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The past decade has seen the rise of highly successful cache replacement policies that are based on binary prediction. For example, the Hawkeye policy learns whether lines loaded by a given PC are Cache Friendly (likely to remain in the cache if Belady’s MIN policy had been used) or Cache Averse (likely to be evicted by Belady’s MIN policy). In this paper, we instead present a cache replacement policy that is based on multiclass prediction, which allows it to directly mimic Belady’s MIN policy in a surprisingly simple and effective way. Our policy uses a PC-based predictor to learn each cache line’s reuse distance; it then evicts lines based on their predicted time of reuse. We show that our use of multiclass prediction is more effective than binary prediction because it allows for a finer-grained ordering of cache lines during eviction and because it is more robust to prediction errors.Our empirical results show that our new policy, which we refer to as Mockingjay, outperforms the previous state-of-the-art on both single-core and multi-core platforms and both with and without a prefetcher. For example, with no prefetcher, on a mix of 100 multi-core workloads from the SPEC 2006, SPEC 2017, and GAP benchmark suites, Mockingjay sees an average improvement over LRU of 15.2%, compared to 7.6% for SHiP and 12.9% for Hawkeye. On a single-core platform, Mockingjay’s improvement over LRU is 5.7%, which approaches the 6.0% improvement of Belady MIN’s unrealizable policy. On a single-core platform (with a prefetcher) running the high-MPKI CVP workloads, Mockingjay’s improvement over LRU is 20.1%, compared to 13.4% for Hawkeye.