Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Regularization Causes Modularity Causes Generalization, published by dkirmani on January 1, 2022 on LessWrong.
Epistemic Status: Exploratory
Things That Cause Modularity In Neural Networks
Modularity is when a neural network can be easily split into several modules: groups of neurons that connect strongly with each other, but have weaker connections to outside neurons. What, empirically, makes a network become modular? Several things:
Filan et al.[1]:
Training a model with dropout
Weight pruning
L1/L2 regularization
Kashtan & Alon: Switching between one objective function and a different (but related[2]) objective function every 20 generations
Clune et al.: Adding penalties for connections between neurons
Modularity Improves Generalization
What good is modularity? Both Clune et al. and Kashtan & Alon agree: more modular networks are more adaptable. They make much more rapid progress towards their goals than their non-modular counterparts do:
Modular neural networks, being more adaptable, make faster progress towards their own goals. Not only that, but their adaptability allows them to rapidly advance on related[2:1] goals as well; if their objective function was to suddenly switch to a related goal, they would adapt to it much quicker than their non-modular counterparts.
In fact, modular neural networks are so damn adaptable that they do better on related goals despite never training on them. That's what generalization is: the ability to perform well at tasks with little to no previous exposure to them. That's why we use L1/L2 regularization, dropout, and other similar tricks to make our models generalize from their training data to their validation data. These tricks work because they increase modularity, which, in turn, makes our models better at generalizing to new data.
How Dropout Causes Modularity
What's true for the group is also true for the individual. It's simple: overspecialize, and you breed in weakness. It's slow death.
Major Kusanagi, Ghost in the Shell
Training with dropout is when you train a neural network, but every neuron has a chance of 'dropping out': outputting zero, regardless of its input. In practice, making 20-50% of your model's neurons spontaneously fail during training usually makes it much better at generalizing to previously unseen data.
Ant colonies have dropout. Ants die all the time; they die to war, to famine, and to kids with magnifying glasses. In response, anthills have a high bus factor. Not only do anthills have specialist ants that are really good at nursing, foraging, and fighting, they also have all-rounder ants that can do any of those jobs in an emergency:
Dropout incentivizes robustness to random module failures. One way to be robust to random module failures is to have modules that have different specialties, but can also cover for each other in a pinch. Another way is to have a bunch of modules that all do the exact same thing. For a static objective function, from the perspective of an optimizer:
If you expect a really high failure rate (like 95%), you should make a bunch of jack-of-all-trades modules that're basically interchangeable.
If you expect a moderate failure rate (like 30%), you should make your modules moderately specialized, but somewhat redundant. Like ants!
If you expect no failures at all, you should let modules be as specialized as possible in order to maximize performance.
Do that, and your modules end up hyperspecialized and interdependent. The borders between different modules wither away; you no longer have functionally distinct modules to speak of. You have a spaghetti tower.
Why would modules blur together? "Typically, there are many possible connections that break modularity and increase fitness. Thus, even an initially modular solution rapidly evolves into one of many possible non-modular soluti...
