A fundamental aspect of shape optimization is the choice of geometry representation. Implicit formulations, in which the surface is defined as the zero-level set of a scalar field, provide a geometry representation that has become a well-established approach in this field. Recently, advances in using neural networks for implicit geometry representation have demonstrated significant potential. In this work, we adopt a neural network–based implicit representation for shape optimization, building on the Deep Local Shapes. The approach decomposes the design domain into local regions, each parameterized by a latent code. A shared neural decoder maps spatial coordinates and the corresponding latent code to signed distance values. The global surface is reconstructed as the zero-level set of the assembled local fields. Compared to global object-level approaches, this method offers improved scalability and can handle complex topologies. Furthermore, training data can be generated easily from primitive shapes, and the representation generalizes across a wide variety of geometries, ranging from simple test cases to complex, industry-relevant geometries such as extrusion dies. Within the shape optimization framework, the latent codes serve as design variables and are updated iteratively during the optimization process. A differentiable surface extraction method is employed to transform the implicit representation into a computational mesh. Together with the differentiable nature of the neural decoder, this ensures that sensitivities can be propagated through the geometry model, enabling efficient gradient-based optimization.