I think the implication here is that it is learned during pre-training. You'll usually do some sort of pre-training (think running a model through imagenet) that boils the image down into the vector embeddings, and then you have the model reconstruct the original image using only the vectors. This is basically a reduced order modeling approach. After you have an encoder that is able to turn images into vector embeddings that contain enough information to reconstrust the original image, you can then use that pre-trained network and apply it to another task with similar images. e.g. you pre-trained on imagenet reconstruction, and then you adjust the task to detect whether there is a dog riding a bicycle in the image through regular supervised training. This approach has proven to be better than just training a network from scratch (or a generic pre-trained network) to detect bicycle dogs.

> to detect bicycle dogs.

What?

Educational videos should have a section saying: "This video was tested on the following audiences: ..." And "they had many questions, which I incorporated back into the talk".

Without this, you might as well be watching "Introduction to X, for experts in X". Or "Introduction to X, by someone who is trying to figure out X".

So a transformer is just a "graph" network. You have a bunch of nodes in the graph, and depending on the kind of transformer, the nodes form different topologies. Now, here is the catch, with graph neural networks, we may reorder the nodes, and as long as the edges are kept okay, we are fine.

This is because graph networks are permutation invariant, but vision tasks are not. Nodes do not necessarily know their ordering with respect to the input. We use positional embeddings to inform the nodes where they are with respect to the input, because it matters.

To see how, or why, take any image, flip it upside down, cut it into patches, and then flip the patches.

The patches know what their content is, but not where. The edges in the graph merely point to the neighbours for further computation.

Positional embeddings are just vectors that you index or compute at runtime. These vectors then are concatenated or added onto the vectors of the patches or tokens.

We use positional embeddings for all sorts of tasks, such as text (position of token), vision tasks (position of patch), or even sound tasks (e.g. point in time).

Hi, author of the article here.

They act as a "position signal" that modifies the patch embedding. The learned signals are similar to other neighbouring position signals, and the later layers of the model will use the "similarity" between signals to identify the proximity/order of different patches.

There is no explicit mechanism that tells the network to make neighboring position embeddings similar, it's just a result of the training that fortunately works and seems logical.

I can definitely try to explain further if needed

What’s the advantage of learning this positional embedding vs hardcoding one that has the desired properties of location similarity?

Hi! Are these positional embeddings literally made by concatenating the patch embedding with a number, then passing that through the next layer, as suggested by the figure under "Images to Patch Embeddings"?

It's the most confusing part of transformers for me. How do we train the module that creates these embeddings?

That... still doesn't explain anything to me?

Like, say the embedding of a patch was just a vector (a, b, c, d). To have the attention layer "understand" position, you could just concatenate the patch's position to get (a, b, c, d, x, y). I understand that.

What I don't understand is:

- Why on earth are cosines involved?

- What does that mean:

> During training, these embeddings converge into vector spaces where they show high similarity to their neighboring position embeddings — particularly those sharing the same column and row

Does it just mean that the network learns that "x = 1" is similar to "x = 2"? Because presumably, that's not very valuable by itself, is it? It's something you could easily hardcode.

Presumably there's a step where the network goes "if there is pattern A and pattern B and both patterns have a short distance between them in the positional embedding then we have C" where A B and C are neural network magic... but your article is explaining that step, I don't understand the explanation.

I think something that can help this situation is to not use "big" machine learning words such as "patch embedding".

This is one of the issues with a lot of machine learning articles out there (not to nitpick on you, sorry); there are almost always easy and illustrative examples that you can use to break this down into a simpler explanation.

In NLP, the simplest positional embeddings are just a sequence of [0, 1, 2, 3, 4, .. n] with n being the length of a sentence. Once you start processing text, you split it into individual embeddings for each word, getting a list of embeddings [E_1, E_2, E_3, ... E_n]. Then you just sum up this embedding vector and positional embeddings vector across the first axis, so each embedding is increased by its positional embedding in other dimensions. This somehow works for encoding position as attention is dumb and doesn't keep positions in mind but you just added some sort of a positional signal attention will recognize. There are many ways to model positional embeddings, e.g. by generating sine/cosine curves etc. You can extend this approach to ViTs.