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Weiyan Chen

Publications and source records attributed to Weiyan Chen.

18 recordsLinked to original sources
arXiv2026

Geometry-Aware Resource Allocation for Network-Level ISAC Systems

Network-level integrated sensing and communication (ISAC) is recognized as a transformative technology for next-generation mobile radio systems. By enabling collaboration among multiple transceivers, network-level ISAC can significantly enhance both communication and sensing performance through spatial diversity. However, existing resource allocation strategies typically overlook the impact of spatial geometry, where identical time-frequency resources contribute differently to sensing accuracy depending on the transceiver's location. This leaves the fundamental coupling between spatial topology and resource efficacy unclear, rendering optimal resource allocation a critical challenge for unlocking the full potential of network-level ISAC.To address this challenge, this paper investigates the optimal distribution of time-frequency resources across spatially distributed transceivers through a theoretically grounded two-stage framework. First, we analytically derive the optimal time and frequency aperture distributions for sensing, defined as the variances of the allocated symbol and subcarrier indices, respectively, under both two-transmitter and multi-transmitter scenarios. By exploiting the mathematical isomorphism between delay and Doppler estimation, we prove that the optimal resource allocation strategy follows the gradient direction of the Cramer-Rao Lower Bound (CRLB) with respect to the apertures. Second, to bridge the gap between theoretical aperture values and practical OFDMA constraints, such as the minimized communication rate of each user equipment (UE), we formulate the resource allocation as a combinatorial integer partitioning problem. To tackle the NP-hard nature of the formulated problem, a low-complexity Variance-Guided Partitioning Algorithm (VGPA) is proposed to jointly optimize the subcarrier and symbol patterns for communication and sensing.

eess.SP↗
arXiv2026

When Preference Labels Fall Short: Aligning Diffusion Models from Real Data

Preference alignment aims to guide generative models by learning from comparisons between preferred and non-preferred samples. In practice, most existing approaches rely on preference pairs constructed from model-generated images. Such supervision is inherently relative and can be ambiguous when both samples exhibit artifacts or limited visual quality, making it difficult to infer what constitutes a truly desirable output. In this work, we investigate whether real data can serve as an alternative source of supervision for preference alignment. We adopt a data-centric perspective and study a curation strategy that treats real images as reference points and constructs preference signals by contrasting them with generated or perturbed samples, without requiring manually annotated preference pairs. Through empirical analysis, we show that real-data-based supervision provides effective guidance for aligning diffusion models and achieves performance comparable to existing preference-based methods. Our results suggest that real data offers a practical and complementary source of supervision for preference alignment and highlight directions of label-efficient alignment strategies. Code and models are available at https://cwyxx.github.io/RealAlign.

cs.CV↗
arXiv2026

Robust Conditional Conformal Prediction via Branched Normalizing Flow

Conformal prediction (CP) constructs prediction sets with marginal coverage guarantees under the assumption that the calibration and test distributions are identical. However, under distribution shift, existing approaches primarily align marginal conformal score distributions, which is sufficient to preserve marginal coverage but does not control the conditional coverage error at individual test inputs. As a consequence, CP can remain unreliable in regions where the conditional score distributions are mismatched. In this work, we bound the conditional invalidity of CP under distribution shift in terms of the Wasserstein distance between the calibration and test distributions. This result highlights the role of invertible transport in mitigating conditional coverage degradation. Motivated by this insight, we introduce Branched Normalizing Flow (BNF), a two-branch architecture that normalizes a test input to the calibration distribution and transforms the prediction set of the normalized input back to the test distribution while preserving conditional guarantees. Empirically, BNF consistently improves conditional coverage robustness on nine datasets across a wide range of confidence levels.

cs.LG↗
arXiv2026

Unveiling Perceptual Artifacts: A Fine-Grained Benchmark for Interpretable AI-Generated Image Detection

Current AI-Generated Image (AIGI) detection approaches predominantly rely on binary classification to distinguish real from synthetic images, often lacking interpretable or convincing evidence to substantiate their decisions. This limitation stems from existing AIGI detection benchmarks, which, despite featuring a broad collection of synthetic images, remain restricted in their coverage of artifact diversity and lack detailed, localized annotations. To bridge this gap, we introduce a fine-grained benchmark towards eXplainable AI-Generated image Detection, named X-AIGD, which provides pixel-level, categorized annotations of perceptual artifacts, spanning low-level distortions, high-level semantics, and cognitive-level counterfactuals. These comprehensive annotations facilitate fine-grained interpretability evaluation and deeper insight into model decision-making processes. Our extensive investigation using X-AIGD provides several key insights: (1) Existing AIGI detectors demonstrate negligible reliance on perceptual artifacts, even at the most basic distortion level. (2) While AIGI detectors can be trained to identify specific artifacts, they still substantially base their judgment on uninterpretable features. (3) Explicitly aligning model attention with artifact regions can increase the interpretability and generalization of detectors. The data and code are available at: https://github.com/Coxy7/X-AIGD.

cs.CV↗
arXiv2025

The normal closure of a homological genus 0 bounding pair map

Justin Lanier and the authors recently determined the group normally generated by a single bounding pair map of genus $n$. We related this subgroup with the Chillingworth subgroup and the Casson--Morita's $d$ map. In this paper, we extend the results to the case when $n=0$. Let $\mathcal{M}_g^1$ be the mapping class group, $\text{Ch}_g^1$ be the Chillingworth subgroup and $d$ be the Casson--Morita's $d$-map. We show that $\text{Ker}(d)=[\text{Ch}_g^1,\mathcal{M}_g^1]$ and it is generated by a single homological genus 0 bounding pair map. We also construct an element $H_0\in \text{Ch}_g^1$, and show that $\text{Ch}_g^1$ is normally generated by this single element $H_0$.

math.GT↗
arXiv2025

Federated Conditional Conformal Prediction via Generative Models

Conformal Prediction (CP) provides distribution-free uncertainty quantification by constructing prediction sets that guarantee coverage of the true labels. This reliability makes CP valuable for high-stakes federated learning scenarios such as multi-center healthcare. However, standard CP assumes i.i.d. data, which is violated in federated settings where client distributions differ substantially. Existing federated CP methods address this by maintaining marginal coverage on each client, but such guarantees often fail to reflect input-conditional uncertainty. In this work, we propose Federated Conditional Conformal Prediction (Fed-CCP) via generative models, which aims for conditional coverage that adapts to local data heterogeneity. Fed-CCP leverages generative models, such as normalizing flows or diffusion models, to approximate conditional data distributions without requiring the sharing of raw data. This enables each client to locally calibrate conformal scores that reflect its unique uncertainty, while preserving global consistency through federated aggregation. Experiments on real datasets demonstrate that Fed-CCP achieves more adaptive prediction sets.

cs.LG↗
arXiv2024

Topological complexity of enumerative problems and classifying spaces of $PU_n$

We study the topological complexity, in the sense of Smale, of three enumerative problems in algebraic geometry: finding the 27 lines on cubic surfaces, the 28 bitangents and the 24 inflection points on quartic curves. In particular, we prove lower bounds for the topological complexity of any algorithm that finds solutions to the three problems and for the Schwarz genera of their associated covers. The key is to understand cohomology classes of the classifying spaces of projective unitary groups $PU_n$.

math.AT↗
arXiv2023

Topological complexity of finding flex points on cubic plane curves

We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus of a cover associated to this problem. We also show that our lower bound for the complexity is close to be the best possible.

math.GT↗
arXiv2023

The normal closure of a bounding pair map in its mapping class group

Johnson showed that the normal subgroup of a mapping class group generated by the genus $1$ bounding pair maps is equal to the Torelli group. Generalizing Johnson's result, we give two descriptions of the normal subgroup generated by the genus $n$ bounding pair maps using the Chillingworth and the Casson--Morita invariants.

math.GT↗
arXiv2021

Choosing points on cubic plane curves: rigidity and flexibility

Every smooth cubic plane curve has 9 flex points and 27 sextatic points. We study the following question asked by Farb: Is it true that the known algebraic structures give all the possible ways to continuously choose $n$ distinct points on every smooth cubic plane curve, for each given positive integer $n$? We give an affirmative answer to the question when $n=9$ and 18 (the smallest open cases), and a negative answer for infinitely many $n$'s.

math.AG↗
arXiv2019

Convolutional Sparse Coding for Compressed Sensing CT Reconstruction

Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. Qualitative and quantitative results demonstrate that the proposed methods achieve better performance than several existing state-of-the-art methods.

physics.med-ph↗
arXiv2018

Obstructions to choosing distinct points on cubic plane curves

Every smooth cubic plane curve has 9 inflection points, 27 sextatic points, and 72 ``points of type nine". Motivated by these classical algebro-geometric constructions, we study the following topological question: Is it possible to continuously choose $n$ distinct unordered points on each smooth cubic plane curve for a natural number $n$? This question is equivalent to asking if certain fiber bundle admits a continuous section or not. We prove that the answer is no when $n$ is not a multiple of 9. Our result resolves a conjecture of Benson Farb.

math.GT↗
arXiv2017

Homology of braid groups, the Burau representation, and $\mathbb{F}_q$-points on superelliptic curves

The reduced Burau representation $V_n$ of the braid group $B_n$ is obtained from the action of $B_n$ on the homology of an infinite cyclic cover of the disc with $n$ punctures. The group homology $H_*(B_n;V_n)$ of braid groups with coefficients in the complexified reduced Burau representation is calculated. Our topological calculation has the following arithmetic interpretation (which also has different algebraic proofs): the expected number of points on a random superelliptic curve of a fixed genus over $\mathbb{F}_q$ is exactly $q$.

math.GT↗
arXiv2016

Analytic number theory for 0-cycles

There is a well-known analogy between integers and polynomials over $F_q$, and a vast literature on analytic number theory for polynomials. From a geometric point of view, polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to 0-cycles on more general varieties? In this paper we study prime factorization of effective 0-cycles on an arbitrary connected variety $V$ over $F_q$, emphasizing the analogy between integers and 0-cycles. For example, inspired by the works of Granville and Rhoades, we prove that the prime factors of 0-cycles are typically Poisson distributed.

math.AG↗
arXiv2016

Twisted cohomology of configuration spaces and spaces of maximal tori via point-counting

We consider two families of algebraic varieties $Y_n$ indexed by natural numbers $n$: the configuration space of unordered $n$-tuples of distinct points on $\mathbb{C}$, and the space of unordered $n$-tuples of linearly independent lines in $\mathbb{C}^n$. Let $W_n$ be any sequence of virtual $S_n$-representations given by a character polynomial, we compute $H^i(Y_n; W_n)$ for all $i$ and all $n$ in terms of double generating functions. One consequence of the computation is a new recurrence phenomenon: the stable twisted Betti numbers $\lim_{n\to\infty}\dim H^i(Y_n; W_n)$ are linearly recurrent in $i$. Our method is to compute twisted point-counts on the $F_q$-points of certain algebraic varieties, and then pass through the Grothendieck-Lefschetz fixed point formula to prove results in topology. We also generalize a result of Church-Ellenberg-Farb about the configuration spaces of the affine line to those of a general smooth variety.

math.GT↗
arXiv2014

Optimal control with reset-renewable resources

We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and stochastic shortest path problems with full budget resets in all preferred nodes. In the continuous case, we derive augmented PDEs of optimal control, which are then solved numerically on the extended state space with a full/instantaneous budget reset on the preferred subset. We introduce an iterative algorithm for solving these problems efficiently. The method's performance is demonstrated on a range of computational examples, including the optimal path planning with constraints on prolonged visibility by a static enemy observer. In addition, we also develop an algorithm that works on the original state space to solve a related but simpler problem: finding the subsets of the domain "reachable-within-the-budget". This manuscript is an extended version of the paper accepted for publication by SIAM J. on Control and Optimization. In the journal version, Section 3 and the Appendix were omitted due to space limitations.

math.OC↗