This short note is written for rapid communication of long context training
and to share the idea of how to train it with low memory usage. In the note, we
generalize the attention algorithm and neural network of Generative Pre-Trained
Transformers and reinterpret it in Path integral formalism. First, the role of
the transformer is understood as the time evolution of the token state and
second, it is suggested that the all key-token states in the same time as the
query-token can attend to the attention with the query token states. As a
result of the repetitive time evolution, it is discussed that the token states
in the past sequence meats the token states in the present sequence so that the
attention between separated sequences becomes possible for maintaining infinite
contextual information just by using low memory for limited size of sequence.
For the experiment, the $12$ input token window size was taken and one GPU with
$24$GB memory was used for the pre-training. It was confirmed that more than
$150$ length context is preserved. The sampling result of the training, the
code and the other details will be included in the revised version of this note
later.

利用生成式预训练变形器的注意力算法和神经网络在路径积分形式上进行推广，将变形器的作用解释为令牌状态的时间演变，并建议在相同时间内，所有关键 - 令牌状态都可以与查询令牌状态进行关注，从而通过使用有限的序列大小的低内存来保持分离序列之间的无限上下文信息的注意力。