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What Trace Powers Reveal About Log-Determinants: Closed-Form Estimators, Certificates, and Failure Modes

Sao, Piyush

arXiv.org Machine Learning

Computing $\log\det(A)$ for large symmetric positive definite matrices arises in Gaussian process inference and Bayesian model comparison. Standard methods combine matrix-vector products with polynomial approximations. We study a different model: access to trace powers $p_k = \tr(A^k)$, natural when matrix powers are available. Classical moment-based approximations Taylor-expand $\log(λ)$ around the arithmetic mean. This requires $|λ- \AM| < \AM$ and diverges when $κ> 4$. We work instead with the moment-generating function $M(t) = \E[X^t]$ for normalized eigenvalues $X = λ/\AM$. Since $M'(0) = \E[\log X]$, the log-determinant becomes $\log\det(A) = n(\log \AM + M'(0))$ -- the problem reduces to estimating a derivative at $t = 0$. Trace powers give $M(k)$ at positive integers, but interpolating $M(t)$ directly is ill-conditioned due to exponential growth. The transform $K(t) = \log M(t)$ compresses this range. Normalization by $\AM$ ensures $K(0) = K(1) = 0$. With these anchors fixed, we interpolate $K$ through $m+1$ consecutive integers and differentiate to estimate $K'(0)$. However, this local interpolation cannot capture arbitrary spectral features. We prove a fundamental limit: no continuous estimator using finitely many positive moments can be uniformly accurate over unbounded conditioning. Positive moments downweight the spectral tail; $K'(0) = \E[\log X]$ is tail-sensitive. This motivates guaranteed bounds. From the same traces we derive upper bounds on $(\det A)^{1/n}$. Given a spectral floor $r \leq λ_{\min}$, we obtain moment-constrained lower bounds, yielding a provable interval for $\log\det(A)$. A gap diagnostic indicates when to trust the point estimate and when to report bounds. All estimators and bounds cost $O(m)$, independent of $n$. For $m \in \{4, \ldots, 8\}$, this is effectively constant time.


Enhancing Dimensionality Prediction in Hybrid Metal Halides via Feature Engineering and Class-Imbalance Mitigation

Karabin, Mariia, Armstrong, Isaac, Beck, Leo, Apanel, Paulina, Eisenbach, Markus, Mitzi, David B., Terletska, Hanna, Heinz, Hendrik

arXiv.org Artificial Intelligence

We present a machine learning framework for predicting the structural dimensionality of hybrid metal halides (HMHs), including organic-inorganic perovskites, using a combination of chemically-informed feature engineering and advanced class-imbalance handling techniques. The dataset, consisting of 494 HMH structures, is highly imbalanced across dimensionality classes (0D, 1D, 2D, 3D), posing significant challenges to predictive modeling. This dataset was later augmented to 1336 via the Synthetic Minority Oversampling Technique (SMOTE) to mitigate the effects of the class imbalance. We developed interaction-based descriptors and integrated them into a multi-stage workflow that combines feature selection, model stacking, and performance optimization to improve dimensionality prediction accuracy. Our approach significantly improves F1-scores for underrepresented classes, achieving robust cross-validation performance across all dimensionalities.


VS-Graph: Scalable and Efficient Graph Classification Using Hyperdimensional Computing

Poursiami, Hamed, Snyder, Shay, Cong, Guojing, Potok, Thomas, Parsa, Maryam

arXiv.org Artificial Intelligence

Graph classification is a fundamental task in domains ranging from molecular property prediction to materials design. While graph neural networks (GNNs) achieve strong performance by learning expressive representations via message passing, they incur high computational costs, limiting their scalability and deployment on resource-constrained devices. Hyperdimensional Computing (HDC), also known as Vector Symbolic Architectures (VSA), offers a lightweight, brain-inspired alternative, yet existing HDC-based graph methods typically struggle to match the predictive performance of GNNs. In this work, we propose VS-Graph, a vector-symbolic graph learning framework that narrows the gap between the efficiency of HDC and the expressive power of message passing. VS-Graph introduces a Spike Diffusion mechanism for topology-driven node identification and an Associative Message Passing scheme for multi-hop neighborhood aggregation entirely within the high-dimensional vector space. Without gradient-based optimization or backpropagation, our method achieves competitive accuracy with modern GNNs, outperforming the prior HDC baseline by 4-5% on standard benchmarks such as MUTAG and DD. It also matches or exceeds the performance of the GNN baselines on several datasets while accelerating the training by a factor of up to 450x. Furthermore, VS-Graph maintains high accuracy even with the hypervector dimensionality reduced to D=128, demonstrating robustness under aggressive dimension compression and paving the way for ultra-efficient execution on edge and neuromorphic hardware.


Social Media Data Mining of Human Behaviour during Bushfire Evacuation

Wu, Junfeng, Zhou, Xiangmin, Kuligowski, Erica, Singh, Dhirendra, Ronchi, Enrico, Kinateder, Max

arXiv.org Artificial Intelligence

Traditional data sources on bushfire evacuation behaviour, such as quantitative surveys and manual observations have severe limitations. Mining social media data related to bushfire evacuations promises to close this gap by allowing the collection and processing of a large amount of behavioural data, which are low-cost, accurate, possibly including location information and rich contextual information. However, social media data have many limitations, such as being scattered, incomplete, informal, etc. Together, these limitations represent several challenges to their usefulness to better understand bushfire evacuation. To overcome these challenges and provide guidance on which and how social media data can be used, this scoping review of the literature reports on recent advances in relevant data mining techniques. In addition, future applications and open problems are discussed. We envision future applications such as evacuation model calibration and validation, emergency communication, personalised evacuation training, and resource allocation for evacuation preparedness. We identify open problems such as data quality, bias and representativeness, geolocation accuracy, contextual understanding, crisis-specific lexicon and semantics, and multimodal data interpretation.


ConStellaration: A dataset of QI-like stellarator plasma boundaries and optimization benchmarks

Cadena, Santiago A., Merlo, Andrea, Laude, Emanuel, Bauer, Alexander, Agrawal, Atul, Pascu, Maria, Savtchouk, Marija, Guiraud, Enrico, Bonauer, Lukas, Hudson, Stuart, Kaiser, Markus

arXiv.org Artificial Intelligence

Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations, considered as a promising path to commercial fusion due to their inherent resilience to current driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset along with benchmark problems and baselines, we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.


Leveraging AI for Productive and Trustworthy HPC Software: Challenges and Research Directions

Teranishi, Keita, Menon, Harshitha, Godoy, William F., Balaprakash, Prasanna, Bau, David, Ben-Nun, Tal, Bhatele, Abhinav, Franchetti, Franz, Franusich, Michael, Gamblin, Todd, Georgakoudis, Giorgis, Goldstein, Tom, Guha, Arjun, Hahn, Steven, Iancu, Costin, Jin, Zheming, Jones, Terry, Low, Tze Meng, Mankad, Het, Miniskar, Narasinga Rao, Monil, Mohammad Alaul Haque, Nichols, Daniel, Parasyris, Konstantinos, Pophale, Swaroop, Valero-Lara, Pedro, Vetter, Jeffrey S., Williams, Samuel, Young, Aaron

arXiv.org Artificial Intelligence

We discuss the challenges and propose research directions for using AI to revolutionize the development of high-performance computing (HPC) software. AI technologies, in particular large language models, have transformed every aspect of software development. For its part, HPC software is recognized as a highly specialized scientific field of its own. We discuss the challenges associated with leveraging state-of-the-art AI technologies to develop such a unique and niche class of software and outline our research directions in the two US Department of Energy--funded projects for advancing HPC Software via AI: Ellora and Durban.


Vector Quantized-Elites: Unsupervised and Problem-Agnostic Quality-Diversity Optimization

Tsakonas, Constantinos, Chatzilygeroudis, Konstantinos

arXiv.org Artificial Intelligence

Quality-Diversity algorithms have transformed optimization by prioritizing the discovery of diverse, high-performing solutions over a single optimal result. However, traditional Quality-Diversity methods, such as MAP-Elites, rely heavily on predefined behavior descriptors and complete prior knowledge of the task to define the behavior space grid, limiting their flexibility and applicability. In this work, we introduce Vector Quantized-Elites (VQ-Elites), a novel Quality-Diversity algorithm that autonomously constructs a structured behavior space grid using unsupervised learning, eliminating the need for prior task-specific knowledge. At the core of VQ-Elites is the integration of Vector Quantized Variational Autoencoders, which enables the dynamic learning of behavior descriptors and the generation of a structured, rather than unstructured, behavior space grid -- a significant advancement over existing unsupervised Quality-Diversity approaches. This design establishes VQ-Elites as a flexible, robust, and task-agnostic optimization framework. To further enhance the performance of unsupervised Quality-Diversity algorithms, we introduce behavior space bounding and cooperation mechanisms, which significantly improve convergence and performance, as well as the Effective Diversity Ratio and Coverage Diversity Score, two novel metrics that quantify the actual diversity in the unsupervised setting. We validate VQ-Elites on robotic arm pose-reaching, mobile robot space-covering, and MiniGrid exploration tasks. The results demonstrate its ability to efficiently generate diverse, high-quality solutions, emphasizing its adaptability, scalability, robustness to hyperparameters, and potential to extend Quality-Diversity optimization to complex, previously inaccessible domains.


FATHOMS-RAG: A Framework for the Assessment of Thinking and Observation in Multimodal Systems that use Retrieval Augmented Generation

Hildebrand, Samuel, Taylor, Curtis, Oesch, Sean, Ghawaly, James M Jr, Sadovnik, Amir, Shivers, Ryan, Schreiber, Brandon, Kurian, Kevin

arXiv.org Artificial Intelligence

Abstract--Retrieval-augmented generation (RAG) has emerged as a promising paradigm for improving factual accuracy in large language models (LLMs). We introduce a benchmark designed to evaluate RAG pipelines as a whole, evaluating a pipeline's ability to ingest, retrieve, and reason about several modalities of information, differentiating it from existing benchmarks that focus on particular aspects such as retrieval. We present (1) a small, human-created dataset of 93 questions designed to evaluate a pipeline's ability to ingest textual data, tables, images, and data spread across these modalities in one or more documents; (2) a phrase-level recall metric for correctness; (3) a nearest-neighbor embedding classifier to identify potential pipeline hallucinations; (4) a comparative evaluation of 2 pipelines built with open-source retrieval mechanisms and 4 closed-source foundation models; and (5) a third-party human evaluation of the alignment of our correctness and hallucination metrics. We find that closed-source pipelines significantly outperform open-source pipelines in both correctness and hallucination metrics, with wider performance gaps in questions relying on multimodal and cross-document information. Human evaluation of our metrics showed average agreement of 4.62 for correctness and 4.53 for hallucination detection on a 1-5 Likert scale (5 indicating "strongly agree"). Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT -Battelle, LLC, for the U. S. Department of Energy. Notice: This manuscript has been authored by UT -Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.


A Primer on Quantum Machine Learning

Chang, Su Yeon, Cerezo, M.

arXiv.org Machine Learning

Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization, supervised, unsupervised and reinforcement learning, and generative modeling-among other tasks-more efficiently than classical models. Here we offer a high level overview of QML, focusing on settings where the quantum device is the primary learning or data generating unit. We outline the field's tensions between practicality and guarantees, access models and speedups, and classical baselines and claimed quantum advantages-flagging where evidence is strong, where it is conditional or still lacking, and where open questions remain. By shedding light on these nuances and debates, we aim to provide a friendly map of the QML landscape so that the reader can judge when-and under what assumptions-quantum approaches may offer real benefits.