2025/05/19 by Nishant Suresh Aswani, Aswani, Nishant Suresh, Saif Eddin Jabari +1
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing
paper · pdf · doi:10.48550/arxiv.2505.12809
openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers, treating these representations as states in a dynamical system. Our approach learns a surrogate model that predicts how neural representations transform from input to output, with two key advantages. First, by way of lifting the original states via an autoencoder, it operates in a linear space, making editing the dynamics straightforward. Second, it preserves the topologies of the original representations by regularizing the autoencoding objective. We demonstrate that these surrogate models naturally replicate the progressive topological simplification observed in neural networks. As a practical application, we show how our approach enables targeted class unlearning in the Yin-Yang and MNIST classification tasks.