Recurrent Spectral Network (RSN): Shaping a discrete map to reach automated classification

Lorenzo Chicchi, Duccio Fanelli, Lorenzo Giambagli, Lorenzo Buffoni, Timoteo Carletti

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A novel strategy to automated classification is introduced which exploits a fully trained dynamical system to steer items belonging to different categories towards distinct asymptotic target destinations. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms act for a transient and allow to disentangle the data supplied as initial condition to the discrete dynamical system. The system effectively aligns along assigned directions, which reflect the specificity of the provided input and that are encoded in the loss function via suitable spectral projections. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification, that we here term Recurrent Spectral Network (RSN), is successfully challenged against a simple test-bed model, created for illustrative purposes, as well as a standard dataset for image processing training.
Original languageEnglish
Article number113128
Number of pages11
Journal Chaos, Solitons & Fractals: the interdisciplinary journal of nonlinear science, and nonequilibrium and complex phenomena
Issue number113128
Publication statusPublished - 1 Mar 2023


  • Machine Learning
  • dynamical systems
  • spectral theory
  • Spectral learning
  • Machine learning
  • Dynamical systems


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