Machine learning models are vulnerable to adversarial attacks. One approach
to addressing this vulnerability is certification, which focuses on models that
are guaranteed to be robust for a given perturbation size. A drawback of recent
certified models is that they are stochastic: they require multiple
computationally expensive model evaluations with random noise added to a given
input. In our work, we present a deterministic certification approach which
results in a certifiably robust model. This approach is based on an equivalence
between training with a particular regularized loss, and the expected values of
Gaussian averages. We achieve certified models on ImageNet-1k by retraining a
model with this loss for one epoch without the use of label information.

本文提出了一种基于确定性证明的机器学习模型认证方法，通过基于正则化损失的训练，以及对高斯平均数期望值的估算，实现了在无需标签信息的情况下，针对 ImageNet-1k 数据集的模型认证，并使得机器学习模型对抗攻击具有抵抗性。

Adversarial Boot Camp: 一步完成的无标签认证鲁棒性

Adversarial Boot Camp: label free certified robustness in one epoch

This article investigates, by probabilistic methods, various geometric
questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms
of independent random variables of several distributions on B_p^n, including
the normalized volume measure. These representations allow us to unify and
extend the known results of the sub-independence of coordinate slabs in B_p^n.
As another application, we compute moments of linear functionals on B_p^n,
which gives sharp constants in Khinchine's inequalities on B_p^n and determines
the \psi_2-constant of all directions on B_p^n. We also study the extremal
values of several Gaussian averages on sections of B_p^n (including mean width
and \ell-norm), and derive several monotonicity results as p varies.
Applications to balancing vectors in \ell_2 and to covering numbers of
polyhedra complete the exposition.

利用概率方法，研究了 B_p^n 上的各种几何问题，包括坐标板的子独立性、线性泛函的矩、Gaussian 平均值在 B_p^n 的截面上的极值等，并对向量平衡和多面体的覆盖数等问题进行了应用。