François CholletVerified account

Generalization in deep learning is interpolation along a latent manifold (or rather a learned approximation of it). It has little to do with your model itself and everything to do with the natural organization of your data

Differentiability & minibatch SGD are the strengths of DL: besides making the learning practically tractable, the smoothness & continuity of the function & the incrementality of its fitting work great to learn to approximate latent manifold. But its strengths are also its limits

The whole setup breaks down when you are no longer doing pattern recognition -- when you no longer have a latent manifold (any kind of discrete problem) or no longer have a dense sampling of it. Or when your manifold changes over time.

The game of go and chess are highly discrete. One slightly wrong move and the game is lost. Still AlphaZero does very well. Even move proposals from a ResNet (without search) beats very good amateur go players.

These games involve a mixture of pattern recognition (what a player would call 'intuition') and explicit reasoning. It's not all or nothing. The better you are at pattern recognition, the less you need to rely on reasoning, and inversely.

AlphaZero illustrates this trade-off well: the better the convnet the lesser the need to rely on MCTS. It also really shows how explicit reasoning (e.g. MCTS) enables much greater experience-efficiency in achieving high skill (i.e. greater intelligence): (cont)

playing purely based on pattern recognition (intuition) requires an insane amount of training data (a dense sampling of the manifold). That's not how humans play: for best efficiency, we rely on an interconnected *mix* of intuition and explicit reasoning & planning.

The amount of training data is irrelevant. The fact that AlphaZero captures the discrete landscape of chess and go better than (most) humans demonstrates that DL does not require a continuous domain to work well.