Length generalization (LG) is a challenging problem in learning to reason. It
refers to the phenomenon that when trained on reasoning problems of smaller
lengths or sizes, the resulting model struggles with problems of larger sizes
or lengths. Although LG has been studied by many researchers, the challenge
remains. This paper proposes a theoretical study of LG for problems whose
reasoning processes can be modeled as DAGs (directed acyclic graphs). The paper
first identifies and proves the conditions under which LG can be achieved in
learning to reason. It then designs problem representations based on the theory
to learn to solve challenging reasoning problems like parity, addition, and
multiplication, using a Transformer to achieve perfect LG.

针对学习推理中的长度泛化问题，本文通过理论研究提出一种可以模拟成有向无环图（DAGs）的问题的长度泛化条件，并设计了基于该理论的问题表示方法，使用 Transformer 模型完美解决了诸如奇偶性、加法和乘法等具有挑战性的推理问题。

学习推理中长度泛化的理论

A Theory for Length Generalization in Learning to Reason

We study the problem of learning to reason in large scale knowledge graphs
(KGs). More specifically, we describe a novel reinforcement learning framework
for learning multi-hop relational paths: we use a policy-based agent with
continuous states based on knowledge graph embeddings, which reasons in a KG
vector space by sampling the most promising relation to extend its path. In
contrast to prior work, our approach includes a reward function that takes the
accuracy, diversity, and efficiency into consideration. Experimentally, we show
that our proposed method outperforms a path-ranking based algorithm and
knowledge graph embedding methods on Freebase and Never-Ending Language
Learning datasets.

本文提出了一种基于强化学习的多跳关系路径学习框架，利用知识图谱嵌入、采样方式和奖励函数提高路径推理的精度、多样性和效率，并在 Freebase 和 Never-Ending Language Learning 数据集上展示了其优异性能。