What does 的 mean in 随着学习的深入 (a verb modifies a verb via 的)?
songyuanyao wrote:


  深入 is considered as a noun here


songyuanyao is right, 深入(advance) is a noun here


  随着(following) 学习的 (of study) 深入 (advance)


Notice 随着 (following) is the verb, advance is the object, and 学习的 is the adjectival phrase that describe 'advance'-- (advance of what? Advance of the study of course.)

'的' at the end of '学习的' turns the noun '学习' (study) into an adjectival phrase (of study)

Let me give another example of [noun + 的] = [of noun]:  

战斗 : to battle (v); battle (n)

战斗的 = of battle

加劇: to intensify(v); intensification (n)

"战斗的加劇" = "intensification of battle" 

Both 战斗 and 加劇 are noun here and 的 turns 战斗 to an adjectival phrase for 'intensification' (intensification of the battle)

In '战斗加劇', '战斗'(battle) is the object noun ; and 加劇 (intensify) is a verb 

In '学习得深入', '学习' is a verb and  '得' is a 'degree adverbial particle' that turns the verb '深入' into an adverbial phrase for it (describe the degree of the verb 学习) 

In '深入地学习', '地' turn the verb 深入 into an adverbial phrase for the verb 学习 (describe the manner of the verb 学习)