Research on learned cardinality estimation has achieved significant progress in recent years. However, existing methods still face distinct challenges that hinder their practical deployment in production environments. We conceptualize these challenges as the "Trilemma of Cardinality Estimation", where learned cardinality estimation methods struggle to balance generality, accuracy, and updatability. To address these challenges, we introduce DistJoin, a join cardinality estimator based on efficient distribution prediction using multi-autoregressive models. Our contributions are threefold: (1) We propose a method for estimating both equi and non-equi join cardinality by leveraging the conditional probability distributions of individual tables in a decoupled manner. (2) To meet the requirements of efficient training and inference for DistJoin, we develop Adaptive Neural Predicate Modulation (ANPM), a high-throughput conditional probability distribution estimation model. (3) We formally analyze the variance of existing similar methods and demonstrate that such approaches suffer from variance accumulation issues. To mitigate this problem, DistJoin employs a selectivity-based approach rather than a count-based approach to infer join cardinality, effectively reducing variance. In summary, DistJoin not only represents the first data-driven method to effectively support both equi and non-equi joins but also demonstrates superior accuracy while enabling fast and flexible updates. We evaluate DistJoin on JOB-light and JOB-light-ranges, extending the evaluation to non-equi join conditions. The results demonstrate that our approach achieves the highest accuracy, robustness to data updates, generality, and comparable update and inference speed relative to existing methods.

Neurosymbolic (NeSy) AI studies the integration of neural networks (NNs) and symbolic reasoning based on logic. Usually, NeSy techniques focus on learning the neural, probabilistic and/or fuzzy parameters of NeSy models. Learning the symbolic or logical structure of such models has, so far, received less attention. We introduce neurosymbolic decision trees (NDTs), as an extension of decision trees together with a novel NeSy structure learning algorithm, which we dub NeuID3. NeuID3 adapts the standard top-down induction of decision tree algorithms and combines it with a neural probabilistic logic representation, inherited from the DeepProbLog family of models. The key advantage of learning NDTs with NeuID3 is the support of both symbolic and subsymbolic data (such as images), and that they can exploit background knowledge during the induction of the tree structure, In our experimental evaluation we demonstrate the benefits of NeSys structure learning over more traditonal approaches such as purely data-driven learning with neural networks.

Training visual reinforcement learning (RL) in practical scenarios presents a significant challenge, $\textit{i.e.,}$ RL agents suffer from low sample efficiency in environments with variations. While various approaches have attempted to alleviate this issue by disentanglement representation learning, these methods usually start learning from scratch without prior knowledge of the world. This paper, in contrast, tries to learn and understand underlying semantic variations from distracting videos via offline-to-online latent distillation and flexible disentanglement constraints. To enable effective cross-domain semantic knowledge transfer, we introduce an interpretable model-based RL framework, dubbed Disentangled World Models (DisWM). Specifically, we pretrain the action-free video prediction model offline with disentanglement regularization to extract semantic knowledge from distracting videos. The disentanglement capability of the pretrained model is then transferred to the world model through latent distillation. For finetuning in the online environment, we exploit the knowledge from the pretrained model and introduce a disentanglement constraint to the world model. During the adaptation phase, the incorporation of actions and rewards from online environment interactions enriches the diversity of the data, which in turn strengthens the disentangled representation learning. Experimental results validate the superiority of our approach on various benchmarks.

In recent years, the exceptional performance of generative models in generative tasks has sparked significant interest in their integration into decision-making processes. Due to their ability to handle complex data distributions and their strong model capacity, generative models can be effectively incorporated into decision-making systems by generating trajectories that guide agents toward high-reward state-action regions or intermediate sub-goals. This paper presents a comprehensive review of the application of generative models in decision-making tasks. We classify seven fundamental types of generative models: energy-based models, generative adversarial networks, variational autoencoders, normalizing flows, diffusion models, generative flow networks, and autoregressive models. Regarding their applications, we categorize their functions into three main roles: controllers, modelers and optimizers, and discuss how each role contributes to decision-making. Furthermore, we examine the deployment of these models across five critical real-world decision-making scenarios. Finally, we summarize the strengths and limitations of current approaches and propose three key directions for advancing next-generation generative directive models: high-performance algorithms, large-scale generalized decision-making models, and self-evolving and adaptive models.

On-robot Reinforcement Learning is a promising approach to train embodiment-aware policies for legged robots. However, the computational constraints of real-time learning on robots pose a significant challenge. We present a framework for efficiently learning quadruped locomotion in just 8 minutes of raw real-time training utilizing the sample efficiency and minimal computational overhead of the new off-policy algorithm CrossQ. We investigate two control architectures: Predicting joint target positions for agile, high-speed locomotion and Central Pattern Generators for stable, natural gaits. While prior work focused on learning simple forward gaits, our framework extends on-robot learning to omnidirectional locomotion. We demonstrate the robustness of our approach in different indoor and outdoor environments.

Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on Gaussian process (GP) priors which seamlessly combine empirical measurements and mechanistic knowledge. As such, they quantify uncertainties arising from e.g. noisy or missing data, unknown PDE parameters or discretization error by design. Prior work has established connections to classical PDE solvers and provided solid theoretical guarantees. However, scaling such methods to large-scale problems remains a fundamental challenge primarily due to dense covariance matrices. Our approach addresses the scalability issues by leveraging the Markov property of many commonly used GP priors. It has been shown that such priors are solutions to stochastic PDEs (SPDEs) which when discretized allow for highly efficient GP regression through sparse linear algebra. In this work, we show how to leverage this prior class to make probabilistic PDE solvers practical, even for large-scale nonlinear PDEs, through greatly accelerated inference mechanisms. Additionally, our approach also allows for flexible and physically meaningful priors beyond what can be modeled with covariance functions. Experiments confirm substantial speedups and accelerated convergence of our physics-informed priors in nonlinear settings.

In recent years, humanoid robots have garnered significant attention from both academia and industry due to their high adaptability to environments and human-like characteristics. With the rapid advancement of reinforcement learning, substantial progress has been made in the walking control of humanoid robots. However, existing methods still face challenges when dealing with complex environments and irregular terrains. In the field of perceptive locomotion, existing approaches are generally divided into two-stage methods and end-to-end methods. Two-stage methods first train a teacher policy in a simulated environment and then use distillation techniques, such as DAgger, to transfer the privileged information learned as latent features or actions to the student policy. End-to-end methods, on the other hand, forgo the learning of privileged information and directly learn policies from a partially observable Markov decision process (POMDP) through reinforcement learning. However, due to the lack of supervision from a teacher policy, end-to-end methods often face difficulties in training and exhibit unstable performance in real-world applications. This paper proposes an innovative two-stage perceptive locomotion framework that combines the advantages of teacher policies learned in a fully observable Markov decision process (MDP) to regularize and supervise the student policy. At the same time, it leverages the characteristics of reinforcement learning to ensure that the student policy can continue to learn in a POMDP, thereby enhancing the model's upper bound. Our experimental results demonstrate that our two-stage training framework achieves higher training efficiency and stability in simulated environments, while also exhibiting better robustness and generalization capabilities in real-world applications.

As one transitions from statistical to causal learning, one is seeking the most appropriate causal model. Dynamic Bayesian networks are a popular model, where a weighted directed acyclic graph represents the causal relationships. Stochastic processes are represented by its vertices, and weighted oriented edges suggest the strength of the causal relationships. When there are confounders, one would like to utilize both oriented edges (when the direction of causality is clear) and edges that are not oriented (when there is a confounder), yielding mixed graphs. A little-studied extension of acyclicity to this mixed-graph setting is known as maximally ancestral graphs. We propose a score-based learning algorithm for learning maximally ancestral graphs. A mixed-integer quadratic program is formulated, and an algorithmic approach is proposed, in which the pre-generation of exponentially many constraints is avoided by generating only violated constraints in the so-called branch-and-cut (``lazy constraint'') method. Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 25 variables.

Wireless signal recognition (WSR) is a crucial technique for intelligent communications and spectrum sharing in the next six-generation (6G) wireless communication networks. It can be utilized to enhance network performance and efficiency, improve quality of service (QoS), and improve network security and reliability. Additionally, WSR can be applied for military applications such as signal interception, signal race, and signal abduction. In the past decades, great efforts have been made for the research of WSR. Earlier works mainly focus on model-based methods, including likelihood-based (LB) and feature-based (FB) methods, which have taken the leading position for many years. With the emergence of artificial intelligence (AI), intelligent methods including machine learning-based (ML-based) and deep learning-based (DL-based) methods have been developed to extract the features of the received signals and perform the classification. In this work, we provide a comprehensive review of WSR from the view of applications, main tasks, recent advances, datasets and evaluation metrics, challenges, and future directions. Specifically, intelligent WSR methods are introduced from the perspective of model, data, learning and implementation. Moreover, we analyze the challenges for WSR from the view of complex, dynamic, and open 6G wireless environments and discuss the future directions for WSR. This survey is expected to provide a comprehensive overview of the state-of-the-art WSR techniques and inspire new research directions for WSR in 6G networks.

Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous graphs, many real-world graphs exhibit heterogeneous patterns where nodes and edges have multiple types. This paper fills this gap by introducing the first approach for heterogeneous graph structure learning (HGSL). To this end, we first propose a novel statistical model for the data-generating process (DGP) of heterogeneous graph data, namely hidden Markov networks for heterogeneous graphs (H2MN). Then we formalize HGSL as a maximum a-posterior estimation problem parameterized by such DGP and derive an alternating optimization method to obtain a solution together with a theoretical justification of the optimization conditions. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate that our proposed method excels in learning structure on heterogeneous graphs in terms of edge type identification and edge weight recovery.