Stochastic approximation (SA) algorithms, first introduced by Robbins and Monro in the 1950's [24], has become one of the most important classes of stochastic numerical methods. Originally aimed at finding the the root of a continuous function given noisy observations, SA is now a fundamental tool in a range of areas such as statistics, optimization, electrical engineering, and machine learning, to mention but a few. Within the latter, the importance of SA algorithms is illustrated by the fact that a specific subclass of methods--stochastic gradient descent (SGD) methods--is central to the training of deep learning methods, and in reinforcement learning the standard methods (Q-learning and temporal-difference-learning) are variants of SA. The general class that is SA algorithms with state-dependent noise (see below for the definition) therefore constitute a rich and important family of stochastic recursive algorithms. In addition to the examples already mentioned (SGD, reinforcement learning), this class also includes persistent contrastive divergence, adaptive Markov chain Monte-Carlo (MCMC) and extended ensemble algorithms such as the Wang-Landau algorithm. The theory of SA stems from the pioneering work of Robbins and Monro [24] and Kiefer and Wolfowitz [20], and remains an active research area within probability theory. This is in part due to the many and diverse applications of SA algorithms where, due to the complex nature of the systems under considerations, different variants of the original Robbins-Monro algorithm are needed. In turn, developing the theoretical foundation for SA algorithms, such as, e.g., convergence results, central limit theorems, concentration results and results on deviations, is of fundamental importance; monographs covering many of the standard results of

The EU AI Act underscores the importance of transparency, user-centricity, and robustness in AI systems, particularly for high-risk systems. In response, we present advancements in XentricAI, an explainable hand gesture recognition (HGR) system designed to meet these regulatory requirements. XentricAI adresses fundamental challenges in HGR, such as the opacity of black-box models using explainable AI methods and the handling of distributional shifts in real-world data through transfer learning techniques. We extend an existing radar-based HGR dataset by adding 28,000 new gestures, with contributions from multiple users across varied locations, including 24,000 out-of-distribution gestures. Leveraging this real-world dataset, we enhance XentricAI's capabilities by integrating a variational autoencoder module for improved gesture anomaly detection, incorporating user-specific thresholding. This integration enables the identification of 11.50% more anomalous gestures. Our extensive evaluations demonstrate a 97.5% sucess rate in characterizing these anomalies, significantly improving system explainability. Furthermore, the implementation of transfer learning techniques has shown a substantial increase in user adaptability, with an average improvement of at least 15.17%. This work contributes to the development of trustworthy AI systems by providing both technical advancements and regulatory compliance, offering a commercially viable solution that aligns with the EU AI Act requirements.

Recent advancements in machine learning (ML), natural language processing (NLP), and foundational models have shown promise for real-life applications in critical, albeit compute-constrainted fields like healthcare. In such areas, combining foundational models with supervised ML offers potential for automating tasks like diagnosis and treatment planning, but the limited availability of onsite computational resources pose significant challenges before applying these technologies effectively: Current approaches either yield subpar results when using pretrained models without task-specific adaptation, or require substantial computational resources for fine-tuning, which is often a barrier to entry in such environments. This renders them inaccessible in applications where performance and quality standards are high, but computational resources are scarce. To bridge the gap between best-in-class performance and accessibility, we propose a novel method for adapting foundational, multimodal embeddings to downstream tasks, without the need of expensive fine-tuning processes. Our method leverages frozen embeddings from Large Language Models (LLMs) and Vision Models, and uses contrastive learning to train a small, task-specific nonlinear projection that can be used in the downstream task, without having to fine-tune the original foundational models. We show that this efficient procedure leads to significant performance improvements across various downstream tasks, and perhaps more importantly with minimal computational overhead, offering a practical solution for the use of advanced, foundational ML models in resource-constrained settings.

This tutorial intends to introduce readers with a background in AI to quantum machine learning (QML) -- a rapidly evolving field that seeks to leverage the power of quantum computers to reshape the landscape of machine learning. For self-consistency, this tutorial covers foundational principles, representative QML algorithms, their potential applications, and critical aspects such as trainability, generalization, and computational complexity. In addition, practical code demonstrations are provided in https://qml-tutorial.github.io/ to illustrate real-world implementations and facilitate hands-on learning. Together, these elements offer readers a comprehensive overview of the latest advancements in QML. By bridging the gap between classical machine learning and quantum computing, this tutorial serves as a valuable resource for those looking to engage with QML and explore the forefront of AI in the quantum era.

Machine learning models are routinely trained on a mixture of different data domains. Different domain weights yield very different downstream performances. We propose the Soup-of-Experts, a novel architecture that can instantiate a model at test time for any domain weights with minimal computational cost and without re-training the model. Our architecture consists of a bank of expert parameters, which are linearly combined to instantiate one model. We learn the linear combination coefficients as a function of the input domain weights. To train this architecture, we sample random domain weights, instantiate the corresponding model, and backprop through one batch of data sampled with these domain weights. We demonstrate how our approach obtains small specialized models on several language modeling tasks quickly. Soup-of-Experts are particularly appealing when one needs to ship many different specialist models quickly under a model size constraint.

Diffusion models have emerged as powerful generative models capable of producing high-quality contents such as images, videos, and audio, demonstrating their potential to revolutionize digital content creation. However, these capabilities come at the cost of their significant computational resources and lengthy generation time, underscoring the critical need to develop efficient techniques for practical deployment. In this survey, we provide a systematic and comprehensive review of research on efficient diffusion models. We organize the literature in a taxonomy consisting of three main categories, covering distinct yet interconnected efficient diffusion model topics from algorithm-level, system-level, and framework perspective, respectively. We have also created a GitHub repository where we organize the papers featured in this survey at https://github.com/AIoT-MLSys-Lab/Efficient-Diffusion-Model-Survey. We hope our survey can serve as a valuable resource to help researchers and practitioners gain a systematic understanding of efficient diffusion model research and inspire them to contribute to this important and exciting field.

The prevalence of drawing causal conclusions from observational studies has raised concerns about potential exaggeration in science communication. While some believe causal language should only apply to randomized controlled trials, others argue that rigorous methods can justify causal claims in observational studies. Ideally, causal language should align with the strength of the evidence. However, through the analysis of over 80,000 observational study abstracts using computational linguistic and regression methods, we found that causal language is more frequently used by less experienced authors, smaller research teams, male last authors, and authors from countries with higher uncertainty avoidance indices. These findings suggest that the use of causal language may be influenced by external factors such as the sociocultural backgrounds of authors and the dynamics of research collaboration. This newly identified link deepens our understanding of how such factors help shape scientific conclusions in causal inference and science communication.

Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous theoretical error analysis. This paper bridges the gap: we prove error bounds for the SKI Gram matrix and examine the error's effect on hyperparameter estimation and posterior inference. We further provide a practical guide to selecting the number of inducing points under convolutional cubic interpolation: they should grow as $n^{d/3}$ for error control. Crucially, we identify two dimensionality regimes governing the trade-off between SKI Gram matrix spectral norm error and computational complexity. For $d \leq 3$, any error tolerance can achieve linear time for sufficiently large sample size. For $d > 3$, the error must increase with sample size to maintain linear time. Our analysis provides key insights into SKI's scalability-accuracy trade-offs, establishing precise conditions for achieving linear-time GP inference with controlled approximation error.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

Weak-to-strong generalization, where weakly supervised strong models outperform their weaker teachers, offers a promising approach to aligning superhuman models with human values. To deepen the understanding of this approach, we provide theoretical insights into its capabilities and limitations. First, in the classification setting, we establish upper and lower generalization error bounds for the strong model, identifying the primary limitations as stemming from the weak model's generalization error and the optimization objective itself. Additionally, we derive lower and upper bounds on the calibration error of the strong model. These theoretical bounds reveal two critical insights: (1) the weak model should demonstrate strong generalization performance and maintain well-calibrated predictions, and (2) the strong model's training process must strike a careful balance, as excessive optimization could undermine its generalization capability by over-relying on the weak supervision signals. Finally, in the regression setting, we extend the work of Charikar et al. (2024) to a loss function based on Kullback-Leibler (KL) divergence, offering guarantees that the strong student can outperform its weak teacher by at least the magnitude of their disagreement. We conduct sufficient experiments to validate our theory.