In this work, we investigate the fundamental trade-off regarding accuracy and parameter efficiency in the parameterization of neural network weights using predictor networks. We present a surprising finding that, when recovering the original model accuracy is the sole objective, it can be achieved effectively through the weight reconstruction objective alone. Additionally, we explore the underlying factors for improving weight reconstruction under parameter-efficiency constraints, and propose a novel training scheme that decouples the reconstruction objective from auxiliary objectives such as knowledge distillation that leads to significant improvements compared to state-of-the-art approaches. Finally, these results pave way for more practical scenarios, where one needs to achieve improvements on both model accuracy and predictor network parameter-efficiency simultaneously.
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