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.

We focus on learning the smoothing distribution, i.e. the joint distribution of the latent states given the observations, using a variational approach together with Monte Carlo importance sampling. We propose an efficient algorithm for computing the gradient of the evidence lower bound (ELBO) in the context of streaming data, where observations arrive sequentially. Our contributions include a computationally efficient online ELBO estimator, demonstrated performance in offline and true online settings, and adaptability for computing general expectations under joint smoothing distributions.

To effectively express and satisfy network application requirements, intent-based network management has emerged as a promising solution. In intent-based methods, users and applications express their intent in a high-level abstract language to the network. Although this abstraction simplifies network operation, it induces many challenges to efficiently express applications' intents and map them to different network capabilities. Therefore, in this work, we propose an AI-based framework for intent profiling and translation. We consider a scenario where applications interacting with the network express their needs for network services in their domain language. The machine-to-machine communication (i.e., between applications and the network) is complex since it requires networks to learn how to understand the domain languages of each application, which is neither practical nor scalable. Instead, a framework based on emergent communication is proposed for intent profiling, in which applications express their abstract quality-of-experience (QoE) intents to the network through emergent communication messages. Subsequently, the network learns how to interpret these communication messages and map them to network capabilities (i.e., slices) to guarantee the requested Quality-of-Service (QoS). Simulation results show that the proposed method outperforms self-learning slicing and other baselines, and achieves a performance close to the perfect knowledge baseline.

The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically estimating the local learning coefficient, but so far these methods have not been extended to the scale of modern deep learning architectures or data sets. Using a method developed in {\tt arXiv:2308.12108 [stat.ML]} we empirically show how the LLC may be measured accurately and self-consistently for deep linear networks (DLNs) up to 100M parameters. We also show that the estimated LLC has the rescaling invariance that holds for the theoretical quantity.

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks because PCs can solve marginal inference (MAR) tasks in time that scales linearly in the size of the network. Unfortunately, the maximum-a-posteriori (MAP) and marginal MAP (MMAP) tasks remain NP-hard in these models. Inspired by the recent work on using neural networks for generating near-optimal solutions to optimization problems such as integer linear programming, we propose an approach that uses neural networks to approximate (M)MAP inference in PCs. The key idea in our approach is to approximate the cost of an assignment to the query variables using a continuous multilinear function, and then use the latter as a loss function. The two main benefits of our new method are that it is self-supervised and after the neural network is learned, it requires only linear time to output a solution. We evaluate our new approach on several benchmark datasets and show that it outperforms three competing linear time approximations, max-product inference, max-marginal inference and sequential estimation, which are used in practice to solve MMAP tasks in PCs.

Bike-Sharing Systems provide eco-friendly urban mobility, contributing to the alleviation of traffic congestion and to healthier lifestyles. Efficiently operating such systems and maintaining high customer satisfaction is challenging due to the stochastic nature of trip demand, leading to full or empty stations. Devising effective rebalancing strategies using vehicles to redistribute bikes among stations is therefore of uttermost importance for operators. As a promising alternative to classical mathematical optimization, reinforcement learning is gaining ground to solve sequential decision-making problems. This paper introduces a spatio-temporal reinforcement learning algorithm for the dynamic rebalancing problem with multiple vehicles. We first formulate the problem as a Multi-agent Markov Decision Process in a continuous time framework. This allows for independent and cooperative vehicle rebalancing, eliminating the impractical restriction of time-discretized models where vehicle departures are synchronized. A comprehensive simulator under the first-arrive-first-serve rule is then developed to facilitate the learning process by computing immediate rewards under diverse demand scenarios. To estimate the value function and learn the rebalancing policy, various Deep Q-Network configurations are tested, minimizing the lost demand. Experiments are carried out on various datasets generated from historical data, affected by both temporal and weather factors. The proposed algorithms outperform benchmarks, including a multi-period Mixed-Integer Programming model, in terms of lost demand. Once trained, it yields immediate decisions, making it suitable for real-time applications. Our work offers practical insights for operators and enriches the integration of reinforcement learning into dynamic rebalancing problems, paving the way for more intelligent and robust urban mobility solutions.

Autonomous agents trained using deep reinforcement learning (RL) often lack the ability to successfully generalise to new environments, even when they share characteristics with the environments they have encountered during training. In this work, we investigate how the sampling of individual environment instances, or levels, affects the zero-shot generalisation (ZSG) ability of RL agents. We discover that, for deep actor-critic architectures sharing their base layers, prioritising levels according to their value loss minimises the mutual information between the agent's internal representation and the set of training levels in the generated training data. This provides a novel theoretical justification for the implicit regularisation achieved by certain adaptive sampling strategies. We then turn our attention to unsupervised environment design (UED) methods, which have more control over the data generation mechanism. We find that existing UED methods can significantly shift the training distribution, which translates to low ZSG performance. To prevent both overfitting and distributional shift, we introduce in-context environment design (ICED). ICED generates levels using a variational autoencoder trained over an initial set of level parameters, reducing distributional shift, and achieves significant improvements in ZSG over adaptive level sampling strategies and UED methods.

We develop a multi-agent reinforcement learning (MARL) algorithm to minimize the total energy consumption of multiple massive MIMO (multiple-input multiple-output) base stations (BSs) in a multi-cell network while preserving the overall quality-of-service (QoS) by making decisions on the multi-level advanced sleep modes (ASMs) and antenna switching of these BSs. The problem is modeled as a decentralized partially observable Markov decision process (DEC-POMDP) to enable collaboration between individual BSs, which is necessary to tackle inter-cell interference. A multi-agent proximal policy optimization (MAPPO) algorithm is designed to learn a collaborative BS control policy. To enhance its scalability, a modified version called MAPPO-neighbor policy is further proposed. Simulation results demonstrate that the trained MAPPO agent achieves better performance compared to baseline policies. Specifically, compared to the auto sleep mode 1 (symbol-level sleeping) algorithm, the MAPPO-neighbor policy reduces power consumption by approximately 8.7% during low-traffic hours and improves energy efficiency by approximately 19% during high-traffic hours, respectively.

Stochastic Gradient Descent (SGD) with adaptive steps is now widely used for training deep neural networks. Most theoretical results assume access to unbiased gradient estimators, which is not the case in several recent deep learning and reinforcement learning applications that use Monte Carlo methods. This paper provides a comprehensive non-asymptotic analysis of SGD with biased gradients and adaptive steps for convex and non-convex smooth functions. Our study incorporates time-dependent bias and emphasizes the importance of controlling the bias and Mean Squared Error (MSE) of the gradient estimator. In particular, we establish that Adagrad and RMSProp with biased gradients converge to critical points for smooth non-convex functions at a rate similar to existing results in the literature for the unbiased case. Finally, we provide experimental results using Variational Autoenconders (VAE) that illustrate our convergence results and show how the effect of bias can be reduced by appropriate hyperparameter tuning.

Stochastic approximation is a class of algorithms that update a vector iteratively, incrementally, and stochastically, including, e.g., stochastic gradient descent and temporal difference learning. One fundamental challenge in analyzing a stochastic approximation algorithm is to establish its stability, i.e., to show that the stochastic vector iterates are bounded almost surely. In this paper, we extend the celebrated Borkar-Meyn theorem for stability from the Martingale difference noise setting to the Markovian noise setting, which greatly improves its applicability in reinforcement learning, especially in those off-policy reinforcement learning algorithms with linear function approximation and eligibility traces. Central to our analysis is the diminishing asymptotic rate of change of a few functions, which is implied by both a form of strong law of large numbers and a commonly used V4 Lyapunov drift condition and trivially holds if the Markov chain is finite and irreducible.