Compression is a subtle and powerful thing. The ability to compress is closely related to prediction: if you can predict 95% of the moves a chess grandmaster wi

Compression is a subtle and powerful thing. The ability to compress is closely related to prediction: if you can predict 95% of the moves a chess grandmaster will make, you can compress the game by explicitly representing only the other 5% of moves. If you could perfectly predict (or equivalently, compress) the actions of a real-world human being, you'd have solved AI. Despite their simplicity, Markov chains are used throughout modern statistical AI, e.g., the Google Translate language model is essentially a big Markov chain. The fact that deep networks can apparently form better generative models across a wide range of applications (no one has ever actually gotten these kinds of image generation results from Markov chains) means that they really are getting at more interesting structure. They're not a panacea, but it's still a pretty big deal.