In particular, we conjecture and empirically illustrate that, the celebrated batch normalization (BN) technique actually adapts the "normalized" bias such that it approximates

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The purpose of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy. Previous works on statistical analysis of distributional TD learning focus mainly on the tabular case. We first consider the linear function approximation setting and conduct a fine-grained analysis of the linear-categorical Bellman equation. Building on this analysis, we further incorporate variance reduction techniques in our new algorithms to establish tight sample complexity bounds independent of the support size $K$ when $K$ is large. Our theoretical results imply that, when employing distributional TD learning with linear function approximation, learning the full distribution of the return function from streaming data is no more difficult than learning its expectation. This work provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO\textsubscript{1}), faces a fundamental tradeoff between logic fidelity and computational efficiency. This work establishes a Grounding-Skolemization dichotomy to systematically analyze this challenge and motivate a paradigm shift in CQA. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO\textsubscript{1} queries with low computational complexity. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.

The integration of different learning paradigms has long been a focus of machine learning research, aimed at overcoming the inherent limitations of individual methods. Fuzzy rule-based models excel in interpretability and have seen widespread application across diverse fields. However, they face challenges such as complex design specifications and scalability issues with large datasets. The fusion of different techniques and strategies, particularly Gradient Boosting, with Fuzzy Rule-Based Models offers a robust solution to these challenges. This paper proposes an Integrated Fusion Framework that merges the strengths of both paradigms to enhance model performance and interpretability. At each iteration, a Fuzzy Rule-Based Model is constructed and controlled by a dynamic factor to optimize its contribution to the overall ensemble. This control factor serves multiple purposes: it prevents model dominance, encourages diversity, acts as a regularization parameter, and provides a mechanism for dynamic tuning based on model performance, thus mitigating the risk of overfitting. Additionally, the framework incorporates a sample-based correction mechanism that allows for adaptive adjustments based on feedback from a validation set. Experimental results substantiate the efficacy of the presented gradient boosting framework for fuzzy rule-based models, demonstrating performance enhancement, especially in terms of mitigating overfitting and complexity typically associated with many rules. By leveraging an optimal factor to govern the contribution of each model, the framework improves performance, maintains interpretability, and simplifies the maintenance and update of the models.

Multivariate time series data come as a collection of time series describing different aspects of a certain temporal phenomenon. Anomaly detection in this type of data constitutes a challenging problem yet with numerous applications in science and engineering because anomaly scores come from the simultaneous consideration of the temporal and variable relationships. In this paper, we propose a clustering-based approach to detect anomalies concerning the amplitude and the shape of multivariate time series. First, we use a sliding window to generate a set of multivariate subsequences and thereafter apply an extended fuzzy clustering to reveal a structure present within the generated multivariate subsequences. Finally, a reconstruction criterion is employed to reconstruct the multivariate subsequences with the optimal cluster centers and the partition matrix. We construct a confidence index to quantify a level of anomaly detected in the series and apply Particle Swarm Optimization as an optimization vehicle for the problem of anomaly detection. Experimental studies completed on several synthetic and six real-world datasets suggest that the proposed methods can detect the anomalies in multivariate time series. With the help of available clusters revealed by the extended fuzzy clustering, the proposed framework can detect anomalies in the multivariate time series and is suitable for identifying anomalous amplitude and shape patterns in various application domains such as health care, weather data analysis, finance, and disease outbreak detection.

The sim-to-real gap, where agents trained in a simulator face significant performance degradation during testing, is a fundamental challenge in reinforcement learning. Extansive works adopt the framework of distributionally robust RL, to learn a policy that acts robustly under worst case environment shift. Within this framework, our objective is to devise algorithms that are sample efficient with interactive data collection and large state spaces. By assuming d-rectangularity of environment dynamic shift, we identify a fundamental hardness result for learning in online Markov game, and address it by adopting minimum value assumption. Then, a novel least square value iteration type algorithm, DR-CCE-LSI, with exploration bonus devised specifically for multiple agents, is proposed to find an \episilon-approximate robust Coarse Correlated Equilibrium(CCE). To obtain sample efficient learning, we find that: when the feature mapping function satisfies certain properties, our algorithm, DR-CCE-LSI, is able to achieve ε-approximate CCE with a regret bound of O{dHmin{H,1/min{σ_i}}\sqrt{K}}, where K is the number of interacting episodes, H is the horizon length, d is the feature dimension, and \simga_i represents the uncertainty level of player i. Our work introduces the first sample-efficient algorithm for this setting, matches the best result so far in single agent setting, and achieves minimax optimalsample complexity in terms of the feature dimension d. Meanwhile, we also conduct simulation study to validate the efficacy of our algorithm in learning a robust equilibrium.

In the era of smart manufacturing, predictive maintenance (PdM) plays a pivotal role in improving equipment reliability and reducing operating costs. In this paper, we propose a novel Markov Decision Process (MDP) framework that integrates advanced soft computing techniques - Fourier Neural Operator (FNO), Denoising Autoencoder (DAE), Graph Neural Network (GNN), and Proximal Policy Optimisation (PPO) - to address the multidimensional challenges of predictive maintenance in complex manufacturing systems. Specifically, the proposed framework innovatively combines the powerful frequency-domain representation capability of FNOs to capture high-dimensional temporal patterns; DAEs to achieve robust, noise-resistant latent state embedding from complex non-Gaussian sensor data; and GNNs to accurately represent inter-device dependencies for coordinated system-wide maintenance decisions. Furthermore, by exploiting PPO, the framework ensures stable and efficient optimisation of long-term maintenance strategies to effectively handle uncertainty and non-stationary dynamics. Experimental validation demonstrates that the approach significantly outperforms multiple deep learning baseline models with up to 13% cost reduction, as well as strong convergence and inter-module synergy. The framework has considerable industrial potential to effectively reduce downtime and operating expenses through data-driven strategies.

Label learning is a fundamental task in machine learning that aims to construct intelligent models using labeled data, encompassing traditional single-label and multi-label classification models. Traditional methods typically rely on logical labels, such as binary indicators (e.g., "yes/no") that specify whether an instance belongs to a given category. However, in practical applications, label annotations often involve significant uncertainty due to factors such as data noise, inherent ambiguity in the observed entities, and the subjectivity of human annotators. Therefore, representing labels using simplistic binary logic can obscure valuable information and limit the expressiveness of label learning models. To overcome this limitation, this paper introduces the concept of fuzzy labels, grounded in fuzzy set theory, to better capture and represent label uncertainty. We further propose an efficient fuzzy labeling method that mines and generates fuzzy labels from the original data, thereby enriching the label space with more informative and nuanced representations. Based on this foundation, we present fuzzy-label-enhanced algorithms for both single-label and multi-label learning, using the classical K-Nearest Neighbors (KNN) and multi-label KNN algorithms as illustrative examples. Experimental results indicate that fuzzy labels can more effectively characterize the real-world labeling information and significantly enhance the performance of label learning models.