Neural Network Renormalization Group

By Shuo-Hui Li, Lei Wang. 2018

145 citations recorded by the source corpus.

We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural network directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Model Architectures

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Citations in the corpus

Stochastic Normalizing Flows (2020, methodology): “Derivation via weight maximization If we draw samples in latent space via z ∼ µ Z ( z ) and transform them to samples x through the SNF, a sufﬁcient condition to sample x ∼ µ X ( x ) is to respect path-based detailed balance: This can be achieved by running MCMC in path-space and accepting paths wit”
Equivariant Flows: exact likelihood generative learning for symmetric densities (2020, background): “Copyright 2020 by the author(s). approach is widely applicable in the physical sciences, and has also been employed in the sampling of spin lattice states (Nicoli et al., 2019; Li & Wang, 2018) and nuclear physics models (Albergo et al., 2019).”
A high-bias, low-variance introduction to Machine Learning for physicists (2018, unknown): “This basic logic is reminiscent of renormalization procedures that seek to decorrelate layers at each step (Li and Wang, 2018; Mehta and Schwab, 2014; Vidal, 2007).”
Machine learning and the physical sciences (2019, background): “First attempts in this direction appeared in (Koch-Janusz and Ringel, 2018; Li and Wang, 2018).”
Unsupervised Learning Methods for Molecular Simulation Data (2021, background): “173 This is a promising direction for combining the tasks of dimensionality reduction and rare-event sampling in the molecular sciences.”
Monge-Ampère Flow for Generative Modeling (2018, methodology): “Dinh et al. (2014; 2016); Li & Wang (2018); Kingma & Dhariwal (2018) strive the balance between expressibility and efﬁciency of the bijective networks by imposing block structures in the Jacobian matrix.”