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FaceMath: An Algebra of Ideas in A.I.

I like to call it “an algebra of ideas”, because we are using basic math to add concepts together, forming compound concepts.

Back in this cartoon AI article, we saw how blocks of text could be turned into special fixed-length lists of numbers (embedded into vectors), with the clustering of those vectors revealing information about the topic of groups of comics.

By finding good encodings (i.e., embeddings) for a set of images, you can start to do the same kind of “feature math” we did on words, to modify the pictures in cool ways.

However, the neural network used to model faces (e.g., autoencoder or gan) is different than the type of math used to model words and their relationships to each other (word embedding with word2vec, gloVe, fastText, ELMo, BERT, XLNet, etc.).

We see on page 10 that the vectors for “man with glasses” minus “man withough glasses” plus “woman without glasses” gives us a face of a woman with glasses.

It’s basically the machine learning version of a zip file: you take an image, compress it down to a small amount of data, and then try to use that data to redraw the original image.

This basically means that the neural network needs to learn to compress and then decompress the image, and in doing so, it learns the essential features that make up faces.

If it can learn about faces, then we can use the trained model to do cool things like generate new faces, morph between faces, and add concepts to faces, like adding glasses, or subtracting one gender and adding another, or reducing age, and so on.

The overall equation for this was: “original face” — “average of faces original face’s age” + “average face of new age” And so to turn someone 35 into a 5 year old, you would go: i=image of 35 year old a=average vector of the embeddings of 35 year old faces n=average vector of the embeddings of 5 year old faces and when you push into the decoder of the autoencoder the vector i-a+n, you get a baby face version of the original face.

This turned out to work a lot better for very young faces than very old faces, since the blurriness of the images made it hard to show wrinkles and that kind of thing.

And here is the gif of this magical process: Adding Glasses worked pretty well: And it worked on me as well: The following is a morph of Sam face maximizing feminine features: And now let’s talk about gneerating brand new faces.

We can do a random walk in the embedding space to get faces like this: And the model seems to understand lighting: And faces nearby in the embedding space look similar: The generated faces can be pretty detailed when you blow them up:

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