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In this work, we propose FUSE, a novel GPU cache system that integrates spin-transfer torque magnetic random-access memory (STT-MRAM) into the on-chip L1D cache. FUSE can minimize the number of outgoing memory accesses over the interconnection network of GPU's multiprocessors, which in turn can considerably improve the level of massive computing parallelism in GPUs. Specifically, FUSE predicts a read-level of GPU memory accesses by extracting GPU runtime information and places write-once-read-multiple (WORM) data blocks into the STT-MRAM, while accommodating write-multiple data blocks over a small portion of SRAM in the L1D cache. To further reduce the off-chip memory accesses, FUSE also allows WORM data blocks to be allocated anywhere in the STT-MRAM by approximating the associativity with the limited number of tag comparators and I/O peripherals. Our evaluation results show that, in comparison to a traditional GPU cache, our proposed heterogeneous cache reduces the number of outgoing memory references by 32% across the interconnection network, thereby improving the overall performance by 217% and reducing energy cost by 53%.