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Optical computing offers a promising solution for achieving high-performance neural networks without relying heavily on electronic computing power. This work introduces a novel framework for implementing programmable neural networks. The framework enables both linear and nonlinear transformations at low optical power by leveraging multiple scattering and data repetition to achieve high-order nonlinearities. By combining linear optics and structural nonlinearity, it offers scalability and programmability for optical computing, particularly in artificial intelligence applications. The framework's ability to synthesize a learnable linear and nonlinear data transform bridges the gap between optical and digital neural networks.