We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs approximate solutions to partial differential equations (PDEs) by minimizing residual losses over sampled collocation and boundary points. We formalize both operator-level and variational notions of consistency, proving that residual minimization in Sobolev norms leads to convergence in energy and uniform norms under mild regularity. Deterministic stability bounds quantify how bounded perturbations to the network outputs propagate through the full composite loss, while probabilistic concentration results via McDiarmid's inequality yield sample complexity guarantees for residual-based generalization. A unified generalization bound links residual consistency, projection error, and perturbation sensitivity. Empirical results on elliptic, parabolic, and nonlinear PDEs confirm the predictive accuracy of our theoretical bounds across regimes. The framework identifies key structural principles, such as operator coercivity, activation smoothness, and sampling admissibility, that underlie robust and generalizable PINN training, offering principled guidance for the design and analysis of PDE-informed learning systems.

Large Language Models (LLMs) are increasingly used for cybersecurity threat analysis, but their deployment in security-sensitive environments raises trust and safety concerns. With over 21,000 vulnerabilities disclosed in 2025, manual analysis is infeasible, making scalable and verifiable AI support critical. When querying LLMs, dealing with emerging vulnerabilities is challenging as they have a training cut-off date. While Retrieval-Augmented Generation (RAG) can inject up-to-date context to alleviate the cut-off date limitation, it remains unclear how much LLMs rely on retrieved evidence versus the model's internal knowledge, and whether the retrieved information is meaningful or even correct. This uncertainty could mislead security analysts, mis-prioritize patches, and increase security risks. Therefore, this work proposes LLM Embedding-based Attribution (LEA) to analyze the generated responses for vulnerability exploitation analysis. More specifically, LEA quantifies the relative contribution of internal knowledge vs. retrieved content in the generated responses. We evaluate LEA on 500 critical vulnerabilities disclosed between 2016 and 2025, across three RAG settings -- valid, generic, and incorrect -- using three state-of-the-art LLMs. Our results demonstrate LEA's ability to detect clear distinctions between non-retrieval, generic-retrieval, and valid-retrieval scenarios with over 95% accuracy on larger models. Finally, we demonstrate the limitations posed by incorrect retrieval of vulnerability information and raise a cautionary note to the cybersecurity community regarding the blind reliance on LLMs and RAG for vulnerability analysis. LEA offers security analysts with a metric to audit RAG-enhanced workflows, improving the transparent and trustworthy deployment of AI in cybersecurity threat analysis.

Current AutoML platforms leave substantial performance untapped. Testing 180 fine-tuning tasks across models from 70M to 70B parameters, we found that HuggingFace AutoTrain, TogetherAI, Databricks, and Google Cloud consistently produce suboptimal configurations. Gradients, built on the Bittensor network, attacks this problem through competition. Independent miners race to find optimal hyperparameters, earning rewards proportional to their models' performance. This tournament drives exploration of configuration spaces that single-strategy methods never examine. In our experiments, Gradients achieved a 100\% win rate against TogetherAI, Databricks, and Google Cloud, and beat HuggingFace AutoTrain in 82.8\% of experiments. Mean improvements reached 42.1\% against commercial platforms. Retrieval-augmented generation tasks saw 30-40\% gains; diffusion models improved 23.4\% on person-specific generation. When miners compete for rewards, they develop optimization strategies that centralized approaches overlook. These findings demonstrate that decentralized systems with economic incentives can systematically outperform traditional AutoML, suggesting market dynamics may be key to achieving superior fine-tuning results. Code is available at https://github.com/rayonlabs/G.O.D.

Diffusion Transformers (DiT) are powerful generative models but remain computationally intensive due to their iterative structure and deep transformer stacks. To alleviate this inefficiency, we propose F astCache, a hidden-state-level caching and compression framework that accelerates DiT inference by exploiting redundancy within the model's internal representations. FastCache introduces a dual strategy: (1) a spatial-aware token selection mechanism that adaptively filters redundant tokens based on hidden state saliency, and (2) a transformer-level cache that reuses latent activations across timesteps when changes are statistically insignificant. These modules work jointly to reduce unnecessary computation while preserving generation fidelity through learnable linear approximation. Theoretical analysis shows that FastCache maintains bounded approximation error under a hypothesis-testing-based decision rule. Empirical evaluations across multiple DiT variants demonstrate substantial reductions in latency and memory usage, with best generation output quality compared to other cache methods, as measured by FID and t-FID.

Early detection of cognitive decline is crucial for enabling interventions that can slow neurodegenerative disease progression. Traditional diagnostic approaches rely on labor-intensive clinical assessments, which are impractical for frequent monitoring. Our pilot study investigates voice assistant systems (VAS) as non-invasive tools for detecting cognitive decline through longitudinal analysis of speech patterns in voice commands. Over an 18-month period, we collected voice commands from 35 older adults, with 15 participants providing daily at-home VAS interactions. To address the challenges of analyzing these short, unstructured and noisy commands, we propose Cog-TiPRO, a framework that combines (1) LLM-driven iterative prompt refinement for linguistic feature extraction, (2) HuBERT-based acoustic feature extraction, and (3) transformer-based temporal modeling. Using iTransformer, our approach achieves 73.80% accuracy and 72.67% F1-score in detecting MCI, outperforming its baseline by 27.13%. Through our LLM approach, we identify linguistic features that uniquely characterize everyday command usage patterns in individuals experiencing cognitive decline.

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

Autoregressive models (ARMs), which predict subsequent tokens one-by-one ``from left to right,'' have achieved significant success across a wide range of sequence generation tasks. However, they struggle to accurately represent sequences that require satisfying sophisticated constraints or whose sequential dependencies are better addressed by out-of-order generation. Masked Diffusion Models (MDMs) address some of these limitations, but the process of unmasking multiple tokens simultaneously in MDMs can introduce incoherences, and MDMs cannot handle arbitrary infilling constraints when the number of tokens to be filled in is not known in advance. In this work, we introduce Insertion Language Models (ILMs), which learn to insert tokens at arbitrary positions in a sequence -- that is, they select jointly both the position and the vocabulary element to be inserted. By inserting tokens one at a time, ILMs can represent strong dependencies between tokens, and their ability to generate sequences in arbitrary order allows them to accurately model sequences where token dependencies do not follow a left-to-right sequential structure. To train ILMs, we propose a tailored network parameterization and use a simple denoising objective. Our empirical evaluation demonstrates that ILMs outperform both ARMs and MDMs on common planning tasks. Furthermore, we show that ILMs outperform MDMs and perform on par with ARMs in an unconditional text generation task while offering greater flexibility than MDMs in arbitrary-length text infilling. The code is available at: https://dhruveshp.com/projects/ilm .

Accurate extraction of key information from 2D engineering drawings is crucial for high - precision manufacturing. Manual extraction is slow and labor - intensive, while traditional Optical Character Recognition (OCR) techniques often struggle with complex layouts and overlapping symbols, resulting in unstructured outputs . To address these challenges, this paper proposes a novel hybrid deep learning framework for structured information extraction by integrat ing an O riented B ounding B ox (OBB) detection model with a transformer - based document parsing model (Donut). An in - house annotated dataset is used to train YOLOv11 for detect ing nine key categories: Geometric Dimensioning and Tolerancing (GD&T), General Tolerances, Measures, Materials, Notes, Radii, Surface Roughness, Threads, and Title Blocks. Detected OBBs are cropped into image s and labeled to fine - tune Donut for structured JSON output. Fine - tuning strategies include a single model trained across all categories and category - specific models . Results show that the single model consistently outperforms category - specific ones across all evaluation metrics, achieving higher precision (94.77% for GD&T), recall (100% for most categories), and F1 score (97.3%), while reducing hallucination s (5.23%) . The proposed framework improves accuracy, reduces manual effort, and supports scalable deployment in precision - driven industries.

Legal practitioners, particularly those early in their careers, face complex, high-stakes tasks that require adaptive, context-sensitive reasoning. While AI holds promise in supporting legal work, current datasets and models are narrowly focused on isolated subtasks and fail to capture the end-to-end decision-making required in real-world practice. To address this gap, we introduce LawFlow, a dataset of complete end-to-end legal workflows collected from trained law students, grounded in real-world business entity formation scenarios. Unlike prior datasets focused on input-output pairs or linear chains of thought, LawFlow captures dynamic, modular, and iterative reasoning processes that reflect the ambiguity, revision, and client-adaptive strategies of legal practice. Using LawFlow, we compare human and LLM-generated workflows, revealing systematic differences in structure, reasoning flexibility, and plan execution. Human workflows tend to be modular and adaptive, while LLM workflows are more sequential, exhaustive, and less sensitive to downstream implications. Our findings also suggest that legal professionals prefer AI to carry out supportive roles, such as brainstorming, identifying blind spots, and surfacing alternatives, rather than executing complex workflows end-to-end. Our results highlight both the current limitations of LLMs in supporting complex legal workflows and opportunities for developing more collaborative, reasoning-aware legal AI systems. All data and code are available on our project page (https://minnesotanlp.github.io/LawFlow-website/).

Cardiac magnetic resonance imaging is the gold standard for non-invasive cardiac assessment, offering rich spatio-temporal views of the cardiac anatomy and physiology. Patient-level health factors, such as demographics, metabolic, and lifestyle, are known to substantially influence cardiovascular health and disease risk, yet remain uncaptured by CMR alone. To holistically understand cardiac health and to enable the best possible interpretation of an individual's disease risk, CMR and patient-level factors must be jointly exploited within an integrated framework. Recent multi-modal approaches have begun to bridge this gap, yet they often rely on limited spatio-temporal data and focus on isolated clinical tasks, thereby hindering the development of a comprehensive representation for cardiac health evaluation. To overcome these limitations, we introduce ViTa, a step toward foundation models that delivers a comprehensive representation of the heart and a precise interpretation of individual disease risk. Leveraging data from 42,000 UK Biobank participants, ViTa integrates 3D+T cine stacks from short-axis and long-axis views, enabling a complete capture of the cardiac cycle. These imaging data are then fused with detailed tabular patient-level factors, enabling context-aware insights. This multi-modal paradigm supports a wide spectrum of downstream tasks, including cardiac phenotype and physiological feature prediction, segmentation, and classification of cardiac and metabolic diseases within a single unified framework. By learning a shared latent representation that bridges rich imaging features and patient context, ViTa moves beyond traditional, task-specific models toward a universal, patient-specific understanding of cardiac health, highlighting its potential to advance clinical utility and scalability in cardiac analysis.