Can the word "subsubsection" be used in a thesis?
The next subsubsection discusses so and so.
It is not listed in English dictionaries.
What do you think?
One very important point has yet to be touched on. Indeed, subsubsection is not a dictionary word -- and even if it were, it's awfully cumbersome. Saying "section 1.2.3" is neater and more informative, as it tells the reader exactly where to go.
The most important reason to use numbered references is if the order of your text changes. For example, if you move a particular subsection to another section or chapter, any references to it in the form of "the next subsection" will now be invalid. By using numbered references and attaching these to either the subsection header or a key sentence (as appropriate), the numbers will automatically update and your referencing will remain correct.
The above is applicable to references to anything. It is very dangerous to write such things as "in the following...", "in the previous section we introduced...", etc. Such phrases do not refer to an exact place, and they can easily became invalid as you add, remove, or change parts of the text. Proof-reading will also be more difficult.
It's better to avoid it if you can. Rephrase it with something like "Later we will...", "further in the text...", "in the following we will...", etc. You can also refer to it specifically as "in Sec. X.Y."
By definition, (although the word is not in the dictionary), subsection is a division of a section, hence, does not have a meaning of its own. Section, however, if isolated, has a meaning of its own. Each section can be read and understood without reading the other sections. If necessary, other sections can be referred.
In this experiment, we validate the theorem presented in Section 4.
is a fine sentence. Whereas, a subsection might be entitled Experiments with Abnormal Data, such that one cannot understand before reading the definition of abnormal data (which is probably given at the beginning of the section).
Therefore, instead of
The next subsection discusses the effects of abnormal data to our super-duper proposed solution
We examine the effects of abnormal data to our super-duper proposed solution in detail, in Section 4.3
I think the problem with "subsubsection" is that it leads to troublesome situations for the reader.
In your case, if you are in a section, then you will introduce a subsection.
If you are in a subsection, then you will introduce a subsubsection.
If you are in a subsubsection, then you will introduce a subsubsubsection.
And so on.
This is a situation you are going to get into if you want to be consistent in your thesis, and as it is not convenient, I suggest you to avoid it early. Use labels for referencing portions of your work. Just like Dimitry says in his answer.