arXiv subjects

Junpeng Li

Publications and source records attributed to Junpeng Li.

11 recordsLinked to original sources

arXiv2026

Compact balanced threefolds and LCK manifolds with constant holomorphic sectional curvature

A long-standing conjecture in Hermitian geometry says that a compact Hermitian manifold with constant Chern holomorphic sectional curvature $c$ is K\"ahler for $c\neq 0$ and Chern flat for $c=0$. Although the conjecture has been established in complex dimension two, it remains open in general in higher dimensions. We verify the conjecture for compact balanced threefolds when $c\leq 0$. For compact locally conformally K\"ahler manifolds, Chen, Chen, and Nie established the case $c\leq 0$, while Huang and Wan recently settled the remaining case. Inspired by the approach of Huang and Wan, we investigate a generalization of the conjecture for canonical metric connections and establish it for connected compact locally conformally K\"ahler manifolds.

math.DG↗

arXiv2026

Risk-Consistent Multiclass Learning from Random Label-Subset Membership Queries

Obtaining accurate class labels is often costly or unreliable, and may also be limited by privacy or other practical conditions. Compared with asking an annotator to provide the exact class, it is often easier to ask whether the true label belongs to a certain label subset. This query-response form defines a distinct weak-supervision mechanism: weak supervision information is generated through feedback on a label subset. Although weakly supervised learning has studied many learning frameworks, most existing work starts from established weak label objects. A systematic characterization is still lacking for weakly supervised learning generated directly by such query response observations. This paper proposes a multiclass learn ing framework under random label-subset queries. We model the data-generating distribution of query-response observations and derive an unbiased estimator of the target risk under the empirical risk minimization (ERM) framework. To address negative empirical risk and the associated overfitting problem, we introduce corrected risk estimators based on non-negative and absolute-value corrections. Theoretical analysis establishes a conditional generalization and excess-risk bound for the unbiased estimator, and a bias-and-consistency result for the corrected risk estimator. Experiments under the matched random-query mechanism demonstrate the feasibility of direct query-response learning and the stabilization effect of risk correction.

cs.LG↗

arXiv2026

Sensoformer: Robust Sim-to-Real Inference on Variable-Geometry Sensor Sets via Physics-Structured Randomization

Inferring high-dimensional physical states from sparse, ad-hoc sensor arrays is a fundamental challenge across AI for Science and industrial IoT. Standard machine learning architectures struggle in these domains due to irregular, variable-cardinality sensor geometries and the profound sim-to-real distribution shift caused by unmodeled physical heterogeneities. To address these challenges, we propose Sensoformer, a set-attention framework integrated with Physics-Structured Domain Randomization (PSDR). By explicitly randomizing the underlying physical dynamics (e.g., propagation media, extreme noise, and network availability dropout) rather than just visual features, PSDR enforces the learning of domain-invariant physical operators. Using seismic source inversion as a rigorous real-world testbed, Sensoformer is pre-trained on 100,000 synthetics and evaluated on a highly complex real-world catalog. We demonstrate that Sensoformer achieves state-of-the-art precision and outperforms Message Passing Neural Networks (MPNNs) and Neural Operators (e.g., DeepONet) which struggle with extreme spatial sparsity and mixed-modality inputs. Furthermore, interpretability analysis reveals that the attention mechanism autonomously discovers optimal experimental design principles, dynamically prioritizing sparse orthogonal sensors to overcome information bottlenecks.

cs.LG↗

arXiv2025

A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guarantees

Weakly supervised learning has emerged as a practical alternative to fully supervised learning when complete and accurate labels are costly or infeasible to acquire. However, many existing methods are tailored to specific supervision patterns -- such as positive-unlabeled (PU), unlabeled-unlabeled (UU), complementary-label (CLL), partial-label (PLL), or similarity-unlabeled annotations -- and rely on post-hoc corrections to mitigate instability induced by indirect supervision. We propose a principled, unified framework that bypasses such post-hoc adjustments by directly formulating a stable surrogate risk grounded in the structure of weakly supervised data. The formulation naturally subsumes diverse settings -- including PU, UU, CLL, PLL, multi-class unlabeled, and tuple-based learning -- under a single optimization objective. We further establish a non-asymptotic generalization bound via Rademacher complexity that clarifies how supervision structure, model capacity, and sample size jointly govern performance. Beyond this, we analyze the effect of class-prior misspecification on the bound, deriving explicit terms that quantify its impact, and we study identifiability, giving sufficient conditions -- most notably via supervision stratification across groups -- under which the target risk is recoverable. Extensive experiments show consistent gains across class priors, dataset scales, and class counts -- without heuristic stabilization -- while exhibiting robustness to overfitting.

cs.LG↗

arXiv2025

Cost-Sensitive Unbiased Risk Estimation for Multi-Class Positive-Unlabeled Learning

Positive--Unlabeled (PU) learning considers settings in which only positive and unlabeled data are available, while negatives are missing or left unlabeled. This situation is common in real applications where annotating reliable negatives is difficult or costly. Despite substantial progress in PU learning, the multi-class case (MPU) remains challenging: many existing approaches do not ensure \emph{unbiased risk estimation}, which limits performance and stability. We propose a cost-sensitive multi-class PU method based on \emph{adaptive loss weighting}. Within the empirical risk minimization framework, we assign distinct, data-dependent weights to the positive and \emph{inferred-negative} (from the unlabeled mixture) loss components so that the resulting empirical objective is an unbiased estimator of the target risk. We formalize the MPU data-generating process and establish a generalization error bound for the proposed estimator. Extensive experiments on \textbf{eight} public datasets, spanning varying class priors and numbers of classes, show consistent gains over strong baselines in both accuracy and stability.

cs.LG↗

arXiv2025

Learning from N-Tuple Data with M Positive Instances: Unbiased Risk Estimation and Theoretical Guarantees

Weakly supervised learning often operates with coarse aggregate signals rather than instance labels. We study a setting where each training example is an $n$-tuple containing exactly m positives, while only the count m per tuple is observed. This NTMP (N-tuple with M positives) supervision arises in, e.g., image classification with region proposals and multi-instance measurements. We show that tuple counts admit a trainable unbiased risk estimator (URE) by linking the tuple-generation process to latent instance marginals. Starting from fixed (n,m), we derive a closed-form URE and extend it to variable tuple sizes, variable counts, and their combination. Identification holds whenever the effective mixing rate is separated from the class prior. We establish generalization bounds via Rademacher complexity and prove statistical consistency with standard rates under mild regularity assumptions. To improve finite-sample stability, we introduce simple ReLU corrections to the URE that preserve asymptotic correctness. Across benchmarks converted to NTMP tasks, the approach consistently outperforms representative weak-supervision baselines and yields favorable precision-recall and F1 trade-offs. It remains robust under class-prior imbalance and across diverse tuple configurations, demonstrating that count-only supervision can be exploited effectively through a theoretically grounded and practically stable objective.

cs.LG↗

arXiv2025

Structure-Preserving Margin Distribution Learning for High-Order Tensor Data with Low-Rank Decomposition

The Large Margin Distribution Machine (LMDM) is a recent advancement in classifier design that optimizes not just the minimum margin (as in SVM) but the entire margin distribution, thereby improving generalization. However, existing LMDM formulations are limited to vectorized inputs and struggle with high-dimensional tensor data due to the need for flattening, which destroys the data's inherent multi-mode structure and increases computational burden. In this paper, we propose a Structure-Preserving Margin Distribution Learning for High-Order Tensor Data with Low-Rank Decomposition (SPMD-LRT) that operates directly on tensor representations without vectorization. The SPMD-LRT preserves multi-dimensional spatial structure by incorporating first-order and second-order tensor statistics (margin mean and variance) into the objective, and it leverages low-rank tensor decomposition techniques including rank-1(CP), higher-rank CP, and Tucker decomposition to parameterize the weight tensor. An alternating optimization (double-gradient descent) algorithm is developed to efficiently solve the SPMD-LRT, iteratively updating factor matrices and core tensor. This approach enables SPMD-LRT to maintain the structural information of high-order data while optimizing margin distribution for improved classification. Extensive experiments on diverse datasets (including MNIST, images and fMRI neuroimaging) demonstrate that SPMD-LRT achieves superior classification accuracy compared to conventional SVM, vector-based LMDM, and prior tensor-based SVM extensions (Support Tensor Machines and Support Tucker Machines). Notably, SPMD-LRT with Tucker decomposition attains the highest accuracy, highlighting the benefit of structure preservation. These results confirm the effectiveness and robustness of SPMD-LRT in handling high-dimensional tensor data for classification.

cs.LG↗

arXiv2025

A Unified Empirical Risk Minimization Framework for Flexible N-Tuples Weak Supervision

To alleviate the annotation burden in supervised learning, N-tuples learning has recently emerged as a powerful weakly-supervised method. While existing N-tuples learning approaches extend pairwise learning to higher-order comparisons and accommodate various real-world scenarios, they often rely on task-specific designs and lack a unified theoretical foundation. In this paper, we propose a general N-tuples learning framework based on empirical risk minimization, which systematically integrates pointwise unlabeled data to enhance learning performance. This paper first unifies the data generation processes of N-tuples and pointwise unlabeled data under a shared probabilistic formulation. Based on this unified view, we derive an unbiased empirical risk estimator that generalizes a broad class of existing N-tuples models. We further establish a generalization error bound for theoretical support. To demonstrate the flexibility of the framework, we instantiate it in four representative weakly supervised scenarios, each recoverable as a special case of our general model. Additionally, to address overfitting issues arising from negative risk terms, we adopt correction functions to adjust the empirical risk. Extensive experiments on benchmark datasets validate the effectiveness of the proposed framework and demonstrate that leveraging pointwise unlabeled data consistently improves generalization across various N-tuples learning tasks.

stat.ML↗

arXiv2025

Learning from M-Tuple Dominant Positive and Unlabeled Data

Label Proportion Learning (LLP) addresses the classification problem where multiple instances are grouped into bags and each bag contains information about the proportion of each class. However, in practical applications, obtaining precise supervisory information regarding the proportion of instances in a specific class is challenging. To better align with real-world application scenarios and effectively leverage the proportional constraints of instances within tuples, this paper proposes a generalized learning framework \emph{MDPU}. Specifically, we first mathematically model the distribution of instances within tuples of arbitrary size, under the constraint that the number of positive instances is no less than that of negative instances. Then we derive an unbiased risk estimator that satisfies risk consistency based on the empirical risk minimization (ERM) method. To mitigate the inevitable overfitting issue during training, a risk correction method is introduced, leading to the development of a corrected risk estimator. The generalization error bounds of the unbiased risk estimator theoretically demonstrate the consistency of the proposed method. Extensive experiments on multiple datasets and comparisons with other relevant baseline methods comprehensively validate the effectiveness of the proposed learning framework.

cs.LG↗

arXiv2024

Combining Supervised Learning and Reinforcement Learning for Multi-Label Classification Tasks with Partial Labels

Traditional supervised learning heavily relies on human-annotated datasets, especially in data-hungry neural approaches. However, various tasks, especially multi-label tasks like document-level relation extraction, pose challenges in fully manual annotation due to the specific domain knowledge and large class sets. Therefore, we address the multi-label positive-unlabelled learning (MLPUL) problem, where only a subset of positive classes is annotated. We propose Mixture Learner for Partially Annotated Classification (MLPAC), an RL-based framework combining the exploration ability of reinforcement learning and the exploitation ability of supervised learning. Experimental results across various tasks, including document-level relation extraction, multi-label image classification, and binary PU learning, demonstrate the generalization and effectiveness of our framework.

cs.CL↗

arXiv2023

Semi-automatic Data Enhancement for Document-Level Relation Extraction with Distant Supervision from Large Language Models

Document-level Relation Extraction (DocRE), which aims to extract relations from a long context, is a critical challenge in achieving fine-grained structural comprehension and generating interpretable document representations. Inspired by recent advances in in-context learning capabilities emergent from large language models (LLMs), such as ChatGPT, we aim to design an automated annotation method for DocRE with minimum human effort. Unfortunately, vanilla in-context learning is infeasible for document-level relation extraction due to the plenty of predefined fine-grained relation types and the uncontrolled generations of LLMs. To tackle this issue, we propose a method integrating a large language model (LLM) and a natural language inference (NLI) module to generate relation triples, thereby augmenting document-level relation datasets. We demonstrate the effectiveness of our approach by introducing an enhanced dataset known as DocGNRE, which excels in re-annotating numerous long-tail relation types. We are confident that our method holds the potential for broader applications in domain-specific relation type definitions and offers tangible benefits in advancing generalized language semantic comprehension.

cs.CL↗