arXiv subjects

Yi Ouyang

Publications and source records attributed to Yi Ouyang.

At least 19 recordsLinked to original sources

arXiv2026

Smoothness of Shortest Isogenies to Frobenius Conjugates

Let $E$ be chosen uniformly from the geometric isomorphism classes of supersingular elliptic curves over $\overline{\mathbb{F}}_p$ and $δ_E$ be the minimum degree of isogenies from $E$ to its Frobenius conjugate $E^{(p)}$. We establish bounds for the smoothness probability of $δ_E$ and hence affirm Wesolowski's $p^{1/3+o(1)}$ attack on the supersingular endomorphism ring problem is unconditional. We also establish a uniform asymptotic formula, with a main term expressed in terms of Dirichlet $L$ values, for the probability that a connection isogeny of degree $n$ exists between $E$ and $E^{(p)}$.

math.NT↗

arXiv2026

GLARE: Generating Listening Heads with Appropriate Reactions

While talking head generation has advanced rapidly, generating natural listener behavior in dyadic conversations, which know when to react, how to react, and with what type of response, remains underexplored. Existing dyadic datasets lack fine-grained listener reaction annotations, and prevailing evaluation metrics inherited from talking-head and video generation measure visual realism rather than whether a listener reacted appropriately. We address these gaps along three aspects. First, we curate a listening-head-specific dataset built from RealTalk and Seamless Interaction, comprising approximately 147 hours of paired speaker-listener videos with 64,557 event-level reaction annotations across six categories: nodding, head shaking, smiling, laughing, frowning, and surprised. Second, we introduce an audio-driven baseline built on a flow-matching transformer, namely GLARE, with prosody conditioning derived from Qwen2-Audio and a temporal reaction loss that explicitly supervises frame-wise reactions. Third, we propose a reaction-oriented evaluation protocol that jointly measures reaction occurrence (R-F1), temporal alignment (R-tIoU), asymmetric temporal deviation (R-ATD), and reaction-region visual quality (R-FID), giving a more behaviorally grounded assessment than visual-quality-only metrics. Experiment results show consistent gains over prior listening-head methods in both visual fidelity and reaction-level metrics, suggesting that reaction-aware data, modeling, and evaluation are critical for natural listening behavior.

cs.CV↗

arXiv2026

Beyond Words: Multimodal LLM Knows When to Speak

Chatbots via large language models (LLMs) generate fluent responses but often struggle with when to speak, especially for brief, timely listener reactions during ongoing dialogue. We present a multimodal strategy for LLMs, which leverages synchronized video, audio, and text cues to improve conversational timing awareness. The strategy reformulates response timing as a dense response-type prediction task, enabling an agent to decide whether to remain silent, produce a short reaction, or start a full response under streaming constraints. Therefore, we introduce a curated multimodal dataset from real-world dyadic conversational videos with temporally aligned modalities and fine-grained reaction type annotations. Moreover, we design a multimodal strategy, MM-When2Speak, with a multimodal integration module on top of an LLM backbone. Experiments across various modality settings and strong LLM baselines show that MM-When2Speak achieves up to a 3x improvement in response type prediction performance, highlighting the importance of multimodal perception for natural and engaging conversational interaction.

cs.CV↗

arXiv2026

On quadratic binomial vectorial functions with maximal bent components

Assume $n=2m\geq 2$ and let $F(x)=x^{d_1}+x^{d_2}$ be a binomial vectorial function over $\F_{2^n}$ possessing the maximal number (i.e. $2^n-2^m$) of bent components. Suppose the $2$-adic Hamming weights $\wt_2(d_1)$ and $\wt_2(d_2)$ are both at most $2$, we prove that $F(x)$ is affine equivalent to either $x^{2^m+1}$ or $x^{2^i}(x+x^{2^m})$, provided that \[ \ell(n):=\min_{γ:~\F_2(γ)=\F_{2^n}} \dim_{\F_2}\F_2[σ]γ>m, \] where $σ$ is the Frobenius $(x\mapsto x^2)$ on $\F_{2^n}$, and $\gcd(d_1,d_2,2^m-1)>1$. Under this condition, we also establish two bounds on the nonlinearity and the differential uniformity of $F$ by means of the cardinality of its image set.

cs.IT↗

arXiv2026

Sub-optimality bounds for certainty equivalent policies in partially observed systems

In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as follows: the optimal action at each time is obtained by evaluating the optimal state-feedback policy of the stochastic linear system at the minimum mean square error (MMSE) estimate of the state. Motivated by this interpretation, we consider certainty equivalent policies for general (non-linear) partially observed stochastic systems that allow for any state estimate rather than restricting to MMSE estimates. In such settings, the certainty equivalent policy is not optimal. For models where the cost and the dynamics are smooth in an appropriate sense, we derive upper bounds on the sub-optimality of certainty equivalent policies. We present several examples to illustrate the results.

math.OC↗

arXiv2025

When Top-ranked Recommendations Fail: Modeling Multi-Granular Negative Feedback for Explainable and Robust Video Recommendation

Existing video recommendation systems, relying mainly on ID-based embedding mapping and collaborative filtering, often fail to capture in-depth video content semantics. Moreover, most struggle to address biased user behaviors (e.g., accidental clicks, fast skips), leading to inaccurate interest modeling and frequent negative feedback in top recommendations with unclear causes. To tackle this issue, we collect real-world user video-watching sequences, annotate the reasons for users' dislikes, and construct a benchmark dataset for personalized explanations. We then introduce the Agentic Explainable Negative Feedback (ENF) framework, which integrates three core components: (1) the Profile Agent, extracting behavioral cues from users' historical data to derive psychological and personality profiles; (2) the Video Agent, performing comprehensive multimodal video analysis; and (3) the Reason Agent, synthesizing information from the other two agents to predict user engagement and generate explanations. Additionally, we propose the S-GRPO algorithm, enabling the model to progressively address complex tasks during reinforcement fine-tuning. Experimental results on the collected dataset show that our method significantly outperforms state-of-the-art baselines in negative feedback prediction and reason explanation. Notably, it achieves an 8.6% improvement over GPT-4o in reason classification. Deployment on the business platform further validates its benefits: increasing average user watch time by 6.2%, reducing the fast-skip rate by 9.4%, and significantly enhancing user satisfaction.

cs.MM↗

arXiv2025

Generalized connectedness and Bertini-type theorems over real closed fields

In this paper, we establish a real closed analogue of Bertini's theorem. Let $R$ be a real closed field and $X$ a formally real integral algebraic variety over $R$. We show that if the zero locus of a nonzero global section $s$ of an invertible sheaf on $X$ has a formally real generic point, then $s$ does not change sign on $X$, and vice versa under certain conditions. As a consequence, we demonstrate that there exists a nonempty open subset of hypersurface sections preserving formal reality and integrality for quasi-projective varieties of dimension $\geq 2$ under these conditions.

math.AG↗

arXiv2025

Finiteness of Pythagoras numbers of finitely generated real algebras

In this paper, we establish two finiteness results and propose a conjecture concerning the Pythagoras number $P(A)$ of a finitely generated real algebra $A$. Let $X \hookrightarrow \mathbb{P}^n$ be an integral projective surface over $\mathbb{R}$, let $\widetilde{X}$ be the normalization of $X$, and let $s \in Γ(X,\mathcal{O}_X(1))$ be a nonzero section such that $\bigl(\widetilde{X}_{s=0}\bigr)^{\mathrm{red}}$ is formally real. We prove $P\bigl(Γ(X_{s\neq 0})\bigr)=\infty$. As a corollary, the Pythagoras numbers of integral smooth affine curves over $\mathbb{R}$ are shown to be unbounded. For any finitely generated $\mathbb{R}$-algebra $A$, if the Zariski closure of the real points of $\mathrm{Spec}(A)$ has dimension less than two, we demonstrate $P(A)<\infty$.

math.NT↗

arXiv2025

Divide, Weight, and Route: Difficulty-Aware Optimization with Dynamic Expert Fusion for Long-tailed Recognition

Long-tailed visual recognition is challenging not only due to class imbalance but also because of varying classification difficulty across categories. Simply reweighting classes by frequency often overlooks those that are intrinsically hard to learn. To address this, we propose \textbf{DQRoute}, a modular framework that combines difficulty-aware optimization with dynamic expert collaboration. DQRoute first estimates class-wise difficulty based on prediction uncertainty and historical performance, and uses this signal to guide training with adaptive loss weighting. On the architectural side, DQRoute employs a mixture-of-experts design, where each expert specializes in a different region of the class distribution. At inference time, expert predictions are weighted by confidence scores derived from expert-specific OOD detectors, enabling input-adaptive routing without the need for a centralized router. All components are trained jointly in an end-to-end manner. Experiments on standard long-tailed benchmarks demonstrate that DQRoute significantly improves performance, particularly on rare and difficult classes, highlighting the benefit of integrating difficulty modeling with decentralized expert routing.

cs.CV↗

arXiv2025

AutoPal: Autonomous Adaptation to Users for Personal AI Companionship

Previous research has demonstrated the potential of AI agents to act as companions that can provide constant emotional support for humans. In this paper, we emphasize the necessity of autonomous adaptation in personal AI companionship, an underexplored yet promising direction. Such adaptability is crucial as it can facilitate more tailored interactions with users and allow the agent to evolve in response to users' changing needs. However, imbuing agents with autonomous adaptability presents unique challenges, including identifying optimal adaptations to meet users' expectations and ensuring a smooth transition during the adaptation process. To address them, we devise a hierarchical framework, AutoPal, that enables controllable and authentic adjustments to the agent's persona based on user interactions. A personamatching dataset is constructed to facilitate the learning of optimal persona adaptations. Extensive experiments demonstrate the effectiveness of AutoPal and highlight the importance of autonomous adaptability in AI companionship.

cs.CL↗

arXiv2025

On imaginary quadratic fields with non-cyclic class groups

For a fixed abelian group $H$, let $N_H(X)$ be the number of square-free positive integers $d\leq X$ such that H is a subgroup of $CL(\mathbb{Q}(\sqrt{-d}))$. We obtain asymptotic lower bounds for $N_H(X)$ as $X\to\infty$ in two cases: $H=\mathbb{Z}/g_1\mathbb{Z}\times (\mathbb{Z}/2\mathbb{Z})^l$ for $l\geq 2$ and $2\nmid g_1\geq 3$, $H=(\mathbb{Z}/g\mathbb{Z})^2$ for $2\nmid g\geq 5$. More precisely, for any $ε>0$, we showed $N_H(X)\gg X^{\frac{1}{2}+\frac{3}{2g_1+2}-ε}$ when $H=\mathbb{Z}/g_1\mathbb{Z}\times (\mathbb{Z}/2\mathbb{Z})^l$ for $l\geq 2$ and $2\nmid g_1\geq 3$. For the second case, under a well known conjecture for square-free density of integral multivariate polynomials, for any $ε>0$, we showed $N_H(X)\gg X^{\frac{1}{g-1}-ε}$ when $H=(\mathbb{Z}/g\mathbb{Z})^2$ for $ g\geq 5$. The first case is an adaptation of Soundararajan's results for $H=\mathbb{Z}/g\mathbb{Z}$, and the second conditionally improves the bound $X^{\frac{1}{g}-ε}$ due to Byeon and the bound $X^{\frac{1}{g}}/(\log X)^{2}$ due to Kulkarni and Levin.

math.NT↗

arXiv2025

A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization

We study the set of continuous functions that admit no spurious local optima (i.e. local minima that are not global minima) which we term \textit{global functions}. They satisfy various powerful properties for analyzing nonconvex and nonsmooth optimization problems. For instance, they satisfy a theorem akin to the fundamental uniform limit theorem in the analysis regarding continuous functions. Global functions are also endowed with useful properties regarding the composition of functions and change of variables. Using these new results, we show that a class of nonconvex and nonsmooth optimization problems arising in tensor decomposition applications are global functions. This is the first result concerning nonconvex methods for nonsmooth objective functions. Our result provides a theoretical guarantee for the widely-used $\ell_1$ norm to avoid outliers in nonconvex optimization.

math.OC↗

arXiv2024

Semi-supervised Credit Card Fraud Detection via Attribute-Driven Graph Representation

Credit card fraud incurs a considerable cost for both cardholders and issuing banks. Contemporary methods apply machine learning-based classifiers to detect fraudulent behavior from labeled transaction records. But labeled data are usually a small proportion of billions of real transactions due to expensive labeling costs, which implies that they do not well exploit many natural features from unlabeled data. Therefore, we propose a semi-supervised graph neural network for fraud detection. Specifically, we leverage transaction records to construct a temporal transaction graph, which is composed of temporal transactions (nodes) and interactions (edges) among them. Then we pass messages among the nodes through a Gated Temporal Attention Network (GTAN) to learn the transaction representation. We further model the fraud patterns through risk propagation among transactions. The extensive experiments are conducted on a real-world transaction dataset and two publicly available fraud detection datasets. The result shows that our proposed method, namely GTAN, outperforms other state-of-the-art baselines on three fraud detection datasets. Semi-supervised experiments demonstrate the excellent fraud detection performance of our model with only a tiny proportion of labeled data.

cs.LG↗

arXiv2024

COOL: Comprehensive Knowledge Enhanced Prompt Learning for Domain Adaptive Few-shot Fake News Detection

Most Fake News Detection (FND) methods often struggle with data scarcity for emerging news domain. Recently, prompt learning based on Pre-trained Language Models (PLM) has emerged as a promising approach in domain adaptive few-shot learning, since it greatly reduces the need for labeled data by bridging the gap between pre-training and downstream task. Furthermore, external knowledge is also helpful in verifying emerging news, as emerging news often involves timely knowledge that may not be contained in the PLM's outdated prior knowledge. To this end, we propose COOL, a Comprehensive knOwledge enhanced prOmpt Learning method for domain adaptive few-shot FND. Specifically, we propose a comprehensive knowledge extraction module to extract both structured and unstructured knowledge that are positively or negatively correlated with news from external sources, and adopt an adversarial contrastive enhanced hybrid prompt learning strategy to model the domain-invariant news-knowledge interaction pattern for FND. Experimental results demonstrate the superiority of COOL over various state-of-the-arts.

cs.CL↗

arXiv2024

Divisibility of class numbers of quadratic fields and a conjecture of Iizuka

Assume $x,\ y,\ n$ are positive integers and $n$ is odd. In this note, we show that the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{x^{2}-y^{n}})$ is divisible by $n$ for fixed $x, n$ if $\gcd(2x,y)=1$ and $y>C$ where $C$ is a constant depending only on $x$ and $n$. Based on this result, for any odd integer $n$ and any positive integer $m$, we construct an infinite family of $m+1$ successive imaginary quadratic fields $\mathbb{Q}(\sqrt{d})$, $\mathbb{Q}(\sqrt{d+1^{2}})$, $\cdots$, $\mathbb{Q}(\sqrt{d+m^{2}})$ $(d\in \mathbb{Z})$ whose class numbers are all divisible by $n$.

math.NT↗

arXiv2024

Generation is better than Modification: Combating High Class Homophily Variance in Graph Anomaly Detection

Graph-based anomaly detection is currently an important research topic in the field of graph neural networks (GNNs). We find that in graph anomaly detection, the homophily distribution differences between different classes are significantly greater than those in homophilic and heterophilic graphs. For the first time, we introduce a new metric called Class Homophily Variance, which quantitatively describes this phenomenon. To mitigate its impact, we propose a novel GNN model named Homophily Edge Generation Graph Neural Network (HedGe). Previous works typically focused on pruning, selecting or connecting on original relationships, and we refer to these methods as modifications. Different from these works, our method emphasizes generating new relationships with low class homophily variance, using the original relationships as an auxiliary. HedGe samples homophily adjacency matrices from scratch using a self-attention mechanism, and leverages nodes that are relevant in the feature space but not directly connected in the original graph. Additionally, we modify the loss function to punish the generation of unnecessary heterophilic edges by the model. Extensive comparison experiments demonstrate that HedGe achieved the best performance across multiple benchmark datasets, including anomaly detection and edgeless node classification. The proposed model also improves the robustness under the novel Heterophily Attack with increased class homophily variance on other graph classification tasks.

cs.LG↗

arXiv2024

Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces

For two supersingular elliptic curves $E$ and $E'$ defined over $\mathbb{F}_{p^2}$, let $[E \times E']$ be the superspecial abelian surface with the principal polarization $\{0\} \times E' + E \times \{0\}$. We determine local structure of the vertices $[E \times E']$ in the $(\ell, \ell)$-isogeny graph of principally polarized superspecial abelian surfaces where either $E$ or $E'$ is defined over $\mathbb{F}_p$. We also present a simple new proof of the main theorem in \cite{LOX20}.

math.NT↗

arXiv2024

Model approximation in MDPs with unbounded per-step cost

We consider the problem of designing a control policy for an infinite-horizon discounted cost Markov decision process $\mathcal{M}$ when we only have access to an approximate model $\hat{\mathcal{M}}$. How well does an optimal policy $\hatπ^{\star}$ of the approximate model perform when used in the original model $\mathcal{M}$? We answer this question by bounding a weighted norm of the difference between the value function of $\hatπ^\star $ when used in $\mathcal{M}$ and the optimal value function of $\mathcal{M}$. We then extend our results and obtain potentially tighter upper bounds by considering affine transformations of the per-step cost. We further provide upper bounds that explicitly depend on the weighted distance between cost functions and weighted distance between transition kernels of the original and approximate models. We present examples to illustrate our results.

math.OC↗