The paper introduces a novel neural network-based computational pipeline, called Neural Slicer, for multi-axis 3D printing. This pipeline is designed to handle models with diverse representations and complex topologies by optimizing a mapping function that defines curved layers for printing. The key contributions include: 1. Formulating the curved slicing problem as an optimization task for two continuous functions, $\mathbf{q}(\mathbf{x})$ and $\mathbf{s}(\mathbf{x})$, which define a mapping $\lambda(\mathbf{q}(\mathbf{x}), \mathbf{s}(\mathbf{x}))$ and a scalar field $G(\mathbf{x})$. 2. Developing a differentiable pipeline of neural networks for optimization, where loss functions are directly based on $\nabla G(\mathbf{x})$ (local printing directions), reducing dependency on initial guesses. 3. Deriving loss functions within the neural pipeline to address manufacturing objectives such as support-free and strength reinforcement. The pipeline uses a volumetric mesh to cage the input model, which is independent of the discrete representation of the input model. The scalar field $G(\mathbf{x})$ is optimized using loss functions that ensure support-free and strength-reinforced printing. The method is validated through physical fabrication experiments, demonstrating improved slicing solutions compared to conventional planar layer-based 3D printing methods.The paper introduces a novel neural network-based computational pipeline, called Neural Slicer, for multi-axis 3D printing. This pipeline is designed to handle models with diverse representations and complex topologies by optimizing a mapping function that defines curved layers for printing. The key contributions include: 1. Formulating the curved slicing problem as an optimization task for two continuous functions, $\mathbf{q}(\mathbf{x})$ and $\mathbf{s}(\mathbf{x})$, which define a mapping $\lambda(\mathbf{q}(\mathbf{x}), \mathbf{s}(\mathbf{x}))$ and a scalar field $G(\mathbf{x})$. 2. Developing a differentiable pipeline of neural networks for optimization, where loss functions are directly based on $\nabla G(\mathbf{x})$ (local printing directions), reducing dependency on initial guesses. 3. Deriving loss functions within the neural pipeline to address manufacturing objectives such as support-free and strength reinforcement. The pipeline uses a volumetric mesh to cage the input model, which is independent of the discrete representation of the input model. The scalar field $G(\mathbf{x})$ is optimized using loss functions that ensure support-free and strength-reinforced printing. The method is validated through physical fabrication experiments, demonstrating improved slicing solutions compared to conventional planar layer-based 3D printing methods.