High-strength metal alloys achieve their performance via careful control of the nucleation, growth, and kinetics of precipitation. Alloy mechanical properties are then controlled by atomic scale phenomena such as shearing of the precipitates by dislocations. Atomistic modeling to understand the operative mechanisms requires length and time scales far larger than those accessible by first-principles methods. Here, a family of Behler-Parinello neural-network potentials (NNPs) for the Al-Mg-Si system is developed to enable quantitative studies of Al-6xxx alloys. The NNP is trained on metallurgically-important quantities computed by first principles density functional theory (DFT) leading to high fidelity predictions of intermetallic compounds, elastic constants, dilute solid-solution energetics, precipitate/matrix interfaces, Al stacking fault energies, antisite defect energies, and other quantities. A preliminary examination of early-stage clustering kinetics and energetics in Al-6xxx is then made, showing the formation of low-energy Mg-Si structures and the trapping of vacancies in these clusters. The Generalized Stacking Fault Energy surfaces (GSFE) for the three prevalent β" precipitate compositions in peak-aged Al-6xxx are then computed with the NNP, and are validated by DFT computations at key points. The NNP thus shows significant transferability across structures, making it a powerful approach for chemically-accurate simulations of metallurgical phenomena in Al-Mg-Si alloys.