This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential equations. Moreover, PrINNs extend the concept of Physics-Informed Neural Networks (PINNs) and their variants, offering a platform for the integration of diverse forms of perception precisiation, including singular, probability distribution, possibility distribution, interval, and fuzzy graph. In fact, PrINNs allow neural networks to model dynamical systems by integrating expert knowledge and perception-based information through loss functions, enabling the creation of modern data-driven models. Some of the key contributions include Mixture of Experts Informed Neural Networks (MOEINNs), which combine heterogeneous expert knowledge into the network, and Transformed-Knowledge Informed Neural Networks (TKINNs), which facilitate the incorporation of meta-information for enhanced model performance. Additionally, Fuzzy-Informed Neural Networks (FINNs) as a modern class of fuzzy deep neural networks leverage fuzzy logic constraints within a deep learning architecture, allowing online training without pre-training and eliminating the need for defuzzification. PrINNs represent a significant step forward in bridging the gap between traditional physics-based modeling and modern data-driven approaches, enabling neural networks to learn from both structured physics laws and flexible perception-based rules. This approach empowers neural networks to operate in uncertain environments, model complex systems, and discover new forms of differential equations, making PrINNs a powerful tool for advancing computational science and engineering.

Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding of \emph{general} function approximation schemes largely remains missing. In this paper, we establish the first provably efficient RL algorithm with general value function approximation. We show that if the value functions admit an approximation with a function class \mathcal{F}, our algorithm achieves a regret bound of \widetilde{O}(\mathrm{poly}(dH)\sqrt{T}) where d is a complexity measure of \mathcal{F} that depends on the eluder dimension [Russo and Van Roy, 2013] and log-covering numbers, H is the planning horizon, and T is the number interactions with the environment. Moreover, our algorithm is model-free and provides a framework to justify the effectiveness of algorithms used in practice.

Reinforcement Learning (RL) utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results. We consider kernel-based function approximation for RL in the infinite horizon average reward setting, also referred to as the undiscounted setting. We propose an optimistic algorithm, similar to acquisition function based algorithms in the special case of bandits. We establish novel no-regret performance guarantees for our algorithm, under kernel-based modelling assumptions.

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions. This is the focus of this work, where we study function approximation with two-layer neural networks (considering both ReLU and polynomial activation functions). Our first result is a computationally and statistically efficient algorithm in the generative model setting under completeness for two-layer neural networks. Our second result considers this setting but under only realizability of the neural net function class.

This paper focuses on the impact of rule representation in Michigan-style Learning Fuzzy-Classifier Systems (LFCSs) on its classification performance. A well-representation of the rules in an LFCS is crucial for improving its performance. However, conventional rule representations frequently need help addressing problems with unknown data characteristics. To address this issue, this paper proposes a supervised LFCS (i.e., Fuzzy-UCS) with a self-adaptive rule representation mechanism, entitled Adaptive-UCS. Adaptive-UCS incorporates a fuzzy indicator as a new rule parameter that sets the membership function of a rule as either rectangular (i.e., crisp) or triangular (i.e., fuzzy) shapes. The fuzzy indicator is optimized with evolutionary operators, allowing the system to search for an optimal rule representation. Results from extensive experiments conducted on continuous space problems demonstrate that Adaptive-UCS outperforms other UCSs with conventional crisp-hyperrectangular and fuzzy-hypertrapezoidal rule representations in classification accuracy. Additionally, Adaptive-UCS exhibits robustness in the case of noisy inputs and real-world problems with inherent uncertainty, such as missing values, leading to stable classification performance.

--Fuzzy rough feature selection (FRFS) is an effective means of addressing the curse of dimensionality in high-dimensional data. By removing redundant and irrelevant features, FRFS helps mitigate classifier overfitting, enhance generalization performance, and lessen computational overhead. However, most existing FRFS algorithms primarily focus on reducing uncertainty in pattern classification, neglecting that lower uncertainty does not necessarily result in improved classification performance, despite it commonly being regarded as a key indicator of feature selection effectiveness in the FRFS literature. T o bridge uncertainty characterization and pattern classification, we propose a Margin-aware Fuzzy Rough Feature Selection (MAFRFS) framework that considers both the compactness and separation of label classes. MAFRFS effectively reduces uncertainty in pattern classification tasks, while guiding the feature selection towards more separable and discriminative label class structures. Extensive experiments on 15 public datasets demonstrate that MAFRFS is highly scalable and more effective than FRFS. The algorithms developed using MAFRFS outperform six state-of-the-art feature selection algorithms. ITH the rapid advancement of data acquisition technologies and storage solutions, real-world data in various applications often appear in high-dimensional form, accompanied by a multitude of features. Some of these features are essential for learning processes, whereas others may be redundant or irrelevant. The presence of unnecessary features not only reduces the generalization performance of learning models but also increases computational overhead. Feature selection, guided by multiple evaluation criteria, provides an effective mechanism to eliminate irrelevant or redundant features.

Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of CTRL remains limited, especially in settings with general function approximation. In this work, we propose a model-based CTRL algorithm that achieves both sample and computational efficiency. Our approach leverages optimism-based confidence sets to establish the first sample complexity guarantee for CTRL with general function approximation, showing that a near-optimal policy can be learned with a suboptimality gap of $\tilde{O}(\sqrt{d_{\mathcal{R}} + d_{\mathcal{F}}}N^{-1/2})$ using $N$ measurements, where $d_{\mathcal{R}}$ and $d_{\mathcal{F}}$ denote the distributional Eluder dimensions of the reward and dynamic functions, respectively, capturing the complexity of general function approximation in reinforcement learning. Moreover, we introduce structured policy updates and an alternative measurement strategy that significantly reduce the number of policy updates and rollouts while maintaining competitive sample efficiency. We implemented experiments to backup our proposed algorithms on continuous control tasks and diffusion model fine-tuning, demonstrating comparable performance with significantly fewer policy updates and rollouts.

Autonomous systems that rely on Machine Learning (ML) utilize online fault tolerance mechanisms, such as runtime monitors, to detect ML prediction errors and maintain safety during operation. However, the lack of human-interpretable explanations for these errors can hinder the creation of strong assurances about the system's safety and reliability. This paper introduces a novel fuzzy-based monitor tailored for ML perception components. It provides human-interpretable explanations about how different operating conditions affect the reliability of perception components and also functions as a runtime safety monitor. We evaluated our proposed monitor using naturalistic driving datasets as part of an automated driving case study. The interpretability of the monitor was evaluated and we identified a set of operating conditions in which the perception component performs reliably. Additionally, we created an assurance case that links unit-level evidence of \textit{correct} ML operation to system-level \textit{safety}. The benchmarking demonstrated that our monitor achieved a better increase in safety (i.e., absence of hazardous situations) while maintaining availability (i.e., ability to perform the mission) compared to state-of-the-art runtime ML monitors in the evaluated dataset.

The rising incidence of skin cancer, coupled with limited public awareness and a shortfall in clinical expertise, underscores an urgent need for advanced diagnostic aids. Artificial Intelligence (AI) has emerged as a promising tool in this domain, particularly for distinguishing malignant from benign skin lesions. Leveraging publicly available datasets of skin lesions, researchers have been developing AI-based diagnostic solutions. However, the integration of such computer systems in clinical settings is still nascent. This study aims to bridge this gap by employing a fusion of image processing techniques and machine learning algorithms, specifically neuro-fuzzy and colonial competition approaches. Applied to dermoscopic images from the ISIC database, our method achieved a notable accuracy of 94% on a dataset of 560 images. These results underscore the potential of our approach in aiding clinicians in the early detection of melanoma, thereby contributing significantly to skin cancer diagnostics.

Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, exhibiting overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.