一、remember 作“记得、回忆起”意义解时，后接的非谓语动词的动作时间是谓语动作之前发生过的。通常正式语体用动名词的完成体，非正式语体用动名词的一般体形式表示。但也有用不定式的完成体表示的，这是少数情况。以下为COCA语料库的几个例句，用不定式的完成体作宾语，表示记得或不记得以前发生过某事。

I remember to have heard it observed by a very learned man upon such an occasion.

On the other hand, there was picked up from the floor a green eye-patch, which the housekeeper could not remember to have seen before.

By the way, we do not remember to have seen this presented in any chapter or passage of our author's writings, and justice to him requires it to be stated.

如果remember作“记着要作某事、没忘记要做某事”这个意义解时，作宾语非谓语动词的动作在谓语时间还没有发生，要用不定式to do作宾语，不能用不定式完成体。非谓语动词的体的形式应该首先由谓语的时间所决定。所以你的二个句子均为错误：

I remember to have finished my homework when my father comes home. （X）

Tom has asked to have been paid by the end of nex month. (X)

要表达你的意思，改为如下：

I remember to finish my homework before my father comes home.

I must finish my homework before my father comes home.

Tom has asked to be paid before the end of next month.

二、I have decided to have being working until tomorrow night. （X)

我已决定一直工作到明晚。

改为：I have decided to continue working until tomorrow night.

我已决定一直工作到明晚。

三、不定式完成体和完成进行体例句：

Tom seems to have sold his house. 不定式的动作先于谓语时间。

Tom is said to have been writing a new book. 不定式的动作从过去持续到谓语时间。