If an optimization problem admits efficient direct-product aggregation with decodable optimal solutions, then mild average-case hardness can be amplified to strong average-case hardness for the same problem on larger instances.
List-decoding using the XOR lemma
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Hardness Amplification of Optimization Problems
If an optimization problem admits efficient direct-product aggregation with decodable optimal solutions, then mild average-case hardness can be amplified to strong average-case hardness for the same problem on larger instances.