We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional Flow Matching and a practical implementation for efficient training and sampling. We also introduce an $x_1$-prediction variant that improves stability over the original $u$-prediction form. The resulting framework is a practical one-step Flow Matching method applicable to a wide range of functional data generation tasks such as time series, images, PDEs, and 3D geometry.

Training neural operators to approximate mappings between infinite-dimensional function spaces often requires extensive datasets generated by either demanding experimental setups or computationally expensive numerical solvers. This dependence on solver-based data limits scalability and constrains exploration across physical systems. Here we introduce the Method of Manufactured Learning (MML), a solver-independent framework for training neural operators using analytically constructed, physics-consistent datasets. Inspired by the classical method of manufactured solutions, MML replaces numerical data generation with functional synthesis, i.e., smooth candidate solutions are sampled from controlled analytical spaces, and the corresponding forcing fields are derived by direct application of the governing differential operators. During inference, setting these forcing terms to zero restores the original governing equations, allowing the trained neural operator to emulate the true solution operator of the system. The framework is agnostic to network architecture and can be integrated with any operator learning paradigm. In this paper, we employ Fourier neural operator as a representative example. Across canonical benchmarks including heat, advection, Burgers, and diffusion-reaction equations. MML achieves high spectral accuracy, low residual errors, and strong generalization to unseen conditions. By reframing data generation as a process of analytical synthesis, MML offers a scalable, solver-agnostic pathway toward constructing physically grounded neural operators that retain fidelity to governing laws without reliance on expensive numerical simulations or costly experimental data for training.

This paper presents a transformer-based approach for classifying hope expressions in text. We developed and compared three architectures (BERT, GPT-2, and DeBERTa) for both binary classification (Hope vs. Not Hope) and multiclass categorization (five hope-related categories). Our initial BERT implementation achieved 83.65% binary and 74.87% multiclass accuracy. In the extended comparison, BERT demonstrated superior performance (84.49% binary, 72.03% multiclass accuracy) while requiring significantly fewer computational resources (443s vs. 704s training time) than newer architectures. GPT-2 showed lowest overall accuracy (79.34% binary, 71.29% multiclass), while DeBERTa achieved moderate results (80.70% binary, 71.56% multiclass) but at substantially higher computational cost (947s for multiclass training). Error analysis revealed architecture-specific strengths in detecting nuanced hope expressions, with GPT-2 excelling at sarcasm detection (92.46% recall). This study provides a framework for computational analysis of hope, with applications in mental health and social media analysis, while demonstrating that architectural suitability may outweigh model size for specialized emotion detection tasks.

Deep neural networks achieve state of the art performance but remain difficult to interpret mechanistically. In this work, we propose a control theoretic framework that treats a trained neural network as a nonlinear state space system and uses local linearization, controllability and observability Gramians, and Hankel singular values to analyze its internal computation. For a given input, we linearize the network around the corresponding hidden activation pattern and construct a state space model whose state consists of hidden neuron activations. The input state and state output Jacobians define local controllability and observability Gramians, from which we compute Hankel singular values and associated modes. These quantities provide a principled notion of neuron and pathway importance: controllability measures how easily each neuron can be excited by input perturbations, observability measures how strongly each neuron influences the output, and Hankel singular values rank internal modes that carry input output energy. We illustrate the framework on simple feedforward networks, including a 1 2 2 1 SwiGLU network and a 2 3 3 2 GELU network. By comparing different operating points, we show how activation saturation reduces controllability, shrinks the dominant Hankel singular value, and shifts the dominant internal mode to a different subset of neurons. The proposed method turns a neural network into a collection of local white box dynamical models and suggests which internal directions are natural candidates for pruning or constraints to improve interpretability.

Clinical electroencephalogram (EEG) reports encode domain-specific linguistic conventions that general-purpose language models (LMs) fail to capture. We introduce NeuroLex, a lightweight domain-adaptive language model trained purely on EEG report text from the Harvard Electroencephalography Database. Unlike existing biomedical LMs, NeuroLex is tailored to the linguistic and diagnostic characteristics of EEG reporting, enabling it to serve as both an independent textual model and a decoder backbone for multimodal EEG-language systems. Using span-corruption pretraining and instruction-style fine-tuning on report polishing, paragraph summarization, and terminology question answering, NeuroLex learns the syntax and reasoning patterns characteristic of EEG interpretation. Comprehensive evaluations show that it achieves lower perplexity, higher extraction and summarization accuracy, better label efficiency, and improved robustness to negation and factual hallucination compared with general models of the same scale. With an EEG-aware linguistic backbone, NeuroLex bridges biomedical text modeling and brain-computer interface applications, offering a foundation for interpretable and language-driven neural decoding.

Online change detection (OCD) aims to rapidly identify change points in streaming data and is critical in applications such as power system monitoring, wireless network sensing, and financial anomaly detection. Existing OCD methods typically assume precise system knowledge, which is unrealistic due to estimation errors and environmental variations. Moreover, existing OCD methods often struggle with efficiency in large-scale systems. To overcome these challenges, we propose RoS-Guard, a robust and optimal OCD algorithm tailored for linear systems with uncertainty. Through a tight relaxation and reformulation of the OCD optimization problem, RoS-Guard employs neural unrolling to enable efficient parallel computation via GPU acceleration. The algorithm provides theoretical guarantees on performance, including expected false alarm rate and worst-case average detection delay. Extensive experiments validate the effectiveness of RoS-Guard and demonstrate significant computational speedup in large-scale system scenarios.

The proliferation of generative AI has led to hyper-realistic synthetic videos, escalating misuse risks and outstripping binary real/fake detectors. We introduce SAGA (Source Attribution of Generative AI videos), the first comprehensive framework to address the urgent need for AI-generated video source attribution at a large scale. Unlike traditional detection, SAGA identifies the specific generative model used. It uniquely provides multi-granular attribution across five levels: authenticity, generation task (e.g., T2V/I2V), model version, development team, and the precise generator, offering far richer forensic insights. Our novel video transformer architecture, leveraging features from a robust vision foundation model, effectively captures spatio-temporal artifacts. Critically, we introduce a data-efficient pretrain-and-attribute strategy, enabling SAGA to achieve state-of-the-art attribution using only 0.5\% of source-labeled data per class, matching fully supervised performance. Furthermore, we propose Temporal Attention Signatures (T-Sigs), a novel interpretability method that visualizes learned temporal differences, offering the first explanation for why different video generators are distinguishable. Extensive experiments on public datasets, including cross-domain scenarios, demonstrate that SAGA sets a new benchmark for synthetic video provenance, providing crucial, interpretable insights for forensic and regulatory applications.

We present a systematic evaluation of representation learning objectives for particle physics within a unified framework. Our study employs a shared transformer-based particle-cloud encoder with standardized preprocessing, matched sampling, and a consistent evaluation protocol on a jet classification dataset. We compare contrastive (supervised and self-supervised), masked particle modeling, and generative reconstruction objectives under a common training regimen. In addition, we introduce targeted supervised architectural modifications that achieve state-of-the-art performance on benchmark evaluations. This controlled comparison isolates the contributions of the learning objective, highlights their respective strengths and limitations, and provides reproducible baselines. We position this work as a reference point for the future development of foundation models in particle physics, enabling more transparent and robust progress across the community.

Catastrophic forgetting is a longstanding challenge in continual learning, where models lose knowledge from earlier tasks when learning new ones. While various mitigation strategies have been proposed for Multi-Layer Perceptrons (MLPs), recent architectural advances like Kolmogorov-Arnold Networks (KANs) have been suggested to offer intrinsic resistance to forgetting by leveraging localized spline-based activations. However, the practical behavior of KANs under continual learning remains unclear, and their limitations are not well understood. To address this, we present a comprehensive study of catastrophic forgetting in KANs and develop a theoretical framework that links forgetting to activation support overlap and intrinsic data dimension. We validate these analyses through systematic experiments on synthetic and vision tasks, measuring forgetting dynamics under varying model configurations and data complexity. Further, we introduce KAN-LoRA, a novel adapter design for parameter-efficient continual fine-tuning of language models, and evaluate its effectiveness in knowledge editing tasks. Our findings reveal that while KANs exhibit promising retention in low-dimensional algorithmic settings, they remain vulnerable to forgetting in high-dimensional domains such as image classification and language modeling. These results advance the understanding of KANs' strengths and limitations, offering practical insights for continual learning system design.

Assessing journal impact is central to scholarly communication, yet existing open resources rarely capture how collaboration structures and artificial intelligence (AI) research jointly shape venue prestige in biomedicine. We present BioMedJImpact, a large-scale, biomedical-oriented dataset designed to advance journal-level analysis of scientific impact and AI engagement. Built from 1.74 million PubMed Central articles across 2,744 journals, BioMedJImpact integrates bibliometric indicators, collaboration features, and LLM-derived semantic indicators for AI engagement. Specifically, the AI engagement feature is extracted through a reproducible three-stage LLM pipeline that we propose. Using this dataset, we analyze how collaboration intensity and AI engagement jointly influence scientific impact across pre- and post-pandemic periods (2016-2019, 2020-2023). Two consistent trends emerge: journals with higher collaboration intensity, particularly those with larger and more diverse author teams, tend to achieve greater citation impact, and AI engagement has become an increasingly strong correlate of journal prestige, especially in quartile rankings. To further validate the three-stage LLM pipeline we proposed for deriving the AI engagement feature, we conduct human evaluation, confirming substantial agreement in AI relevance detection and consistent subfield classification. Together, these contributions demonstrate that BioMedJImpact serves as both a comprehensive dataset capturing the intersection of biomedicine and AI, and a validated methodological framework enabling scalable, content-aware scientometric analysis of scientific impact and innovation dynamics. Code is available at https://github.com/JonathanWry/BioMedJImpact.