arXiv subjects

Qihang Wang

Publications and source records attributed to Qihang Wang.

9 recordsLinked to original sources

arXiv2026

Fr\"oberg's Conjecture for Quintics and Septics in Four Variables

Let $k$ be a field of characteristic zero and let $S=k[x_1,x_2,x_3,x_4]$. We prove Fr\"oberg's predicted Hilbert series for ideals generated by $r$ general forms of equal degree $d$ for every $r\geq1$ in each of the two cases $d=5$ and $d=7$. Relative to the classical cases $r\leq5$ and the equal-degree theorem through degree $d+2$ of Boij--Dannetun--Lundqvist, the generator-count ranges requiring new input are $6\leq r\leq11$ for quintics and $6\leq r\leq21$ for septics. The proof reduces each slice to finitely many endpoint ranks of Macaulay multiplication matrices. For quintics, ten exact endpoint computations based on twenty-one sparse forms suffice. For septics, a nested family of 120 integral forms supplies fifteen endpoint computations. In every endpoint certificate for these new ranges, an explicitly recorded maximal minor is nonzero modulo $2$, hence is a nonzero integer. The case $r=5$ is the classical strong Lefschetz instance; for quintics we also record a matching modular rank and Koszul bound. Zariski openness then gives the result over every characteristic-zero field. The unrestricted Fr\"oberg conjecture remains outside the scope of the paper. The main results of this paper were obtained through a generative-AI workflow using OpenAI GPT-5.6 Sol, Anthropic Claude Fable 5, and Grok 4.6. Further details appear in the disclosure at the end of the paper.

math.AC↗

arXiv2026

Complementary Quantum Correlations Are Universal for Qubits

Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.

quant-ph↗

arXiv2026

When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification

Mutually unbiased measurements are commonly expected to expose independent facets of a quantum state: a correlation that is classical in one basis should disappear in a complementary basis. In higher dimensions, however, this intuition becomes particularly subtle because correlations recovered in different settings need not represent different information. To expose this loophole, we propose a two-branch classical null test: before the setting is chosen, a shared bit selects one of two orthogonal product preparations, producing a rank-two classical--classical state, and the candidate protocol then runs unchanged. Different settings can read the same bit through different outcome patterns. This two-branch classical architecture disproves the complementary-quantum correlation (CQC) conjecture in every dimension $d\geq3$. A distinct rank-two classical--classical state disproves its complete-basis extension (ECQC) at $d=7$, with an overrun that grows without bound along prime dimensions. Its qutrit CQC instance also gives classical false positives for a proposed quantum-correlation measure and a proposed one-sided semi-device-independent steering criterion, and refutes a conditional-probability conjecture. The failures identify the missing requirement: information read in different settings must be nonredundant. In experiments and applications, the same low-overhead architecture can serve as a calibration test before a multibasis score is assigned quantum meaning.

quant-ph↗

arXiv2026

Residual bounds for Schur-stable polynomials

Let $r_n$ be the infimum of \[ \frac{\lVert P'-P'(0)P\rVert_{H^2}}{\lVert P\rVert_{H^2}} \] over all degree-$n$ polynomials $P$ satisfying $P(0)=1$ whose zeros lie in the closed unit disk. We prove the quantitative residual bound \[ r_n\geq \exp\!\bigl(-(1+o(1))\sqrt n\log n\bigr) \qquad(n\to\infty). \] As an application, we answer Erd\H{o}s Problem 973 on exterior power sums in the negative, in a form quantitatively stronger than the answer first obtained by Luo, Yang, and Zhu.

math.CV↗

arXiv2026

Automated SVA Generation with LLMs

Functional verification remains a dominant cost in modern IC development, and SystemVerilog Assertions (SVAs) are critical for simulation-based monitoring and formal property checking. However, writing SVAs by hand is time-consuming and error-prone. Directly prompting general-purpose large language models (LLMs) is also unreliable: the generated properties are often syntactically invalid or semantically incorrect, and the problem is exacerbated by scarce, high-quality domain training data. We present SVA Generator, a data-centric framework that translates natural-language SVA Descriptions (SVADs) into executable SVAs. It uses AST-grounded constraint injection and an automated supervision pipeline that enforces structural consistency and reduces hallucinations via de-duplication and constraint checks. To enable rigorous evaluation, we introduce a benchmark suite stratified by AST depth and use formal property equivalence checking to quantify semantic correctness separately from syntax validity, by checking mutual implication between the generated and reference properties under the same clocking and environment assumptions. Across all difficulty tiers, SVA Generator achieves comparable Syntax Pass Rate (SPR) to strong general LLM baselines, while delivering substantially higher Semantic Equivalence Rate (SER) on deeper tiers: +24.5 pp on D2, +26.0 pp on D3, and +17.5 pp on D4 relative to the best-performing general LLM, corresponding to a +22.7 pp SER improvement on average over D2--D4. These results highlight that high-fidelity data construction and depth-stratified benchmarking are key to reliable, semantics-preserving SVA generation.

cs.AR↗

arXiv2025

TDEdit: A Unified Diffusion Framework for Text-Drag Guided Image Manipulation

This paper explores image editing under the joint control of text and drag interactions. While recent advances in text-driven and drag-driven editing have achieved remarkable progress, they suffer from complementary limitations: text-driven methods excel in texture manipulation but lack precise spatial control, whereas drag-driven approaches primarily modify shape and structure without fine-grained texture guidance. To address these limitations, we propose a unified diffusion-based framework for joint drag-text image editing, integrating the strengths of both paradigms. Our framework introduces two key innovations: (1) Point-Cloud Deterministic Drag, which enhances latent-space layout control through 3D feature mapping, and (2) Drag-Text Guided Denoising, dynamically balancing the influence of drag and text conditions during denoising. Notably, our model supports flexible editing modes - operating with text-only, drag-only, or combined conditions - while maintaining strong performance in each setting. Extensive quantitative and qualitative experiments demonstrate that our method not only achieves high-fidelity joint editing but also matches or surpasses the performance of specialized text-only or drag-only approaches, establishing a versatile and generalizable solution for controllable image manipulation. Code will be made publicly available to reproduce all results presented in this work.

cs.CV↗

arXiv2025

Image2Net: Datasets, Benchmark and Hybrid Framework to Convert Analog Circuit Diagrams into Netlists

Large Language Model (LLM) exhibits great potential in designing of analog integrated circuits (IC) because of its excellence in abstraction and generalization for knowledge. However, further development of LLM-based analog ICs heavily relies on textual description of analog ICs, while existing analog ICs are mostly illustrated in image-based circuit diagrams rather than text-based netlists. Converting circuit diagrams to netlists help LLMs to enrich the knowledge of analog IC. Nevertheless, previously proposed conversion frameworks face challenges in further application because of limited support of image styles and circuit elements. Up to now, it still remains a challenging task to effectively convert complex circuit diagrams into netlists. To this end, this paper constructs and opensources a new dataset with rich styles of circuit diagrams as well as balanced distribution of simple and complex analog ICs. And a hybrid framework, named Image2Net, is proposed for practical conversion from circuit diagrams to netlists. The netlist edit distance (NED) is also introduced to precisely assess the difference between the converted netlists and ground truth. Based on our benchmark, Image2Net achieves 80.77% successful rate, which is 34.62%-45.19% higher than previous works. Specifically, the proposed work shows 0.116 averaged NED, which is 62.1%-69.6% lower than state-of-the-arts. Our datasets and benchmark are available at https://github.com/LAD021/ci2n_datasets.

cs.AR↗

arXiv2024

Combining Radiomics and Machine Learning Approaches for Objective ASD Diagnosis: Verifying White Matter Associations with ASD

Autism Spectrum Disorder is a condition characterized by a typical brain development leading to impairments in social skills, communication abilities, repetitive behaviors, and sensory processing. There have been many studies combining brain MRI images with machine learning algorithms to achieve objective diagnosis of autism, but the correlation between white matter and autism has not been fully utilized. To address this gap, we develop a computer-aided diagnostic model focusing on white matter regions in brain MRI by employing radiomics and machine learning methods. This study introduced a MultiUNet model for segmenting white matter, leveraging the UNet architecture and utilizing manually segmented MRI images as the training data. Subsequently, we extracted white matter features using the Pyradiomics toolkit and applied different machine learning models such as Support Vector Machine, Random Forest, Logistic Regression, and K-Nearest Neighbors to predict autism. The prediction sets all exceeded 80% accuracy. Additionally, we employed Convolutional Neural Network to analyze segmented white matter images, achieving a prediction accuracy of 86.84%. Notably, Support Vector Machine demonstrated the highest prediction accuracy at 89.47%. These findings not only underscore the efficacy of the models but also establish a link between white matter abnormalities and autism. Our study contributes to a comprehensive evaluation of various diagnostic models for autism and introduces a computer-aided diagnostic algorithm for early and objective autism diagnosis based on MRI white matter regions.

eess.IV↗

arXiv2024

On the First and the Second Borel-Cantelli Lemmas

Let $\{A_n\}_{n=1}^\infty$ be a sequence of events and let $\displaystyle S:=\sum_{n=1}^\infty 1_{A_n}$. We present in this note equivalent characterizations for the statements $\mathbb{P} (S<\infty)=1$ and $\mathbb{P} (S=\infty)=1$ respectively. These characterizations are of Borel-Cantelli lemma type and of Kochen-Stone lemma type respectively, which could be regarded as the most general version of the first and the second Borel-Cantelli Lemmas.

math.PR↗