Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable estimation, especially for high-dimensional data. This paper suggests a flexible parametric structure to tails, and this enables us to conduct the estimation at quantile levels with rich observations and then to extrapolate the fitted structures to far tails. The proposed model depends on some quantile indices and hence is called the quantile index regression. Moreover, the composite quantile regression method is employed to obtain non-crossing quantile estimators, and this paper further establishes their theoretical properties, including asymptotic normality for the case with low-dimensional covariates and non-asymptotic error bounds for that with high-dimensional covariates. Simulation studies and an empirical example are presented to illustrate the usefulness of the new model.
In intelligent education, personalized mathematics question generation aims to produce mathematics questions that satisfy educational requirements while supporting adaptive assessment and learning. Existing LLM-based single-agent and multi-agent methods improve generation flexibility, but they still tend to rely on aggregated feedback or model randomness, making it difficult to jointly ensure dimension-wise objective alignment and controllable diversity. To address these challenges, we propose EduAgentQG, a multi-agent collaborative framework for personalized mathematics question generation with explicit diversity and objective-aware evaluation. EduAgentQG organizes question generation as a closed-loop process of planning, writing, evaluation, refinement, and checking: structured generation plans and multiple generation directions guide candidate generation, while fine-grained evaluation verifies logical correctness, solvability, and objective alignment in knowledge concepts, difficulty, grade level, and core competencies. We first construct a mathematics question generation benchmark containing 10,273 questions across Grades 1-9, covering 634 knowledge concepts, 16 core competencies, and three difficulty levels; for evaluation, it is organized into two subsets: MathChoice, with 489 educational objectives for multiple-choice question generation, and MathBlank, with 500 educational objectives for fill-in-the-blank question generation. Experiments using Gemini-2.5-Flash, GPT-4o-mini, and Qwen2.5-72B-Instruct show that EduAgentQG consistently outperforms COT, COTN, ReAct, and EQPR in diversity, Objective Consistency, and Win Rate. On Gemini-2.5-Flash, EduAgentQG improves Win Rate by 3.90 and 4.75 percentage points on MathChoice and MathBlank, respectively, over the strongest baseline, demonstrating its ability to generate diverse, solvable, and educationally aligned personalized mathematics questions with stronger controllability.
Multi-task visual grounding (MTVG) covers two sub-tasks: Referring Expression Comprehension (REC) and Referring Expression Segmentation (RES). Existing approaches typically follow a pipeline of independent visual and linguistic feature extraction, a cross-modal interaction module, and separate prediction heads. Despite this progress, this line has two limitations: (1) lacking a careful design of where to inject language into the visual backbone, they need an extra cross-modal fusion module, increasing model complexity and computational cost; (2) the relationship between REC and RES is underexploited, although the two tasks target the same object and share the same center. To address these issues, we propose a Progressive Language-guided Visual Learning framework (PLVL), which mines the inherent visual features while progressively injecting language information to learn linguistic-related visual features. Thus PLVL fully leverages language guidance without an additional cross-modal fusion module. Moreover, since RES is a pixel-wise classification task and both tasks target the same object, their center cues may be correlated. We therefore adopt a shared-representation multi-task head with grouped feature routing while keeping separate task-specific losses. Experiments on RefCOCO validate our language-guided backbone and shared-representation head for both REC and RES. On RefCOCOg val(U), PLVL surpasses EEVG by 1.98% (REC) and 1.06% (RES) under traditional training, and by 4.01% (REC) and 3.69% (RES) with multi-dataset pre-training. Code is available at https://github.com/jcwang0602/PLVL
This paper introduces an interactive continual learning paradigm in which AI models dynamically learn new skills from real-time human feedback while retaining prior knowledge. This paradigm addresses two key limitations of traditional continual learning: (1) it enables dynamic model updates using streaming, real-time human-annotated data, rather than static datasets with fixed labels, and (2) it relaxes the assumption of clean labels by explicitly handling the noisy feedback common in real-world interactions. To tackle these challenges, we propose RiCL, a Reinforced interactive Continual Learning framework that leverages Large Language Models (LLMs) to learn new skills effectively from dynamic feedback. RiCL incorporates three key components: a temporal consistency-aware purifier to automatically discern clean samples from noisy ones in data streams; an interaction-aware direct preference optimization strategy to align model behavior with human intent by reconciling AI-generated and human-provided feedback; and a noise-resistant contrastive learning module that captures robust representations by exploiting inherent data relationships, thereby reducing reliance on potentially unreliable labels. Extensive experiments on two benchmark datasets (FewRel and Tacred), contaminated with realistic noise patterns, demonstrate that our RiCL approach substantially outperforms existing integrations of state-of-the-art online continual learning and noisy-label learning methods.
For a graph F, let h_F(n,q) be the minimum number of copies of F in an n-vertex graph with ex(n,F)+q edges, where ex(n,F) is the maximum number of edges in an n-vertex F-free graph. Let c(n,F) be the minimum number of copies obtained by adding one edge to an extremal F-free graph. Mubayi's supersaturation conjecture predicts, under a stability hypothesis, that h_F(n,q)≥ q c(n,F). Ma and Yuan recently constructed stable graph counterexamples for every fixed q≥4; they asked whether the one-edge equality h_F(n,1)=c(n,F) might still hold for every graph F containing a cycle. We give a negative answer to their question. For each integer t≥6, let H_t be obtained from the t-vertex path by replacing each edge with a 3t-page book, using disjoint page vertices for different path edges. Then h_H_t(n,1)<c(n,H_t) for infinitely many values of n. Moreover, by taking t large, the ratio h_H_t(n,1)/c(n,H_t) can be made arbitrarily small along infinitely many values of n.
