François CholletVerified account

Once you have such a curve, you can walk on the curve to make sense of *samples you've never seen before* (that are interpolated from samples you have seen). This is how a GAN can generate faces that weren't in the training data, or how a MNIST classifier can recognize new digits

If you're in a high-dimensional encoding space, this curve is, of course, a high-dimensional curve. But that's because it needs to deal with the encoding space, not because the problem is intrinsically high-dimensional (as mentioned earlier).

Now, how do you learn such a curve? That's where deep learning comes in.

I'm back, just wanted to add one important note to conclude the thread: deep learning models are basically big curves fitted via gradient, that approximate the latent manifold of a dataset. The *quality of this approximation* determines how well the model will generalize.

The ideal model literally just encodes the latent space -- it would be able to perfectly generalize to *any* new sample. An imperfect model will partially deviate from the latent space, leading to possible errors.

Being able to fit a curve that approximates the latent space relies critically on two factors: 1. The structure of the latent space itself! (a property of the data, not of your model) 2. The availability of a "sufficiently dense" sampling of the latent manifold, i.e. enough data

You *cannot* generalize in this way to a problem where the manifold hypothesis does not apply (i.e. a true discrete problem, like finding prime numbers).