The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially-private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

With advancements in generative models, evaluating their performance using rigorous, clearly defined metrics and We propose a comprehensive sample-based criteria has become increasingly essential. Disambiguating method for assessing the quality of generative true from modeled distributions is especially pertinent in models. The proposed approach enables the estimation light of the growing emphasis on AI safety within the community, of the probability that two sets of samples as well as in scientific domains where stringent standards are drawn from the same distribution, providing of rigor and uncertainty quantification are needed for a statistically rigorous method for assessing the the adoption of machine learning methods. When evaluating performance of a single generative model or the generative models, we are interested in three qualitative comparison of multiple competing models trained properties (Stein et al., 2023; Jiralerspong et al., 2023): Fidelity on the same dataset. This comparison can be conducted refers to the quality and realism of individual outputs by dividing the space into non-overlapping generated by a model. It assesses how indistinguishable regions and comparing the number of data samples each generated sample is from real data.

We introduce PACOH-RL, a novel model-based Meta-Reinforcement Learning (Meta-RL) algorithm designed to efficiently adapt control policies to changing dynamics. PACOH-RL meta-learns priors for the dynamics model, allowing swift adaptation to new dynamics with minimal interaction data. Existing Meta-RL methods require abundant meta-learning data, limiting their applicability in settings such as robotics, where data is costly to obtain. To address this, PACOH-RL incorporates regularization and epistemic uncertainty quantification in both the meta-learning and task adaptation stages. When facing new dynamics, we use these uncertainty estimates to effectively guide exploration and data collection. Overall, this enables positive transfer, even when access to data from prior tasks or dynamic settings is severely limited. Our experiment results demonstrate that PACOH-RL outperforms model-based RL and model-based Meta-RL baselines in adapting to new dynamic conditions. Finally, on a real robotic car, we showcase the potential for efficient RL policy adaptation in diverse, data-scarce conditions.

Graph neural networks (GNNs) have gained popularity for various graph-related tasks. However, similar to deep neural networks, GNNs are also vulnerable to adversarial attacks. Empirical studies have shown that adversarially robust generalization has a pivotal role in establishing effective defense algorithms against adversarial attacks. In this paper, we contribute by providing adversarially robust generalization bounds for two kinds of popular GNNs, graph convolutional network (GCN) and message passing graph neural network, using the PAC-Bayesian framework. Our result reveals that spectral norm of the diffusion matrix on the graph and spectral norm of the weights as well as the perturbation factor govern the robust generalization bounds of both models. Our bounds are nontrivial generalizations of the results developed in (Liao et al., 2020) from the standard setting to adversarial setting while avoiding exponential dependence of the maximum node degree. As corollaries, we derive better PAC-Bayesian robust generalization bounds for GCN in the standard setting, which improve the bounds in (Liao et al., 2020) by avoiding exponential dependence on the maximum node degree.

We study the in-context learning dynamics of large language models (LLMs) using three instrumental learning tasks adapted from cognitive psychology. We find that LLMs update their beliefs in an asymmetric manner and learn more from better-than-expected outcomes than from worse-than-expected ones. Furthermore, we show that this effect reverses when learning about counterfactual feedback and disappears when no agency is implied. We corroborate these findings by investigating idealized in-context learning agents derived through meta-reinforcement learning, where we observe similar patterns. Taken together, our results contribute to our understanding of how in-context learning works by highlighting that the framing of a problem significantly influences how learning occurs, a phenomenon also observed in human cognition.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Diffusion Models (DMs) have disrupted the image Super-Resolution (SR) field and further closed the gap between image quality and human perceptual preferences. They are easy to train and can produce very high-quality samples that exceed the realism of those produced by previous generative methods. Despite their promising results, they also come with new challenges that need further research: high computational demands, comparability, lack of explainability, color shifts, and more. Unfortunately, entry into this field is overwhelming because of the abundance of publications. To address this, we provide a unified recount of the theoretical foundations underlying DMs applied to image SR and offer a detailed analysis that underscores the unique characteristics and methodologies within this domain, distinct from broader existing reviews in the field. This survey articulates a cohesive understanding of DM principles and explores current research avenues, including alternative input domains, conditioning techniques, guidance mechanisms, corruption spaces, and zero-shot learning approaches. By offering a detailed examination of the evolution and current trends in image SR through the lens of DMs, this survey sheds light on the existing challenges and charts potential future directions, aiming to inspire further innovation in this rapidly advancing area.

Maximum likelihood estimation (MLE) of latent variable models is often recast as an optimization problem over the extended space of parameters and probability distributions. For example, the Expectation Maximization (EM) algorithm can be interpreted as coordinate descent applied to a suitable free energy functional over this space. Recently, this perspective has been combined with insights from optimal transport and Wasserstein gradient flows to develop particle-based algorithms applicable to wider classes of models than standard EM. Drawing inspiration from prior works which interpret `momentum-enriched' optimisation algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical systems-inspired approach to minimizing the free energy functional over the extended space of parameters and probability distributions. The result is a dynamic system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we establish quantitative convergence of the proposed system to the unique minimiser of the functional in continuous time. We then propose a numerical discretization of this system which enables its application to parameter estimation in latent variable models. Through numerical experiments, we demonstrate that the resulting algorithm converges faster than existing methods and compares favourably with other (approximate) MLE algorithms.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

This comprehensive review article delves into the intricate realm of fault-tolerant control (FTC) schemes tailored for robotic manipulators. Our exploration spans the historical evolution of FTC, tracing its development over time, and meticulously examines the recent breakthroughs fueled by the synergistic integration of cutting-edge technologies such as artificial intelligence (AI), machine learning (ML), and digital twin technologies (DTT). The article places a particular emphasis on the transformative influence these contemporary trends exert on the landscape of robotic manipulator control and fault tolerance. By delving into the historical context, our aim is to provide a comprehensive understanding of the evolution of FTC schemes. This journey encompasses the transition from model-based and signal-based schemes to the role of sensors, setting the stage for an exploration of the present-day paradigm shift enabled by AI, ML, and DTT. The narrative unfolds as we dissect the intricate interplay between these advanced technologies and their applications in enhancing fault tolerance within the domain of robotic manipulators. Our review critically evaluates the impact of these advancements, shedding light on the novel methodologies, techniques, and applications that have emerged in recent times. The overarching goal of this article is to present a comprehensive perspective on the current state of fault diagnosis and fault-tolerant control within the context of robotic manipulators, positioning our exploration within the broader framework of AI, ML, and DTT advancements. Through a meticulous examination of both historical foundations and contemporary innovations, this review significantly contributes to the existing body of knowledge, offering valuable insights for researchers, practitioners, and enthusiasts navigating the dynamic landscape of robotic manipulator control.