At , ten seeds of the symmetrised convolutional classifier, trained on one fixed set…

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · High-performance and data-driven computational physics · High-performance and data-driven computational physics

Scientific Computing for Physicists, Ch Neural networks on physical data: backpropagation, convolution and symmetry

Problem

L=64

, ten seeds of the symmetrised convolutional classifier, trained on one fixed set of training runs, give a mean half-crossing of

2.276\,J/k_B

, with a standard deviation of

0.053\,J/k_B

across the ten seeds; each seed's crossing is read from four independent Monte Carlo evaluation sets pooled. Taken one set at a time, the ensemble-mean crossing has a standard deviation of

0.006\,J/k_B

across the four sets. A side test at

L=32

moved the unlabelled training window from

[1.9,2.4]

[2.1,2.8]\,J/k_B

and shifted the crossing from

2.199

2.277\,J/k_B

; assume the same shift at

L=64

. ((a)) Compute the training-randomness line

u_{\rm seed}

(the standard error of the mean over seeds), the statistics line

u_{\rm stat}

(the standard error over the four evaluation sets) and the training-window line

u_{\rm win}

(half the shift between the two windows). ((b)) Combine the three lines in quadrature and report the crossing with its uncertainty. ((c)) Compare the crossing with Onsager's exact

k_BT_c/J=2.269185

. ((d)) A colleague proposes training forty seeds instead of ten to tighten the result, assuming the seed spread stays the same. Compute the new total uncertainty and say what would shrink it more.

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