kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning

kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and continuous-time infinitesimal generators. By learning these operators, users can analyze dynamical systems via spectral methods, derive data-driven reduced-order models, and forecast future states and observables. kooplearn's interface is compliant with the scikit-learn API, facilitating its integration into existing machine learning and data science workflows. Additionally, kooplearn includes curated benchmark datasets to support experimentation, reproducibility, and the fair comparison of learning algorithms. The software is available at https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.

An Empirical Bernstein Inequality for Dependent Data in Hilbert Spaces and Applications

Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert space. Our inequalities apply to both stationary and non-stationary processes and exploit the potential rapid decay of correlations between temporally separated variables to improve estimation. We demonstrate the utility of these bounds by applying them to covariance operator estimation in the Hilbert-Schmidt norm and to operator learning in dynamical systems, achieving novel risk bounds. Finally, we perform numerical experiments to illustrate the practical implications of these bounds in both contexts.

BioLCNet: Reward-modulated Locally Connected Spiking Neural Networks

Recent studies have shown that convolutional neural networks (CNNs) are not the only feasible solution for image classification. Furthermore, weight sharing and backpropagation used in CNNs do not correspond to the mechanisms present in the primate visual system. To propose a more biologically plausible solution, we designed a locally connected spiking neural network (SNN) trained using spike-timing-dependent plasticity (STDP) and its reward-modulated variant (R-STDP) learning rules. The use of spiking neurons and local connections along with reinforcement learning (RL) led us to the nomenclature BioLCNet for our proposed architecture. Our network consists of a rate-coded input layer followed by a locally connected hidden layer and a decoding output layer. A spike population-based voting scheme is adopted for decoding in the output layer. We used the MNIST dataset to obtain image classification accuracy and to assess the robustness of our rewarding system to varying target responses.