arXiv subjects

Yuanyuan Chen

Publications and source records attributed to Yuanyuan Chen.

At least 19 recordsLinked to original sources

arXiv2026

Filtration theorems, Hilbert functions, and generic freeness

Let $M$ be a finitely generated module over a ring $R$ that is a finitely generated algebra over a Noetherian ring $A$ by $r$ elements. We prove that there are finitely many primes $P_1, \ldots, P_k$ of $A$ such that $M$ has a countable ascending filtration by finitely generated $A$-modules with the property that every factor $F_n$ has a filtration by cyclic modules of the form $A/P_i$, $1 \leq i \leq k$ such that the number of copies $H_i(n)$ of $A/P_i$ that occur in the filtration of $F_n$ is an eventually polynomial function of $n$. We prove a number of bounds on the degrees of these eventually polynomial functions: $r-1$ is always a bound, and the dimension of $\dim(M_P)-1$ is a bound under mild hypotheses. One application is an immediate proof Grothedieck's classic theorem on generic freeness. Several other applications are given.

math.AC↗

arXiv2026

Minimizing the spectral radius of unicyclic graphs with fixed order and dissociation number

A dissociation set of a graph G is a vertex subset S contained in V(G) such that the induced subgraph G[S] has maximum degree at most 1, and the dissociation number of G is the cardinality of a maximum dissociation set denoted by Φ(G). In this paper, we first derive a sharp lower bound on the dissociation number for all unicyclic graphs. Furthermore, we also study the graphs with minimum spectral radius among all unicyclic graphs with given order and dissociation number and explicitly identify all extremal graphs for $n-4 \le Φ(G) \le n-1$.

math.CO↗

arXiv2026

RSI Arena: Towards Recursive Self-Improvement with Human Feedback

Can AI agents autonomously train useful language models and improve them using feedback from users? We introduce RSI Arena, a two-stage study of autonomous post-training as a step toward recursive self-improvement. Ten frontier models act as training agents, each starting from NVIDIA Nemotron 3.5 Lightning 30B-A3B Base. During a six-day first stage, each agent has 1,000 GPU-hours and $300 in API credit on a shared 64-GPU cluster, independently selecting data, implementing training procedures, and choosing checkpoints. We evaluate their models on 20 benchmarks and through blind human evaluations. All ten agents produce working assistants, with the strongest model, trained by GPT-6 Astra, closing a median of 76% of the base-to-Instruct gap across 12 capability benchmarks. Its human-preference rating is also close to NVIDIA Instruct after statistical adjustment for answer length and formatting. In Stage 2, each agent receives the comparison records and votes involving its Stage 1 model and is given three additional days for further training. Using NVIDIA Instruct as a common reference across the two evaluation rounds, we observe an improvement from Stage 1 to Stage 2 in the style-adjusted relative rating of eight of the ten models. We show that benchmark gains were modest, with no clear link to preference gains, while some agents encouraged longer responses and one model showed increased harmful compliance on StrongREJECT. RSI Arena provides an auditable setting for studying how human feedback can guide autonomous model development. It takes a step toward recursive self-improvement with human feedback (RSIHF), in which people help define what improvement means for the AI systems they use.

cs.CL↗

arXiv2026

On the maximal index of $C_4^-$-free unbalanced signed graphs of prescribed size

The extremal problem of determining the graphs with maximum spectral radius among all graphs with a prescribed number of edges was resolved by Rowlinson [Linear Algebra Appl. 110 (1988) 43--53]. A signed graph $Γ=(G,σ)$ is called $C_k^-$-free if it contains no negative $k$-cycle as a signed subgraph. The index of a signed graph is defined as the largest eigenvalue of its adjacency matrix. This paper addresses the maximization of the index of unbalanced signed graphs. For signed graphs of a prescribed order, Wang and Lin [Discrete Appl. Math. 372 (2025) 164--172] determined the maximum index of $C_4^{-}$-free unbalanced signed graphs. Subsequently, Wang, Peng and Hou [Discrete Math. 349 (2026) 114871] characterized the unbalanced signed graphs of prescribed size with maximum index. This paper treats the edge spectral Turán-type problem for $C_4^-$-free unbalanced signed graphs. The all-positive signed graph with underlying graph $G$ is denoted by $(G,+)$. Evidently, $A((G,+))=A(G)$. In particular, $(H_{d,t},+)$ is the all-positive signed graph whose underlying graph is $H_{d,t}$, where $H_{d,0}=K_d$ and for $t>0$, $H_{d,t}$ is obtained from $K_d$ by adding a single vertex adjacent to exactly $t$ vertices of $K_d$. Let $m-3=\binom{d}{2}+t$ with $0\le t\le d-1$. Up to switching isomorphism and the addition of isolated vertices, the unique extremal unbalanced signed graph is obtained by attaching a negative triangle to a specified vertex of the all-positive signed graph $(H_{d,t},+)$.

math.CO↗

arXiv2026

Spectral extremal problems on 1-planar graphs without Friendship graph

Let $\textit{spex}_{\mathcal{P}_1}(n,F)$ be the maximum spectral radius among all $n$-vertex $F$-free $1$-planar graphs. Define $F_t$ as the friendship graph formed by $t$ triangles sharing exactly one common vertex. Tait and Tobin (2017)~\cite{Tait2017} used the fundamental structure of spectral extremal graphs to determine the unique planar graph with maximum spectral radius for sufficiently large order. Subsequently, Zhang, Wang and Wang (2024)~\cite{Zhang2024} characterized the corresponding extremal graph in the class of $1$-planar graphs. In this paper, we focus on $F_t$-free $1$-planar graphs and establish a structural theorem for their spectral extremal graphs for all $t\geq1$ and sufficiently large $n$. More precisely, every extremal graph is connected and contains a copy of $K_{2,n-2}$, and for $t\geq2$ the two distinguished vertices are adjacent and the subgraph induced by the remaining vertices is a bipartite graph. Based on this structure result together with the drawing properties of $K_{3,6}$, we determine $\textit{spex}_{\mathcal{P}_1}(n,F_t)$ and characterize its unique extremal graph.

math.CO↗

arXiv2026

Independence number, essential connectivity and the distance spectral radius of graphs

An independent set of a graph G is a subset of VG, no two of which are adjacent. The cardinality of a maximum independent set in a graph G is called the independence number of G, denoted by alpha(G). The essential connectivity kappa'(G) of a graph G is denoted as the minimum number of vertices of G whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the n-vertex connected graphs with given independence number and essential connectivity that attain the minimum distance spectral radius, and fully characterize the corresponding extremal graphs.

math.CO↗

arXiv2026

Toward Federated Large Language Models in Medicine: A Parameter-Efficient Framework for Privacy-Preserving, Multi-Institutional Adaptation

Large language models (LLMs) are increasingly adapted for medical applications, but most are trained using data from a single institution because privacy and governance constraints prevent multi-institutional data sharing. As a result, these models often generalize poorly across heterogeneous healthcare systems. We address this gap by introducing Fed-MedLoRA and Fed-MedLoRA+, a parameter-efficient federated framework for collaborative LLM adaptation across healthcare institutions. Fed-MedLoRA transmits only low-rank adapters rather than full model weights, reducing communication overhead. We also evaluate a privacy-preserving variant that applies Gaussian perturbation to transmitted adapter updates. Fed-MedLoRA+ further incorporates adaptive aggregation to better address cross-site heterogeneity in patient populations, annotation practices, and disease distributions. We evaluate the framework on clinical information extraction across five independent patient cohorts totaling 42,198 entities and 41,570 relations, and compare it with zero-shot and fine-tuned LLMs, domain-specific BERT models, and federated baselines. Across all settings, the proposed methods consistently improve extraction performance and generalize better to heterogeneous cohorts. In a real-world case study using clinical notes from the Yale New Haven Health System, the framework demonstrates strong performance under low-resource new-site deployment. These results suggest that federated, parameter-efficient LLM adaptation is feasible, scalable, and effective for multi-institutional clinical deployment.

cs.CL↗

arXiv2026

Spectral extremal problems on planar and outerplanar graphs without $C_{k,l}

Let $\emph{spex}_{\mathcal{P}}(n,F)$ and $\emph{spex}_{\mathcal{OP}}(n,F)$ be the maximum spectral radius among all $n$-vertex $F$-free planar graphs and outerplanar graphs, respectively. Define $C_{k,l}$ as a graph obtained from $C_k \cup C_l$ such that the two cycles share a common vertex, where $l \ge k \ge 3$. In the 1990s, Cvetković and Rowlinson conjectured $K_1 + P_{n-1}$ maximizes spectral radius in outerplanar graphs on $n$ vertices, while Boots and Royle (independently, Cao and Vince) conjectured $K_2 + P_{n-2} $ does so in planar graphs. Tait and Tobin [J. Combin. Theory Ser. B, 2017] determined the fundamental structure as the key to confirming these two conjectures for sufficiently large $n$. Recently, Yin and Li [Discrete Mathematics, 2026] characterized the extremal graphs for $\emph{spex}_{\mathcal{P}}(n,B_{t,l})$ and $\emph{spex}_{\mathcal{OP}}(n,B_{t,l})$ in planar and outerplanar graphs on the basis of this key idea, where $B_{t,l}$ denotes the graph obtained by $t$ edge-disjoint $l$-cycles sharing a common vertex. In this paper, we focus on planar and outerplanar graphs without $C_{k,l}$, and determine $\emph{spex}_{\mathcal{P}}(n,C_{k,l})$ and $\emph{spex}_{\mathcal{OP}}(n,C_{k,l})$ along with their unique extremal graphs for all $l \geq k \geq 3$ and large $n$.

math.CO↗

arXiv2026

Towards Interpretable Federated Learning

Federated learning (FL) enables multiple data owners to build machine learning models collaboratively without exposing their private local data. In order for FL to achieve widespread adoption, it is important to balance the need for performance, privacy-preservation and interpretability, especially in mission critical applications such as finance and healthcare. Thus, interpretable federated learning (IFL) has become an emerging topic of research attracting significant interest from the academia and the industry alike. Its interdisciplinary nature can be challenging for new researchers to pick up. In this paper, we bridge this gap by providing (to the best of our knowledge) the first survey on IFL. We propose a unique IFL taxonomy which covers relevant works enabling FL models to explain the prediction results, support model debugging, and provide insights into the contributions made by individual data owners or data samples, which in turn, is crucial for allocating rewards fairly to motivate active and reliable participation in FL. We conduct comprehensive analysis of the representative IFL approaches, the commonly adopted performance evaluation metrics, and promising directions towards building versatile IFL techniques.

cs.LG↗

arXiv2026

Visual Aesthetic Benchmark: Can Frontier Models Judge Beauty?

Multimodal large language models (MLLMs) are now routinely deployed for visual understanding, generation, and curation. A substantial fraction of these applications require an explicit aesthetic judgment. Most existing solutions reduce this judgment to predicting a scalar score for a single image. We first ask whether such scores faithfully capture comparative preference: in a controlled study with eight expert annotators, score-derived rankings align poorly with the same annotators' direct comparisons, while direct ranking yields substantially higher inter-annotator agreement on best- and worst-image labels. Motivated by this finding, we introduce the Visual Aesthetic Benchmark (VAB), which casts aesthetic evaluation as comparative selection over candidate sets with matched subject matter. VAB contains 400 tasks and 1,195 images across fine art, photography, and illustration, with labels derived from the consensus of 10 independent expert judges per task. Evaluating 20 frontier MLLMs and six dedicated visual-quality reward models, we find that the strongest system identifies both the best and the worst image correctly across three random permutations of the candidate order in only 26.5% of tasks, far below the 68.9% achieved by human experts. Fine-tuning a 35B-parameter model on 2,000 expert examples brings its accuracy close to that of a 397B-parameter open-weight model, suggesting that the comparative signal in VAB is transferable. Together, these results expose a clear and measurable gap between current multimodal models and expert aesthetic judgment, and VAB provides the first set-based, expert-grounded testbed on which that gap can be tracked and closed.

cs.CV↗

arXiv2026

Spectral radius, toughness and $k$-factor of graphs

A $k$-regular spanning subgraph of $G$ is called a $k$-factor. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] presented a tight sufficient condition in terms of the spectral radius for a connected 1-tough graph to contain a connected 2-factor (Hamilton cycle). Then it is interesting to consider the following problem: What is the spectral radius condition to guarantee the existence of a $k$-factor with $k\ge3$ in a connected 1-tough graph $G$ with $δ(G)\ge k$? In this paper, we completely solve this problem.

math.CO↗

arXiv2025

Dynamical control of quantum photon-photon interaction with phase change material

Quantum interference can produce a pivotal effective photon-photon interaction, enabling the exploration of various quantum information technologies that beyond the possibilities of classical physics. While such an effective interaction is fundamentally limited to the bosonic nature of photons and the restricted phase responses from commonly used unitary optical elements, loss-induced nonunitary operation provides an alternative degree of freedom to control the quantum interference. Here, we propose and experimentally demonstrate a concise yet powerful tool to unravel fundamental features of quantum interference based on the phase change material vanadium dioxide. Since the insulator-metal transition in an elaborate vanadium dioxide thin film can create any desired particle exchange phase response, we show its tunability over the effective photon-photon interaction between paired photons that are entangled in the symmetric and anti-symmetric forms, which may introduce sophisticated nonunitary operations and functionalities into programmable optical platforms. These results provide an alternative approach to investigate the quantum light-matter interaction, and facilitate the use of quantum interference for various quantum information processing tasks such as quantum simulation and quantum computation.

quant-ph↗

arXiv2025

Self-Aware Adaptive Alignment: Enabling Accurate Perception for Intelligent Transportation Systems

Achieving top-notch performance in Intelligent Transportation detection is a critical research area. However, many challenges still need to be addressed when it comes to detecting in a cross-domain scenario. In this paper, we propose a Self-Aware Adaptive Alignment (SA3), by leveraging an efficient alignment mechanism and recognition strategy. Our proposed method employs a specified attention-based alignment module trained on source and target domain datasets to guide the image-level features alignment process, enabling the local-global adaptive alignment between the source domain and target domain. Features from both domains, whose channel importance is re-weighted, are fed into the region proposal network, which facilitates the acquisition of salient region features. Also, we introduce an instance-to-image level alignment module specific to the target domain to adaptively mitigate the domain gap. To evaluate the proposed method, extensive experiments have been conducted on popular cross-domain object detection benchmarks. Experimental results show that SA3 achieves superior results to the previous state-of-the-art methods.

cs.CV↗

arXiv2025

Classifying and characterizing the evolution of minimum orbit intersection distance for near-Earth asteroids

In this paper, the minimum orbit intersection distances (MOIDs) of near-Earth asteroids (NEAs) over the next 200 years were computed and analyzed in detail. It was shown that the MOID of a NEA relative to the Earth-Moon barycenter (EMB) is usually a superior metric for predicting a potential impact than that relative to the Earth. Subsequently, a novel MOID Evolution Index (MEI) spanning from 0.0 to 9.9 was proposed and the orbits of NEAs are classified into 100 distinct categories by considering the variations of the MOID over time, which is useful for quickly screening and prioritizing hazardous asteroids for future research. Furthermore, it was demonstrated that a linear fitting to the MOID evolution provides a simple yet valid approach for most of the NEAs, which is useful for quickly estimating the MOID value without the need to perform an orbit propagation. As a result, a scheme with several parameters was proposed to characterize the MOID variations as well as the relative position information of the critical points along the orbits associated with the minimum distances. A database incorporating these parameters and the MEI values was therefore established for the cataloged NEAs, enabling the derivation of statistically constrained upper bounds for secular MOID drift rate as function of the semi-major axes. Finally, some special orbital configurations and dynamical mechanisms that may lead to a large deviation from the linear fit or multiple orbit crossings were also investigated, indicating the intricate nature in the patterns of MOID evolution for some NEAs.

astro-ph.EP↗

arXiv2025

HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HYDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HYDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HYDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra_8686.

cs.LG↗

arXiv2025

FedOBD: Opportunistic Block Dropout for Efficiently Training Large-scale Neural Networks through Federated Learning

Large-scale neural networks possess considerable expressive power. They are well-suited for complex learning tasks in industrial applications. However, large-scale models pose significant challenges for training under the current Federated Learning (FL) paradigm. Existing approaches for efficient FL training often leverage model parameter dropout. However, manipulating individual model parameters is not only inefficient in meaningfully reducing the communication overhead when training large-scale FL models, but may also be detrimental to the scaling efforts and model performance as shown by recent research. To address these issues, we propose the Federated Opportunistic Block Dropout (FedOBD) approach. The key novelty is that it decomposes large-scale models into semantic blocks so that FL participants can opportunistically upload quantized blocks, which are deemed to be significant towards training the model, to the FL server for aggregation. Extensive experiments evaluating FedOBD against four state-of-the-art approaches based on multiple real-world datasets show that it reduces the overall communication overhead by more than 88% compared to the best performing baseline approach, while achieving the highest test accuracy. To the best of our knowledge, FedOBD is the first approach to perform dropout on FL models at the block level rather than at the individual parameter level.

cs.LG↗

arXiv2025

Ultrasensitive Transverse Deflection Measurement with Two-photon Interference

Hong-Ou-Mandel (HOM) interference is an intrinsic quantum phenomena that goes beyond the possibilities of classical physics, and enables various applications in quantum metrology. While the timing resolution of HOM-based sensor is generally investigated, the ultimate quantum sensitivity in the estimation of transverse deflection or displacement between paired photons interfering at a balanced beam splitter has been explored relatively little. Here, we present an experimental demonstration of a spatial HOM interferometry for measuring the transverse deflection of an optical beam by using transverse momentum sampling measurements. This feasible scheme suffices to achieve great precision with comparatively little technological effort, which circumvents the stringent requirement in direct imaging resolution at the diffraction limit. We can adaptively determine optimum working points using a Fisher information analysis, and demonstrate an optimized spatial HOM interferometry according to practical applications. These results may significantly facilitate the use of quantum interference for high precision spatial sensing, and pave the way to more complex quantum imaging techniques like nanoscopic microscopy.

quant-ph↗

arXiv2025

Can Textual Gradient Work in Federated Learning?

Recent studies highlight the promise of LLM-based prompt optimization, especially with TextGrad, which automates differentiation'' via texts and backpropagates textual feedback. This approach facilitates training in various real-world applications that do not support numerical gradient propagation or loss calculation. In this paper, we systematically explore the potential and challenges of incorporating textual gradient into Federated Learning (FL). Our contributions are fourfold. Firstly, we introduce a novel FL paradigm, Federated Textual Gradient (FedTextGrad), that allows clients to upload locally optimized prompts derived from textual gradients, while the server aggregates the received prompts. Unlike traditional FL frameworks, which are designed for numerical aggregation, FedTextGrad is specifically tailored for handling textual data, expanding the applicability of FL to a broader range of problems that lack well-defined numerical loss functions. Secondly, building on this design, we conduct extensive experiments to explore the feasibility of FedTextGrad. Our findings highlight the importance of properly tuning key factors (e.g., local steps) in FL training. Thirdly, we highlight a major challenge in FedTextGrad aggregation: retaining essential information from distributed prompt updates. Last but not least, in response to this issue, we improve the vanilla variant of FedTextGrad by providing actionable guidance to the LLM when summarizing client prompts by leveraging the Uniform Information Density principle. Through this principled study, we enable the adoption of textual gradients in FL for optimizing LLMs, identify important issues, and pinpoint future directions, thereby opening up a new research area that warrants further investigation.

cs.LG↗