Arguably, the central achievement of the deep learning era is multi-layer neural networks' ability to learn useful intermediate feature representations using a supervised learning signal. In a supervised task, it's easy to define what makes a feature representation useful: the fact that's easier for a subsequent layer to use to make the final class prediction. When we want to learn features in an unsupervised way, things get a bit trickier. There's the obvious problem of what kinds of problem structures and architectures work to extract representations at all. But there's also a deeper problem: when we ask for a good feature representation, outside of the context of any given task, what are we asking for? Are there some inherent aspects of a representation that can be analyzed without ground truth labels to tell you whether the representations you've learned are good are not? 

The notion of "disentangled" features is one answer to that question: it suggests that a representation is good when the underlying "factors of variation" (things that are independently variable in the underlying generative process of the data) are captured in independent dimensions of the feature representation. That is, if your representation is a ten-dimensional vector, and it just so happens that there are ten independent factors along which datapoints differ (color, shape, rotation, etc), you'd ideally want each dimension to correspond to each factor. 

This criteria has an elegance to it, and it's previously been shown useful in predicting when the representations learned by a model will be useful in predicting the values of the factors of variation. This paper goes one step further, and tests the value representations for solving a visual reasoning task that involves the factors of variation, but doesn't just involve predicting them. In particular, the authors use learned representations to solve a task patterned on a human IQ test, where some factors stay fixed across a row in a grid, and some vary, and the model needs to generate the image that "fits the pattern". 

https://i.imgur.com/O1aZzcN.png

To test the value of disentanglement, they looked at a few canonical metrics of disentanglement, including scores that represent "how many factors are captured in each dimension" and "how many dimensions is a factor spread across". They measured the correlation of these metrics with task performance, and compared that with the correlation between simple autoencoder reconstruction error and performance.

They found that at early stages of training on top of the representations, the disentanglement metrics were more predictive of performance than reconstruction accuracy. This distinction went away as the model learning on top of the representations had more time to train. It makes reasonable sense that you'd mostly see value for disentangled features in a low-data regime, since after long enough the fine-tuning network can learn its own features regardless. But, this paper does appear to contribute to evidence that disentangled features are predictive of task performance, at least when that task directly involves manipulation of specific, known, underlying factors of variation.