Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic $L^2(Ω)$-error bounds for FK-PINNs with $\tanh$ activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of $\tanh$ neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schrödinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.

Physics-Aware Query-Conditioned Graph Attention Networks for Radio Map Estimation

Radio map estimation from sparse measurements is fundamental to wireless network planning, optimization, and localized map updating. Most recent learning-based approaches formulate the problem as dense map completion over a predefined grid, whereas many practical deployments require estimating transmitter-specific received signal strength only at queried locations or refining an existing map after local changes. This paper proposes a physics-aware query-conditioned hierarchical graph attention network for transmitter-resolved point-wise radio map estimation. For each queried target--transmitter pair, the proposed encoder constructs a bounded local graph over sampled reference observations and aggregates reference-to-query evidence through transmitter-referenced geometric descriptors. A global graph then exchanges representation-level context among nearby target locations to improve neighborhood consistency without revisiting a large number of reference measurements. On top of this shared architecture, we instantiate three operating regimes: direct RSS estimation, prior-conditioned residual correction, and post-hoc gated attenuation of the learned correction. The framework uses only measurement-side quantities and does not rely on environment-side inputs. Simulations on the DeepMIMO scenario show that, in the direct regime, the proposed HGAT achieves the lowest RMSE and MAE among the evaluated learning-based baselines on all reported sites. When conventional prior estimate is available, the residual and gated regimes further reduce the prior error.

Generative Path-Finding Method for Wasserstein Gradient Flow

Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the full path from an arbitrary initial distribution to equilibrium is challenging, especially in high dimensions. Eulerian methods suffer from the curse of dimensionality, while existing Lagrangian approaches based on particles or generative maps do not naturally improve efficiency through time step tuning. We propose GenWGP, a generative path finding framework for Wasserstein gradient paths. GenWGP learns a generative flow that transports mass from an initial density to an unknown equilibrium distribution by minimizing a path loss that encodes the full trajectory and its terminal equilibrium condition. The loss is derived from a geometric action functional motivated by Dawson Gartner large deviation theory for empirical distributions of interacting diffusion systems. We formulate both a finite horizon action under physical time parametrization and a reparameterization invariant geometric action based on Wasserstein arclength. Using normalizing flows, GenWGP computes a geometric curve toward equilibrium while enforcing approximately constant intrinsic speed between adjacent network layers, so that discretized distributions remain nearly equidistant in the Wasserstein metric along the path. This avoids delicate time stepping constraints and enables stable training that is largely independent of temporal or geometric discretization. Experiments on Fokker Planck and aggregation type problems show that GenWGP matches or exceeds high fidelity reference solutions with only about a dozen discretization points while capturing complex dynamics.

Human Gaze-based Dual Teacher Guidance Learning for Semi-Supervised Medical Image Segmentation

In the field of medical image segmentation, the scarcity of labeled data poses a major challenge for existing models to accurately perceive target regions. Compared with manual annotation, gaze data is easier and cheaper to obtain. As a classical semi-supervised learning framework, mean-teacher can effectively use a large number of unlabeled medical images for stable training through self-teaching and collaborative optimization. Our study is based on the mean-teacher framework. By combining gaze data, it aims to address two crucial issues in semi-supervised medical image segmentation: 1) expand the scale and diversity of the dataset with limited labeled data; 2) enhance the network's perception ability. We propose the Human Gaze-based Dual Teacher Guidance Learning model (HG-DTGL). In this model, human gaze serves as an additional hidden `teacher' in the mean-teacher architecture. We introduce the GazeMix to generate reliable mixed data to expand the diversity and scale of the dataset, and the Multi-scale Gaze Perception (MGP) module is used to extract the multi-scale perception of the network. A Gaze Loss is designed to align the model's perception with human gaze. We have verified HG-DTGL on multiple datasets of different modalities and achieved superior performance on a total of ten different organs/tissues, with extensive experiments. This demonstrates that our method has strong generalization ability for medical images of different modalities, and shows the great application potential of gaze data in semi-supervised medical image segmentation.

Semantic Surgery: Zero-Shot Concept Erasure in Diffusion Models

Concept erasure in text-to-image diffusion models is crucial for mitigating harmful content, yet existing methods often compromise generative quality. We introduce Semantic Surgery, a novel training-free, zero-shot framework for concept erasure that operates directly on text embeddings before the diffusion process. It dynamically estimates the presence of target concepts in a prompt and performs a calibrated vector subtraction to neutralize their influence at the source, enhancing both erasure completeness and locality. The framework includes a Co-Occurrence Encoding module for robust multi-concept erasure and a visual feedback loop to address latent concept persistence. As a training-free method, Semantic Surgery adapts dynamically to each prompt, ensuring precise interventions. Extensive experiments on object, explicit content, artistic style, and multi-celebrity erasure tasks show our method significantly outperforms state-of-the-art approaches. We achieve superior completeness and robustness while preserving locality and image quality (e.g., 93.58 H-score in object erasure, reducing explicit content to just 1 instance, and 8.09 H_a in style erasure with no quality degradation). This robustness also allows our framework to function as a built-in threat detection system, offering a practical solution for safer text-to-image generation.

EmotionHallucer: Evaluating Emotion Hallucinations in Multimodal Large Language Models

Emotion understanding is a critical yet challenging task. Recent advances in Multimodal Large Language Models (MLLMs) have significantly enhanced their capabilities in this area. However, MLLMs often suffer from hallucinations, generating irrelevant or nonsensical content. To the best of our knowledge, despite the importance of this issue, there has been no dedicated effort to evaluate emotion-related hallucinations in MLLMs. In this work, we introduce EmotionHallucer, the first benchmark for detecting and analyzing emotion hallucinations in MLLMs. Unlike humans, whose emotion understanding stems from the interplay of biology and social learning, MLLMs rely solely on data-driven learning and lack innate emotional instincts. Fortunately, emotion psychology provides a solid foundation of knowledge about human emotions. Building on this, we assess emotion hallucinations from two dimensions: emotion psychology knowledge and real-world multimodal perception. To support robust evaluation, we utilize an adversarial binary question-answer (QA) framework, which employs carefully crafted basic and hallucinated pairs to assess the emotion hallucination tendencies of MLLMs. By evaluating 38 LLMs and MLLMs on EmotionHallucer, we reveal that: i) most current models exhibit substantial issues with emotion hallucinations; ii) closed-source models outperform open-source ones in detecting emotion hallucinations, and reasoning capability provides additional advantages; iii) existing models perform better in emotion psychology knowledge than in multimodal emotion perception. As a byproduct, these findings inspire us to propose the PEP-MEK framework, which yields an average improvement of 9.90% in emotion hallucination detection across selected models. Resources will be available at https://github.com/xxtars/EmotionHallucer.

Graph Convolutional Network with Connectivity Uncertainty for EEG-based Emotion Recognition

Automatic emotion recognition based on multichannel Electroencephalography (EEG) holds great potential in advancing human-computer interaction. However, several significant challenges persist in existing research on algorithmic emotion recognition. These challenges include the need for a robust model to effectively learn discriminative node attributes over long paths, the exploration of ambiguous topological information in EEG channels and effective frequency bands, and the mapping between intrinsic data qualities and provided labels. To address these challenges, this study introduces the distribution-based uncertainty method to represent spatial dependencies and temporal-spectral relativeness in EEG signals based on Graph Convolutional Network (GCN) architecture that adaptively assigns weights to functional aggregate node features, enabling effective long-path capturing while mitigating over-smoothing phenomena. Moreover, the graph mixup technique is employed to enhance latent connected edges and mitigate noisy label issues. Furthermore, we integrate the uncertainty learning method with deep GCN weights in a one-way learning fashion, termed Connectivity Uncertainty GCN (CU-GCN). We evaluate our approach on two widely used datasets, namely SEED and SEEDIV, for emotion recognition tasks. The experimental results demonstrate the superiority of our methodology over previous methods, yielding positive and significant improvements. Ablation studies confirm the substantial contributions of each component to the overall performance.

ECG-CL: A Comprehensive Electrocardiogram Interpretation Method Based on Continual Learning

Electrocardiogram (ECG) monitoring is one of the most powerful technique of cardiovascular disease (CVD) early identification, and the introduction of intelligent wearable ECG devices has enabled daily monitoring. However, due to the need for professional expertise in the ECGs interpretation, general public access has once again been restricted, prompting the need for the development of advanced diagnostic algorithms. Classic rule-based algorithms are now completely outperformed by deep learning based methods. But the advancement of smart diagnostic algorithms is hampered by issues like small dataset, inconsistent data labeling, inefficient use of local and global ECG information, memory and inference time consuming deployment of multiple models, and lack of information transfer between tasks. We propose a multi-resolution model that can sustain high-resolution low-level semantic information throughout, with the help of the development of low-resolution high-level semantic information, by capitalizing on both local morphological information and global rhythm information. From the perspective of effective data leverage and inter-task knowledge transfer, we develop a parameter isolation based ECG continual learning (ECG-CL) approach. We evaluated our model's performance on four open-access datasets by designing segmentation-to-classification for cross-domain incremental learning, minority-to-majority class for category incremental learning, and small-to-large sample for task incremental learning. Our approach is shown to successfully extract informative morphological and rhythmic features from ECG segmentation, leading to higher quality classification results. From the perspective of intelligent wearable applications, the possibility of a comprehensive ECG interpretation algorithm based on single-lead ECGs is also confirmed.

A Causal Intervention Scheme for Semantic Segmentation of Quasi-periodic Cardiovascular Signals

Precise segmentation is a vital first step to analyze semantic information of cardiac cycle and capture anomaly with cardiovascular signals. However, in the field of deep semantic segmentation, inference is often unilaterally confounded by the individual attribute of data. Towards cardiovascular signals, quasi-periodicity is the essential characteristic to be learned, regarded as the synthesize of the attributes of morphology (Am) and rhythm (Ar). Our key insight is to suppress the over-dependence on Am or Ar while the generation process of deep representations. To address this issue, we establish a structural causal model as the foundation to customize the intervention approaches on Am and Ar, respectively. In this paper, we propose contrastive causal intervention (CCI) to form a novel training paradigm under a frame-level contrastive framework. The intervention can eliminate the implicit statistical bias brought by the single attribute and lead to more objective representations. We conduct comprehensive experiments with the controlled condition for QRS location and heart sound segmentation. The final results indicate that our approach can evidently improve the performance by up to 0.41% for QRS location and 2.73% for heart sound segmentation. The efficiency of the proposed method is generalized to multiple databases and noisy signals.

Neural network facilitated ab initio derivation of linear formula: A case study on formulating the relationship between DNA motifs and gene expression

Developing models with high interpretability and even deriving formulas to quantify relationships between biological data is an emerging need. We propose here a framework for ab initio derivation of sequence motifs and linear formula using a new approach based on the interpretable neural network model called contextual regression model. We showed that this linear model could predict gene expression levels using promoter sequences with a performance comparable to deep neural network models. We uncovered a list of 300 motifs with important regulatory roles on gene expression and showed that they also had significant contributions to cell-type specific gene expression in 154 diverse cell types. This work illustrates the possibility of deriving formulas to represent biology laws that may not be easily elucidated. (https://github.com/Wang-lab-UCSD/Motif_Finding_Contextual_Regression)