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Pipelining between data loading and computation is a critical tensor program optimization for GPUs. In order to unleash the high performance of latest GPUs, we must perform a synergetic optimization of multi-stage pipelining across the multi-level buffer hierarchy of GPU. Existing frameworks rely on hand-written libraries such as cuBLAS to perform pipelining optimization, which is inextensible to new operators and un-composable with prior tensor compiler optimizations. This paper presents ALCOP, the first framework that is compiler-native and fully supports multi-stage multi-level pipelining. ALCOP overcomes three critical obstacles in generating code for pipelining: detection of pipelining-applicable buffers, program transformation for multi-level multi-stage pipelining, and efficient schedule parameter search by incorporating static analysis. Experiments show that ALCOP can generate programs with 1.23x speedup on average (up to 1.73x) over vanilla TVM. On end-to-end models, ALCOP can improve upon TVM by up to 1.18x, and XLA by up to 1.64x. Besides, our performance model significantly improves the efficiency of the schedule tuning process and can find schedules with 99% of the performance given by exhaustive search while costing 40x fewer trials.