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The transition from monolithic to multi-component neural architectures in advanced neural network controllers poses substantial challenges due to the high computational complexity of the latter. Conventional model compression techniques for complexity reduction, such as structured pruning based on norm-based metrics to estimate the relative importance of distinct parameter groups, often fail to capture functional significance. This paper introduces a component-aware pruning framework that utilizes gradient information to compute three distinct importance metrics during training: Gradient Accumulation, Fisher Information, and Bayesian Uncertainty. Experimental results with an autoencoder and a TD-MPC agent demonstrate that the proposed framework reveals critical structural dependencies and dynamic shifts in importance that static heuristics often miss, supporting more informed compression decisions.