Design an efficient system that can dynamically determine which subset of many neural networks should be run on a given input image. Explain how this approach improves performance compared to traditional lookup tables or rule-based approaches.

Implement a neural network with dynamic structure internally, where the architecture adapts based on information from the input image. This reduces the computational overhead of model selection by dynamically determining which subset of features (hidden units) to compute given the input data. The system can handle out-of-distribution inputs and adapt to changing user preferences and input distributions.