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I'm writing my master thesis in English as a non-native speaker. I start a lot of sentences without an article and one of my lectors (a non-native speaker like myself) found this to be odd and marked every occurrence. My question to the native speakers is: which method would be considered better?

A few examples:

Identification of such failures is usually a tedious manual task.

Automatic identification of such failures would be highly beneficial.

Examination of test data reveals...

Literature review confirms that...

Application of these models shows poor results.

My lector would correct all these examples with a definite article:

The identification of such failures is usually a tedious manual task.

The automatic identification of such failures would be highly beneficial.

The examination of test data reveals...

The literature review confirms that...

The application of these models shows poor results.

I'm a native speaker who occasionally works professionally as a technical writer and editor, including writing scientific journal articles. In my opinion, your versions of the sentences, without the leading article, are more conventional.

Adding the article isn't wrong, but it's not the customary way to express those facts in academic writing. You're invoking the subject noun as an abstract concept, e.g. "identification of such failures" as an idea or possibility to entertain, not as a specific occurrence of identifying certain, specific failures. You can write the to indicate that you intend a noun to be taken as an abstraction rather than an instance, as is commonly done in many languages with a definite article, but in contemporary English this is usually done only with a small range of nouns. For example, it's done with species and organs, such as "the elephant" and "the stomach". With most nouns, we determine them abstractly by omitting the article entirely.

You would say "The literature review confirms that…" only if you were referring to a specific literature review already introduced. If the sentence introduces your literature review, expressing it without the article is customary. It suggests that literature review in general, or some unspecified amount of literature review, confirms your conclusion. There's really no distinction here between treating "literature review" as an abstraction or as a mass noun; either way, it takes no article. You could introduce your literature review with "A literature review confirms that…", but this leaves open the possibility that you're referring to someone else's literature review. That could be OK if the following text makes it obvious that you mean your literature review.

Sentences 1, 2, and 5 are fine either way in my opinion. I slightly prefer no article.

The third sentence should be either your way, or "An examination". I prefer your way with no article. "The examination" would make sense if you were referring to a particular examination that had been done in the past. Like, "The examination of the data revealed ..." But you're using present tense, which means "examination" is used in a more abstract sense. That logic does not apply to the other sentences because "the identification" could also make sense as the process of identification, not a particular identification that had been done.

The fourth sentence sounds better as "A review of the literature confirms that...", or "Review of the literature..." but if you don't mind sounding a little clipped, you could also put it your way, or "A literature review...".

You should not omit the article. Doing so is not common, whether in academic writing or not.

Perhaps you picked up the habit after noticing and subtly misanalyzing mass nouns. One of the features of academic writing is coining new terms by converting a mass noun to a count noun or vice versa. For example, "pedagogy" has recently been pluralized now that academic writing has turned its attention to different types of pedagogy (e.g. Indigenous vs. Western pedagogy).

So let's imagine that you've seen the word "pedagogies" and it seems like a count noun in your mental grammar. Later, you come across this sentence:

Pedagogy is a question not only of the means of teaching, but also of its ends.

Then you might (incorrectly) conclude that the determiner has been dropped from the beginning. In reality, it's being used as a mass noun here.

Let's look at your examples. All four of your opening nouns (identification, examination, application, review) are abstract and exist in this limbo between count and mass noun. However, the meaning they have in your sentences does not appear to be the mass meaning. This would be right:

Academics prefer to write about theory rather than application.

But this would be wrong:

We decided to investigate possible application of our theory.

Note that in the titles of academic publications, much like in newspaper headlines, none of this applies and you are certainly free to drop the determiner.