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

ConnectX is a two-player game that generalizes the popular game Connect 4.
The objective is to get X coins across a row, column, or diagonal of an M x N
board. The first player to do so wins the game. The parameters (M, N, X) are
allowed to change in each game, making ConnectX a novel and challenging
problem. In this paper, we present our work on the implementation and
modification of various reinforcement learning algorithms to play ConnectX.

本研究介绍了使用不同的强化学习算法来玩 ConnectX 游戏的实现和修改工作，让这个基于 M x N 棋盘的双人游戏成为一个新颖而具有挑战性的问题。