Researchers have established a lower bound for sparse least squares optimization, confirming a conjecture by Axiotis and Sviridenko. This finding, conditional on a specific hypothesis related to randomized exact-volume Small-Set Expansion, demonstrates that polynomial-time algorithms cannot improve upon the linear dependence on the restricted condition number. Notably, the proof was initially generated by a Gemini-based agentic system developed at Google, with the authors subsequently verifying and refining the result. AI
IMPACT Demonstrates AI's capability in assisting with complex mathematical proofs, potentially accelerating research in optimization and related fields.
RANK_REASON The cluster describes a mathematical proof published on arXiv, detailing a lower bound for sparse least squares optimization.
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