Yes, it arguably includes technical training according to the List of Dual-Use Goods and Technologies and Munitions List (Wa-List (14) 2). Exploitation, as used in your question, can take many forms of course.
First, take a look at the definition of technology for GTN and both lists1:
Technology is defined as information.
The information can take the form of technical assistance.
Technical assistance may take the form of training.
Now we need to look to see if "exploitation" is on any of the lists and then if technology for exploitation is included.
The best I can find is at on the Dual Use List - Category 4 - Computers:
4.E.1.c "Technology" for the "development" of "intrusion software".
Note that technology appears in quotes. This means that the term takes on the meaning defined in the List of Definitions (found on p. 201 of Wa-List (14) 2). I also think that "Intrusion software" as defined (page 212) comports with what you call exploitation.
There are probably others, but we need to know more about what you mean by exploitation. For now I think this is enough. If you need more, I think that more answers will come from really understanding the definitions and how the defined words and phrases are used in the Wa-List.
Specific information necessary for the "development", "production" or
"use" of a product. The information takes the form of 'technical data'
or 'technical assistance'. Controlled "technology" for the Dual-Use
List is defined in the General Technology Note and in the Dual-Use
List. Controlled “technology” for the Munitions List is specified in
ML22. Technical Notes.
1. 'Technical data' may take forms such as blueprints, plans, diagrams, models, formulae, tables, engineering designs and
specifications, manuals and instructions written or recorded on other
media or devices such as disk, tape, read-only memories.
2. 'Technical assistance' may take forms such as instruction, skills, training, working knowledge, consulting services.
'Technical assistance' may involve transfer of 'technical data'.