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Artificial neural networks have been widely adopted as ansatzes to studyclassical and quantum systems. However, some notably hard systems such as thoseexhibiting glassiness and frustration have mainly achieved unsatisfactoryresults despite their representational power and entanglement content, thus,suggesting a potential conservation of computational complexity in the learningprocess. We explore this possibility by implementing the neural annealingmethod with autoregressive neural networks on a model that exhibits glassy andfractal dynamics: the two-dimensional Newman-Moore model on a triangularlattice. We find that the annealing dynamics is globally unstable because ofhighly chaotic loss landscapes. Furthermore, even when the correct ground stateenergy is found, the neural network generally cannot find degenerateground-state configurations due to mode collapse. These findings indicate thatthe glassy dynamics exhibited by the Newman-Moore model caused by the presenceof fracton excitations in the configurational space likely manifests itselfthrough trainability issues and mode collapse in the optimization landscape.

Neural annealing and visualization of autoregressive neural networks in the Newman-Moore model