Mechanical metamaterials derive their effective elastic properties primarily from the geometry of their periodic microstructure rather than from the constituent material alone. This work presents a neural implicit topology optimization framework for the inverse homogenization of two-dimensional metamaterial unit cells in which the principal design requirements are satisfied exactly by construction rather than through penalty terms. The pseudo-density field is represented by a coordinate-based neural network whose input is an integer-frequency Fourier embedding, which makes the field exactly periodic and gives explicit control over its spatial bandwidth and hence the minimum feature size. A per-iteration bisection on a logit offset enforces the volume-fraction constraint exactly. The optimization problems are formulated for different objectives: maximizing the bulk modulus, shear modulus, and effective elastic modulus, and minimizing Poisson’s ratio. A loss function is constructed based on the target elastic property. The gradients of the loss function are backpropagated through the finite element analysis pipeline to update the neural network parameters via gradient-based optimization. This framework allows the generation of optimized metamaterial unit-cell layouts without relying on conventional iterative density-update schemes. Numerical results demonstrate that the our framework can discover mechanically efficient unit-cell topologies with improved stiffness characteristics and reduced Poisson’s ratio. The results show that embedding physical requirements directly in the network architecture provides a compact and robust route to metamaterial design. This methodology shows potential for the discovery of microstructures with tailored mechanical properties for lightweight and multifunctional engineering applications.