations among arithmetic groups in Deligne--Mostow theory.

math.AG↗

arXiv2026

PACT: Privileged Trace Co-Training for Multi-Turn Tool-Use Agents

Multi-turn tool-use agents must reason, call tools, and adapt to observations across several interaction turns. Post-training such agents is challenging, as reinforcement learning often suffers from sparse rewards and weak credit assignment despite matching the prompt-only inference setting, while supervised fine-tuning on expert traces provides dense process supervision but can over-constrain the model to fixed trajectories. To tackle this, we propose PACT, a Privileged trAce Co-Training framework for multi-turn tool-use agents. The key idea is to use expert traces only as training-time optimization signals rather than rollout-time hints. PACT keeps rollout generation prompt-only, then uses expert traces to guide optimization through two complementary signals: a trace-conditioned RL surrogate that evaluates prompt-only rollouts under expert-trace context, and a component-aware SFT loss that supervises reasoning prefixes and tool-calls with annealed strength. To reduce over-reliance on the training-only trace context, PACT further introduces a prompt-only anchoring. We also provide a latent-trace view that connects the two trace-based objectives and explains how expert traces can guide optimization without being used during rollout generation. Experiments on FTRL, BFCL, and ToolHop show that PACT consistently improves over strong SFT- and RL-based baselines, highlighting the value of privileged trace co-training for multi-turn tool-use learning.

cs.CL↗

arXiv2026

Omnidirectional photonic chiral flatband in nonlocal membrane metasurfaces

Omnidirectional flat-band resonances, characterized by an enhanced photonic density of states and inherent angular robustness, are highly sought-after in integrated nanophotonic devices, particularly when integrated with chiral functionality. Here we realize such resonances in a nonlocal silicon membrane metasurface patterned with periodic square-lattice air-hole arrays. Increasing the lattice period not only compresses the Brillouin zone but, crucially, weakens the evanescent coupling between neighbouring Bloch modes associated with the same-order guided resonances. Driven by the tight-binding model in the limit of weak inter-unit-cell coupling, the pronounced band flattening of the degenerate guided resonance along both $k_{x}$ and $k_{y}$ yields, giving rise to an omnidirectional flat-band resonance. Remarkably, both numerical simulations and experiments reveal a universal route for endowing flat-band guided resonances with optical chirality through the deliberate breaking of the mirror symmetry of air holes. As a result, the omnidirectional chiral flat-band resonance emerges along both principal in-plane directions, with $Q$-factors exceeding 10$^{3}$ and circular dichroism greater than 0.9 over a wide angular range of $\pm 5^{\circ}$. Nonlinear measurements further show that the resulting resonance not only drives highly efficient third-harmonic generation but also imparts a pronounced spin-selective character to the nonlinear process. Simultaneously, the highly efficient nonlinear process also enables chirality-controlled frequency-upconversion imaging. Our results establish a general paradigm for engineering omnidirectional chiral flat-band resonances in planar silicon platforms, opening new opportunities for nonlinear nanophotonics and chiral imaging.

physics.optics↗

arXiv2026

Scalable RF Simulation in Generative 4D Worlds

Radio Frequency (RF) sensing has emerged as a powerful, privacy-preserving alternative to vision-based methods for various perception tasks. However, building high-quality RF datasets in dynamic and diverse environments remains a major challenge. To address this, we introduce WaveVerse, a prompt-based, scalable framework that simulates realistic RF signals from generated indoor scenes with human motions guided by spatial paths, enabling diverse and feasible behaviors without manual trajectory design. WaveVerse features a language-guided 4D world generator and a physics-based signal simulator that enables realistic simulation of RF signals in diverse environments. It employs a phase-coherent ray tracer that preserves both spatial and temporal phase consistency. The simulated signals show high fidelity on phase-sensitive benchmarks, and closely align with both real-world collected measurements and simulations from a proprietary electromagnetic solver. When used for data augmentation, WaveVerse consistently improves performance in downstream tasks like RF imaging and human activity recognition, with gains that grow with the amount of simulated data and surpass existing methods. Code and additional materials are available on the webpage.

cs.CV↗

arXiv2026

Next-Scale Autoregressive Models for Text-to-Motion Generation

Autoregressive (AR) models offer stable and efficient training, but standard next-token prediction is not well aligned with the temporal structure required for text-conditioned motion generation. We introduce MoScale, a next-scale AR framework that generates motion hierarchically from coarse to fine temporal resolutions. By providing global semantics at the coarsest scale and refining them progressively, MoScale establishes a causal hierarchy better suited for long-range motion structure. To improve robustness under limited text-motion data, we further incorporate cross-scale hierarchical refinement for improving per-scale initial predictions and in-scale temporal refinement for selective bidirectional re-prediction. MoScale achieves SOTA text-to-motion performance with high training efficiency, scales effectively with model size, and generalizes zero-shot to diverse motion generation and editing tasks.

cs.CV↗

arXiv2026

Degenerations to secant cubic hypersurfaces and limiting Hodge structure

The secant variety of the Veronese surface is a singular cubic fourfold. Degenerations to this specific cubic fourfold and the associated limiting Hodge structures are key ingredients for Hassett and Laza in studying the moduli space of cubic fourfolds and the period mapping. We generalize some results to the cubic hypersurfaces of secant type. Specifically, we compute the limit mixed Hodge structure for families of smooth cubic hypersurfaces degenerating to the cubic hypersurface of secant type. Using Usui's partial compactification and the resulting limit mixed Hodge structure, we characterize a local extension of the period map associated with the degenerating family.

math.AG↗

arXiv2026

Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions $F_D$

The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric functions using Deligne--Mostow theory and the geometric correspondence between curves and surfaces. In this paper, we apply the same construction to obtain transformation formulas among these hypergeometric functions. This also provides an alternative approach to some of Goursat's quadratic transformations via double integrals and Fubini's theorem.

math.CA↗

arXiv2026

LaCoGSEA: Unsupervised deep learning for pathway analysis via latent correlation

Motivation: Pathway enrichment analysis is widely used to interpret gene expression data. Standard approaches, such as GSEA, rely on predefined phenotypic labels and pairwise comparisons, which limits their applicability in unsupervised settings. Existing unsupervised extensions, including single-sample methods, provide pathway-level summaries but primarily capture linear relationships and do not explicitly model gene-pathway associations. More recently, deep learning models have been explored to capture non-linear transcriptomic structure. However, their interpretation has typically relied on generic explainable AI (XAI) techniques designed for feature-level attribution. As these methods are not designed for pathway-level interpretation in unsupervised transcriptomic analyses, their effectiveness in this setting remains limited. Results: To bridge this gap, we introduce LaCoGSEA (Latent Correlation GSEA), an unsupervised framework that integrates deep representation learning with robust pathway statistics. LaCoGSEA employs an autoencoder to capture non-linear manifolds and proposes a global gene-latent correlation metric as a proxy for differential expression, generating dense gene rankings without prior labels. We demonstrate that LaCoGSEA offers three key advantages: (i) it achieves improved clustering performance in distinguishing cancer subtypes compared to existing unsupervised baselines; (ii) it recovers a broader range of biologically meaningful pathways at higher ranks compared with linear dimensionality reduction and gradient-based XAI methods; and (iii) it maintains high robustness and consistency across varying experimental protocols and dataset sizes. Overall, LaCoGSEA provides state-of-the-art performance in unsupervised pathway enrichment analysis. Availability and implementation: https://github.com/willyzzz/LaCoGSEA

cs.LG↗

arXiv2026

TwinPurify: Purifying gene expression data to reveal tumor-intrinsic transcriptional programs via self-supervised learning

Advances in single-cell and spatial transcriptomic technologies have transformed tumor ecosystem profiling at cellular resolution. However, large scale studies on patient cohorts continue to rely on bulk transcriptomic data, where variation in tumor purity obscures tumor-intrinsic transcriptional signals and constrains downstream discovery. Many deconvolution methods report strong performance on synthetic bulk mixtures but fail to generalize to real patient cohorts because of unmodeled biological and technical variation. Here, we introduce TwinPurify, a representation learning framework that adapts the Barlow Twins self-supervised objective, representing a fundamental departure from the deconvolution paradigm. Rather than resolving the bulk mixture into discrete cell-type fractions, TwinPurify instead learns continuous, high-dimensional tumor embeddings by leveraging adjacent-normal profiles within the same cohort as "background" guidance, enabling the disentanglement of tumor-specific signals without relying on any external reference. Benchmarked against multiple large cancer cohorts across RNA-seq and microarray platforms, TwinPurify outperforms conventional representation learning baselines like auto-encoders in recovering tumor-intrinsic and immune signals. The purified embeddings improve molecular subtype and grade classification, enhance survival model concordance, and uncover biologically meaningful pathway activities compared to raw bulk profiles. By providing a transferable framework for decontaminating bulk transcriptomics, TwinPurify extends the utility of existing clinical datasets for molecular discovery.

cs.LG↗

arXiv2025

Moduli spaces of sextic curves with simple singularities and their compactifications

In this paper, we study moduli spaces of sextic curves with simple singularities. Through period maps of K3 surfaces with ADE singularities, we prove that such moduli spaces admit algebraic open embeddings into arithmetic quotients of type IV domains. For all cases, we prove the identifications of GIT compactifications and Looijenga compactifications. We also describe Picard lattices in an explicit way for many cases. For nodal cases, we prove that the orbifold structures on the two sides of the period map are isomorphic.

math.AG↗