We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is particularly effective for Hadamard matrices of Goethals--Seidel type, where Fourier methods permit fast scoring and optimisation. For orders between 100 and 200, it produces large numbers of inequivalent Hadamard matrices, and for larger orders, it succeeds where local search from random initialisation fails. The largest example found by our method has order 252. In addition to these new constructions, our experiments reveal that the transformer can discover and exploit useful hidden symmetry in the search space.

Objective: To develop a robust and compact deep learning model for automated knee cartilage segmentation on point-of-care ultrasound (POCUS) devices. Methods: We propose MonoUNet, a novel, highly compact segmentation model consisting of (i) an aggressively reduced U-Net backbone, (ii) a trainable monogenic block that extracts multi-scale local phase features from the input, and (iii) a gating mechanism that injects these features into the encoder stages to reduce sensitivity to variations in ultrasound image appearance. MonoUNet segmentation performance was evaluated on a multi-site, multi-device knee cartilage ultrasound dataset using Dice score and mean average surface distance (MASD). Agreement between MonoUNet and manual cartilage outcomes (thickness and echo intensity) was assessed using Bland-Altman analysis with 95% limits of agreement, and reliability was assessed using intraclass correlation coefficient (ICC$_{2,k}$). Results: Overall, MonoUNet outperformed existing lightweight segmentation models, with average Dice scores ranging from 92.62% to 94.82% and MASD values between 0.133 mm and 0.254 mm. MonoUNet reduces the number of parameters by 10x--700x and computational cost by 14x--2000x relative to existing lightweight models. MonoUNet cartilage outcomes showed excellent reliability and agreement with the manual outcomes: intraclass correlation coefficients (ICC$_{2,k})$=0.96 and bias=2.00% (0.047 mm) for average thickness, and ICC$_{2,k}$=0.99 and bias=0.80% (0.328 a.u.) for echo intensity. Conclusion: Incorporating trainable local phase features improves the robustness of highly compact neural networks for knee cartilage segmentation across varying acquisition settings and could support scalable ultrasound-based assessment and monitoring of knee osteoarthritis using POCUS devices. The code is publicly available at https://github.com/alvinkimbowa/monounet.

Production deployment of AI coding agents requires fast, reproducible evaluation signals. Existing industrial practices trade off speed and fidelity: online A/B testing takes weeks and risks user experience, shadow deployment yields signals that are not reproducible across runs, and public benchmarks diverge from production workloads in language distribution, prompt style, and codebase structure. This paper presents REAP (Relevance and Execution-Audited Pipeline), an automated curation pipeline that constructs production-derived benchmarks from real developer-agent sessions without manual labeling. Such curation, while in-distribution to production usage, runs into several challenges. Untestable prompts, misaligned tests, and test flakiness all compromise evaluation reliability. While tasks can be manually audited to ensure only high-quality tasks remain in the benchmark, this approach is infeasible in the monorepo setting: the build infrastructure state is often ephemeral in large monorepos and requires the benchmark to be continuously re-curated against the current codebase. As manual verification cannot be sustained at this cadence, REAP adds an automated verification layer using LLM-based task classification, agentic test-relevance validation, and multi-run stability checks to ensure the executable benchmark yields trustworthy signals. We use REAP to curate Harvest, a benchmark where each task feeds the coding agent a real developer prompt and verifies the resulting code change against fail-to-pass tests retrieved from production. Harvest's distribution spans more than four programming languages with a majority of tasks drawn from Hack. Model and harness evaluations reveal that solve rates range from 42.9% to 58.2% across five frontier models, surfacing capability differences that inform concrete deployment decisions.

The rapid evolution of end-to-end spoken dialogue systems demands transcending mere textual semantics to incorporate paralinguistic nuances and the spontaneous nature of human conversation. However, current methods struggle with two critical gaps: the modality gap, involving prosody and emotion, and the colloquialness gap, distinguishing written scripts from natural speech. To address these challenges, we introduce SDiaReward, an end-to-end multi-turn reward model trained on SDiaReward-Dataset, a novel collection of episode-level preference pairs explicitly targeting these gaps. It operates directly on full multi-turn speech episodes and is optimized with pairwise preference supervision, enabling joint assessment of modality and colloquialness in a single evaluator. We further establish ESDR-Bench, a stratified benchmark for robust episode-level evaluation. Experiments demonstrate that SDiaReward achieves state-of-the-art pairwise preference accuracy, significantly outperforming general-purpose audio LLMs. Further analysis suggests that SDiaReward captures relative conversational expressiveness beyond superficial synthesis cues, improving generalization across domains and recording conditions. Code, data, and demos are available at https://github.com/MM-Speech/SDiaReward/.

We propose glaucoma lesion evaluation and analysis with multimodal imaging (GLEAM), the first publicly available tri-modal glaucoma dataset comprising scanning laser ophthalmoscopy fundus images, circumpapillary OCT images, and visual field pattern deviation maps, annotated with four disease stages, enabling effective exploitation of multimodal complementary information and facilitating accurate diagnosis and treatment across disease stages. To effectively integrate cross-modal information, we propose hierarchical attentive masked modeling (HAMM) for multimodal glaucoma classification. Our framework employs hierarchical attentive encoders and light decoders to focus cross-modal representation learning on the encoder.

Many large-scale platforms and networked control systems have a centralized decision maker interacting with a massive population of agents under strict observability constraints. Motivated by such applications, we study a cooperative Markov game with a global agent and $n$ homogeneous local agents in a communication-constrained regime, where the global agent only observes a subset of $k$ local agent states per time step. We propose an alternating learning framework $(\texttt{ALTERNATING-MARL})$, where the global agent performs subsampled mean-field $Q$-learning against a fixed local policy, and local agents update by optimizing in an induced MDP. We prove that these approximate best-response dynamics converge to an $\widetilde{O}(1/\sqrt{k})$-approximate Nash Equilibrium, while separating the sample complexities between the joint state and action spaces. Finally, we validate our results in numerical simulations for multi-robot control.

Cancer is often driven by specific combinations of an estimated two to nine gene mutations, known as multi-hit combinations. Identifying these multi-hit combinations of gene mutations that drive cancer is critical for understanding carcinogenesis and designing targeted therapies. We formalize this challenge as the Multi-Hit Cancer Driver Set Cover Problem (MHCDSCP), optimizing the selection of gene combinations to maximize tumor coverage while strictly minimizing normal sample misclassification. While existing approaches rely on exhaustive enumeration and massive parallelization, we introduce fast heuristics based on constraint programming and mixed integer programming formulations. Evaluated on real-world cancer genomics data, our framework matches state-of-the-art supercomputing methods using a single commodity CPU in under a minute. We also propose a price-and-branch heuristic which, by solving the root node to optimality, provides the first provably optimal solutions for over half of the benchmark instances, thereby verifying the near-optimality of our fast heuristics. These findings demonstrate that on real-world problem instances, the MHCDSCP is far less computationally demanding than previously believed, providing an accessible baseline that enables the exploration of previously intractable multi-hit modeling assumptions.

Room impulse responses (RIRs) are essential for many acoustic signal processing tasks, yet measuring them densely across space is often impractical. In this work, we propose RIR-Former, a grid-free, one-step feed-forward model for RIR reconstruction. By introducing a sinusoidal encoding module into a transformer backbone, our method effectively incorporates microphone position information, enabling interpolation at arbitrary array locations. Furthermore, a segmented multi-branch decoder is designed to separately handle early reflections and late reverberation, improving reconstruction across the entire RIR. Experiments on diverse simulated acoustic environments demonstrate that RIR-Former consistently outperforms state-of-the-art baselines in terms of normalized mean square error (NMSE) and cosine distance (CD), under varying missing rates and array configurations. These results highlight the potential of our approach for practical deployment and motivate future work on scaling from randomly spaced linear arrays to complex array geometries, dynamic acoustic scenes, and real-world environments.

Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet its typically sequential structure and hard constraints make efficient accelerator implementations difficult. This paper introduces Nested Slice Sampling (NSS), a GPU-friendly, vectorized formulation of Nested Sampling that uses Hit-and-Run Slice Sampling for constrained updates. A tuning analysis yields a simple near-optimal rule for setting the slice width, improving high-dimensional behavior and making per-step compute more predictable for parallel execution. Experiments on challenging synthetic targets, high dimensional Bayesian inference, and Gaussian process hyperparameter marginalization show that NSS maintains accurate evidence estimates and high-quality posterior samples, and is particularly robust on difficult multimodal problems where current state-of-the-art methods such as tempered SMC baselines can struggle. An open-source implementation is released to facilitate adoption and reproducibility.

Interactive recommender systems can dynamically adapt to user feedback, but often suffer from content homogeneity and filter bubble effects due to overfitting short-term user preferences. While recent efforts aim to improve content diversity, they predominantly operate in static or one-shot settings, neglecting the long-term evolution of user interests. Reinforcement learning provides a principled framework for optimizing long-term user satisfaction by modeling sequential decision-making processes. However, its application in recommendation is hindered by sparse, long-tailed user-item interactions and limited semantic planning capabilities. In this work, we propose LLM-Enhanced Reinforcement Learning (LERL), a novel hierarchical recommendation framework that integrates the semantic planning power of LLM with the fine-grained adaptability of RL. LERL consists of a high-level LLM-based planner that selects semantically diverse content categories, and a low-level RL policy that recommends personalized items within the selected semantic space. This hierarchical design narrows the action space, enhances planning efficiency, and mitigates overexposure to redundant content. Extensive experiments on real-world datasets demonstrate that LERL significantly improves long-term user satisfaction when compared with state-of-the-art baselines. The implementation of LERL is available at https://github.com/1163710212/LERL.

Recent advances in audio-aware large language models have shown strong performance on audio question answering. However, existing benchmarks mainly cover answerable questions and overlook the challenge of unanswerable ones, where no reliable answer can be inferred from the audio. Such cases are common in real-world settings, where questions may be misleading, ill-posed, or incompatible with the information. To address this gap, we present AQUA-Bench, a benchmark for Audio Question Unanswerability Assessment. It systematically evaluates three scenarios: Absent Answer Detection (the correct option is missing), Incompatible Answer Set Detection (choices are categorically mismatched with the question), and Incompatible Audio Question Detection (the question is irrelevant or lacks sufficient grounding in the audio). By assessing these cases, AQUA-Bench offers a rigorous measure of model reliability and promotes the development of audio-language systems that are more robust and trustworthy. Our experiments suggest that while models excel on standard answerable tasks, they often face notable challenges with unanswerable ones, pointing to a blind spot in current audio-language understanding.

Graph-based recommendation has achieved great success in recent years. The classical graph recommendation model utilizes ID embedding to store essential collaborative information. However, this ID-based paradigm faces challenges in transferring to a new domain, making it hard to build a pre-trained graph recommendation model. This phenomenon primarily stems from two inherent challenges: (1) the non-transferability of ID embeddings due to isolated domain-specific ID spaces, and (2) structural incompatibility between heterogeneous interaction graphs across domains. To address these issues, we propose TextBridgeGNN, a pre-training and fine-tuning framework that can effectively transfer knowledge from a pre-trained GNN to downstream tasks. We believe the key lies in how to build the relationship between domains. Specifically, TextBridgeGNN uses text as a semantic bridge to connect domains through multi-level graph propagation. During the pre-training stage, textual information is utilized to break the data islands formed by multiple domains, and hierarchical GNNs are designed to learn both domain-specific and domain-global knowledge with text features, ensuring the retention of collaborative signals and the enhancement of semantics. During the fine-tuning stage, a similarity transfer mechanism is proposed. This mechanism initializes ID embeddings in the target domain by transferring from semantically related nodes, successfully transferring the ID embeddings and graph pattern. Experiments demonstrate that TextBridgeGNN outperforms existing methods in cross-domain, multi-domain, and training-free settings, highlighting its ability to integrate Pre-trained Language Model (PLM)-driven semantics with graph-based collaborative filtering without costly language model fine-tuning or real-time inference overhead.

Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields, reducing either speed or spin count. We demonstrate an amplitude-only, rank-free spatial photonic Ising machine in which arbitrary Ising Hamiltonians are encoded as Hadamard products on aligned amplitude and binary spatial modulators and read out by a single-pixel intensity measurement. The machine directly programs fully connected 797-spin Ising models with external fields at nearly 9-bit precision and operates at a constant iteration rate of ~200 Hz. By removing zero-valued product terms, the same architecture scales to sparse problems and experimentally solves a Max-Cut instance on a 424,108-vertex Mobius ladder graph. We also observe the phase transition of the Sherrington-Kirkpatrick model, demonstrating programmable optical simulation beyond low-rank couplings. These results establish amplitude modulation as a scalable route to programmable photonic Ising machines.

Quantum machine learning has emerged as a promising approach to improve feature extraction and classification tasks in high-dimensional data domains such as medical imaging. In this work, we present a hybrid Quantum-Classical Convolutional Neural Network (QCNN) architecture designed for the binary classification of the BreastMNIST dataset, a standardized benchmark for distinguishing between benign and malignant breast tumors. Our architecture integrates classical convolutional feature extraction with two distinct quantum circuits: an amplitude-encoding variational quantum circuit (VQC) and an angle-encoding VQC circuit with circular entanglement, both implemented on four qubits. These circuits generate quantum feature embeddings that are fused with classical features to form a joint feature space, which is subsequently processed by a fully connected classifier. To ensure fairness, the hybrid QCNN is parameter-matched against a baseline classical CNN, allowing us to isolate the contribution of quantum layers. Both models are trained under identical conditions using the Adam optimizer and binary cross-entropy loss. Experimental evaluation in five independent runs demonstrates that the hybrid QCNN achieves statistically significant improvements in classification accuracy compared to the classical CNN, as validated by a one-sided Wilcoxon signed rank test (p = 0.03125) and supported by large effect size of Cohen's d = 2.14. Our results indicate that hybrid QCNN architectures can leverage entanglement and quantum feature fusion to enhance medical image classification tasks. This work establishes a statistical validation framework for assessing hybrid quantum models in biomedical applications and highlights pathways for scaling to larger datasets and deployment on near-term quantum hardware.

Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors used to identify counterfactual quantities via eigendecomposition tasks. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.

We propose Fast-MIA (https://github.com/Nikkei/fast-mia), a Python library for efficiently evaluating membership inference attacks (MIA) against large language models (LLMs). MIA has emerged as a crucial technique for auditing privacy risks and copyright infringement in LLMs. However, computational demands have grown substantially: recent methods rely on repeated inference, while practical auditing requires large-scale evaluation. Progress is further hindered by existing implementations that execute methods independently, redundantly computing shared intermediate results such as log-probabilities. To address these challenges, Fast-MIA combines two strategies: (1) high-throughput batch inference via vLLM, achieving approximately 5$\times$ speedup, and (2) a cross-method caching architecture that computes intermediate results once and shares them across methods. The library includes representative MIA methods under a unified framework, integrates with established benchmarks, and supports flexible YAML configuration. We release Fast-MIA under the Apache License 2.0 to support scalable and reproducible MIA research.

Large Language Models (LLMs) remain vulnerable to jailbreak attacks, where adversarially crafted prompts induce policy-violating responses despite safety alignment. Existing defenses typically improve safety through external filtering, auxiliary guardrails, or decoding-time control. However, these interventions often reduce practical deployability because they may require additional model access, introduce extra inference cost, or affect benign-task utility. In this paper, we propose Safety-Aware Intent Defense (SAID), a training-free jailbreak defense framework based on intent-level safety probing. SAID first distills potentially obfuscated user inputs into concise core intents using the target model itself. It then applies a validated safety prefix to probe each distilled intent and elicit the model's safety-aware response. Finally, a conservative aggregation rule rejects the original request if any distilled intent is identified as unsafe. This design enables black-box-compatible defense without updating model parameters or modifying the decoding process. Experiments on four open-source LLMs under six representative jailbreak attacks show that SAID achieves state-of-the-art defense performance in reducing harmful responses while maintaining competitive utility on benign tasks. Further analyses on prefix variants, hierarchical distillation, and inference efficiency demonstrate that SAID provides a practical safety-utility trade-off for securing LLMs against jailbreak threats.

The growing prevalence of speech deepfakes has raised serious concerns, particularly in real-world scenarios such as telephone fraud and identity theft. While many anti-spoofing systems have demonstrated promising performance on lab-generated synthetic speech, they often fail when confronted with physical replay attacks-a common and low-cost form of attack used in practical settings. Our experiments show that models trained on existing datasets exhibit severe performance degradation, with average accuracy dropping to 59.6% when evaluated on replayed audio. To bridge this gap, we present EchoFake, a comprehensive dataset comprising more than 120 hours of audio from over 13,000 speakers, featuring both cutting-edge zero-shot text-to-speech (TTS) speech and physical replay recordings collected under varied devices and real-world environmental settings. Additionally, we evaluate three baseline detection models and show that models trained on EchoFake achieve lower average EERs across datasets, indicating better generalization. By introducing more practical challenges relevant to real-world deployment, EchoFake offers a more realistic foundation for advancing spoofing detection methods.

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust feasibility is ensured. This work introduces a novel approach integrating it with the directional sensor networks to enhance coverage using a distributed greedy algorithm. In particular, we provide an exact formula for the radius of robust feasibility of sensors in a directional sensor network. The proposed model strategically orients the sensors in regions with high coverage potential, accounting for robustness in the face of uncertainty. We analyze the algorithm's adaptability in dynamic environments, demonstrating its ability to enhance efficiency and robustness. Experimental results validate its efficacy in maximizing coverage and optimizing sensor orientations, highlighting its practical advantages for real-world scenarios.

We study spectral graph clustering under edge differential privacy. We propose a matrix shuffling mechanism that combines randomized edge flipping with a random permutation of the adjacency matrix. While edge flipping alone provides only a constant $\varepsilon$ guarantee as the graph grows, shuffling amplifies privacy so that the effective $\varepsilon$ tends to zero with the number of nodes. We develop a unified error analysis framework -- based on Davis--Kahan perturbation theory and a classification-margin bound -- that gives explicit misclassification rates for all the mechanisms considered as a function of the privacy budget, eigengap, and number of communities. Applying this framework, we show that the matrix shuffling mechanism achieves an error rate scaling of $\tilde{O}(1/n)$, a clear improvement over two canonical DP baselines from the private PCA literature: the Gaussian mechanism applied directly to the adjacency matrix (Analyze Gauss) and the noisy power method, both of which scale as $\tilde{O}(1)$ in $n$. We further propose a private spectral gap detection algorithm for estimating the number of communities. Experiments on synthetic and real-world networks validate our theoretical findings.

With the rapid advancement of smart glasses, voice interaction has been widely adopted due to its naturalness and convenience. However, its practical deployment is often undermined by vulnerability to spoofing attacks, while no public dataset currently exists for voice liveness detection and authentication in smart-glasses scenarios. To address this challenge, we first collect a multi-acoustic-modal dataset comprising 16-channel audio data from 42 subjects, along with corresponding attack samples covering two attack categories. Based on insights derived from this collected data, we propose AuthG-Live, a sound-field-based voice liveness detection method, and AuthG-Net, a multi-acoustic-modal authentication model. We further benchmark seven voice liveness detection methods and four authentication methods across diverse acoustic modalities. The results demonstrate that our proposed approach achieves state-of-the-art performance on four benchmark tasks, and extensive ablation studies validate the generalizability of our methods \red{under real-world constraints}. Finally, we release this dataset, termed AuthGlass, to facilitate future research on voice liveness detection and authentication for smart glasses.

Estimating causal effects on networks is challenging because treatments may affect both treated units and their neighbors, while network homophily induces dependence and confounding. These challenges are amplified when causal effects are heterogeneous across units and edges. We propose a two-stage orthogonal learning framework for estimating heterogeneous direct and spillover effects on networks. The first stage uses graph neural networks to estimate nuisance components that capture complex dependence on covariates and network structure. The second stage residualizes these nuisance components and estimates causal effects through an interpretable attention-based interference model, yielding edge-level spillover estimates as well as node- and population-level summaries. Neyman orthogonalization and cross-fitting reduce sensitivity to first-stage estimation error, so nuisance errors enter only at higher order. We further develop a bootstrap-based uncertainty quantification procedure for the estimated spillover matrix, enabling pointwise and simultaneous inference for heterogeneous edge- and node-level effects. Experiments show that our method improves heterogeneous effect estimation while supporting interpretable downstream analyses such as influential-neighbor detection and spillover-sign recovery.

The increase in cardiac and pulmonary diseases presents an alarming and pervasive health challenge on a global scale responsible for unexpected and premature mortalities. In spite of how serious these conditions are, existing methods of detection and treatment encounter challenges, particularly in achieving timely diagnosis for effective medical intervention. Manual screening processes commonly used for primary detection of cardiac and respiratory problems face inherent limitations, increased by a scarcity of skilled medical practitioners in remote or under-resourced areas. To address this, our study introduces an innovative yet efficient model which integrates AI for diagnosing lung and heart conditions concurrently using the auscultation sounds. Unlike the already high-priced digital stethoscope, our proposed model has been particularly designed to deploy on low-cost embedded devices and thus ensure applicability in under-developed regions that actually face an issue of accessing medical care. Our proposed model incorporates MFCC feature extraction and engineering techniques to ensure that the signal is well analyzed for accurate diagnostics through the hybrid model combining Gated Recurrent Unit with CNN in processing audio signals recorded from the low-cost stethoscope. Beyond its diagnostic capabilities, the model generates digital audio records that facilitate in classifying six pulmonary and five cardiovascular diseases. Hence, the integration of a cost effective stethoscope with an efficient AI empowered model deployed on a web app providing real-time analysis, represents a transformative step towards standardized healthcare

Identifying brain hemorrhages from magnetic resonance imaging (MRI) is a critical task for healthcare professionals. The diverse nature of MRI acquisitions with varying contrasts and orientation introduce complexity in identifying hemorrhage using neural networks. For acquisitions with varying orientations, traditional methods often involve resampling images to a fixed plane, which can lead to information loss. To address this, we propose a 3D multi-plane vision transformer (MP-ViT) for hemorrhage classification with varying orientation data. It employs two separate transformer encoders for axial and sagittal contrasts, using cross-attention to integrate information across orientations. MP-ViT also includes a modality indication vector to provide missing contrast information to the model. The effectiveness of the proposed model is demonstrated with extensive experiments on real world clinical dataset consists of 10,084 training, 1,289 validation and 1,496 test subjects. MP-ViT achieved substantial improvement in area under the curve (AUC), outperforming the vision transformer (ViT) by 5.5% and CNN-based architectures by 1.8%. These results highlight the potential of MP-ViT in improving performance for hemorrhage detection when different orientation contrasts are needed.

Training effective dense retrieval models typically relies on hard negative (HN) examples mined from large document corpora using methods such as BM25 or cross-encoders, which require full corpus access and expensive index construction. We propose generating synthetic hard negatives directly from a provided query and positive passage, using Large Language Models(LLMs). We fine-tune DistilBERT using synthetic negatives generated by four state-of-the-art LLMs ranging from 4B to 30B parameters (Qwen3, LLaMA3, Phi4) and evaluate performance across 10 BEIR benchmark datasets. Contrary to the prevailing assumption that stronger generative models yield better synthetic data, find that our generative pipeline consistently underperforms traditional corpus-based mining strategies (BM25 and Cross-Encoder). Furthermore, we observe that scaling the generator model does not monotonically improve retrieval performance and find that the 14B parameter model outperforms the 30B model and in some settings it is the worst performing.

This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused on general mathematics problems and the currently infeasible objective of automated theorem proving. In the first part of this paper, we relax our ambition and focus on a more specialized domain: we evaluate the performance of the state-of-the-art open-source large language model Qwen2.5-Math-7B-Instruct on algorithmic and computational tasks in algorithmic number theory. On a benchmark of thirty algorithmic problems and thirty computational questions taken from classical number-theoretic textbooks and Math StackExchange, the model achieves at least 0.95 accuracy (relative to the true answer) on every problem or question when given an optimal non-spoiling hint. The second part of the paper empirically verifies a folklore conjecture in analytic number theory stating that the modulus \(q\) of a Dirichlet character \(χ\) is uniquely determined by the initial nontrivial zeros \(\{ρ_1,\dots,ρ_k\}\) (for some \(k\in\mathbb{N}\)) of the corresponding Dirichlet \(L\)-function \(L(s,χ)\). We train a LightGBM multiclass classifier to predict the conductor \(q\) for 214 randomly chosen Dirichlet \(L\)-functions from a vector of statistical features of their initial zeros (moments, finite-difference statistics, FFT magnitudes, etc.). The model empirically verifies the conjecture for small \(q\), achieving at least 93.9\% test accuracy when sufficient statistical properties of the zeros are incorporated. For the second part of the paper, code and dataset are available.

How to allocate limited resources to projects that will yield the greatest long-term benefits is a problem that often arises in decision-making under uncertainty. For example, organizations may need to evaluate and select innovation projects with risky returns. Similarly, when allocating resources to research projects, funding agencies are tasked with identifying the most promising proposals based on idiosyncratic criteria. Finally, in participatory budgeting, a local community may need to select a subset of public projects to fund. Regardless of context, agents must estimate the uncertain values of a potentially large number of projects. Developing parsimonious methods to compare these projects, and aggregating agent evaluations so that the overall benefit is maximized, are critical in assembling the best project portfolio. Unlike in standard sorting algorithms, evaluating projects on the basis of uncertain long-term benefits introduces additional complexities. We propose comparison rules based on Quicksort and the Bradley--Terry model, which connects rankings to pairwise "win" probabilities. In our model, each agent determines win probabilities of a pair of projects based on his or her specific evaluation of the projects' long-term benefit. The win probabilities are then appropriately aggregated and used to rank projects. Several of the methods we propose perform better than the two most effective aggregation methods currently available. Additionally, our methods can be combined with sampling techniques to significantly reduce the number of pairwise comparisons. We also discuss how the Bradley--Terry portfolio selection approach can be implemented in practice.

Battery degradation significantly impacts the reliability and efficiency of energy storage systems, particularly in electric vehicles and industrial applications. Predicting the remaining useful life (RUL) of lithium-ion batteries is crucial for optimizing maintenance schedules, reducing costs, and improving safety. Traditional RUL prediction methods often struggle with nonlinear degradation patterns and uncertainty quantification. To address these challenges, we propose a hybrid survival analysis framework integrating survival data reconstruction, survival model learning, and survival probability estimation. Our approach transforms battery voltage time series into time-to-failure data using path signatures. The multiple Cox-based survival models and machine-learning-based methods, such as DeepHit and MTLR, are learned to predict battery failure-free probabilities over time. Experiments conducted on the Toyota battery and NASA battery datasets demonstrate the effectiveness of our approach, achieving high time-dependent AUC and concordance index (C-Index) while maintaining a low integrated Brier score. The data and source codes are available to the public at https://github.com/okic-ca/rul

Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs) for solving question-answer (QA) tasks. The state-of-the-art RAG approaches often use the graph data as the external data since they capture the rich semantic information and link relationships between entities. However, existing graph-based RAG approaches cannot accurately identify the relevant information from the graph and also consume large numbers of tokens in the online retrieval process. To address these issues, we introduce a novel graph-based RAG approach, called Attributed Community-based Hierarchical RAG (ArchRAG), by augmenting the question using attributed communities, and also introducing a novel LLM-based hierarchical clustering method. To retrieve the most relevant information from the graph for the question, we build a novel hierarchical index structure for the attributed communities and develop an effective online retrieval method. Experimental results demonstrate that ArchRAG outperforms existing methods in both accuracy and token cost.

Graph Neural Networks (GNNs) are widely deployed in industry, making their intellectual property valuable. However, protecting GNNs from unauthorized use remains a challenge. Watermarking offers a solution by embedding ownership information into models. Existing watermarking methods have two limitations: First, they rarely focus on graph data or GNNs. Second, the de facto backdoor-based method relies on manipulating training data, which can introduce ownership ambiguity through misclassification and vulnerability to data poisoning attacks that can interrupt the backdoor mechanism. Our explanation-based watermarking inherits the strengths of backdoor-based methods (e.g., black-box verification) without data manipulation, eliminating ownership ambiguity and data dependencies. In particular, we watermark GNN explanations such that these explanations are statistically distinct from others, so ownership claims must be verified through statistical significance. We theoretically prove that, even with full knowledge of our method, locating the watermark is NP-hard. Empirically, our method demonstrates robustness to fine-tuning and pruning attacks. By addressing these challenges, our approach significantly advances GNN intellectual property protection.