Adversarial representation learning is a promising paradigm for obtaining
data representations that are invariant to certain sensitive attributes while
retaining the information necessary for predicting target attributes. Existing
approaches solve this problem through iterative adversarial minimax
optimization and lack theoretical guarantees. In this paper, we first study the
"linear" form of this problem i.e., the setting where all the players are
linear functions. We show that the resulting optimization problem is both
non-convex and non-differentiable. We obtain an exact closed-form expression
for its global optima through spectral learning and provide performance
guarantees in terms of analytical bounds on the achievable utility and
invariance. We then extend this solution and analysis to non-linear functions
through kernel representation. Numerical experiments on UCI, Extended Yale B
and CIFAR-100 datasets indicate that, (a) practically, our solution is ideal
for "imparting" provable invariance to any biased pre-trained data
representation, and (b) empirically, the trade-off between utility and
invariance provided by our solution is comparable to iterative minimax
optimization of existing deep neural network based approaches. Code is
available at this https URL

通过对非凸和非可微最优化问题的研究和核表示方法，我们提供了一种通过谱学习实现数据的不变性、得出全局最优解的解决方案，并在 UCI、Extended Yale B 和 CIFAR-100 数据集上进行了实验验证，得出我们的解决方案能够实现与现有神经网络解决方案迭代最小化相当的效果。

核化对抗表示学习的全局最优解

On the Global Optima of Kernelized Adversarial Representation Learning

We develop a new bisimulation (pseudo)metric for weighted finite automata
(WFA) that generalizes Boreale's linear bisimulation relation. Our metrics are
induced by seminorms on the state space of WFA. Our development is based on
spectral properties of sets of linear operators. In particular, the joint
spectral radius of the transition matrices of WFA plays a central role. We also
study continuity properties of the bisimulation pseudometric, establish an
undecidability result for computing the metric, and give a preliminary account
of applications to spectral learning of weighted automata.

本文提出了一种基于 WFA 状态空间上的半范数的新型仿射（伪）度量，以线性算子集的谱性质为基础，研究了其连续性和应用于加权自动机谱学习的初步结果，并且发现其计算难度为不可判定问题。

加权自动机的等价关系度量

Bisimulation Metrics for Weighted Automata

We describe an approach to create a diverse set of predictions with spectral
learning of latent-variable PCFGs (L-PCFGs). Our approach works by creating
multiple spectral models where noise is added to the underlying features in the
training set before the estimation of each model. We describe three ways to
decode with multiple models. In addition, we describe a simple variant of the
spectral algorithm for L-PCFGs that is fast and leads to compact models. Our
experiments for natural language parsing, for English and German, show that we
get a significant improvement over baselines comparable to state of the art.
For English, we achieve the $F_1$ score of 90.18, and for German we achieve the
$F_1$ score of 83.38.

本文以 L-PCFGs 谱学习方法为基础，创建多种不同预测模型，添加噪声以及进行多模型演示，并尝试提高自然语言解析的性能，取得了明显提升。其中，英文的 F1 值为 90.18，德文的 F1 值为 83.38。