We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces dimensionality at the cost of interpretability, PCA QS retains the original feature space while using leading principal components solely to guide a quantile based stratification scheme. This principled design ensures that sampling remains representative without distorting the underlying data semantics. We establish rigorous theoretical guarantees, deriving convergence rates for empirical quantiles, Kullback Leibler divergence, and Wasserstein distance, thus quantifying the distributional fidelity of PCA QS samples. Practical guidelines for selecting the number of principal components, quantile bins, and sampling rates are provided based on these results. Extensive empirical studies on both synthetic and real-world datasets show that PCA QS consistently outperforms simple random sampling, yielding better structure preservation and improved downstream model performance. Together, these contributions position PCA QS as a scalable, interpretable, and theoretically grounded solution for efficient data summarization in modern machine learning workflows.

This study quantifies the association between non-adherence to antipsychotic medications and adverse outcomes in individuals with schizophrenia. We frame the problem using survival analysis, focusing on the time to the earliest of several adverse events (early death, involuntary hospitalization, jail booking). We extend standard causal inference methods (T-learner, S-learner, nearest neighbor matching) to utilize various survival models to estimate individual and average treatment effects, where treatment corresponds to medication non-adherence. Analyses are repeated using different amounts of longitudinal information (3, 6, 9, and 12 months). Using data from Allegheny County in western Pennsylvania, we find strong evidence that non-adherence advances adverse outcomes by approximately 1 to 4 months. Ablation studies confirm that county-provided risk scores adjust for key confounders, as their removal amplifies the estimated effects. Subgroup analyses by medication formulation (injectable vs. oral) and medication type consistently show that non-adherence is associated with earlier adverse events. These findings highlight the clinical importance of adherence in delaying psychiatric crises and show that integrating survival analysis with causal inference tools can yield policy-relevant insights. We caution that although we apply causal inference, we only make associative claims and discuss assumptions needed for causal interpretation.

Stochastic Gradient Descent (SGD) is fundamental for training deep neural networks, especially in non-convex settings. Understanding SGD's generalization properties is crucial for ensuring robust model performance on unseen data. In this paper, we analyze the generalization error bounds of SGD for non-convex learning by introducing the Type II perturbed SGD (T2pm-SGD), which accommodates both sub-Gaussian and bounded loss functions. The generalization error bound is decomposed into two components: the trajectory term and the flatness term. Our analysis improves the trajectory term to $O(n^{-1})$, significantly enhancing the previous $O((nb)^{-1/2})$ bound for bounded losses, where n is the number of training samples and b is the batch size. By selecting an optimal variance for the perturbation noise, the overall bound is further refined to $O(n^{-2/3})$. For sub-Gaussian loss functions, a tighter trajectory term is also achieved. In both cases, the flatness term remains stable across iterations and is smaller than those reported in previous literature, which increase with iterations. This stability, ensured by T2pm-SGD, leads to tighter generalization error bounds for both loss function types. Our theoretical results are validated through extensive experiments on benchmark datasets, including MNIST and CIFAR-10, demonstrating the effectiveness of T2pm-SGD in establishing tighter generalization bounds.

Lipschitz continuity characterizes the worst-case sensitivity of neural networks to small input perturbations; yet its dynamics (i.e. temporal evolution) during training remains under-explored. We present a rigorous mathematical framework to model the temporal evolution of Lipschitz continuity during training with stochastic gradient descent (SGD). This framework leverages a system of stochastic differential equations (SDEs) to capture both deterministic and stochastic forces. Our theoretical analysis identifies three principal factors driving the evolution: (i) the projection of gradient flows, induced by the optimization dynamics, onto the operator-norm Jacobian of parameter matrices; (ii) the projection of gradient noise, arising from the randomness in mini-batch sampling, onto the operator-norm Jacobian; and (iii) the projection of the gradient noise onto the operator-norm Hessian of parameter matrices. Furthermore, our theoretical framework sheds light on such as how noisy supervision, parameter initialization, batch size, and mini-batch sampling trajectories, among other factors, shape the evolution of the Lipschitz continuity of neural networks. Our experimental results demonstrate strong agreement between the theoretical implications and the observed behaviors.

Sensitive data captured by Industrial Control Systems (ICS) play a large role in the safety and integrity of many critical infrastructures. Detection of anomalous or malicious data, or Anomaly Detection (AD), with machine learning is one of many vital components of cyberphysical security. Quantum kernel-based machine learning methods have shown promise in identifying complex anomalous behavior by leveraging the highly expressive and efficient feature spaces of quantum computing. This study focuses on the parameterization of Quantum Hybrid Support Vector Machines (QSVMs) using three popular datasets from Cyber-Physical Systems (CPS). The results demonstrate that QSVMs outperform traditional classical kernel methods, achieving 13.3% higher F1 scores. Additionally, this research investigates noise using simulations based on real IBMQ hardware, revealing a maximum error of only 0.98% in the QSVM kernels. This error results in an average reduction of 1.57% in classification metrics. Furthermore, the study found that QSVMs show a 91.023% improvement in kernel-target alignment compared to classical methods, indicating a potential "quantum advantage" in anomaly detection for critical infrastructures. This effort suggests that QSVMs can provide a substantial advantage in anomaly detection for ICS, ultimately enhancing the security and integrity of critical infrastructures.

Large Language Models (LLMs) are increasingly used in applications requiring long context lengths, but the key-value (KV) cache often becomes a memory bottleneck on GPUs as context grows. To address this, we propose Commutative Vector Quantization (CommVQ) to significantly reduce memory usage for long-context LLM inference. We first introduce additive quantization with a lightweight encoder and codebook to compress the KV cache, which can be decoded via simple matrix multiplication. To further reduce computational costs during decoding, we design the codebook to be commutative with Rotary Position Embedding (RoPE) and train it using an Expectation-Maximization (EM) algorithm. This enables efficient integration of decoding into the self-attention mechanism. Our approach achieves high accuracy with additive quantization and low overhead via the RoPE-commutative codebook. Experiments on long-context benchmarks and GSM8K show that our method reduces FP16 KV cache size by 87.5% with 2-bit quantization, while outperforming state-of-the-art KV cache quantization methods. Notably, it enables 1-bit KV cache quantization with minimal accuracy loss, allowing a LLaMA-3.1 8B model to run with a 128K context length on a single RTX 4090 GPU. The source code is available at: https://github.com/UMass-Embodied-AGI/CommVQ.

Standard datasets often present limitations, particularly due to the fixed nature of input data sensors, which makes it difficult to compare methods that actively adjust sensor parameters to suit environmental conditions. This is the case with Automatic-Exposure (AE) methods, which rely on environmental factors to influence the image acquisition process. As a result, AE methods have traditionally been benchmarked in an online manner, rendering experiments non-reproducible. Building on our prior work, we propose a methodology that utilizes an emulator capable of generating images at any exposure time. This approach leverages BorealHDR, a unique multi-exposure stereo dataset, along with its new extension, in which data was acquired along a repeated trajectory at different times of the day to assess the impact of changing illumination. In total, BorealHDR covers 13.4 km over 59 trajectories in challenging lighting conditions. The dataset also includes lidar-inertial-odometry-based maps with pose estimation for each image frame, as well as Global Navigation Satellite System (GNSS) data for comparison. We demonstrate that by using images acquired at various exposure times, we can emulate realistic images with a Root-Mean-Square Error (RMSE) below 1.78% compared to ground truth images. Using this offline approach, we benchmarked eight AE methods, concluding that the classical AE method remains the field's best performer. To further support reproducibility, we provide in-depth details on the development of our backpack acquisition platform, including hardware, electrical components, and performance specifications. Additionally, we share valuable lessons learned from deploying the backpack over more than 25 km across various environments. Our code and dataset are available online at this link: https://github.com/norlab-ulaval/TFR24 BorealHDR

In the study of drug function and precision medicine, identifying new drug-microbe associations is crucial. However, current methods isolate association and similarity analysis of drug and microbe, lacking effective inter-view optimization and coordinated multi-view feature fusion. In our study, a multi-view Divergence-Convergence Feature Augmentation framework for Drug-related Microbes Prediction (DCFA_DMP) is proposed, to better learn and integrate association information and similarity information. In the divergence phase, DCFA_DMP strengthens the complementarity and diversity between heterogeneous information and similarity information by performing Adversarial Learning method between the association network view and different similarity views, optimizing the feature space. In the convergence phase, a novel Bidirectional Synergistic Attention Mechanism is proposed to deeply synergize the complementary features between different views, achieving a deep fusion of the feature space. Moreover, Transformer graph learning is alternately applied on the drug-microbe heterogeneous graph, enabling each drug or microbe node to focus on the most relevant nodes. Numerous experiments demonstrate DCFA_DMP's significant performance in predicting drug-microbe associations. It also proves effectiveness in predicting associations for new drugs and microbes in cold start experiments, further confirming its stability and reliability in predicting potential drug-microbe associations.

We investigate language generation in the limit - a model by Kleinberg and Mullainathan [NeurIPS 2024] and extended by Li, Raman, and Tewari [COLT 2025]. While Kleinberg and Mullainathan proved generation is possible for all countable collections, Li et al. defined a hierarchy of generation notions (uniform, non-uniform, and generatable) and explored their feasibility for uncountable collections. Our first set of results resolve two open questions of Li et al. by proving finite unions of generatable or non-uniformly generatable classes need not be generatable. These follow from a stronger result: there is a non-uniformly generatable class and a uniformly generatable class whose union is non-generatable. This adds to the aspects along which language generation in the limit is different from traditional tasks in statistical learning theory like classification, which are closed under finite unions. In particular, it implies that given two generators for different collections, one cannot combine them to obtain a single "more powerful" generator, prohibiting this notion of boosting. Our construction also addresses a third open question of Li et al. on whether there are uncountable classes that are non-uniformly generatable and do not satisfy the eventually unbounded closure (EUC) condition introduced by Li, Raman, and Tewari. Our approach utilizes carefully constructed classes along with a novel diagonalization argument that could be of independent interest in the growing area of language generation.

Federated learning (FL) has emerged as a groundbreaking paradigm in machine learning (ML), offering privacy-preserving collaborative model training across diverse datasets. Despite its promise, FL faces significant hurdles in non-identically and independently distributed (non-IID) data scenarios, where most existing methods often struggle with data heterogeneity and lack robustness in performance. This paper introduces Federated Loss Exploration (FedLEx), an innovative approach specifically designed to tackle these challenges. FedLEx distinctively addresses the shortcomings of existing FL methods in non-IID settings by optimizing its learning behavior for scenarios in which assumptions about data heterogeneity are impractical or unknown. It employs a federated loss exploration technique, where clients contribute to a global guidance matrix by calculating gradient deviations for model parameters. This matrix serves as a strategic compass to guide clients' gradient updates in subsequent FL rounds, thereby fostering optimal parameter updates for the global model. FedLEx effectively navigates the complex loss surfaces inherent in non-IID data, enhancing knowledge transfer in an efficient manner, since only a small number of epochs and small amount of data are required to build a strong global guidance matrix that can achieve model convergence without the need for additional data sharing or data distribution statics in a large client scenario. Our extensive experiments with state-of-the art FL algorithms demonstrate significant improvements in performance, particularly under realistic non-IID conditions, thus highlighting FedLEx's potential to overcome critical barriers in diverse FL applications.