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Researchers prove near-optimal cryptographic hardness for learning halfspaces under Gaussian distributions

By PulseAugur Editorial · [3 sources] ·

Two new research papers explore the computational hardness of learning with halfspaces under Gaussian distributions. The first paper focuses on homogeneous halfspaces, proving near-optimal hardness results under the Learning With Errors assumption and extending prior work to this specific case. The second paper provides improved hardness results for learning intersections of halfspaces, offering unconditional bounds in the statistical query framework and narrowing the gap between upper and lower bounds for learning multiple halfspaces. AI

IMPACT These theoretical findings could inform the development of more efficient and secure machine learning algorithms by establishing fundamental limits on learnability.

RANK_REASON Two academic papers published on arXiv presenting new theoretical results on computational hardness in machine learning.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

Researchers prove near-optimal cryptographic hardness for learning halfspaces under Gaussian distributions

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COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · Jizhou Huang, Brendan Juba ·

    Near-Optimal Cryptographic Hardness of Learning With Homogeneous Halfspaces Under Gaussian Marginals

    arXiv:2604.26446v1 Announce Type: new Abstract: We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples $(…

  2. arXiv cs.LG TIER_1 English(EN) · Brendan Juba ·

    Near-Optimal Cryptographic Hardness of Learning With Homogeneous Halfspaces Under Gaussian Marginals

    We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples $(\mathbf{x}, \mathrm{y})$ drawn from an unknown d…

  3. arXiv stat.ML TIER_1 English(EN) · Stefan Tiegel ·

    Improved Hardness Results for Learning Intersections of Halfspaces

    arXiv:2402.15995v2 Announce Type: replace-cross Abstract: We show strong (and surprisingly simple) lower bounds for weakly learning intersections of halfspaces in the improper setting. Strikingly little is known about this problem. For instance, it is not even known if there is a…

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