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Qiyuan Chen

Publications and source records attributed to Qiyuan Chen.

At least 19 recordsLinked to original sources
arXiv2026

Turán problems for multilinear maps

We study Turán-type extremal problems for alternating and unrestricted multilinear maps. For alternating order-$d$ multilinear maps $T: (\mathbb F^n)^d\to \mathbb{F}^m$, we determine, over algebraically closed fields of arbitrary characteristic, the largest $k$ such that every $T$ vanishes identically on $\mathbb{V}^d$ for some $k$-dimensional subspace $\mathbb{V}$. This extends the bilinear formula of Buhler, Gupta, and Harris [J. Algebra, 1987] to arbitrary order and resolves a question of Qiao [Discrete Anal., 2023]. We also solve the analogous problem for arbitrary, not necessarily alternating, multilinear maps by determining the largest $k$ such that every $T$ vanishes on $\mathbb{V}_1\times\cdots\times \mathbb{V}_d$ for some $k$-dimensional subspaces $\mathbb{V}_1,\dots,\mathbb{V}_d$. These results yield exact values, over algebraically closed fields, of the Feldman--Propp number [Adv. Math., 1992], the Turán number [Discrete Anal., 2023], and the Gow--Quinlan number [Linear Multilinear Algebra, 2006] associated with alternating multilinear maps. Finally, motivated by the Erdős box problem, we give a purely algebraic derivation of the Conlon--Pohoata--Zakharov lower bound [Discrete Anal., 2021] by combining analytic and partition rank estimates with an incidence count. In the relevant parameter range, we further show that every multilinear map defined over a finite field has many isotropic tuples of $2$-dimensional subspaces over extensions of sufficiently divisible degree. This rules out the natural route to improving the Conlon--Pohoata--Zakharov exponent by selecting multilinear maps with substantially fewer bad isotropic configurations.

math.CO↗
arXiv2026

Lower bounds on the strength of the determinant

We establish new lower bounds for the strength and partition rank of the determinant. For every prime $p$, we prove the exact identity \[ \operatorname{str}(\mathrm{det}_p)=p. \] A weak monotonicity argument, combined with a bound for gaps between consecutive primes, then gives $\operatorname{str}(\mathrm{det}_n)\ge (1-o(1))n^{0.475}$ for sufficiently large $n$. Since the Birch rank of $\mathrm{det}_n$ is always $4$, this gives the first explicit family showing that the dependence on the degree in bounds for strength in terms of Birch rank is unavoidable. Viewing $\mathrm{det}_n$ as an $n$-linear form in its columns, we also prove that its partition rank is at least the largest prime not exceeding $n$. Consequently, \[ n-n^{0.525}\le \operatorname{prk}(\mathrm{det}_n)\le n \] for all sufficiently large $n$, and hence the partition rank of the determinant is $n-o(n)$. The proof introduces an intersection-theoretic method for lower-bounding strength: a short strength decomposition produces a nowhere-vanishing section of a split vector bundle on the complement of the determinantal hypersurface, while a nonzero top Chern class in the Chow ring of $\mathrm{PGL}_n$ obstructs such a section.

math.AC↗
arXiv2026

OASIF: An Efficient Obfuscation-Aware Self-Improving Framework for LLM-Based Assembly Code Instruction Following and Comprehension

Large Language Models (LLMs) have recently shown promise in automated binary analysis, yet they remain brittle under commercial-grade obfuscation. We present OASIF, an Obfuscation-Aware Self-evolving Instruction-Following framework for obfuscated assembly comprehension. OASIF couples a token-efficient assembly encoder with a lightweight projector to expose long obfuscated code to a pretrained code LLM under a bounded context budget and follows a three-phase training: (i) feature-space alignment, (ii) supervised instruction fine-tuning, and (iii) online self-evolving reinforcement learning with hybrid rewards, enabling continual adaptation with minimal manual verification. On VMISA-Bench, a challenging out-of-distribution suite featuring three commercial VM-based obfuscators, OASIF consistently improves open-source backbones; Qwen2.5-Coder-Instruct-14B attains Success Rate gains of +15.9, +5.8, and +16.9 percentage points (pp) on Code Virtualizer, Themida (v3.0.7), and VMProtect (v3.5), respectively, and improves the OASIF-Bench average by +9.8. OASIF further delivers stable gains across seven standard BCSD benchmarks while preserving general and domain-relevant capabilities on HumanEval, VulBench, and HumanEval-Decompile.

cs.SE↗
arXiv2026

Geometric Gradient Rectification for Safe Open-Set Semi-Supervised Learning

Open-set semi-supervised learning aims to leverage unlabeled data that may contain out-of-distribution outliers while maintaining performance on in-distribution classes. Existing methods mainly follow two paradigms: filtering suspicious samples or incorporating unlabeled objectives with soft weighting. We argue that both face a common trade-off: aggressive filtering can discard informative but hard ID samples, whereas utilization can introduce auxiliary gradients that conflict with supervised learning when pseudo labels are wrong. We therefore shift the focus from sample selection to gradient-level control. We propose \textit{Geometric Gradient Rectification} (GGR), a plug-in framework that uses the supervised gradient as an anchor and projects conflicting auxiliary gradients onto an admissible region in gradient space. This makes the applied auxiliary update first-order non-opposing within the rectified coordinate block while preserving orthogonal components that may still carry useful representation signals. We further extend GGR with subspace-aware rectification to stabilize the anchor under noisy mini-batch gradients. Experiments on CIFAR and ImageNet benchmarks show that GGR improves representative OSSL baselines in most settings and yields gains in both closed-set generalization and open-set robustness. Code will be available at https://github.com/JiaheChen2002/GGR.

cs.CV↗
arXiv2026

Spectral Intertwining Operators

We study spectral intertwining operators between spectral Eisenstein series $\operatorname{Eis}_{P^\vee}$, $\operatorname{Eis}_{Q^\vee}$ for two parabolic subgroups $P, Q$ of a $p$-adic reductive group $G$ with the same Levi subgroup $M$, inspired by the analogy with the classical intertwining operators between parabolic induced representations of $p$-adic reductive groups. In particular, we construct the normalized (canonical) intertwining operator that satisfies the transitivity and an unnormalized intertwining operator that is adjoint to a rational section of an analog of the Bruhat-Mackey's filtration. Moreover, the normalized and unnormalized intertwining operators differ by a ratio of L-functions, analogously to the Langlands conjecture about classical ones up to units. Finally we prove that the spectral intertwining operators correspond to classical ones up to units under any conjectural categorical local Langlands correspondence.

math.RT↗
arXiv2026

HO-SFL: Hybrid-Order Split Federated Learning with Backprop-Free Clients and Dimension-Free Aggregation

Fine-tuning large models on edge devices is severely hindered by the memory-intensive backpropagation (BP) in standard frameworks like federated learning and split learning. While substituting BP with zeroth-order optimization can significantly reduce memory footprints, it typically suffers from prohibitively degraded convergence speed. To resolve this dilemma, we propose Hybrid-Order Split Federated Learning (HO-SFL). By reformulating the split learning process within a Lagrangian framework, HO-SFL decouples the optimization landscape: The server performs precise first-order updates (i.e., BP), whereas clients conduct memory-efficient zeroth-order optimization. This hybrid design not only eliminates the need for client-side BP but also enables dimension-free model aggregation, drastically lowering communication costs. Crucially, we provide a theoretical convergence analysis, demonstrating that HO-SFL mitigates the dimension-dependent convergence slowdown of zeroth-order optimization, achieving a convergence rate comparable to first-order methods. Extensive experiments on tasks across vision and language modalities validate that HO-SFL achieves convergence speeds comparable to first-order baselines while significantly reducing communication costs and client memory footprints.

cs.LG↗
arXiv2026

Language-Induced Priors for Domain Adaptation

Domain adaptation faces a fundamental paradox in the cold-start regime. When target data is scarce, statistical methods fail to distinguish relevant source domains from irrelevant ones, which often leads to negative transfer. In this paper, we address this challenge by leveraging expert textual descriptions of the target domain, a resource that is often available but overlooked. We propose a probabilistic framework that translates these semantic descriptions into a choice model, namely a Language-Induced Prior (LIP), that learns the preferences from a pretrained Large Language Model (LLM). The LIP is then integrated into an Expectation-Maximization algorithm to identify source relevance. Methodologically, this framework is compatible with any parametric model where a likelihood is available. It allows the LIP to guide the selection of sources when target signals are weak, while gradually refining these choices as samples accumulate. Theoretically, we prove that the estimator roughly matches an oracle cold-start MSE under a correct prior, while remaining asymptotically consistent regardless of the quality of the LIP. Empirically, we validated the framework on a descriptive (Gaussian estimation), a predictive (C-MAPSS dataset), and a prescriptive task (MuJoCo hopper).

cs.LG↗
arXiv2026

Geometry of multilinear varieties over infinite fields and its applications

Multilinear varieties, defined as the sets of rational points of varieties cut out by multilinear functions, were first introduced and studied by Gowers and Milićević[Proc. Edinb. Math. Soc., 2021] for finite $\mathbb{K}$. In this paper, we investigate multilinear varieties over infinite fields from a geometric perspective. We establish two fundamental results: a codimension formula for the Zariski closure of a multilinear variety, and the existence of a high-dimensional irreducible subvariety passing through any given $\mathbb{K}$-rational point. These results serve as a geometric foundation for analyzing various ranks of tensors and homogeneous polynomials, including partition rank, analytic rank, geometric rank, (collective) strength and (collective) Birch rank. As applications, we resolve the Adiprasito-Kazhdan-Ziegler conjecture [arXiv:2102.03659, 2021] on the stability of partition rank for perfect infinite fields. We thereby settle the stability conjecture for collective strength [Selecta Math., 2024], as well as the conjecture on the linear equivalence between strength and Birch rank [arXiv:2410.00248, 2024] for such fields. Moreover, our results immediately yield a strengthening of the theorems of Bik-Draisma-Snowden [arXiv:2401.02067, 2024] and Lampert-Snowden [arXiv:2406.18498, 2024], for multilinear varieties over infinite fields.

math.AG↗
arXiv2026

Collaborative Contextual Bayesian Optimization

Discovering optimal designs through sequential data collection is essential in many real-world applications. While Bayesian Optimization (BO) has achieved remarkable success in this setting, growing attention has recently turned to context-specific optimal design, formalized as Contextual Bayesian Optimization (CBO). Unlike BO, CBO is inherently more challenging as it must approximate an entire mapping from the context space to its corresponding optimal design, requiring simultaneous exploration across contexts and exploitation within each. In many modern applications, such tasks arise across multiple potentially heterogeneous but related clients, where collaboration can significantly improve learning efficiency. We propose CCBO, Collaborative Contextual Bayesian Optimization, a unified framework enabling multiple clients to jointly perform CBO with controllable contexts, supporting both online collaboration and offline initialization from peers' historical beliefs, with an optional privacy-preserving communication mechanism. We establish sublinear regret guarantees and demonstrate, through extensive simulations and a real-world hot rolling application, that CCBO achieves substantial improvements over existing approaches even under client heterogeneity. The code to reproduce the results can be found at https://github.com/cchihyu/Collaborative-Contextual-Bayesian-Optimization

cs.LG↗
arXiv2026

Learning What Matters: Dynamic Dimension Selection and Aggregation for Interpretable Vision-Language Reward Modeling

Vision-language reward modeling faces a dilemma: generative approaches are interpretable but slow, while discriminative ones are efficient but act as opaque "black boxes." To bridge this gap, we propose VL-MDR (Vision-Language Multi-Dimensional Reward), a framework that dynamically decomposes evaluation into granular, interpretable dimensions. Instead of outputting a monolithic scalar, VL-MDR employs a visual-aware gating mechanism to identify relevant dimensions and adaptively weight them (e.g., Hallucination, Reasoning) for each specific input. To support this, we curate a dataset of 321k vision-language preference pairs annotated across 21 fine-grained dimensions. Extensive experiments show that VL-MDR consistently outperforms existing open-source reward models on benchmarks like VL-RewardBench. Furthermore, we show that VL-MDR-constructed preference pairs effectively enable DPO alignment to mitigate visual hallucinations and improve reliability, providing a scalable solution for VLM alignment.

cs.CL↗
arXiv2026

MM-DADM: Multimodal Drug-Aware Diffusion Model for Virtual Clinical Trials

High failure rates in cardiac drug development necessitate virtual clinical trials via electrocardiogram (ECG) generation to reduce risks and costs. However, existing ECG generation models struggle to balance morphological realism with pathological flexibility, fail to disentangle demographics from genuine drug effects, and are severely bottlenecked by early-phase data scarcity. To overcome these hurdles, we propose the Multimodal Drug-Aware Diffusion Model (MM-DADM), the first generative framework for generating individualized drug-induced ECGs. Specifically, our proposed MM-DADM integrates a Dynamic Cross-Attention (DCA) module that adaptively fuses External Physical Knowledge (EPK) to preserve morphological realism while avoiding the suppression of complex pathological nuances. To resolve feature entanglement, a Causal Feature Encoder (CFE) actively filters out demographic noise to extract pure pharmacological representations. These representations subsequently guide a Causal-Disentangled ControlNet (CDC-Net), which leverages counterfactual data augmentation to explicitly learn intrinsic pharmacological mechanisms despite limited clinical data. Extensive experiments on $9,443$ ECGs across $8$ drug regimens demonstrate that MM-DADM outperforms $10$ state-of-the-art ECG generation models, improving simulation accuracy by at least $6.13\%$ and recall by $5.89\%$, while providing highly effective data augmentation for downstream classification tasks.

cs.LG↗
arXiv2026

Towards Clinical Practice in CT-Based Pulmonary Disease Screening: An Efficient and Reliable Framework

Deep learning models for pulmonary disease screening from Computed Tomography (CT) scans promise to alleviate the immense workload on radiologists. Still, their high computational cost, stemming from processing entire 3D volumes, remains a major barrier to widespread clinical adoption. Current sub-sampling techniques often compromise diagnostic integrity by introducing artifacts or discarding critical information. To overcome these limitations, we propose an Efficient and Reliable Framework (ERF) that fundamentally improves the practicality of automated CT analysis. Our framework introduces two core innovations: (1) A Cluster-based Sub-Sampling (CSS) method that efficiently selects a compact yet comprehensive subset of CT slices by optimizing for both representativeness and diversity. By integrating an efficient k-nearest neighbor search with an iterative refinement process, CSS bypasses the computational bottlenecks of previous methods while preserving vital diagnostic features. (2) An Ambiguity-aware Uncertainty Quantification (AUQ) mechanism, which enhances reliability by specifically targeting data ambiguity arising from subtle lesions and artifacts. Unlike standard uncertainty measures, AUQ leverages the predictive discrepancy between auxiliary classifiers to construct a specialized ambiguity score. By maximizing this discrepancy during training, the system effectively flags ambiguous samples where the model lacks confidence due to visual noise or intricate pathologies. Validated on two public datasets with 2,654 CT volumes across diagnostic tasks for 3 pulmonary diseases, ERF achieves diagnostic performance comparable to the full-volume analysis (over 90% accuracy and recall) while reducing processing time by more than 60%. This work represents a significant step towards deploying fast, accurate, and trustworthy AI-powered screening tools in time-sensitive clinical settings.

eess.IV↗
arXiv2026

Curing Semantic Drift: A Dynamic Approach to Grounding Generation in Large Vision-Language Models

Large Vision-Language Models (LVLMs) face a tug-of-war between powerful linguistic priors and visual evidence, often leading to \emph{semantic drift}: a progressive detachment from the input image that can abruptly emerge at specific decoding steps. Through a token-level diagnosis, we show that hallucination is frequently triggered not by the absence of grounded candidates, but by a failure of selection -- the model chooses a linguistically convenient yet visually unfaithful token even when better grounded alternatives exist. Motivated by this insight, we propose \textbf{D}ynamic \textbf{L}ogits \textbf{C}alibration (DLC), a training-free decoding framework that introduces a lightweight visual referee to intervene exactly when drift happens. At each step, DLC performs a dual-aspect grounding check on top-$k$ candidates: (1) it assesses the intrinsic visual relevance of a candidate token and (2) its contextual visual coherence. These signals are evaluated against an adaptive historical baseline to compute a relative visual advantage, which is then used to dynamically calibrate logits and favor grounded tokens. Extensive experiments on CHAIR, POPE, SHR, GPT-4o evaluation, and MME demonstrate that DLC consistently reduces hallucinations across multiple LVLMs while preserving response quality. Further analyses validate robustness to different vision backbones and demonstrate a favorable trade-off between output quality and computational cost as the candidate pool size varies. Code will be released on https://github.com/JiaheChen2002/DLC.

cs.CV↗
arXiv2026

A base change framework for tensor functions

The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)} slice rank is linearly bounded by geometric rank for any 3-tensors over any field. \emph{(2)} slice rank of any 3-tensors is quasi-supermultiplicative. As a consequence, the asymptotic slice rank exists for any 3-tensors.

math.AC↗
arXiv2025

CC-GSEO-Bench: A Content-Centric Benchmark for Measuring Source Influence in Generative Search Engines

Generative Search Engines (GSEs) synthesize conversational answers from multiple sources, weakening the long-standing link between search ranking and digital visibility. This shift raises a central question for content creators: How can we reliably quantify a source article's influence on a GSE's synthesized answer across diverse intents and follow-up questions? We introduce CC-GSEO-Bench, a content-centric benchmark that couples a large-scale dataset with a creator-centered evaluation framework. The dataset contains over 1,000 source articles and over 5,000 query-article pairs, organized in a one-to-many structure for article-level evaluation. We ground construction in realistic retrieval by combining seed queries from public QA datasets with limited synthesized augmentation and retaining only queries whose paired source reappears in a follow-up retrieval step. On top of this dataset, we operationalize influence along three core dimensions: Exposure, Faithful Credit, and Causal Impact, and two content-quality dimensions: Readability and Structure, and Trustworthiness and Safety. We aggregate query-level signals over each article's query cluster to summarize influence strength, coverage, and stability, and empirically characterize influence dynamics across representative content patterns.

cs.CL↗
arXiv2025

Stability of ranks under field extensions

This paper studies the stability of tensor ranks under field extensions. Our main contributions are fourfold: (1) We prove that the analytic rank is stable under field extensions. (2) We establish the equivalence between the partition rank vs. analytic rank conjecture and the stability conjecture for partition rank. We also prove that they are equivalent to other two important conjectures. (3) We resolve the Adiprasito-Kazhdan-Ziegler conjecture on the stability of the slice rank of linear subspaces under field extensions. (4) As an application of (1), we show that the geometric rank is equal to the analytic rank up to a constant factor.

math.CO↗
arXiv2025

Physical regularized Hierarchical Generative Model for Metallic Glass Structural Generation and Energy Prediction

Disordered materials such as glasses, unlike crystals, lack long range atomic order and have no periodic unit cells, yielding a high dimensional configuration space with widely varying properties. The complexity not only increases computational costs for atomistic simulations but also makes it difficult for generative AI models to deliver accurate property predictions and realistic structure generation. In this work, we introduce GlassVAE, a hierarchical graph variational autoencoder that uses graph representations to learn compact, rotation, translation, and permutation invariant embeddings of atomic configurations. The resulting structured latent space not only enables efficient generation of novel, physically plausible structures but also supports exploration of the glass energy landscape. To enforce structural realism and physical fidelity, we augment GlassVAE with two physics informed regularizers, a radial distribution function (RDF) loss that captures characteristic short and medium range ordering and an energy regression loss that reflects the broad configurational energetics. Both theoretical analysis and experimental results highlight the critical impact of these regularizers. By encoding high dimensional atomistic data into a compact latent vector and decoding it into structures with accurate energy predictions, GlassVAE provides a fast, physics aware path for modeling and designing disordered materials.

cs.CE↗
arXiv2025

Isotropy and completeness indices of multilinear maps

Structures of multilinear maps are characterized by invariants. In this paper we introduce two invariants, named the isotropy index and the completeness index. These invariants capture the tensorial structure of the kernel of a multilinear map. We establish bounds on both indices in terms of the partition rank, geometric rank, analytic rank and height, and present three applications: 1) Using the completeness index as an interpolator, we establish upper bounds on the aforementioned tensor ranks in terms of the subrank. This settles an open problem raised by Kopparty, Moshkovitz and Zuiddam, and consequently answers a question of Derksen, Makam and Zuiddam. 2) We prove a Ramsey-type theorem for the two indices, generalizing a recent result of Qiao and confirming a conjecture of his. 3) By computing the completeness index, we obtain a polynomial-time probabilistic algorithm to estimate the height of a polynomial ideal.

math.CO↗