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arXiv:2509.07893v1 Announce Type: cross Abstract: The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular, can help reduce computational costs. Building on the representation of the expected signature of (inhomogeneous) L'evy processes with absolutely continuous characteristics as the development of an absolutely continuous path in the extended tensor algebra [F.-H.-Tapia, Forum of Mathematics: Sigma (2022), "Unified signature cumulants and generalized Magnus expansions"], we extend the arguments developed for smooth rough paths in [Lemercier-Lyons-Salvi, "Log-PDE Methods for Rough Signature Kernels"] to derive a PDE system for the expected signature of inhomogeneous L'evy processes. As a specific example, we see that the expected signature kernel of Gaussian martingales satisfies a Goursat PDE.

arXiv:2509.06213v2 Announce Type: replace-cross Abstract: We investigate reinforcement learning in the Game Of Hidden Rules (GOHR) environment, a complex puzzle in which an agent must infer and execute hidden rules to clear a 6$times$6 board by placing game pieces into buckets. We explore two state representation strategies, namely Feature-Centric (FC) and Object-Centric (OC), and employ a Transformer-based Advantage Actor-Critic (A2C) algorithm for training. The agent has access only to partial observations and must simultaneously infer the governing rule and learn the optimal policy through experience. We evaluate our models across multiple rule-based and trial-list-based experimental setups, analyzing transfer effects and the impact of representation on learning efficiency.

arXiv:2509.07108v1 Announce Type: new Abstract: Survival analysis is a fundamental tool for modeling time-to-event outcomes in healthcare. Recent advances have introduced flexible neural network approaches for improved predictive performance. However, most of these models do not provide interpretable insights into the association between exposures and the modeled outcomes, a critical requirement for decision-making in clinical practice. To address this limitation, we propose Additive Deep Hazard Analysis Mixtures (ADHAM), an interpretable additive survival model. ADHAM assumes a conditional latent structure that defines subgroups, each characterized by a combination of covariate-specific hazard functions. To select the number of subgroups, we introduce a post-training refinement that reduces the number of equivalent latent subgroups by merging similar groups. We perform comprehensive studies to demonstrate ADHAM's interpretability at the population, subgroup, and individual levels. Extensive experiments on real-world datasets show that ADHAM provides novel insights into the association between exposures and outcomes. Further, ADHAM remains on par with existing state-of-the-art survival baselines in terms of predictive performance, offering a scalable and interpretable approach to time-to-event prediction in healthcare.

arXiv:2508.17180v2 Announce Type: replace Abstract: A key frontier for Multimodal Large Language Models (MLLMs) is the ability to perform deep mathematical and spatial reasoning directly from images, moving beyond their established success in semantic description. Mathematical surface plots provide a rigorous testbed for this capability, as they isolate the task of reasoning from the semantic noise common in natural images. To measure progress on this frontier, we introduce MaRVL-QA (Mathematical Reasoning over Visual Landscapes), a new benchmark designed to quantitatively evaluate these core reasoning skills. The benchmark comprises two novel tasks: Topological Counting, identifying and enumerating features like local maxima; and Transformation Recognition, recognizing applied geometric transformations. Generated from a curated library of functions with rigorous ambiguity filtering, our evaluation on MaRVL-QA reveals that even state-of-the-art MLLMs struggle significantly, often resorting to superficial heuristics instead of robust spatial reasoning. MaRVL-QA provides a challenging new tool for the research community to measure progress, expose model limitations, and guide the development of MLLMs with more profound reasoning abilities.

arXiv:2509.07170v1 Announce Type: new Abstract: Each year millions of people seek help for their legal problems by calling a legal aid program hotline, walking into a legal aid office, or using a lawyer referral service. The first step to match them to the right help is to identify the legal problem the applicant is experiencing. Misdirection has consequences. Applicants may miss a deadline, experience physical abuse, lose housing or lose custody of children while waiting to connect to the right legal help. We introduce and evaluate the FETCH classifier for legal issue classification and describe two methods for improving accuracy: a hybrid LLM/ML ensemble classification method, and the automatic generation of follow-up questions to enrich the initial problem narrative. We employ a novel data set of 419 real-world queries to a nonprofit lawyer referral service. Ultimately, we show classification accuracy (hits@2) of 97.37% using a mix of inexpensive models, exceeding the performance of the current state-of-the-art GPT-5 model. Our approach shows promise in significantly reducing the cost of guiding users of the legal system to the right resource for their problem while achieving high accuracy.

arXiv:2509.07208v1 Announce Type: new Abstract: The evolution of the traditional power grid into the "smart grid" has resulted in a fundamental shift in energy management, which allows the integration of renewable energy sources with modern communication technology. However, this interconnection has increased smart grids' vulnerability to attackers, which might result in privacy breaches, operational interruptions, and massive outages. The SCADA-based smart grid protocols are critical for real-time data collection and control, but they are vulnerable to attacks like unauthorized access and denial of service (DoS). This research proposes a hybrid deep learning-based Intrusion Detection System (IDS) intended to improve the cybersecurity of smart grids. The suggested model takes advantage of Convolutional Neural Networks' (CNN) feature extraction capabilities as well as Long Short-Term Memory (LSTM) networks' temporal pattern recognition skills. DNP3 and IEC104 intrusion detection datasets are employed to train and test our CNN-LSTM model to recognize and classify the potential cyber threats. Compared to other deep learning approaches, the results demonstrate considerable improvements in accuracy, precision, recall, and F1-score, with a detection accuracy of 99.70%.

arXiv:2509.07146v1 Announce Type: new Abstract: The sympathetic nervous system (SNS) plays a central role in regulating the body's responses to stress and maintaining physiological stability. Its dysregulation is associated with a wide range of conditions, from cardiovascular disease to anxiety disorders. Skin nerve activity (SKNA) extracted from high-frequency electrocardiogram (ECG) recordings provides a noninvasive window into SNS dynamics, but its measurement is highly susceptible to electromyographic (EMG) contamination. Traditional preprocessing based on bandpass filtering within a fixed range (e.g., 500--1000 Hz) is susceptible to overlapping EMG and SKNA spectral components, especially during sustained muscle activity. We present a denoising approach using a lightweight one-dimensional convolutional autoencoder with a long short-term memory (LSTM) bottleneck to reconstruct clean SKNA from EMG-contaminated recordings. Using clean ECG-derived SKNA data from cognitive stress experiments and EMG noise from chaotic muscle stimulation recordings, we simulated contamination at realistic noise levels (--4 dB, --8 dB signal-to-noise ratio) and trained the model in the leave-one-subject-out cross-validation framework. The method improved signal-to-noise ratio by up to 9.65 dB, increased cross correlation with clean SKNA from 0.40 to 0.72, and restored burst-based SKNA features to near-clean discriminability (AUROC $geq$ 0.96). Classification of baseline versus sympathetic stimulation (cognitive stress) conditions reached accuracies of 91--98% across severe noise levels, comparable to clean data. These results demonstrate that deep learning--based reconstruction can preserve physiologically relevant sympathetic bursts during substantial EMG interference, enabling more robust SKNA monitoring in naturalistic, movement-rich environments.

arXiv:2509.07159v1 Announce Type: new Abstract: Text-to-SQL models allow users to interact with a database more easily by generating executable SQL statements from natural-language questions. Despite recent successes on simpler databases and questions, current Text-to-SQL methods still suffer from low execution accuracy on industry-scale databases and complex questions involving domain-specific business logic. We present emph{PaVeRL-SQL}, a framework that combines emph{Partial-Match Rewards} and emph{Verbal Reinforcement Learning} to drive self-improvement in reasoning language models (RLMs) for Text-to-SQL. To handle practical use cases, we adopt two pipelines: (1) a newly designed in-context learning framework with group self-evaluation (verbal-RL), using capable open- and closed-source large language models (LLMs) as backbones; and (2) a chain-of-thought (CoT) RL pipeline with a small backbone model (OmniSQL-7B) trained with a specially designed reward function and two-stage RL. These pipelines achieve state-of-the-art (SOTA) results on popular Text-to-SQL benchmarks -- Spider, Spider 2.0, and BIRD. For the industrial-level Spider2.0-SQLite benchmark, the verbal-RL pipeline achieves an execution accuracy 7.4% higher than SOTA, and the CoT pipeline is 1.4% higher. RL training with mixed SQL dialects yields strong, threefold gains, particularly for dialects with limited training data. Overall, emph{PaVeRL-SQL} delivers reliable, SOTA Text-to-SQL under realistic industrial constraints. The code is available at https://github.com/PaVeRL-SQL/PaVeRL-SQL.

arXiv:2509.07122v1 Announce Type: new Abstract: Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - textit{DeepProbLog}, textit{Scallop}, and textit{DomiKnowS}. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.