One of the most basic facts related to the famous Ulam reconstruction
conjecture is that the connectedness of a graph can be determined by the deck
of its vertex-deleted subgraphs, which are considered up to isomorphism. We
strengthen this result by proving that connectedness can still be determined
when the subgraphs in the deck are given up to equivalence under the color
refinement isomorphism test. Consequently, this implies that connectedness is
recognizable by Reconstruction Graph Neural Networks, a recently introduced GNN
architecture inspired by the reconstruction conjecture (Cotta, Morris, Ribeiro
2021).

Ulman 的重构猜想与图的连通性有关，可以通过顶点删除子图的牌堆来确定，我们通过证明，当给定牌堆中的子图通过颜色细化同构测试等价时，仍然可以确定连通性，因此，这意味着通过重构图神经网络可以识别连通性，这是一种新近引入的受重构猜想启发的 GNN 架构。

关于重构颜色细化的表达能力

On the Expressibility of the Reconstructional Color Refinement

Gradient-based saliency maps have been widely used to explain the decisions
of deep neural network classifiers. However, standard gradient-based
interpretation maps, including the simple gradient and integrated gradient
algorithms, often lack desired structures such as sparsity and connectedness in
their application to real-world computer vision models. A frequently used
approach to inducing sparsity structures into gradient-based saliency maps is
to alter the simple gradient scheme using sparsification or norm-based
regularization. A drawback with such post-processing methods is their
frequently-observed significant loss in fidelity to the original simple
gradient map. In this work, we propose to apply adversarial training as an
in-processing scheme to train neural networks with structured simple gradient
maps. We show a duality relation between the regularized norms of the
adversarial perturbations and gradient-based maps, based on which we design
adversarial training loss functions promoting sparsity and group-sparsity
properties in simple gradient maps. We present several numerical results to
show the influence of our proposed norm-based adversarial training methods on
the standard gradient-based maps of standard neural network architectures on
benchmark image datasets.

通过对简单梯度方案进行稀疏性及连接性调整，采用对抗训练作为一种内部处理方案，设计并展示了基于正则化的对抗训练方法对标准神经网络架构在基准图像数据集上的梯度图产生的影响。

基于范数正则化的结构化梯度解释方法

Structured Gradient-based Interpretations via Norm-Regularized  Adversarial Training

Counterfactual post-hoc interpretability approaches have been proven to be
useful tools to generate explanations for the predictions of a trained blackbox
classifier. However, the assumptions they make about the data and the
classifier make them unreliable in many contexts. In this paper, we discuss
three desirable properties and approaches to quantify them: proximity,
connectedness and stability. In addition, we illustrate that there is a risk
for post-hoc counterfactual approaches to not satisfy these properties.

本文探讨了后设反事实解释方法对数据和分类器的基本假设导致其在很多情况下的不可靠性，并提出了近似性、连通性和稳定性三种量化方法和途径。另外，本文还证明了后设反事实方法不满足这些属性的风险。