Deep learning models have increasingly become computationally intensive, necessitating specialized hardware and significant runtime for both training and inference. In this work, we introduce DynaLay, a versatile and dynamic neural network architecture that employs a reinforcement learning agent to adaptively select which layers to execute for a given input. Our approach introduces an element of introspection into neural network architectures by enabling the model to recompute the results on more difficult inputs during inference, balancing the amount of expelled computation, optimizing for both performance and efficiency. The system comprises a main model constructed with Fixed-Point Iterative (FPI) layers, which can approximate complex functions with high fidelity, and an agent that chooses among these layers or a no-operation (NOP) action. Unique to our approach is a multi-faceted reward function that combines classification accuracy, computational time, and a penalty for redundant layer selection, thereby ensuring a harmonious trade-off between performance and cost. Experimental results demonstrate that DynaLay achieves comparable accuracy to conventional deep models while significantly reducing computational overhead. Our approach represents a significant step toward creating more efficient, adaptable, and universally applicable deep learning systems.