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Google's Gemini AI assists in proving mathematical lower bound for sparse least squares

By PulseAugur Editorial · [2 sources] ·

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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AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Google's Gemini AI assists in proving mathematical lower bound for sparse least squares

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Honghao Lin, Vahab Mirrokni, David P. Woodruff ·

    The Condition-Number Barrier in Sparse Least Squares

    arXiv:2608.02588v1 Announce Type: cross Abstract: In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower boun…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    The Condition-Number Barrier in Sparse Least Squares

    In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the…

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