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Multiagent systems aim to accomplish highly complex learning tasks through decentralised consensus seeking dynamics and their use has garnered a great deal of attention in the signal processing and computational intelligence societies. This article examines the behaviour of multiagent networked systems with nonlinear filtering/learning dynamics. To this end, a general formulation for the actions of an agent in multiagent networked systems is presented and conditions for achieving a cohesive learning behaviour is given. Importantly, application of the so derived framework in distributed and federated learning scenarios are presented.

Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.

Neuro-evolutionary methods have proven effective in addressing a wide range of tasks. However, the study of the robustness and generalisability of evolved artificial neural networks (ANNs) has remained limited. This has immense implications in the fields like robotics where such controllers are used in control tasks. Unexpected morphological or environmental changes during operation can risk failure if the ANN controllers are unable to handle these changes. This paper proposes an algorithm that aims to enhance the robustness and generalisability of the controllers. This is achieved by introducing morphological variations during the evolutionary process. As a results, it is possible to discover generalist controllers that can handle a wide range of morphological variations sufficiently without the need of the information regarding their morphologies or adaptation of their parameters. We perform an extensive experimental analysis on simulation that demonstrates the trade-off between specialist and generalist controllers. The results show that generalists are able to control a range of morphological variations with a cost of underperforming on a specific morphology relative to a specialist. This research contributes to the field by addressing the limited understanding of robustness and generalisability in neuro-evolutionary methods and proposes a method by which to improve these properties.

In PDE-constrained optimization, one aims to find design parameters that minimize some objective, subject to the satisfaction of a partial differential equation. A major challenges is computing gradients of the objective to the design parameters, as applying the chain rule requires computing the Jacobian of the design parameters to the PDE's state. The adjoint method avoids this Jacobian by computing partial derivatives of a Lagrangian. Evaluating these derivatives requires the solution of a second PDE with the adjoint differential operator to the constraint, resulting in a backwards-in-time simulation. Particle-based Monte Carlo solvers are often used to compute the solution to high-dimensional PDEs. However, such solvers have the drawback of introducing noise to the computed results, thus requiring stochastic optimization methods. To guarantee convergence in this setting, both the constraint and adjoint Monte Carlo simulations should simulate the same particle trajectories. For large simulations, storing full paths from the constraint equation for re-use in the adjoint equation becomes infeasible due to memory limitations. In this paper, we provide a reversible extension to the family of permuted congruential pseudorandom number generators (PCG). We then use such a generator to recompute these time-reversed paths for the heat equation, avoiding these memory issues.

The escalating surge in data generation presents formidable challenges to information technology, necessitating advancements in storage, retrieval, and utilization. With the proliferation of artificial intelligence and big data, the "Data Age 2025" report forecasts an exponential increase in global data production. The escalating data volumes raise concerns about efficient data processing. The paper addresses the predicament of achieving a lower compression ratio while maintaining or surpassing the compression performance of state-of-the-art techniques. This paper introduces a lossy compression framework grounded in the perceptron model for data prediction, striving for high compression quality. The contributions of this study encompass the introduction of positive and negative factors within the relative-to-absolute domain transformation algorithm, the utilization of a three-layer perceptron for improved predictive accuracy, and data selection rule modifications for parallelized compression within compression blocks. Comparative experiments with SZ2.1's PW_REL mode demonstrate a maximum compression ratio reduction of 17.78%. The article is structured as follows: the introduction highlights the data explosion challenge; related work delves into existing solutions; optimization of mapping algorithms in the relative and absolute domains is expounded in Section 3,the design of the new compression framework is detailed in Section 4,In Section 5 we describe the whole process and give pseudo-code, and in Section 6, our solution is evaluated. Finally, in Section 7, we provide an outlook for future work.

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. On the basis of the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information.

We present a robust deep incremental learning framework for regression tasks on financial temporal tabular datasets which is built upon the incremental use of commonly available tabular and time series prediction models to adapt to distributional shifts typical of financial datasets. The framework uses a simple basic building block (decision trees) to build self-similar models of any required complexity to deliver robust performance under adverse situations such as regime changes, fat-tailed distributions, and low signal-to-noise ratios. As a detailed study, we demonstrate our scheme using XGBoost models trained on the Numerai dataset and show that a two layer deep ensemble of XGBoost models over different model snapshots delivers high quality predictions under different market regimes. We also show that the performance of XGBoost models with different number of boosting rounds in three scenarios (small, standard and large) is monotonically increasing with respect to model size and converges towards the generalisation upper bound. We also evaluate the robustness of the model under variability of different hyperparameters, such as model complexity and data sampling settings. Our model has low hardware requirements as no specialised neural architectures are used and each base model can be independently trained in parallel.

We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and the control acting on the interface, the regularity of solution of the control problem is limited on the whole domain, but smoother on subdomains. The control function with pointwise inequality constraints is served as the flux jump condition which we called Neumann interface control. We use a simple uniform mesh that is independent of the interface. The standard linear finite element method can not achieve optimal convergence when the uniform mesh is used. Therefore the state and adjoint state equations are discretized by piecewise linear immersed finite element method (IFEM). While the accuracy of the piecewise constant approximation of the optimal control on the interface is improved by a postprocessing step which possesses superconvergence properties; as well as the variational discretization concept for the optimal control is used to improve the error estimates. Optimal error estimates for the control, suboptimal error estimates for state and adjoint state are derived. Numerical examples with and without constraints are provided to illustrate the effectiveness of the proposed scheme and correctness of the theoretical analysis.

This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies on the one hand, explore the space and hence facilitate learning but, on the other hand, introduce bias by assigning a positive probability to non-optimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularisation. We study algorithms resulting from two entropy regularisation formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalises policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularisation, we prove that the regret, for both learning algorithms, is of the order $\mathcal{O}(\sqrt{N}) $ (up to a logarithmic factor) over $N$ episodes, matching the best known result from the literature.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.