The layer-by-layer decomposition approach may have limitations in terms of scalability and complexity as the neural network architecture becomes more intricate. One potential limitation is the increasing computational burden as the number of layers or neurons per layer grows, leading to longer computation times. To address this, techniques such as parallel processing or distributed computing could be explored to distribute the computational load across multiple processors or machines, improving efficiency. Additionally, incorporating heuristics or adaptive strategies to dynamically adjust the decomposition process based on the network's structure and complexity could help strike a better balance between computation time and the tightness of the Lipschitz estimate. By optimizing the decomposition strategy based on the network's characteristics, we can potentially enhance the trade-off between computational efficiency and the accuracy of the Lipschitz constant estimation.