https://arxiv.org/ftp/arxiv/papers/2009/2009.07485.pdf, I 've updated in the article also.

What people mean when they say AI is not truly learning is that often the most impressive results are coming from extremely big models. For example, almost all the top AI scientist takes dig on Large language models, because we don't know whether they learned something or it just memorized all the possible combinations. Why people believe AI is not truly learning is that there are papers that show that AI was unable to generalize to simple mathematical equations.

x³ + xy² + y (mod 97), AI was unable to generalize to this simple equation.

https://medium.com/aiguys/paper-review-grokking-generalization-and-over-fitting-9dbbec1055ae

https://arxiv.org/abs/2201.02177

Because VC dimension of kernel SVM is infinite and thus they can create extremely curved boundaries in lower hyperdimension.

What I mean to say by that the biggest cause for Adversarial attacks is that NN creates linear boundaries locally, that's why Kernel SVM are the best defense against adversarial attacks.

Even I don't know how VAE learn that. But recent paper that Neural networks can be written exactly like decision trees proved mathematically that NN are also decision tress but with added hyperspace.

https://arxiv.org/pdf/2210.05189.pdf

Read this paper, it's been proven that neural networks are decision trees, not a mere approximation but precisely that only. 3rd line in the abstract.

The argument goes much further, NNs are not exactly learning the data distribution. If they had, the affine transformation problem would have been already taken care of, there would have been no need for data augmentation by rotating or flipping. Also approximating any algorithm doesn't necessarily mean the underlying data is following a distribution made out of any known algorithm. Also, Neural network struggle even to learn simple mathematical functions, all they do in the approximation is make piecewise assumptions of algorithms.

Here's the grokking paper review that told that NN couldn't generalize to this equation:

x³ + xy² + y (mod 97)

Article: https://medium.com/p/9dbbec1055ae

Original paper: https://arxiv.org/abs/2201.02177

I've tried adding information from a lot of other resources. Not just one paper. And all of them are mentioned in the article.

So the paper which talks about the Spline theory of DL says that even in latent representation NN are incapable of interpolation and that's a very important thing to know about. If we know this then we can design loss functions that works to better understand the global manifold structures.

It might behave in a similar fashion to DT, but DT doesn't make abstract feature representation and that is something important.

It does, if we know that NN behaves like DT then we can design new loss functions that take the internal structure into account. One of the research areas in this regard is Lipschitz Regularization. Adding such regularization makes NN behave more smoothly.

This paper is a bit short, I've drawn conclusions from multiple papers like Spline's theory of Deep learning, why adversarial attacks exist, and the interpolation/extrapolation regime of Neural Nets.