: How can I stop overusing "I" in my writing? I won't edit this question, so you can see how much I use it. The current count is 3 times. I've been told that the solution is to revise, revise,

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Often, you can avoid or elide the subject by adjusting the phrasing. This is more passive, but easily understandable. To avoid too much passive voice, you can also make other items the subject.
The method we used was...
The method used was...
I found that the second device operated more efficiently...
The second device operated more efficiently...
After I modified the algorithm, the result were closer to the ideal case.
With a modified algorithm, the results were closer to the ideal case.
Using a modified algorithm produced results closer to the ideal case.
Technical writers have to do this all the time to avoid portraying computers and software as actors in sentences, and to avoid personifying concepts.

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Generalizing some answers here:

Use a different perspective - "I" is 1st person, switching to a neutral, 3rd person or
2nd person ("you") will implicitly prevent the use of "I".
Alternate "I" with other pronouns:

Third person pronouns - E.g., "one could take", "some say". See DPT's answer for more detail. You should be able to use this style with 1st person perspective.
First person pronouns - Specifically "my". Switching between the two would presumably lead to a 50% reduction in the use of "I". Adding "we" and "our" could be another consideration.

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The following information may just help you to stop overusing “I” in your writing. It's a powerful technique because it draws on nothing less than your desire to stay alive. Got your attention? Then read on.

I'm currently engrossed in a book called Ageless Body, Timeless Mind by Deepak Chopra. In it he describes the implications of a study about Heart Disease by Larry Scherwitz, a University of California psychologist who:

taped the conversations of nearly six hundred men, a third of whom
were suffering from heart disease, the rest of whom were healthy.
Listening to the tapes, he counted how often each man used the words
I, me, and mine. Comparing his results with the frequency of heart
disease, Scherwitz found that men who used the first-person pronoun
most often had the highest risk of heart trouble. In addition, by
following his subjects for several years, he found that the more a man
habitually talked about himself, the greater the chance he would
actually have a coronary.

Counting the times a person said "I" was an ingenious way to quantify
self-absorption, and to me, there's something very fitting in the fact
that the less you open your heart to others, the more your heart
suffers. The antidote, Scherwitz concluded, was to be more giving: "
Listen with regard when others talk. Give your time and energy to
others; let others have their way; do things for reasons other than
furthering your own needs." In those words, he goes beyond the
quantifiable data to issues of love and compassion, which appeal very
much to our intuitive sense that an open, loving person should age
well.

You can draw your own conclusion from this, but if it doesn't give you a little more desire to stop overusing 'I' in your writing then I don't know what will.

Good luck with your writing.

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You can talk about you.
This is a sales letter trick, often used in manuals as well. Make all your "narrative" lines as "you," (the reader), or some equivalent.

I will also try to show that the unrelaxed difference density is still not equivalent to the transition density.

Hopefully you will see the unrelaxed difference density is still not ...

I can't find the definition of {a} in the paper,

You will not find a definition of {a} in the paper ...

Importantly, we always start from the set of ground-state MO coefficients

It is important you start from the set of ground-state MO coefficients ...

Because I don't want to mess with the block-diagonal structure of PΔMO, I will transform T to the MO basis:

You don't want to mess with the block-diagonal structure of PΔMO, so you can transform T to the MO basis:

I am not sure if the MO coefficients in the double sum can be simplified, but it doesn't matter; assume they are unity.

Whether or not the MO coefficients in the double sum can be simplified or not, you will find it does not matter. For example, [you can] assume they are unity.
And so on. Everything you attribute to "I" or "We", rewrite to attribute to the reader.
Several studies of this technique in Sales have shown it is strangely and wildly effective; far more people will read to the end of a sales letter if it addresses them specifically as "you" and "your". It is talking about you, your children, your home, your car, your retirement, your entertainment options. Do you want to put all that at risk? We want to hear from you, listen to you, help you achieve your goals. You might think people would see through such a transparent trick, but you'd be mistaken, it still works for advertisers, and it can work for you too.

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Put it in Neutral.
As if YOU did not write the paper, but must describe the action line by line. An example from your first linked example:

I will also try to show that the unrelaxed difference density is still not equivalent to the transition density.

An attempt will be made to show the unrelaxed ...

I can't find the definition of {a} in the paper,

The paper apparently contains no definition of {a} ...

Importantly, we always start from the set of ground-state MO coefficients

It is important to start from the set of ground-state MO coefficients ...

Because I don't want to mess with the block-diagonal structure of PΔMO, I will transform T to the MO basis:

The block-diagonal structure of PΔMO is preserved by transformation to the MO basis:

I am not sure if the MO coefficients in the double sum can be simplified, but it doesn't matter; assume they are unity.

Whether the MO coefficients in the double sum can be simplified or not will not matter; assume they are unity.
And so on.The "couching in qualifiers" speech pattern is something we called Programmer's Disease when I was in college (four decades ago), but plagues scientists generally; a side-effect of learning that damn near everything has exceptions and to be accurate requires qualifiers. So you gain accuracy by restricting the domain of cases you are describing.
However, to laymen and undergrads, every qualifier subtracts certainty from what you are talking about, thus the more qualifiers you use, the closer you asymptotically approach the state of having said nothing at all they can understand.
If they push back with questions or qualifiers of their own, they prove their ability to process a restricted domain, so acknowledge your overreach in the interest of simplicity and use qualifiers to restrict the domain then.

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I see this a lot in unpublished writing (including my own early drafts): "I entered the room and saw a red couch and a bookcase. I thought it was a particularly nice red. I heard the clock ticking."

Remember that we, the readers, know that the words and ideas are coming from you, the writer. So you can just say stuff rather than saying that you think it.

Look for "I thought..." "I saw..." "I felt..." and in a surprising number of cases you can delete that phrase and tweak the wording a bit.

So... "In the room was a red couch and a bookcase. It was a particularly nice red. The clock ticked."

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As a crazy, obviously not to be taken seriously suggestion: have you considered not writing in English? English places a lot of importance in the subject, and therefore in pronouns. English also places way too much importance on the self. The self is so important, it is written with a capital letter! Maybe it could explain some things about how North American culture shaped itself. Thing is, other languages have many tools to avoid repetition of the singular form of the first person: latin languages have several tools to imply you are talking about yourself without actually using pronouns, and Japanese has several ways to present yourself, which give way more information about your person and your personality than the English "I".

Obviously you can't change your mother language, and learning a new language is not something you can do in a fingersnap, so onto the more realistic side of the answer, consider not using first person when writing literature in English. Many (English) writers consider first person narrators the mark of an amateur, probably because the repetition of the first person pronoun feels wrong, and unless you make a conscious effort to avoid it as much as possible, it will look bad. This phenomenon doesn't happen as much in other languages due to not having to repeat the same pronoun over and over being way easier, contrary to how difficult it is to do in English, depending on what you want to express.

As a more generic advice, consider revising every single one of your sentences containing an "I", and check if you can use conjuctive words to take advantage of your first reference to the subject in order to not have to repeat yourself. Consider as well to refer yourself as "we" when it makes sense, or using the passive voice, and when there is no other way but to refer to yourself and only yourself, not your actions or your work, embrace the "I", for English was designed for this.

As a sidenote, this post was written with avoiding the singular form of the first person in mind. In cursive are marked the expressions where an "I" accidentally slipped in the first draft of the answer. "Maybe" used to be "I guess" (it is uncertain for everyone, so it makes no sense to explicitly self-signal myself, for my guess is as good as everyone else's), and "consider" replaces "I would consider" (because why should you care who makes the recommendation, specially considering it isn't coming from an authority in this subject?). So it is certainly possible to avoid referring to the self when expressing an opinion, it just takes a conscious effort and some proofreading, but it's not like anyone will object if they read a few "I", so don't sweat it too much.

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You go through piece by piece because you will want to assess each instance. Sorry. That's my answer. Someone may have an easier answer, but easy does not mean better. Look at each instance. Just do it.

Start a list of phrases to swap. i'll edit your piece and bold the edit's. This is one quick pass.

I won't edit this question, so you can see how much I use it. The
current count is 3 times. Some say the solution is to revise,
revise, revise, but is there a particular strategy for editing that one could take? I never really learned editing strategies other than
to just...do it. Are there patterns to look out for to avoid this
while writing something, to retrain myself? Are there resources
for writing less casually in the area somewhere between non-fiction
and technical writing? "When is it acceptable to use the first person
in technical reports" doesn't help, because not everything
is a technical report. It could be a comment on GitHub, an email, or
especially some of my longer Stack Exchange posts, where (deleted) my
preferred initial style is to build a narrative that (deleted) communicates a problem or figures something out. Part
of this habit comes from the perceived need to couch every scientific
statement (deleted) with some "I think-" or "Most likely"-type
language, and it seems to have pervaded my writing ever since the end
of undergrad. The result is long blocks of text that ramble too much
and contain anywhere between one "I" every two sentences to two "I"s
every sentence. Writing a science PhD dissertation did not break this
habit. Here and here are concrete examples. Upon rereading, maybe
these aren't so bad, but they seem to overuse "I"
because of their rather casual style.

Are you female? Are you young (under 30)? Here's some reporting that shows youth and gender impact use of first person pronouns.

Knowing that, and knowing that 'old white men' are generally in charge and have been historically within my culture, was enough for me to break habits I did not personally want.

If you'd like to cede your power (as an anonymous individual) in writing, you can ignore that information. When I see a post riddled with "I's" I assume youth.

If you'd like to understand trends in society, you can take the data and interpret it to your best ability, however you like, your schema, what fits your experience.

Again, those particular data were enough to help me break habits. Just do it. There are enough roadblocks up to young people. Appearing self-indulgent works against you.

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