The 'KeOps' library lets you compute generic reductions of very large arrays whose entries are given by a mathematical formula. It combines a tiled reduction scheme with an automatic differentiation engine, and can be used through 'R', 'Matlab', 'NumPy' or 'PyTorch' backends. It is perfectly suited to the computation of Kernel dot products and the associated gradients, even when the full kernel matrix does not fit into the GPU memory.