An optimized Franz-Parisi hardness criterion is proven equivalent to statistical query lower bounds under a verifiable correlation assumption, yielding new average-case hardness results for mixed sparse regression and convex truncation.
Group testing: an information theory perspective
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An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Bounds
An optimized Franz-Parisi hardness criterion is proven equivalent to statistical query lower bounds under a verifiable correlation assumption, yielding new average-case hardness results for mixed sparse regression and convex truncation.