The propagation of scaling factors in the SAN method can be extended beyond the immediate subsequent layer by implementing a multi-layer propagation mechanism. This could involve creating a framework where scaling factors are not only applied to the next layer's parameters but also influence the parameters of subsequent layers in a cascading manner. For instance, scaling factors from layer ( l ) could be propagated to layers ( l+1 ), ( l+2 ), and so forth, potentially through a series of transformations that account for the cumulative effects of these factors across multiple layers.
Potential Benefits:
Enhanced Expressivity: By allowing scaling factors to influence multiple layers, the model can achieve a more nuanced adjustment of parameters, leading to improved performance on complex tasks.
Improved Generalization: This approach could help in capturing long-range dependencies within the network, potentially leading to better generalization on unseen data.
Reduced Overfitting: By distributing the influence of scaling factors across layers, the model may avoid overfitting to specific training data, as the adjustments would be more balanced and less localized.
Challenges:
Increased Complexity: Implementing multi-layer propagation would add complexity to the model architecture and training process, requiring careful design to ensure stability and efficiency.
Computational Overhead: The additional computations required for propagating scaling factors across multiple layers could lead to increased training times and resource consumption.
Diminished Interpretability: As the model becomes more complex, understanding the specific contributions of each layer and the effects of scaling factors may become more challenging, potentially complicating debugging and optimization efforts.