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We introduce a strategy to compute EPRL spin foam amplitudes with manyinternal faces numerically. We work with sl2cfoam-next, the state-of-the-artframework to numerically evaluate spin foam transition amplitudes. We find thatuniform sampling Monte Carlo is exceptionally effective in approximating thesum over internal quantum numbers of a spin foam amplitude, considerablyreducing the computational resources necessary. We apply it to compute largevolume divergences of the theory and find surprising numerical evidence thatthe EPRL vertex renormalization amplitude is instead finite.

Summing bulk quantum numbers with Monte Carlo in spin foam theories