Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators

Anindita Maiti, Keegan Stoner, and Jim Halverson

Northeastern University

Code associated with the paper arxiv.org/abs/2106.xxxx.pdf

Accuracy and Symmetry Breaking

To reproduce the symmetry breaking plots in Fig. 1, showing the two paramters mu and k affect training accuracy, first generate the data by running

symmetry_breaking_paramters.py

with options

--run=[int] to repeat experiments with the same parameters. default = 0

--k=[int, 0 to 10] so that k of the last linear weights will have mean mw (the rest will have mean 0). default = 10

--mw=[float] to set the value of the mean for k of the parameters. If you want ALL parameters to have this mean, set k = 10. default = 0.0

--targets=["hot" or "cold"] to specify the target encoding. default = "hot" onehot

One can then run plot_heatmap.py to generate a heatmap given the ranges of parameters run from the previous script. To change the target encoding simply changed the commented line for the variable targets.

To see the effect of mw on accuracy only, such as in the one-cold plot of Fig. 1, run plot_mw.py.

SO(5) invariance of n-pt functions

As an example of SO(D) invariance of the n-pt functions, we give the code for SO(5) invariance for the 2-pt and 4-pt functions. A demonstration of invariance for other D can be generated similarly with some small changes. In the npt_symmetry directory, run generate_models.py which has arguments

--width=[int] to specify the widths of the generated networks. default = 1000

--d-out=[int] to specify the output dimension of the networks. default = 5

Once the mdoels with d-out = 5 are generated at a variety of widths, e.g. [5, 10, 50, 100, 1000], run npt.py for each width. This will save the 2pt and 4pt function tensors, as well as their statistical errors.

Then to test for SO(5) invariance of the 2- and 4-pt functions, run all cells in so5_sym.ipynb.

Code Authors

Keegan Stoner

Anindita Maiti (aninditamaiti)