Based on a transformer based sequence-to-sequence architecture combined with a dynamic batching algorithm, this work introduces a machine learning framework for automatically simplifying complex expressions involving multiple elliptic Gamma functions, including the q-θ function and the elliptic Gamma function. The model is trained to apply algebraic identities, particularly the SL(2, Z) and SL(3, Z) modular transformations, to reduce heavily scrambled expressions to their canonical forms. Experimental results show that the proposed framework achieves high accuracy on in-distribution tests and maintains robust performance under extrapolation, including substantially deeper scrambling depths than those seen during training. Our results demonstrate that modern sequence-to-sequence Transformer models can identify canonical representatives of expressions related by modular identities, providing a practical framework for automating symbolic manipulations involving special functions arising in supersymmetric quantum field theory and string theory.