Privacy concerns have led to a surge in the creation of synthetic datasets, with diffusion models emerging as a promising avenue. Although prior studies have performed empirical evaluations on these models, there has been a gap in providing a mathematical characterization of their privacy-preserving capabilities. To address this, we present the pioneering theoretical exploration of the privacy preservation inherent in discrete diffusion models (DDMs) for discrete dataset generation. Focusing on per-instance differential privacy (pDP), our framework elucidates the potential privacy leakage for each data point in a given training dataset, offering insights into how the privacy loss of each point correlates with the dataset's distribution. Our bounds also show that training with $s$-sized data points leads to a surge in privacy leakage from $(\epsilon, O(\frac{1}{s^2\epsilon}))$-pDP to $(\epsilon, O(\frac{1}{s\epsilon}))$-pDP of the DDM during the transition from the pure noise to the synthetic clean data phase, and a faster decay in diffusion coefficients amplifies the privacy guarantee. Finally, we empirically verify our theoretical findings on both synthetic and real-world datasets.

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

This paper studies the problem of Anytime-Competitive Markov Decision Process (A-CMDP). Existing works on Constrained Markov Decision Processes (CMDPs) aim to optimize the expected reward while constraining the expected cost over random dynamics, but the cost in a specific episode can still be unsatisfactorily high. In contrast, the goal of A-CMDP is to optimize the expected reward while guaranteeing a bounded cost in each round of any episode against a policy prior. We propose a new algorithm, called Anytime-Competitive Reinforcement Learning (ACRL), which provably guarantees the anytime cost constraints. The regret analysis shows the policy asymptotically matches the optimal reward achievable under the anytime competitive constraints. Experiments on the application of carbon-intelligent computing verify the reward performance and cost constraint guarantee of ACRL.

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling predictions of their temporal evolution and analyses of thermodynamic quantities, including absorbed heat, work done on the system, and entropy production. However, inferring the Langevin equation from observed trajectories remains challenging, particularly for nonlinear and high-dimensional systems. In this study, we present a comprehensive framework that employs Bayesian neural networks for inferring Langevin equations in both overdamped and underdamped regimes. Our framework first provides the drift force and diffusion matrix separately and then combines them to construct the Langevin equation. By providing a distribution of predictions instead of a single value, our approach allows us to assess prediction uncertainties, which can prevent potential misunderstandings and erroneous decisions about the system. We demonstrate the effectiveness of our framework in inferring Langevin equations for various scenarios including a neuron model and microscopic engine, highlighting its versatility and potential impact.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $\eta(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2\eta(x)-1$ and apply the method to real datasets.

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has $\tilde{\mathcal{O}}({T}^{3/4})$ regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret-bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.

In such cases, transferring knowledge from the source domain becomes crucial, particularly because the Machine learning has made substantial advancements in limited initial data in the target domain may be insufficient recent decades, with its applications spanning a wide range of for effective learning. The extensive and diverse information fields such as image and speech recognition, natural language available from the source domains can significantly compensate processing, and autonomous driving. Despite these achievements, for this shortfall, providing a foundational knowledge base machine learning in biomedicine faces significant challenges, that the model can build upon as more target domain data particularly in data collection. The acquisition of labeled becomes available. Therefore, the efficiency and effectiveness data can be very costly or even unfeasible due to factors of learning in the target domain are greatly enhanced by the like ethical considerations, patient privacy, and the scarcity transferred knowledge from the source domains. of certain diseases. These challenges have led researchers to Online transfer learning entails leveraging knowledge from increasingly rely on utilizing data from related domains that a static source domain and applying it to an ongoing, evolving have a more abundant supply of data.

Causal discovery, the task of inferring causal structure from data, promises to accelerate scientific research, inform policy making, and more. However, the per-dataset nature of existing causal discovery algorithms renders them slow, data hungry, and brittle. Inspired by foundation models, we propose a causal discovery framework where a deep learning model is pretrained to resolve predictions from classical discovery algorithms run over smaller subsets of variables. This method is enabled by the observations that the outputs from classical algorithms are fast to compute for small problems, informative of (marginal) data structure, and their structure outputs as objects remain comparable across datasets. Our method achieves state-of-the-art performance on synthetic and realistic datasets, generalizes to data generating mechanisms not seen during training, and offers inference speeds that are orders of magnitude faster than existing models.

Weakly supervised learning generally faces challenges in applicability to various scenarios with diverse weak supervision and in scalability due to the complexity of existing algorithms, thereby hindering the practical deployment. This paper introduces a general framework for learning from weak supervision (GLWS) with a novel algorithm. Central to GLWS is an Expectation-Maximization (EM) formulation, adeptly accommodating various weak supervision sources, including instance partial labels, aggregate statistics, pairwise observations, and unlabeled data. We further present an advanced algorithm that significantly simplifies the EM computational demands using a Non-deterministic Finite Automaton (NFA) along with a forward-backward algorithm, which effectively reduces time complexity from quadratic or factorial often required in existing solutions to linear scale. The problem of learning from arbitrary weak supervision is therefore converted to the NFA modeling of them. GLWS not only enhances the scalability of machine learning models but also demonstrates superior performance and versatility across 11 weak supervision scenarios. We hope our work paves the way for further advancements and practical deployment in this field.

In this work, we review research studies that combine Reinforcement Learning (RL) and Large Language Models (LLMs), two areas that owe their momentum to the development of deep neural networks. We propose a novel taxonomy of three main classes based on the way that the two model types interact with each other. The first class, RL4LLM, includes studies where RL is leveraged to improve the performance of LLMs on tasks related to Natural Language Processing. L4LLM is divided into two sub-categories depending on whether RL is used to directly fine-tune an existing LLM or to improve the prompt of the LLM. In the second class, LLM4RL, an LLM assists the training of an RL model that performs a task that is not inherently related to natural language. We further break down LLM4RL based on the component of the RL training framework that the LLM assists or replaces, namely reward shaping, goal generation, and policy function. Finally, in the third class, RL+LLM, an LLM and an RL agent are embedded in a common planning framework without either of them contributing to training or fine-tuning of the other. We further branch this class to distinguish between studies with and without natural language feedback. We use this taxonomy to explore the motivations behind the synergy of LLMs and RL and explain the reasons for its success, while pinpointing potential shortcomings and areas where further research is needed, as well as alternative methodologies that serve the same goal.