We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a full decomposability over specific subspaces and determine the largest possible subspaces that allow the full decomposability. We derive novel inclusions of the subdifferential of the tensor nuclear norm and study its subgradients in a variety of subspaces of interest. All the results hold for tensors of an arbitrary order. As an immediate application, we establish the statistical performance of the tensor robust principal component analysis, the first such result for tensors of an arbitrary order.

We present spd-metrics-id, a Python package for computing distances and divergences between symmetric positive-definite (SPD) matrices. Unlike traditional toolkits that focus on specific applications, spd-metrics-id provides a unified, extensible, and reproducible framework for SPD distance computation. The package supports a wide variety of geometry-aware metrics, including Alpha-z Bures-Wasserstein, Alpha-Procrustes, affine-invariant Riemannian, log-Euclidean, and others, and is accessible both via a command-line interface and a Python API. Reproducibility is ensured through Docker images and Zenodo archiving. We illustrate usage through a connectome fingerprinting example, but the package is broadly applicable to covariance analysis, diffusion tensor imaging, and other domains requiring SPD matrix comparison. The package is openly available at https://pypi.org/project/spd-metrics-id/.

Policy targets evolve faster than the Couple Model Intercomparison Project cycles, complicating adaptation and mitigation planning that must often contend with outdated projections. Climate model output emulators address this gap by offering inexpensive surrogates that can rapidly explore alternative futures while staying close to Earth System Model (ESM) behavior. We focus on emulators designed to provide inputs to impact models. Using monthly ESM fields of near-surface temperature, precipitation, relative humidity, and wind speed, we show that deep generative models have the potential to model jointly the distribution of variables relevant for impacts. The specific model we propose uses score-based diffusion on a spherical mesh and runs on a single mid-range graphical processing unit. We introduce a thorough suite of diagnostics to compare emulator outputs with their parent ESMs, including their probability densities, cross-variable correlations, time of emergence, or tail behavior. We evaluate performance across three distinct ESMs in both pre-industrial and forced regimes. The results show that the emulator produces distributions that closely match the ESM outputs and captures key forced responses. They also reveal important failure cases, notably for variables with a strong regime shift in the seasonal cycle. Although not a perfect match to the ESM, the inaccuracies of the emulator are small relative to the scale of internal variability in ESM projections. We therefore argue that it shows potential to be useful in supporting impact assessment. We discuss priorities for future development toward daily resolution, finer spatial scales, and bias-aware training. Code is made available at https://github.com/shahineb/climemu.

Despite recent progress in optimal hyperparameter transfer under model and dataset scaling, no unifying explanatory principle has been established. Using the Scion optimizer, we discover that joint optimal scaling across model and dataset sizes is governed by a single invariant: the operator norm of the output layer. Across models with up to 1.3B parameters trained on up to 138B tokens, the optimal learning rate/batch size pair $(η^{\ast}, B^{\ast})$ consistently has the same operator norm value - a phenomenon we term norm transfer. This constant norm condition is necessary but not sufficient: while for each dataset size, multiple $(η, B)$ reach the optimal norm, only a unique $(η^{\ast}, B^{\ast})$ achieves the best loss. As a sufficient condition, we provide the first measurement of $(η^{\ast}, B^{\ast})$ scaling with dataset size for Scion, and find that the scaling rules are consistent with those of the Adam optimizer. Tuning per-layer-group learning rates also improves model performance, with the output layer being the most sensitive and hidden layers benefiting from lower learning rates. We provide practical insights on norm-guided optimal scaling and release our Distributed Scion (Disco) implementation with logs from over two thousand runs to support research on LLM training dynamics at scale.

In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection falls beneath sample-level fluctuations, identifiability fails. Our Fisher Threshold Theorem formalizes this by proving that stability requires the minimal Fisher eigenvalue to exceed an explicit $O(\sqrt{d/n})$ bound. Unlike prior asymptotic or model-specific criteria, this threshold is finite-sample and necessary, marking a sharp phase transition between reliable concentration and inevitable failure. To make the principle constructive, we introduce the Fisher floor, a verifiable spectral regularization robust to smoothing and preconditioning. Synthetic experiments on Gaussian mixtures and logistic models confirm the predicted transition, consistent with $d/n$ scaling. Statistically, the threshold sharpens classical eigenvalue conditions into a non-asymptotic law; learning-theoretically, it defines a spectral sample-complexity frontier, bridging theory with diagnostics for robust high-dimensional inference.

Bayesian Optimization (BO) is widely used for optimizing expensive black-box functions, particularly in hyperparameter tuning. However, standard BO assumes access to precise objective values, which may be unavailable, noisy, or unreliable in real-world settings where only relative or rank-based feedback can be obtained. In this study, we propose Quantile-Scaled Bayesian Optimization (QS-BO), a principled rank-based optimization framework. QS-BO converts ranks into heteroscedastic Gaussian targets through a quantile-scaling pipeline, enabling the use of Gaussian process surrogates and standard acquisition functions without requiring explicit metric scores. We evaluate QS-BO on synthetic benchmark functions, including one- and two-dimensional nonlinear functions and the Branin function, and compare its performance against Random Search. Results demonstrate that QS-BO consistently achieves lower objective values and exhibits greater stability across runs. Statistical tests further confirm that QS-BO significantly outperforms Random Search at the 1\% significance level. These findings establish QS-BO as a practical and effective extension of Bayesian Optimization for rank-only feedback, with promising applications in preference learning, recommendation, and human-in-the-loop optimization where absolute metric values are unavailable or unreliable.

Abstract--In Kigali, Rwanda, motorcycle taxis are a primary mode of transportation, often navigating unpredictably and disregarding traffic rules, posing significant challenges for autonomous driving systems. This study compares four object detection models--YOLOv5, Faster R-CNN, SSD, and RetinaNet--for motorbike detection using a custom dataset of 198 images collected in Kigali. Implemented in PyT orch with transfer learning, the models were evaluated for accuracy, localization, and inference speed to assess their suitability for real-time navigation in resource-constrained settings. We identify implementation challenges, including dataset limitations and model complexities, and recommend simplified architectures for future work to enhance accessibility for autonomous systems in developing countries like Rwanda. In developing countries like Rwanda, motorcycle taxis, locally known as "moto taxis," dominate urban transportation, particularly in Kigali.

-- Software development effort estimation is one of the most critical aspect in software development process, as the success or failure of the entire project depends on the accuracy of estimations. Researchers are still conducting studies on agile effort estimation. The aim of this research is to develop a story point based agile effort estimation model using LASSO and Elastic Net regression techniques. The experimental work is applied to the agile story point approach using 21 software projects collected from six firms. The two algorithms are trained using their default parameters and tuned grid search with 5 - fold cross - validation to get an enhanced model. The experiment result shows LASSO regressio n achieved better predictive performance PRED (8%) and PRED (25%) results of 100.0, The results are also compared with other related literature.

The ability to control LLMs' emulated emotional states and personality traits is essential for enabling rich, human-centered interactions in socially interactive settings. We introduce PsySET, a Psychologically-informed benchmark to evaluate LLM Steering Effectiveness and Trustworthiness across the emotion and personality domains. Our study spans four models from different LLM families paired with various steering strategies, including prompting, fine-tuning, and representation engineering. Our results indicate that prompting is consistently effective but limited in intensity control, whereas vector injections achieve finer controllability while slightly reducing output quality. Moreover, we explore the trustworthiness of steered LLMs by assessing safety, truthfulness, fairness, and ethics, highlighting potential side effects and behavioral shifts. Notably, we observe idiosyncratic effects; for instance, even a positive emotion like joy can degrade robustness to adversarial factuality, lower privacy awareness, and increase preferential bias. Meanwhile, anger predictably elevates toxicity yet strengthens leakage resistance. Our framework establishes the first holistic evaluation of emotion and personality steering, offering insights into its interpretability and reliability for socially interactive applications.

Modern computer systems often rely on syslog, a simple, universal protocol that records every critical event across heterogeneous infrastructure. However, healthcare's rapidly growing clinical AI stack has no equivalent. As hospitals rush to pilot large language models and other AI-based clinical decision support tools, we still lack a standard way to record how, when, by whom, and for whom these AI models are used. Without that transparency and visibility, it is challenging to measure real-world performance and outcomes, detect adverse events, or correct bias or dataset drift. In the spirit of syslog, we introduce MedLog, a protocol for event-level logging of clinical AI. Any time an AI model is invoked to interact with a human, interface with another algorithm, or act independently, a MedLog record is created. This record consists of nine core fields: header, model, user, target, inputs, artifacts, outputs, outcomes, and feedback, providing a structured and consistent record of model activity. To encourage early adoption, especially in low-resource settings, and minimize the data footprint, MedLog supports risk-based sampling, lifecycle-aware retention policies, and write-behind caching; detailed traces for complex, agentic, or multi-stage workflows can also be captured under MedLog. MedLog can catalyze the development of new databases and software to store and analyze MedLog records. Realizing this vision would enable continuous surveillance, auditing, and iterative improvement of medical AI, laying the foundation for a new form of digital epidemiology.