  The quasiparticle effective mass $m^\ast$ of interacting electrons is a
fundamental quantity in the Fermi liquid theory. However, the precise value of
the effective mass of uniform electron gas is still elusive after decades of
research. The newly developed neural canonical transformation approach [Xie et
al., J. Mach. Learn. 1, (2022)] offers a principled way to extract the
effective mass of electron gas by directly calculating the thermal entropy at
low temperature. The approach models a variational many-electron density matrix
using two generative neural networks: an autoregressive model for momentum
occupation and a normalizing flow for electron coordinates. Our calculation
reveals a suppression of effective mass in the two-dimensional spin-polarized
electron gas, which is more pronounced than previous reports in the low-density
strong-coupling region. This prediction calls for verification in
two-dimensional electron gas experiments.
