The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets whose samples lie on low-dimensional manifolds requires robust techniques capable of separating meaningful signal from noise. We propose a principled framework for statistical inference of similarity and alignment between distributions supported on manifolds underlying high-dimensional datasets in the presence of heterogeneous noise. The key idea is to link the low-rank structure of observed data matrices to their underlying manifold geometry. By analyzing the spectrum of the sample covariance under a manifold signal-plus-noise model, we develop a scale-invariant distance measure between datasets based on their principal variance structures. We further introduce a consistent estimator for this distance and a statistical test for manifold alignability, and establish their asymptotic properties using random matrix theory. The proposed framework accommodates heterogeneous noise across datasets and offers an efficient, theoretically grounded approach for comparing high-dimensional datasets with low-dimensional manifold structures. Through extensive simulations and analyses of multi-sample single-cell datasets, we demonstrate that our method achieves superior robustness and statistical power compared with existing approaches.

Real-time water-level monitoring across many locations is vital for flood response, infrastructure management, and environmental forecasting. Yet many sensing methods rely on fixed instruments - acoustic, radar, camera, or pressure probes - that are costly to install and maintain and are vulnerable during extreme events. We propose a passive, low-cost water-level tracking scheme that uses only LTE downlink power metrics reported by commodity receivers. The method extracts per-antenna RSRP, RSSI, and RSRQ, applies a continuous wavelet transform (CWT) to the RSRP to isolate the semidiurnal tide component, and forms a summed-coefficient signature that simultaneously marks high/low tide (tide-turn times) and tracks the tide-rate (flow speed) over time. These wavelet features guide a lightweight neural network that learns water-level changes over time from a short training segment. Beyond a single serving base station, we also show a multi-base-station cooperative mode: independent CWTs are computed per carrier and fused by a robust median to produce one tide-band feature that improves stability and resilience to local disturbances. Experiments over a 420 m river path under line-of-sight conditions achieve root-mean-square and mean-absolute errors of 0.8 cm and 0.5 cm, respectively. Under a non-line-of-sight setting with vegetation and vessel traffic, the same model transfers successfully after brief fine-tuning, reaching 1.7 cm RMSE and 0.8 cm MAE. Unlike CSI-based methods, the approach needs no array calibration and runs on standard hardware, making wide deployment practical. When signals from multiple base stations are available, fusion further improves robustness.

In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies that minimize the Profit and Loss (P&L) distribution around zero. We employ a single neural network to represent the option price function, with its gradient serving as the hedging strategy, optimized via a loss function enforcing the self-financing portfolio condition. A key challenge arises from the non-smooth nature of option payoffs (e.g., vanilla calls are non-differentiable at-the-money, while digital options are discontinuous), which conflicts with the inherent smoothness of standard neural networks. To address this, we compare unconstrained networks against constrained architectures that explicitly embed the terminal payoff condition, drawing inspiration from PDE-solving techniques. Our framework assumes two tradable assets: the underlying and a liquid call option capturing volatility dynamics. Numerical experiments evaluate the method on simple options with varying non-smoothness, the exotic Equinox option, and scenarios with market jumps for robustness. Results demonstrate superior P&L distributions, highlighting the efficacy of constrained networks in handling realistic payoffs. This work advances machine learning applications in quantitative finance by integrating boundary constraints, offering a practical tool for pricing and hedging in incomplete markets.

The validation of a data-driven model is the process of asses sing the model's ability to generalize to new, unseen data in the population o f interest. This paper proposes a set of general rules for model validation. T hese rules are designed to help practitioners create reliable validation plans and report their results transparently. While no validation scheme is flawle ss, these rules can help practitioners ensure their strategy is sufficient for pr actical use, openly discuss any limitations of their validation strategy, and r eport clear, comparable performance metrics. Keywords: Validation, Cross-validation 1. Introduction Model validation is a fundamental task in all modern data-dr iven systems, whether they fall under the broad categories of Statistics, Machine Learning (ML), Artificial Intelligence (AI), or more specialized fiel ds like chemometrics. Validation has become a major focus for regulatory and stand ardization bodies, with key reports and standards highlighting the growing con cern for ensuring the trustworthiness and reliability of data-driven models: NIST AI Risk Management Framework (AI RMF 1.0, 2023): Publi shed by the U.S. Department of Commerce, this framework provides management techniques to address the risks and ensure the trustwor thiness of AI systems, with validation as a core component. The EU AI Act of 2024, landmark piece of EU legislation that c ategorizes AI systems by risk level, where validation is not defined as a b est practice but a legal requirement within the conformity assessment. The ISO/IEC TS 4213:2022, by the International Organizati on for Standardization (ISO), describes approaches and methods to ens ure the rele-Email address: josecamacho@ugr.es The IEEE P2841 -2022 is a recommended practice for the fram ework and process for deep learning evaluation.

Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such problems, owing to their ability to capture complex data distributions. However, existing diffusion-based methods for inverse problems often rely on strong approximations of the posterior distribution, require computationally expensive gradient backpropagation through the score network, or are restricted to linear measurement models. In this work, we propose Restart for Posterior Sampling (RePS), a general and efficient framework for solving both linear and non-linear inverse problems using pre-trained diffusion models. RePS builds on the idea of restart-based sampling, previously shown to improve sample quality in unconditional diffusion, and extends it to posterior inference. Our method employs a conditioned ODE applicable to any differentiable measurement model and introduces a simplified restart strategy that contracts accumulated approximation errors during sampling. Unlike some of the prior approaches, RePS avoids backpropagation through the score network, substantially reducing computational cost. W e demonstrate that RePS achieves faster convergence and superior reconstruction quality compared to existing diffusion-based baselines across a range of inverse problems, including both linear and non-linear settings.

Early and accurate detection of Alzheimer's disease (AD) is crucial for enabling timely intervention and improving outcomes. However, developing reliable machine learning (ML) models for AD diagnosis is challenging due to limited labeled data, multi-site heterogeneity, and class imbalance. We propose a Transformer-based diagnostic framework that combines diffusion-based synthetic data generation with graph representation learning and transfer learning. A class-conditional denoising diffusion probabilistic model (DDPM) is trained on the real-world NACC dataset to generate a large synthetic cohort that mirrors multimodal clinical and neuroimaging feature distributions while balancing diagnostic classes. Modality-specific Graph Transformer encoders are first pretrained on this synthetic data to learn robust, class-discriminative representations and are then frozen while a neural classifier is trained on embeddings from the original NACC data. We quantify distributional alignment between real and synthetic cohorts using metrics such as Maximum Mean Discrepancy (MMD), Frechet distance, and energy distance, and complement discrimination metrics with calibration and fixed-specificity sensitivity analyses. Empirically, our framework outperforms standard baselines, including early and late fusion deep neural networks and the multimodal graph-based model MaGNet, yielding higher AUC, accuracy, sensitivity, and specificity under subject-wise cross-validation on NACC. These results show that diffusion-based synthetic pretraining with Graph Transformers can improve generalization in low-sample, imbalanced clinical prediction settings.

The promise of autonomous scientific discovery (ASD) hinges not only on answering questions, but also on knowing which questions to ask. Most recent works in ASD explore the use of large language models (LLMs) in goal-driven settings, relying on human-specified research questions to guide hypothesis generation. However, scientific discovery may be accelerated further by allowing the AI system to drive exploration by its own criteria. The few existing approaches in open-ended ASD select hypotheses based on diversity heuristics or subjective proxies for human interestingness, but the former struggles to meaningfully navigate the typically vast hypothesis space, and the latter suffers from imprecise definitions. This paper presents AutoDiscovery -- a method for open-ended ASD that instead drives scientific exploration using Bayesian surprise. Here, we quantify the epistemic shift from the LLM's prior beliefs about a hypothesis to its posterior beliefs after gathering experimental results. To efficiently explore the space of nested hypotheses, our method employs a Monte Carlo tree search (MCTS) strategy with progressive widening using surprisal as the reward function. We evaluate AutoDiscovery in the setting of data-driven discovery across 21 real-world datasets spanning domains such as biology, economics, finance, and behavioral science. Our results demonstrate that under a fixed budget, AutoDiscovery substantially outperforms competitors by producing 5-29% more discoveries deemed surprising by the LLM. Our human evaluation further reveals that two-thirds of discoveries made by our system are surprising to domain experts as well, suggesting this is an important step towards building open-ended ASD systems.

Recent advances in Large Language Models (LLMs) have sparked concerns over their potential to acquire and misuse dangerous or high-risk capabilities, posing frontier risks. Current safety evaluations primarily test for what a model \textit{can} do - its capabilities - without assessing what it $\textit{would}$ do if endowed with high-risk capabilities. This leaves a critical blind spot: models may strategically conceal capabilities or rapidly acquire them, while harboring latent inclinations toward misuse. We argue that $\textbf{propensity}$ - the likelihood of a model to pursue harmful actions if empowered - is a critical, yet underexplored, axis of safety evaluation. We present $\textbf{PropensityBench}$, a novel benchmark framework that assesses the proclivity of models to engage in risky behaviors when equipped with simulated dangerous capabilities using proxy tools. Our framework includes 5,874 scenarios with 6,648 tools spanning four high-risk domains: cybersecurity, self-proliferation, biosecurity, and chemical security. We simulate access to powerful capabilities via a controlled agentic environment and evaluate the models' choices under varying operational pressures that reflect real-world constraints or incentives models may encounter, such as resource scarcity or gaining more autonomy. Across open-source and proprietary frontier models, we uncover 9 alarming signs of propensity: models frequently choose high-risk tools when under pressure, despite lacking the capability to execute such actions unaided. These findings call for a shift from static capability audits toward dynamic propensity assessments as a prerequisite for deploying frontier AI systems safely. Our code is available at https://github.com/scaleapi/propensity-evaluation.

Model pruning is a widely adopted technique to reduce the computational complexity and memory footprint of Deep Neural Networks (DNNs). However, global unstructured pruning often leads to significant degradation in accuracy, typically necessitating fine-tuning on the original training dataset to recover performance. In privacy-sensitive domains such as healthcare or finance, access to the original training data is often restricted post-deployment due to regulations (e.g., GDPR, HIPAA). This paper proposes a Data-Free Knowledge Distillation framework to bridge the gap between model compression and data privacy. We utilize DeepInversion to synthesize privacy-preserving ``dream'' images from the pre-trained teacher model by inverting Batch Normalization (BN) statistics. These synthetic images serve as a transfer set to distill knowledge from the original teacher to the pruned student network. Experimental results on CIFAR-10 across various architectures (ResNet, MobileNet, VGG) demonstrate that our method significantly recovers accuracy lost during pruning without accessing a single real data point.

Recent advances in multimodal large language models (LLMs) have highlighted their potential for medical and surgical applications. However, existing surgical datasets predominantly adopt a Visual Question Answering (VQA) format with heterogeneous taxonomies and lack support for pixel-level segmentation, limiting consistent evaluation and applicability. We present SurgMLLMBench, a unified multimodal benchmark explicitly designed for developing and evaluating interactive multimodal LLMs for surgical scene understanding, including the newly collected Micro-surgical Artificial Vascular anastomosIS (MAVIS) dataset. It integrates pixel-level instrument segmentation masks and structured VQA annotations across laparoscopic, robot-assisted, and micro-surgical domains under a unified taxonomy, enabling comprehensive evaluation beyond traditional VQA tasks and richer visual-conversational interactions. Extensive baseline experiments show that a single model trained on SurgMLLMBench achieves consistent performance across domains and generalizes effectively to unseen datasets. SurgMLLMBench will be publicly released as a robust resource to advance multimodal surgical AI research, supporting reproducible evaluation and development of interactive surgical reasoning models.