Spectral Analysis of Hard-Constraint PINNs: The Spatial Modulation Mechanism of Boundary Functions

Physics-Informed Neural Networks with hard constraints (HC-PINNs) are increasingly favored for their ability to strictly enforce boundary conditions via a trial function ansatz $\tilde{u} = A + B \cdot N$, yet the theoretical mechanisms governing their training dynamics have remained unexplored. Unlike soft-constrained formulations where boundary terms act as additive penalties, this work reveals that the boundary function $B$ introduces a multiplicative spatial modulation that fundamentally alters the learning landscape. A rigorous Neural Tangent Kernel (NTK) framework for HC-PINNs is established, deriving the explicit kernel composition law. This relationship demonstrates that the boundary function $B(\vec{x})$ functions as a spectral filter, reshaping the eigenspectrum of the neural network's native kernel. Through spectral analysis, the effective rank of the residual kernel is identified as a deterministic predictor of training convergence, superior to classical condition numbers. It is shown that widely used boundary functions can inadvertently induce spectral collapse, leading to optimization stagnation despite exact boundary satisfaction. Validated across multi-dimensional benchmarks, this framework transforms the design of boundary functions from a heuristic choice into a principled spectral optimization problem, providing a solid theoretical foundation for geometric hard constraints in scientific machine learning.

Early Warning Index for Patient Deteriorations in Hospitals

Hospitals lack automated systems to harness the growing volume of heterogeneous clinical and operational data to effectively forecast critical events. Early identification of patients at risk for deterioration is essential not only for patient care quality monitoring but also for physician care management. However, translating varied data streams into accurate and interpretable risk assessments poses significant challenges due to inconsistent data formats. We develop a multimodal machine learning framework, the Early Warning Index (EWI), to predict the aggregate risk of ICU admission, emergency response team dispatch, and mortality. Key to EWI's design is a human-in-the-loop process: clinicians help determine alert thresholds and interpret model outputs, which are enhanced by explainable outputs using Shapley Additive exPlanations (SHAP) to highlight clinical and operational factors (e.g., scheduled surgeries, ward census) driving each patient's risk. We deploy EWI in a hospital dashboard that stratifies patients into three risk tiers. Using a dataset of 18,633 unique patients at a large U.S. hospital, our approach automatically extracts features from both structured and unstructured electronic health record (EHR) data and achieves C-statistics of 0.796. It is currently used as a triage tool for proactively managing at-risk patients. The proposed approach saves physicians valuable time by automatically sorting patients of varying risk levels, allowing them to concentrate on patient care rather than sifting through complex EHR data. By further pinpointing specific risk drivers, the proposed model provides data-informed adjustments to caregiver scheduling and allocation of critical resources. As a result, clinicians and administrators can avert downstream complications, including costly procedures or high readmission rates and improve overall patient flow.

Towards Optimal Valve Prescription for Transcatheter Aortic Valve Replacement (TAVR) Surgery: A Machine Learning Approach

Transcatheter Aortic Valve Replacement (TAVR) has emerged as a minimally invasive treatment option for patients with severe aortic stenosis, a life-threatening cardiovascular condition. Multiple transcatheter heart valves (THV) have been approved for use in TAVR, but current guidelines regarding valve type prescription remain an active topic of debate. We propose a data-driven clinical support tool to identify the optimal valve type with the objective of minimizing the risk of permanent pacemaker implantation (PPI), a predominant postoperative complication. We synthesize a novel dataset that combines U.S. and Greek patient populations and integrates three distinct data sources (patient demographics, computed tomography scans, echocardiograms) while harmonizing differences in each country's record system. We introduce a leaf-level analysis to leverage population heterogeneity and avoid benchmarking against uncertain counterfactual risk estimates. The final prescriptive model shows a reduction in PPI rates of 26% and 16% compared with the current standard of care in our internal U.S. population and external Greek validation cohort, respectively. To the best of our knowledge, this work represents the first unified, personalized prescription strategy for THV selection in TAVR.

Distributionally Robust Multimodal Machine Learning

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware effects and provide limited insights. We propose a novel distributionally robust optimization (DRO) framework that aims to study both the theoretical and practical insights of multimodal machine learning. We first justify this setup and show the significance of this problem through complexity analysis. We then establish both generalization upper bounds and minimax lower bounds which provide performance guarantees. These results are further extended in settings where we consider encoder-specific error propogations. Empirically, we demonstrate that our approach improves robustness in both simulation settings and real-world datasets. Together, these findings provide a principled foundation for employing multimodal machine learning models in high-stakes applications where uncertainty is unavoidable.

CATCH: A Modular Cross-domain Adaptive Template with Hook

Recent advances in Visual Question Answering (VQA) have demonstrated impressive performance in natural image domains, with models like LLaVA leveraging large language models (LLMs) for open-ended reasoning. However, their generalization degrades significantly when transferred to out-of-domain scenarios such as remote sensing, medical imaging, or math diagrams, due to large distributional shifts and the lack of effective domain adaptation mechanisms. Existing approaches typically rely on per-domain fine-tuning or bespoke pipelines, which are costly, inflexible, and not scalable across diverse tasks. In this paper, we propose CATCH, a plug-and-play framework for cross-domain adaptation that improves the generalization of VQA models while requiring minimal changes to their core architecture. Our key idea is to decouple visual and linguistic adaptation by introducing two lightweight modules: a domain classifier to identify the input image type, and a dual adapter mechanism comprising a Prompt Adapter for language modulation and a Visual Adapter for vision feature adjustment. Both modules are dynamically injected via a unified hook interface, requiring no retraining of the backbone model. Experimental results across four domain-specific VQA benchmarks demonstrate that our framework achieves consistent performance gains without retraining the backbone model, including +2.3 BLEU on MathVQA, +2.6 VQA on MedVQA-RAD, and +3.1 ROUGE on ChartQA. These results highlight that CATCH provides a scalable and extensible approach to multi-domain VQA, enabling practical deployment across diverse application domains.

Hy-Facial: Hybrid Feature Extraction by Dimensionality Reduction Methods for Enhanced Facial Expression Classification

Facial expression classification remains a challenging task due to the high dimensionality and inherent complexity of facial image data. This paper presents Hy-Facial, a hybrid feature extraction framework that integrates both deep learning and traditional image processing techniques, complemented by a systematic investigation of dimensionality reduction strategies. The proposed method fuses deep features extracted from the Visual Geometry Group 19-layer network (VGG19) with handcrafted local descriptors and the scale-invariant feature transform (SIFT) and Oriented FAST and Rotated BRIEF (ORB) algorithms, to obtain rich and diverse image representations. To mitigate feature redundancy and reduce computational complexity, we conduct a comprehensive evaluation of dimensionality reduction techniques and feature extraction. Among these, UMAP is identified as the most effective, preserving both local and global structures of the high-dimensional feature space. The Hy-Facial pipeline integrated VGG19, SIFT, and ORB for feature extraction, followed by K-means clustering and UMAP for dimensionality reduction, resulting in a classification accuracy of 83. 3\% in the facial expression recognition (FER) dataset. These findings underscore the pivotal role of dimensionality reduction not only as a pre-processing step but as an essential component in improving feature quality and overall classification performance.

Bridging the Editing Gap in LLMs: FineEdit for Precise and Targeted Text Modifications

Large Language Models (LLMs) have transformed natural language processing, yet they still struggle with direct text editing tasks that demand precise, context-aware modifications. While models like ChatGPT excel in text generation and analysis, their editing abilities often fall short, addressing only superficial issues rather than deeper structural or logical inconsistencies. In this work, we introduce a dual approach to enhance LLMs editing performance. First, we present InstrEditBench, a high-quality benchmark dataset comprising over 20,000 structured editing tasks spanning Wiki articles, LaTeX documents, code, and database Domain-specific Languages (DSL). InstrEditBench is generated using an innovative automated workflow that accurately identifies and evaluates targeted edits, ensuring that modifications adhere strictly to specified instructions without altering unrelated content. Second, we propose FineEdit, a specialized model trained on this curated benchmark. Experimental results demonstrate that FineEdit achieves significant improvements around {10\%} compared with Gemini on direct editing tasks, convincingly validating its effectiveness.

Generative Video Semantic Communication via Multimodal Semantic Fusion with Large Model

Despite significant advancements in traditional syntactic communications based on Shannon's theory, these methods struggle to meet the requirements of 6G immersive communications, especially under challenging transmission conditions. With the development of generative artificial intelligence (GenAI), progress has been made in reconstructing videos using high-level semantic information. In this paper, we propose a scalable generative video semantic communication framework that extracts and transmits semantic information to achieve high-quality video reconstruction. Specifically, at the transmitter, description and other condition signals (e.g., first frame, sketches, etc.) are extracted from the source video, functioning as text and structural semantics, respectively. At the receiver, the diffusion-based GenAI large models are utilized to fuse the semantics of the multiple modalities for reconstructing the video. Simulation results demonstrate that, at an ultra-low channel bandwidth ratio (CBR), our scheme effectively captures semantic information to reconstruct videos aligned with human perception under different signal-to-noise ratios. Notably, the proposed ``First Frame+Desc." scheme consistently achieves CLIP score exceeding 0.92 at CBR = 0.0057 for SNR > 0 dB. This demonstrates its robust performance even under low SNR conditions.

Rhyme-aware Chinese lyric generator based on GPT

Neural language representation models such as GPT, pre-trained on large-scale corpora, can effectively capture rich semantic patterns from plain text and be fine-tuned to consistently improve natural language generation performance. However, existing pre-trained language models used to generate lyrics rarely consider rhyme information, which is crucial in lyrics. Using a pre-trained model directly results in poor performance. To enhance the rhyming quality of generated lyrics, we incorporate integrated rhyme information into our model, thereby improving lyric generation performance.

Unlock the Correlation between Supervised Fine-Tuning and Reinforcement Learning in Training Code Large Language Models

Automatic code generation has been a longstanding research topic. With the advancement of general-purpose large language models (LLMs), the ability to code stands out as one important measure to the model's reasoning performance. Usually, a two-stage training paradigm is implemented to obtain a Code LLM, namely the pretraining and the fine-tuning. Within the fine-tuning, supervised fine-tuning (SFT), and reinforcement learning (RL) are often used to improve the model's zero-shot ability. A large number of work has been conducted to improve the model's performance on code-related benchmarks with either modifications to the algorithm or refinement of the dataset. However, we still lack a deep insight into the correlation between SFT and RL. For instance, what kind of dataset should be used to ensure generalization, or what if we abandon the SFT phase in fine-tuning. In this work, we make an attempt to understand the correlation between SFT and RL. To facilitate our research, we manually craft 100 basis python functions, called atomic functions, and then a synthesizing pipeline is deployed to create a large number of synthetic functions on top of the atomic ones. In this manner, we ensure that the train and test sets remain distinct, preventing data contamination. Through comprehensive ablation study, we find: (1) Both atomic and synthetic functions are indispensable for SFT's generalization, and only a handful of synthetic functions are adequate; (2) Through RL, the SFT's generalization to target domain can be greatly enhanced, even with the same training prompts; (3) Training RL from scratch can alleviate the over-fitting issue introduced in the SFT phase.