Jianxing He

Junyuan He, Zhonghao Sun, Jizu Huang

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical framework for expressing high-order derivatives of functional TTNs, both with or without constraints. Our framework decomposes the total derivative of a given TTN into a summation of TTNs, each corresponding to the partial derivatives of the original TTN. Using this decomposition, we derive the Taylor expansion of vector-valued functions subject to ordinary differential equation constraints or algebraic constraints imposed by Runge--Kutta (RK) methods. As a concrete application, we employ this framework to construct order conditions for RK methods. Due to the intrinsic tensor properties of partial derivatives and the separable tensor structure in RK methods, the Taylor expansion of numerical solutions can be obtained in a manner analogous to that of exact solutions using tensor operators. This enables the order conditions of RK methods to be established by directly comparing the Taylor expansions of the exact and numerical solutions, eliminating the need for mathematical induction. For a given function $\vector{f}$, we derive sharper order conditions that go beyond the classical ones, enabling the identification of situations where a standard RK scheme of order $p$ achieves unexpectedly higher convergence order for the particular function. These results establish new connections between tensor network theory and classical numerical methods, potentially opening new avenues for both analytical exploration and practical computation.

Hongqiao Dong, Wenhao Chi, Ruobing Liang et al.

Medical expert annotators are scarce, and blind reliance on artificial intelligence (AI) can be misleading, motivating approaches in which humans, particularly junior medical trainees or even non-medical personnel, collaborate with AI to achieve robust medical segmentation. Although the Segment Anything Model (SAM) shows promise for general-purpose image segmentation, its performance in human-AI collaboration for specialized medical tasks has not been thoroughly evaluated. Here we present Hi-Seg, a human-in-the-loop segmentation framework for pulmonary nodules built on SAM. Humans iteratively refine prompts through trial-and-error learning and semantic reasoning, progressively guiding SAM toward higher-quality masks. Using chest CT scans from 1,179 patients across 12 centers, we conducted the first large-scale external validation of collaborative human-SAM segmentation. Across all annotator groups, Hi-Seg achieved a mean Dice score of almost 85%, outperforming five state-of-the-art deep learning models by 10-22% and 13 SAM variants by 1-29%. Hi-Seg improved segmentation accuracy while reducing annotation time for medical annotators, and briefly trained non-medical annotators achieved performance comparable to that of the junior medical student. These findings suggest that human-in-the-loop segmentation can reduce clinician workload, enable scalable crowdsourced annotation, and transform clinical workflows by facilitating the safe and efficient integration of foundation models into routine clinical practice.

Juefei He, Yuexing Peng, Wei Li et al.

Relic landslide, formed over a long period, possess the potential for reactivation, making them a hazardous geological phenomenon. While reliable relic landslide detection benefits the effective monitoring and prevention of landslide disaster, semantic segmentation using high-resolution remote sensing images for relic landslides faces many challenges, including the object visual blur problem, due to the changes of appearance caused by prolonged natural evolution and human activities, and the small-sized dataset problem, due to difficulty in recognizing and labelling the samples. To address these challenges, a semantic segmentation model, termed mask-recovering and interactive-feature-enhancing (MRIFE), is proposed for more efficient feature extraction and separation. Specifically, a contrastive learning and mask reconstruction method with locally significant feature enhancement is proposed to improve the ability to distinguish between the target and background and represent landslide semantic features. Meanwhile, a dual-branch interactive feature enhancement architecture is used to enrich the extracted features and address the issue of visual ambiguity. Self-distillation learning is introduced to leverage the feature diversity both within and between samples for contrastive learning, improving sample utilization, accelerating model convergence, and effectively addressing the problem of the small-sized dataset. The proposed MRIFE is evaluated on a real relic landslide dataset, and experimental results show that it greatly improves the performance of relic landslide detection. For the semantic segmentation task, compared to the baseline, the precision increases from 0.4226 to 0.5347, the mean intersection over union (IoU) increases from 0.6405 to 0.6680, the landslide IoU increases from 0.3381 to 0.3934, and the F1-score increases from 0.5054 to 0.5646.