I was actually agreeing and additionally I'm a neuro computational researcher who studies biologically inspired algorithms.

Since apparently you don't understand the difference between statistical optimization and probabilities I'll give you a lesson.

Statistical optimization is where you'll take a target vector, something like a one hot vector; (Example 1,0,0.. where 0th index is cat, 1st index is dog and 2nd index is fish.) Then you will compare it against the model's guess with Euclidean distance or some other form of accuracy measurement. (Example 0.5,0,0 is the guess and 1,0,0 is the answer. The distance being 0.5) every algorithm and loss function is different.

You'll take this distance and you'll, say, well hey all I have to do to get this answer next time is adjust all the parameters that led to that answer and I'll always classify this input as a cat.

As you have rightly stated, this requires a target vector and that is the label. As you again rightly stated, this is not the way the brain works. Even if a handful of pixels were off I could get a completely different answer and infact that is the basis of adversarial attacks.

What you are incorrect about, is your statement that probabilities need labels and brains don't use probabilities. There are a couple of biologically inspired methods but the type I study are sparse distributed codes. But to your first incorrect statement, probabilities need populations not labels. labels are just easy ways of forcing models to express the probabilities the way we want to see them. Every sound wave has an infinite number of patterns that can be created from slices of it, ranging from the whole sound to tiny portions of it. Every pattern has a probability of occurring again, whether it has a definitive label for what that pattern is, doesn't matter. The pattern exists with or without a label. This is what the brain takes advantage of.

The brain first discretizes patterns into finite ranges. The cones and in your eyes, the stereocilia in your ear, or the taste buds on your tongue, they all convert infinites into discretes. Even though there are infinite portions of light or sound between two arbitrary points, your body evolved to sense specific points on the spectrum at specific intensities. You can think of it as breaking up the infinite definition of the rainbow into 256 color resolution. In this way, your brain can reliably pick out patterns without having to be exact.

It's a lot more complicated, and to be frank technically only theories exist, but essentially your brain saves exactly what it sees. A pattern comes in, it saves it. Your neurons reach out and strengthen on nerves that fire or give a signal. That is your neurons essentially saving information. The interesting part is that they now have created a pattern (code) of neurons that fire. So, other neurons will save that code, but not just to make a new code for a new codes sake. This new code will be based on signals from combining other senses in the body. So in fact, the code that fired for the red ball falling to the ground will be different for the green ball falling to the ground. They will be similar codes, but the color code from your vision will make it a distinct code.

So what do these codes have to do with probabilities. Let's take the ball falling example. Not only are there codes for what a thing looks and smells or feels like. There are codes made from the last time a neuron fired. So in fact, if a ball is suspended in the air, and the next frame of a movie you see it has gone down a little bit, then the next frame a little bit more. We'll shit, what's the probability it continues to go down. The reason your brain can predict this is because there are a general set of codes you developed early in life that light up for falling objects. Regularly and reliably. This is proven with experimental data. You can look up the Bill Clinton neuron. A code similar enough to all falling objects that if you've seen one falling object you can predict closely enough other falling objects.

Their study though can seem to suggest that one face is saved in a single neuron. But that is a bit misleading leading because you'll actually have a whole field of neurons lighting up for a face. We can only test a few.

There are other consequences of sparse distributed codes. I really didn't mention the other features of sparsity or distribution, but you can look them up your self. The sparsity alone has its own powerful implications, you can look up Pentti Kanerva for more info on that. This is already too long though.

Regardless, don't confuse probabilities with statistical optimization. I did when I first started out, but I didn't look like an ass when talking to people about it. Good luck.