The covariance matrix adaptation evolution strategy (CMA-ES) is arguably one of the most powerful real-valued derivative-free optimization algorithms, finding many applications in machine learning. The CMA-ES is a Monte Carlo method, sampling from a sequence of multi-variate Gaussian distributions. Given the function values at the sampled points, updating and storing the covariance matrix dominates the time and space complexity in each iteration of the algorithm. We propose a numerically stable quadratic-time covariance matrix update scheme with minimal memory requirements based on maintaining triangular Cholesky factors. This requires a modification of the cumulative step-size adaption (CSA) mechanism in the CMA-ES, in which we replace the inverse of the square root of the covariance matrix by the inverse of the triangular Cholesky factor. Because the triangular Cholesky factor changes smoothly with the matrix square root, this modification does not change the behavior of the CMA-ES in terms of required objective function evaluations as verified empirically. Thus, the described algorithm can and should replace the standard CMA-ES if updating and storing the covariance matrix matters.

Abstract--Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework that integrates topological conditioning with gradient stabilization mechanisms. The approach employs Forman-Ricci curvature to capture graph topology, Deep Delta Learning for stable rank-one perturbations during constraint projection, and Covariance Matrix Adaptation Evolution Strategy for parameter optimization. Experimental evaluation across multiple problem sizes demonstrates that the method achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate in constraint satisfaction tasks. The framework exhibits seed-independent convergence and graceful scaling behavior up to twenty-node problems, suggesting that topological structure can inform gradient-based optimization without sacrificing interpretability or computational efficiency. Integrating symbolic reasoning with neural learning remains a central challenge in artificial intelligence. While neural networks excel at pattern recognition and gradient-based optimization, they often struggle to maintain explicit constraints or provide interpretable intermediate representations. The opacity of deep neural representations makes it difficult to verify whether learned policies respect domain knowledge or physical laws. Conversely, symbolic systems offer logical transparency and formal guarantees but lack the flexibility to learn from noisy, incomplete data or adapt to distributional shifts.

The covariance matrix adaptation evolution strategy (CMA-ES) is arguably one of the most powerful real-valued derivative-free optimization algorithms, finding many applications in machine learning. The CMA-ES is a Monte Carlo method, sampling from a sequence of multi-variate Gaussian distributions. Given the function values at the sampled points, updating and storing the covariance matrix dominates the time and space complexity in each iteration of the algorithm. We propose a numerically stable quadratic-time covariance matrix update scheme with minimal memory requirements based on maintaining triangular Cholesky factors. This requires a modification of the cumulative step-size adaption (CSA) mechanism in the CMA-ES, in which we replace the inverse of the square root of the covariance matrix by the inverse of the triangular Cholesky factor. Because the triangular Cholesky factor changes smoothly with the matrix square root, this modification does not change the behavior of the CMA-ES in terms of required objective function evaluations as verified empirically. Thus, the described algorithm can and should replace the standard CMA-ES if updating and storing the covariance matrix matters.

The CMA-ES is a Monte Carlo method, sampling from a sequence of multi-variate Gaussian distributions.

The rapid expansion of electric vehicles has intensified the need for accurate and efficient diagnosis of lithium-ion batteries. Parameter identification of electrochemical battery models is widely recognized as a powerful method for battery health assessment. However, conventional metaheuristic approaches suffer from high computational cost and slow convergence, and recent machine learning methods are limited by their reliance on constant current data, which may not be available in practice. To overcome these challenges, we propose deep learning-based framework for parameter identification of electrochemical battery models. The proposed framework combines a neural surrogate model of the single particle model with electrolyte (NeuralSPMe) and a deep learning-based fixed-point iteration method. NeuralSPMe is trained on realistic EV load profiles to accurately predict lithium concentration dynamics under dynamic operating conditions while a parameter update network (PUNet) performs fixed-point iterative updates to significantly reduce both the evaluation time per sample and the overall number of iterations required for convergence. Experimental evaluations demonstrate that the proposed framework accelerates the parameter identification by more than 2000 times, achieves superior sample efficiency and more than 10 times higher accuracy compared to conventional metaheuristic algorithms, particularly under dynamic load scenarios encountered in practical applications.

Wearable robots offer a promising solution for quantitatively monitoring gait and providing systematic, adaptive assistance to promote patient independence and improve gait. However, due to significant interpersonal and intrapersonal variability in walking patterns, it is important to design robot controllers that can adapt to the unique characteristics of each individual. This paper investigates the potential of human-in-the-loop optimisation (HILO) to deliver personalised assistance in gait training. The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) was employed to continuously optimise an assist-as-needed controller of a lower-limb exoskeleton. Six healthy individuals participated over a two-day experiment. Our results suggest that while the CMA-ES appears to converge to a unique set of stiffnesses for each individual, no measurable impact on the subjects' performance was observed during the validation trials. These findings highlight the impact of human-robot co-adaptation and human behaviour variability, whose effect may be greater than potential benefits of personalising rule-based assistive controllers. Our work contributes to understanding the limitations of current personalisation approaches in exoskeleton-assisted gait rehabilitation and identifies key challenges for effective implementation of human-in-the-loop optimisation in this domain.

This paper introduces a methodology for task-specific design optimization of multirotor Micro Aerial Vehicles. By leveraging reinforcement learning, Bayesian optimization, and covariance matrix adaptation evolution strategy, we optimize aerial robot designs guided exclusively by their closed-loop performance in a considered task. Our approach systematically explores the design space of motor pose configurations while ensuring manufacturability constraints and minimal aerodynamic interference. Results demonstrate that optimized designs achieve superior performance compared to conventional multirotor configurations in agile waypoint navigation tasks, including against fully actuated designs from the literature. We build and test one of the optimized designs in the real world to validate the sim2real transferability of our approach.

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

Explainable AI (XAI) methods help identify which image regions influence a model's prediction, but often face a trade-off between detail and interpretability. Layer-wise Relevance Propagation (LRP) offers a model-aware alternative. However, LRP implementations commonly rely on heuristic rule sets that are not optimized for clarity or alignment with model behavior. We introduce EVO-LRP, a method that applies Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to tune LRP hyperparameters based on quantitative interpretability metrics, such as faithfulness or sparseness. EVO-LRP outperforms traditional XAI approaches in both interpretability metric performance and visual coherence, with strong sensitivity to class-specific features. These findings demonstrate that attribution quality can be systematically improved through principled, task-specific optimization.