Logical reasoning over incomplete knowledge graphs to answer complex logical
queries is a challenging task. With the emergence of new entities and relations
in constantly evolving KGs, inductive logical reasoning over KGs has become a
crucial problem. However, previous PLMs-based methods struggle to model the
logical structures of complex queries, which limits their ability to generalize
within the same structure. In this paper, we propose a structure-modeled
textual encoding framework for inductive logical reasoning over KGs. It encodes
linearized query structures and entities using pre-trained language models to
find answers. For structure modeling of complex queries, we design stepwise
instructions that implicitly prompt PLMs on the execution order of geometric
operations in each query. We further separately model different geometric
operations (i.e., projection, intersection, and union) on the representation
space using a pre-trained encoder with additional attention and maxout layers
to enhance structured modeling. We conduct experiments on two inductive logical
reasoning datasets and three transductive datasets. The results demonstrate the
effectiveness of our method on logical reasoning over KGs in both inductive and
transductive settings.

本文提出了一种基于文本编码的结构模型框架，用于在知识图谱上进行归纳逻辑推理，通过设计渐进式的指令和额外的注意力和 maxout 层来增强结构建模，成功处理了复杂查询的逻辑结构，提高了在归纳和转导数据集上的推理效率。

针对知识图谱的归纳逻辑推理的查询结构建模

Query Structure Modeling for Inductive Logical Reasoning Over Knowledge  Graphs

Covariance matrices have attracted attention for machine learning
applications due to their capacity to capture interesting structure in the
data. The main challenge is that one needs to take into account the particular
geometry of the Riemannian manifold of symmetric positive definite (SPD)
matrices they belong to. In the context of deep networks, several architectures
for these matrices have recently been proposed. In our article, we introduce a
Riemannian batch normalization (batchnorm) algorithm, which generalizes the one
used in Euclidean nets. This novel layer makes use of geometric operations on
the manifold, notably the Riemannian barycenter, parallel transport and
non-linear structured matrix transformations. We derive a new
manifold-constrained gradient descent algorithm working in the space of SPD
matrices, allowing to learn the batchnorm layer. We validate our proposed
approach with experiments in three different contexts on diverse data types: a
drone recognition dataset from radar observations, and on emotion and action
recognition datasets from video and motion capture data. Experiments show that
the Riemannian batchnorm systematically gives better classification performance
compared with leading methods and a remarkable robustness to lack of data.

本文介绍了一种基于 Riemann 流形的批量归一化算法，利用 Riemann 流形上的几何操作和结构化矩阵变换进行设计，提出了一种新的流形约束梯度下降算法，在三个不同的数据类型上进行实验证明其可以提高分类性能和鲁棒性。

SPD 神经网络的黎曼批归一化

Riemannian batch normalization for SPD neural networks

Learning low-dimensional embeddings of knowledge graphs is a powerful
approach used to predict unobserved or missing edges between entities. However,
an open challenge in this area is developing techniques that can go beyond
simple edge prediction and handle more complex logical queries, which might
involve multiple unobserved edges, entities, and variables. For instance, given
an incomplete biological knowledge graph, we might want to predict "em what
drugs are likely to target proteins involved with both diseases X and Y?" -- a
query that requires reasoning about all possible proteins that {\em might}
interact with diseases X and Y. Here we introduce a framework to efficiently
make predictions about conjunctive logical queries -- a flexible but tractable
subset of first-order logic -- on incomplete knowledge graphs. In our approach,
we embed graph nodes in a low-dimensional space and represent logical operators
as learned geometric operations (e.g., translation, rotation) in this embedding
space. By performing logical operations within a low-dimensional embedding
space, our approach achieves a time complexity that is linear in the number of
query variables, compared to the exponential complexity required by a naive
enumeration-based approach. We demonstrate the utility of this framework in two
application studies on real-world datasets with millions of relations:
predicting logical relationships in a network of drug-gene-disease interactions
and in a graph-based representation of social interactions derived from a
popular web forum.

本研究提出了一种基于低维嵌入空间中的几何运算来有效处理知识图谱中逻辑查询的框架，能够在处理复杂查询时提高时间复杂度，这种方法应用于真实世界数据中能够提供有用的预测能力。

在知识图谱上嵌入逻辑查询

Embedding Logical Queries on Knowledge Graphs

An established approach for 3D point cloud registration is to estimate the
registration function from 3D keypoint correspondences. Typically, a robust
technique is required to conduct the estimation, since there are false
correspondences or outliers. Current 3D keypoint techniques are much less
accurate than their 2D counterparts, thus they tend to produce extremely high
outlier rates. A large number of putative correspondences must thus be
extracted to ensure that sufficient good correspondences are available. Both
factors (high outlier rates, large data sizes) however cause existing robust
techniques to require very high computational cost. In this paper, we present a
novel preprocessing method called \emph{guaranteed outlier removal} for point
cloud registration. Our method reduces the input to a smaller set, in a way
that any rejected correspondence is guaranteed to not exist in the globally
optimal solution. The reduction is performed using purely geometric operations
which are deterministic and fast. Our method significantly reduces the
population of outliers, such that further optimization can be performed
quickly. Further, since only true outliers are removed, the globally optimal
solution is preserved. On various synthetic and real data experiments, we
demonstrate the effectiveness of our preprocessing method. Demo code is
available as supplementary material.

本文介绍了一种名为 “保证异常值去除” 的预处理方法，该方法使用纯几何操作将输入点云的异常值数量显著减少，以便更快地执行进一步的优化，并保留全局最优解。