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| Hauptverfasser: | , |
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| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2025
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.17369401 |
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Inhaltsangabe:
- <p>The numerical experiments implement the <strong>Near-Equilibrium Propagation</strong> (NEP) algorithm. The simulations integrate the <strong>driven-dissipative Gross-Pitaevskii</strong> equation on discretized one- and two-dimensional grids using a <strong>fourth-order Runge–Kutta</strong> method. Each training step consists of <strong>two steady-state phases</strong>: a <em>free phase</em> without any external drive at the output, and a <em>nudged phase</em> with a small output perturbation applied.</p> <p>Steady-state fields from both phases are compared to <strong>estimate local gradients according to the NEP update rule</strong>. These gradients are then used to update either the real potential or the pumping weights. Each training epoch includes multiple relaxation steps to reach convergence in both phases. The cost function is defined as mean squared error for the <strong>XOR problem</strong> and categorical cross-entropy for the <strong>MNIST tasks</strong>, calculated from the output intensities.</p> <p>The notebook <code>nep_xor.ipynb</code> demonstrates a one-dimensional nine-node system implementing the XOR logical gate, with both potential and pumping optimized.<br>The notebook <code>nep_mnist5.ipynb</code> extends the model to a two-dimensional 5×25 polariton lattice for classification of five MNIST digits using PCA-reduced inputs and one-hot encoded outputs.<br>The notebook <code>nep_mnist10.ipynb</code> performs full ten-class MNIST classification on a 5×50 grid, achieving around 80 percent accuracy under near-equilibrium conditions.</p> <p>All simulations assume weak dissipation and small output nudging, which ensures the validity of the near-equilibrium approximation.</p> <p> </p>