I don't experience the emotion of finding things cute, but I'd like to understand the concept at least from an analytical perspective, both out of intellectual curiosity and to better empathize with people. I may add more mana to the bounty if warranted.
First, what I do know: There's an evolutionary incentive to consider your kids cute until they can take care of themselves. Same for opposite-sex adults, although there seems to be a subtle distinction between "cute" and "hot" that I don't get. Kids have relatively large eyes, so other things with large eyes also look cute, e.g. anime characters (except for https://fma.fandom.com/wiki/Father?file=Homuncurus.jpg I've been told). Similarly, babies have soft skin, and so do furry animals, so furry animals are cute ... except by that reasoning why aren't blankets cute?
Why are miscellaneous non-baby things like architecture (https://hpmor.com/chapter/5), math (https://www.reddit.com/r/math/comments/3citj1/whats_the_cutest_proof_you_know/), adult-size clothes (https://twitter.com/search?q=%22cute%20dress), etc. also called cute? Is there a general explanation, or is "cute" actually multiple distinct emotions that English doesn't have distinct names for?
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Architectural elements can have some properties of cuteness: round, smaller than expected, bringing to mind some small clumsy creature. This is already using the word loosely, I don't think 90% of people could find any building ever half as cute as a puppy.
"Cute" clothing is another indirect usage, probably meaning "associated and evoking childhood". Mostly people don't describe clothing as cute as such, they typically say that the person looks cute wearing it.
Maybe blankets can be sort of cute? But they are flat. Fluffy pillows or a round small bed covered in a nice blanket feels cuter to me.
Proofs can not be cute. When proofs are described as cute, the word is being used in the sense of "neat" or "clever". If you want to stretch thing very far, you could link clever proofs with cuteness via quality of "smaller than usual".
Do you know how the meaning of some words that mean a specific kind of positive/negative quality sometimes drop that "specific kind" part and increasingly come to mean "positive/negative" in general? How "awesome"/"cool"/"cringe" used to mean something specific before the meaning collapsed to almost precisely into "good"/"bad"? "Cute" is not immune to that and sometimes drifts towards just a general expression of liking something.
Distinction between "cute" and "hot" is probably in "young, warm, non-threatening, friendly, approachable" flavouring.
To import the signified "cute" to your mental manifold, I suggest running a text-to-image AI with the following series of prompts: "cute X", for many diverse values of X, as well as the opposite prompt, if supported ("X -cute", which should point at the opposite of cute). X being, for instance, "bear", "child", "sunset", "rhododendron", "medulla", or other typically human-associated series of tokens.
You may also have someone else create a validation and test set of image "X" and "cute X", to assess your loss while your acquire this concept. If you have generation capabilities yourself, a RL-type setup where you would be rewarded/punished by someone else for succeeding/failing to create cute images would speed up your acquisition.
As always, supervised learning is best, but I believe you can acquire this crucial-to-your-performance concept even using self-supervised learning.
This is a fascinating and hilarious use of bounty so I'll add my 2 cents, don't feel obligated to give me mana. Also, the AI making the cover banner for you also had a hard time comprehending cuteness and added some pretty cursed duck bears and baby faces.
Oxford defines cute as "appealing or pretty in an endearing way" and as someone who uses the word frequently I would say this is accurate and straight-forward. I describe something as cute when is is visually appealing and attractive to me. If part of somethings appeal is due to characteristics of being small, innocent, tenderly fragile, or otherwise worthy of protection I might also describe it as such. However, this is still very broad and to your point does encompass many different emotions and situations within one word use. To that point, the secondary dictionary definition of "cute" is "sexually appealing" but is tagged as North American slang. Here it has become blended with "hot" and can have different meaning in context.
I am sure there are things you find visually appealing. At that point its a question of distinction: I find large dark brutalist architecture visually appealing but would describe it as "awe-inspiring" or "epic", never "cute". If I found a small colorful cottage appealing in its architecture I may describe it as "cute". I'm sure due to the many complexities of personal preference some individuals find their aesthetic attraction skewed towards certain things.
Think about what you find aesthetically or emotionally appealing and how you would describe its characteristics. Again, I would imagine you can relate to that feeling (which in my opinion is a broader phenomenon which "cuteness" is one categorization of)
People find things cute due to a combination of factors such as innocence, small size, facial features resembling infants, and positive associations, triggering a nurturing instinct and eliciting positive emotions. I believe there is some amount of social aspect to it as well. Part of the problem is there is alot of people with alot of different opinions on the matter. Plenty of people don't find babies cute at all.