Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential rules (commonly referred to as tuple-generating dependencies) to the fuzzy setting, by allowing for arbitrary t-norms in the place of classical conjunctions in rule bodies. The resulting formalism allows us to perform reasoning about data associated with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for the standard Datalog setting. In particular, we provide fuzzy extensions of Datalog chases which produce fuzzy universal models and we exploit them to show that in important fragments of the language, reasoning has the same complexity as in the classical setting.

Reinforcement learning (RL) [43] has emerged as a powerful framework for sequential decision-making in dynamic and uncertain environments. While traditional RL methods, predominantly focused on maximizing the expected return, have seen significant advancements through approaches such as Q-learning [37, 25] and policy gradients [28, 10], they often fall short in real-world scenarios demanding strict risk control, such as financial investment [9], medical treatment [16], and automous driving [11]. The significance of comprehending risk management in RL has led to the emergence of Risk-Sensitive RL (RSRL). Unlike risk-neutral RL, which primarily focuses on maximizing expected returns, RSRL seeks to optimize risk metrics, such as entropy risk measures (ERM) [17, 18] or conditional value-at-risk (CVaR) [46], of the possible cumulative reward which emphasizes its distributional characteristics. However, traditional RL framework based on Q-learning which typically considers the mean of reward-to-go and corresponding Bellman equation, cannot efficiently capture the characteristics of the cumulative reward's distribution. Therefore, there has been an upsurge of interest in Distributional RL (DisRL) due to its capacity to understand the intrinsic distributional attributes of cumulative rewards, which has already achieved significant empirical success in risk-sensitive tasks [8, 14, 30, 45, 34].

We introduce a modified incremental learning algorithm for evolving Granular Neural Network Classifiers (eGNN-C+). We use double-boundary hyper-boxes to represent granules, and customize the adaptation procedures to enhance the robustness of outer boxes for data coverage and noise suppression, while ensuring that inner boxes remain flexible to capture drifts. The classifier evolves from scratch, incorporates new classes on the fly, and performs local incremental feature weighting. As an application, we focus on the classification of emotion-related patterns within electroencephalogram (EEG) signals. Emotion recognition is crucial for enhancing the realism and interactivity of computer systems. We extract features from the Fourier spectrum of EEG signals obtained from 28 individuals engaged in playing computer games -- a public dataset. Each game elicits a different predominant emotion: boredom, calmness, horror, or joy. We analyze individual electrodes, time window lengths, and frequency bands to assess the accuracy and interpretability of resulting user-independent neural models. The findings indicate that both brain hemispheres assist classification, especially electrodes on the temporal (T8) and parietal (P7) areas, alongside contributions from frontal and occipital electrodes. While patterns may manifest in any band, the Alpha (8-13Hz), Delta (1-4Hz), and Theta (4-8Hz) bands, in this order, exhibited higher correspondence with the emotion classes. The eGNN-C+ demonstrates effectiveness in learning EEG data. It achieves an accuracy of 81.7% and a 0.0029 II interpretability using 10-second time windows, even in face of a highly-stochastic time-varying 4-class classification problem.

We study off-dynamics Reinforcement Learning (RL), where the policy is trained on a source domain and deployed to a distinct target domain. We aim to solve this problem via online distributionally robust Markov decision processes (DRMDPs), where the learning algorithm actively interacts with the source domain while seeking the optimal performance under the worst possible dynamics that is within an uncertainty set of the source domain's transition kernel. We provide the first study on online DRMDPs with function approximation for off-dynamics RL. We find that DRMDPs' dual formulation can induce nonlinearity, even when the nominal transition kernel is linear, leading to error propagation. By designing a d -rectangular uncertainty set using the total variation distance, we remove this additional nonlinear-ity and bypass the error propagation. We then introduce DR-LSVI-UCB, the first provably efficient online DRMDP algorithm for off-dynamics RL with function approximation, and establish a polynomial suboptimal-ity bound that is independent of the state and action space sizes. Our work makes the first step towards a deeper understanding of the provable efficiency of online DRMDPs with linear function approximation. Finally, we substantiate the performance and robustness of DR-LSVI-UCB through different numerical experiments.

In recent years, black-box machine learning approaches have become a dominant modeling paradigm for knowledge extraction in Remote Sensing. Despite the potential benefits of uncovering the inner workings of these models with explainable AI, a comprehensive overview summarizing the used explainable AI methods and their objectives, findings, and challenges in Remote Sensing applications is still missing. In this paper, we address this issue by performing a systematic review to identify the key trends of how explainable AI is used in Remote Sensing and shed light on novel explainable AI approaches and emerging directions that tackle specific Remote Sensing challenges. We also reveal the common patterns of explanation interpretation, discuss the extracted scientific insights in Remote Sensing, and reflect on the approaches used for explainable AI methods evaluation. Our review provides a complete summary of the state-of-the-art in the field. Further, we give a detailed outlook on the challenges and promising research directions, representing a basis for novel methodological development and a useful starting point for new researchers in the field of explainable AI in Remote Sensing.

Anomaly localization, which involves localizing anomalous regions within images, is a significant industrial task. Reconstruction-based methods are widely adopted for anomaly localization because of their low complexity and high interpretability. Most existing reconstruction-based methods only use normal samples to construct model. If anomalous samples are appropriately utilized in the process of anomaly localization, the localization performance can be improved. However, usually only weakly labeled anomalous samples are available, which limits the improvement. In many cases, we can obtain some knowledge of anomalies summarized by domain experts. Taking advantage of such knowledge can help us better utilize the anomalous samples and thus further improve the localization performance. In this paper, we propose a novel reconstruction-based method named knowledge-informed self-training (KIST) which integrates knowledge into reconstruction model through self-training. Specifically, KIST utilizes weakly labeled anomalous samples in addition to the normal ones and exploits knowledge to yield pixel-level pseudo-labels of the anomalous samples. Based on the pseudo labels, a novel loss which promotes the reconstruction of normal pixels while suppressing the reconstruction of anomalous pixels is used. We conduct experiments on different datasets and demonstrate the advantages of KIST over the existing reconstruction-based methods.

Our aim of this paper is to develop new map matching algorithms and to improve upon previous work. We address two key approaches: Analytic Hierarchy Process (AHP) map matching and fuzzy logic map matching. AHP is a decision-making method that combines mathematical analysis with human judgment, and fuzzy logic is an approach to computing based on the degree of truth and aims at modeling the imprecise modes of reasoning from 0 to 1 rather than the usual boolean logic. Of these algorithms, the way of our applying AHP to map matching is newly developed in this paper, meanwhile, our application of fuzzy logic to map matching is mostly the same as existing research except for some small changes. Because of the common characteristic that both methods are designed to handle imprecise information and simplicity for implementation, we decided to use these methods.

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal weights and biases, offering computational efficiency. We demonstrate that there exists a choice of external weights, for any family of such RPNNs, with non-polynomial infinitely differentiable activation functions, that exhibit an exponential convergence rate when approximating any infinitely differentiable function. For illustration purposes, we test the proposed RPNN-based function approximation, with parsimoniously chosen basis functions, across five benchmark function approximation problems. Results show that RPNNs achieve comparable performance to established methods such as Legendre Polynomials, highlighting their potential for efficient and accurate function approximation. Widely used in Machine Learning (ML) tasks, including image classification, signal analysis, speech recognition, text-toimage synthesis and language processing [84, 68, 83, 37, 18, 39], the celebrated universal approximation theorem arXiv:2402.11397v1 Since the 1990s, there has been a notable increase in research focusing on solving numerical analysis problems. Lee and Kang (1990) [59] employed a Hopfield Neural Network to address the numerical solution of differential equations. Rico-Martinez et al. (1992) [76] introduced a recursive multilayer ANNs architecture, emulating the implementation of the 4th-order Runge-Kutta scheme, for the identification of continuous-time ODEs and the construction of their bifurcation diagram from experimental data. Yes ildirek and Lewis (1995) [85] employed a neural network-based controller for the feedback linearization of dynamical systems. Lagaris et al. (1998) [58] systematically investigate the use of FNNs for the solution of linear and nonlinear differential equations, addressing a range of scenarios from initial and boundary value problems. Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications and increased computational power.

We address the problem of non-convergence of online reinforcement learning algorithms (e.g., Q learning and SARSA(A)) by adopt(cid:173) ing an incremental-batch approach that separates the exploration process from the function fitting process. Our BFBP (Batch Fit to Best Paths) algorithm alternates between an exploration phase (during which trajectories are generated to try to find fragments of the optimal policy) and a function fitting phase (during which a function approximator is fit to the best known paths from start states to terminal states). An advantage of this approach is that batch value-function fitting is a global process, which allows it to address the tradeoffs in function approximation that cannot be handled by local, online algorithms. This approach was pioneered by Boyan and Moore with their GROWSUPPORT and ROUT al(cid:173) gorithms. We show how to improve upon their work by applying a better exploration process and by enriching the function fitting procedure to incorporate Bellman error and advantage error mea(cid:173) sures into the objective function.