Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain.

Model combination is a powerful approach to achieve superior performance with a set of models than by just selecting any single one. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs), which have been shown to achieve state-of-the-art macroeconomic time series forecasting results (Ballarin et al., 2024a). Hedge and Follow-the-Leader schemes are discussed, and their online learning guarantees are extended to the case of dependent data. In applications, our proposed Ensemble Echo State Networks show significantly improved predictive performance compared to individual MFESN models.

Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain.

If a product deviates from its desired properties in the injection moulding process, its root cause analysis can be aided by models that relate the input machine settings with the output quality characteristics. The machine learning models tested in the quality prediction are mostly black boxes; therefore, no direct explanation of their prognosis is given, which restricts their applicability in the quality control. The previously attempted explainability methods are either restricted to tree-based algorithms only or do not emphasize on the fact that some explainability methods can lead to wrong root cause identification of a product's deviation from its desired properties. This study first shows that the interactions among the multiple input machine settings do exist in real experimental data collected as per a central composite design. Then, the model-agnostic explainable AI methods are compared for the first time to show that different explainability methods indeed lead to different feature impact analysis in injection moulding. Moreover, it is shown that the better feature attribution translates to the correct cause identification and actionable insights for the injection moulding process. Being model agnostic, explanations on both random forest and multilayer perceptron are performed for the cause analysis, as both models have the mean absolute percentage error of less than 0.05% on the experimental dataset.

Scenario-based testing with driving simulators is extensively used to identify failing conditions of automated driving assistance systems (ADAS) and reduce the amount of in-field road testing. However, existing studies have shown that repeated test execution in the same as well as in distinct simulators can yield different outcomes, which can be attributed to sources of flakiness or different implementations of the physics, among other factors. In this paper, we present MultiSim, a novel approach to multi-simulation ADAS testing based on a search-based testing approach that leverages an ensemble of simulators to identify failure-inducing, simulator-agnostic test scenarios. During the search, each scenario is evaluated jointly on multiple simulators. Scenarios that produce consistent results across simulators are prioritized for further exploration, while those that fail on only a subset of simulators are given less priority, as they may reflect simulator-specific issues rather than generalizable failures. Our case study, which involves testing a deep neural network-based ADAS on different pairs of three widely used simulators, demonstrates that MultiSim outperforms single-simulator testing by achieving on average a higher rate of simulator-agnostic failures by 51%. Compared to a state-of-the-art multi-simulator approach that combines the outcome of independent test generation campaigns obtained in different simulators, MultiSim identifies 54% more simulator-agnostic failing tests while showing a comparable validity rate. An enhancement of MultiSim that leverages surrogate models to predict simulator disagreements and bypass executions does not only increase the average number of valid failures but also improves efficiency in finding the first valid failure.

Memory capacity of nonlinear recurrent networks: Is it informative? Abstract The total memory capacity (MC) of linear recurrent neural networks (RNNs) has been proven to be equal to the rank of the corresponding Kalman controllability matrix, and it is almost surely maximal for connectivity and input weight matrices drawn from regular distributions. This fact questions the usefulness of this metric in distinguishing the performance of linear RNNs in the processing of stochastic signals. This note shows that the MC of random nonlinear RNNs yields arbitrary values within established upper and lower bounds depending just on the input process scale. This confirms that the existing definition of MC in linear and nonlinear cases has no practical value.

We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits of RFNNs. In the case of MSE loss, we obtain closed-form solutions to greedy layer-wise boosting with random features. For general loss functions, we show that fitting random feature residual blocks reduces to solving a quadratically constrained least squares problem. We demonstrate, through numerical experiments on 91 tabular datasets for regression and classification, that RFRBoost significantly outperforms traditional RFNNs and end-to-end trained MLP ResNets, while offering substantial computational advantages and theoretical guarantees stemming from boosting theory.

The increasing demand for privacy-preserving data analytics in finance necessitates solutions for synthetic data generation that rigorously uphold privacy standards. We introduce DP-Fed-FinDiff framework, a novel integration of Differential Privacy, Federated Learning and Denoising Diffusion Probabilistic Models designed to generate high-fidelity synthetic tabular data. This framework ensures compliance with stringent privacy regulations while maintaining data utility. We demonstrate the effectiveness of DP-Fed-FinDiff on multiple real-world financial datasets, achieving significant improvements in privacy guarantees without compromising data quality. Our empirical evaluations reveal the optimal trade-offs between privacy budgets, client configurations, and federated optimization strategies. The results affirm the potential of DP-Fed-FinDiff to enable secure data sharing and robust analytics in highly regulated domains, paving the way for further advances in federated learning and privacy-preserving data synthesis.

Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes the solution sequentially using an inaccurate (fast) solver, and then "corrects" it using an accurate (slow) integrator that runs in parallel across temporal subintervals. This work introduces RandNet-Parareal, a novel method to learn the discrepancy between the coarse and fine solutions using random neural networks (RandNets). RandNet-Parareal achieves speed gains up to x125 and x22 compared to the fine solver run serially and Parareal, respectively. Beyond theoretical guarantees of RandNets as universal approximators, these models are quick to train, allowing the PinT solution of partial differential equations on a spatial mesh of up to $10^5$ points with minimal overhead, dramatically increasing the scalability of existing PinT approaches. RandNet-Parareal's numerical performance is illustrated on systems of real-world significance, such as the viscous Burgers' equation, the Diffusion-Reaction equation, the two- and three-dimensional Brusselator, and the shallow water equation.

The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.