Puppet-CNN: Continuous Parameter Dynamics for Input-Adaptive Convolutional Networks

Modern convolutional neural networks (CNNs) organize com-putation as a discrete stack of layers whose parameters are independentlystored and learned, with the number of layers fixed as an architecturalhyperparameter. In this work, we explore an alternative perspective: cannetwork parameterization itself be modeled as a continuous dynamicalsystem? We introduce Puppet-CNN, a framework that represents con-volutional layer parameters as states evolving along a learned parameterflow governed by a neural ordinary differential equation (ODE). Underthis formulation, layer parameters are generated through continuousevolution in parameter space, and the effective number of generatedlayers is determined by the discretization resolution used to sample thelearned parameter trajectory, which can be modulated by input com-plexity to enable input-adaptive computation. We validate its feasibilityon standard image classification benchmarks and show that continuousparameter dynamics can maintain competitive predictive performancewhile substantially reducing stored trainable parameters. These resultssuggest that viewing neural network parameterization through the lensof dynamical systems provides a structured and flexible design space foradaptive convolutional models.