Integration of machine learning (ML) with topology optimization (TO) has been attempted in many works. However, most works employ ML in a data-driven paradigm, which requires well-defined training data, and the generalization is questionable. This paper aims to utilize the optimization capability of ML for high-resolution structure design. Rather than learning a priori, the neural network (NN) acts as an optimizer in the TO problem. Specifically, the density field is reparametrized into a function representation-based microstructure. The level surface is the design parameter that controls the microstructure’s volume and shape. We reformulate the multiscale TO problem with this new design variable. NN is utilized to map the microstructure parameters into the design domain. The input of NN is spatial coordinates, and the output is the microstructure level surface value. The network parameters are optimized through backpropagation, which leads to optimal design. In this framework, predicting the microstructure’s parameter at any arbitrary point is possible by taking advantage of the mesh size-independent continuous NN. Once the network is optimized, the resolution of structures can be increased accordingly without increasing computational cost. This is crucial to address the sharp transition problem of adjacent microstructures–a common one in the multiscale structure design. Several benchmarks have been studied to validate the proposed method’s effectiveness. Experimental results demonstrate that our work yields high-resolution designs with smooth transitions and improves the overall performance of final structures compared to previous methods.