Neural Annealing and Visualization of Autoregressive Neural Networks in the Newman–Moore Model

Abstract

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, for some notably hard systems, such as those exhibiting glassiness and frustration, they have mainly achieved unsatisfactory results, despite their representational power and entanglement content, thus suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman–Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground-state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman–Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems

“…Several other groups [17][18][19][20] investigated a problem related to sampling, namely that of simulated annealing [31] for finding ground states of optimization problems. This is an a priori slightly easier problem, because simulated annealing does not need to equilibrate at all temperatures to find a solution [32,33].…”

“…A recently developed line of research, see e.g. [13][14][15][16][17][18][19][20], proposed to solve the problem in an elegant and universal way, by machine learning proper MCMC moves. In a nutshell, the idea is to learn an auxiliary probability distribution P a (σ), which (i) can be sampled efficiently (e.g.…”

“…Then, the hope is to use the auxiliary distribution to propose smart MCMC moves. Using this strategy with autoregressive (AR) architectures that ensure efficient sampling, some authors found convergence speedup [13,14,16], but others found less promising results [20].…”

“…Our results confirm that this class of problems are a real challenge for sampling methods, even assisted by smart machine-learned moves. The model investigated in [20] possibly belong to this class. In addition, we discuss some practical issues such as mode-collapse in learning the auxiliary model, which happens when the target probability distribution has multiple peaks and the auxiliary model only learns one (or a subset) of them.…”

Supplementing recurrent neural networks with annealing to solve combinatorial optimization problems

“…In the context of our work, we harness the power of autoregressive models for the purposes of solving optimization problems by sequentially sampling solutions to these problems [3]. This sampling scheme allows to obtain perfect samples as opposed to Metropolis sampling which can produce correlated samples, and which can get stuck in local minima if the optimization problem has a rugged optimization landscape [20].…”