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

ArXi:2604.26446v1 Announce Type: new 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 distribution on $\mathbb{R}^d\times\{-1, +1\}$, whose marginal distribution on $\mathbf{x}$ is standard Gaussian and on $\mathrm{y}$ is arbitrary.