Noa Kaplan

Noa Kaplan, Alberto Padoan, Anastasia Bizyaeva

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a simplified linear and continuous-time reservoir model, we link the dimensionality and structure of the dominant modes directly to the intrinsic dimensionality and information content of the training data. In particular, for training data generated by an autonomous dynamical system, we relate the dominant modes of the trained reservoir to approximations of the Koopman eigenfunctions of the original system, illuminating an explicit connection between reservoir computing and the Dynamic Mode Decomposition algorithm. We illustrate the eigenvalue motion that generates the dominant manifolds during training in simulation, and discuss generalization to nonlinear RC via tangent dynamics and differential p-dominance.

Aliasghar Khani, Arianna Rampini, Bruno Roy et al.

Motion generation, the task of synthesizing realistic motion sequences from various conditioning inputs, has become a central problem in computer vision, computer graphics, and robotics, with applications ranging from animation and virtual agents to human-robot interaction. As the field has rapidly progressed with the introduction of diverse modeling paradigms including GANs, autoencoders, autoregressive models, and diffusion-based techniques, each approach brings its own advantages and limitations. This growing diversity has created a need for a comprehensive and structured review that specifically examines recent developments from the perspective of the generative approach employed. In this survey, we provide an in-depth categorization of motion generation methods based on their underlying generative strategies. Our main focus is on papers published in top-tier venues since 2023, reflecting the most recent advancements in the field. In addition, we analyze architectural principles, conditioning mechanisms, and generation settings, and compile a detailed overview of the evaluation metrics and datasets used across the literature. Our objective is to enable clearer comparisons and identify open challenges, thereby offering a timely and foundational reference for researchers and practitioners navigating the rapidly evolving landscape of motion generation.