  We investigate the lattice regularization of $\mathcal{N} = 4$ supersymmetric
Yang-Mills theory, by stochastically computing the eigenvalue mode number of
the fermion operator. This provides important insight into the non-perturbative
renormalization group flow of the lattice theory, through the definition of a
scale-dependent effective mass anomalous dimension. While this anomalous
dimension is expected to vanish in the conformal continuum theory, the finite
lattice volume and lattice spacing generically lead to non-zero values, which
we use to study the approach to the continuum limit. Our numerical results,
comparing multiple lattice volumes, 't Hooft couplings, and numbers of colors,
confirm convergence towards the expected continuum result, while quantifying
the increasing significance of lattice artifacts at larger couplings.
