Tensor programs \cite{yang1} provide a unified formalism for describing wide neural network architectures and analyzing their infinite-width limits, under appropriate scaling. Classical master theorems establish convergence in distribution of finite-width networks to their infinite-width counterparts, but typically do not provide explicit finite-width error bounds beyond specific settings.

In this work, we prove quantitative master theorems for general tensor programs. Generalizing the main result of \cite{basteri_trevisan}, we establish non-asymptotic bounds in Wasserstein distance between the joint law of the feature variables generated by the finite-width execution and those of the corresponding infinite-width execution. Our results apply under mild assumptions on the activation function and yield explicit convergence rates in terms of the layer widths. As a consequence, we obtain quantitative kernel convergence estimates with matching rates. The proof proceeds by induction over program lines and relies on a detailed analysis of conditional Gaussian updates for matrix multiplication operations, combined with stability estimates the rest of steps in the program.

These results provide a general quantitative refinement of the master theorem in \cite{yang1} and yield explicit finite-width control for a broad class of neural network architectures.