The Grue language doesn’t have words for “blue” or “green”. Instead Grue speakers have the following concepts:

grue: green during the day and blue at night

bleen: blue during the day and green at night

(This example is adapted from the original grue thought experiment.) To us, these concepts seem needlessly complicated. However, to a Grue speaker, it is our language that is unnecessarily complicated. For him, green has the cumbersome definition of “grue during the day and bleen at night”.

How can we wipe the smug smile off this Grue speaker’s face, and convince him of the obvious superiority of our own concepts of blue and green? What we do is sneak into his house at night and blindfold and drug the Grue speaker. We take him to a cave deep underground and leave him there for a few days. When he wakes up, he has no idea whether it is day or night. We remove his blindfold and present him with a simple choice: press the grue button and we let him go, but press the bleen button… Now he’s forced to admit the shortcomings of “grue” as a concept. By withholding irrelevant extra information (the time of day), grue does not provide any information about visual appearance. Obviously, if we told him to press the green button, he’d be much better off.

We say that grue-ness and time of day exhibit “informational synergy” with respect to predicting the visual appearance of an object. Synergy means the “whole is more than the sum of the parts” and in this case, knowing either the time of day or the grue-ness of an object does not help you predict its appearance, but knowing both together gives you perfect information.

Grues in deep learning

This whimsical story is a very close analogy for what happens in the field of “representation learning”. Neural nets and the like learn representations of some data consisting of “neurons” that we can think of as concepts or words in a language, like “grue”. There’s no reason for generic deep learners to prefer a representation involving grue/bleen to one with blue/green because either will have the same ability to make good predictions. And so most learned representations are synergistic and when we look at individual neurons in these representations they have no apparent meaning.

The importance of interpretable models is becoming acutely apparent in biomedical fields where blackbox predictions can be actively dangerous. We would like to quantify and minimize synergies in representation learning to encourage more interpretable and robust representations. Early attempts to do this are described in this paper about synergy and another paper demonstrates some benefits of a less synergistic factor model.

Revenge of the Grue

Now, after making this case, I want to expose our linguo-centrism and provide the Grue apologist’s argument, adapted from a conversation with Jimmy Foulds. It turns out the Grue speakers live on an island that has two species of jellyfish: a bleen-colored one that is deadly poisonous and a grue-colored one which is delicious. Since the Grue people encounter these jellyfish on a daily basis and their very lives are at stake, they find it very convenient to speak of “grue” jellyfish, since in the time it takes them to warn about a “blue during the day but green at night jellyfish”, someone could already be dead. This story doesn’t contradict the previous one but highlights an important point. Synergy only makes sense with respect to a certain set of predicted variables. If we minimize synergies in our mental model of the world, then our most common observations and tasks will determine what constitutes a parsimonious representation of our reality.


I want to thank some of the PhD students who have been integral to this work. Rob Brekelmans did many nice experiments for the synergy paper. He has provided code for the character disentangling benchmark task in the paper. Dave Kale suggested key aspects of this setup. Finally Hrayr Harutyunyan has been doing some amazing work in understanding and improving on different aspects of these models. The code for the disentangled linear factor models is here, I hope to do some in depth posts about different aspects of that model (like blessings of dimensionality!).

The work with Shirley Pepke on using CorEx to find patterns in gene expression data is finally published in BMC Medical Genomics.

Shirley wrote a blog post about it as well. She will present this work at the Harvard Precision Medicine conference and we’ll both present at Berkeley’s Data Edge conference.

The code we used for the paper is online. I’m excited to see what people discover with these techniques, but I also can see we have more to do. If speed is an issue (it took us two days to run on a dataset with 6000 genes… many datasets can have an order of magnitude more genes), please get in touch as we have some experimental versions that are faster. We are also working on making the entire analysis pipeline more automated (i.e. connecting discovered factors with known biology and visualizing predictive factors.)


Edit: Also check out the story by the Washington Post and on

Shirley is a collaborator of mine who works on using gene expression data to get a better understanding of ovarian cancer. She has a remarkable personal story that is featured in a podcast about our work together. I laughed, I cried, I can’t recommend it enough. It can be found on itunes and on soundcloud (link below).

As a physicist, I’m drawn towards simple principles that can explain phenomena that look complex. In biology, on the other hand, explanations tend to be messy and complicated. My recent work has really revolved around trying to use information theory to cut through messy data to discover the strongest signals. My work with Shirley applies this idea to gene expression data for patients with ovarian cancer. Thanks to Shirley’s amazing work, we were able to find a ton of interesting biological signals that could potentially have a real impact on treating this deadly disease. You can see a preprint of our work here.

I want to share one quick result. People often judge clusters discovered in gene expression data based on how well they recover known biological signals. The plot below shows how well our method (CorEx) does compared to a standard method (k-means) and a very popular method in the literature (hierarchical clustering). We are doing a much better job of finding biologically meaningful clusters (at least according to gene ontology databases), and this is very useful for connecting our discovery of hidden factors that affect long-term survival to new drugs that might be useful for treating ovarian cancer.

TCGA clusters



Here’s one way to solve a problem. (1) Visualize what a good solution would look like. (2) Quantify what makes that solution “good”. (3) Search over all potentials solutions for one that optimizes the goodness.

I like working on this whole pipeline, but I have come to the realization that I have been spending too much time on (3). What if there were a easy, general, powerful framework for doing (3) that would work pretty well most of the time? That’s really what tensorflow is. In most cases, I could spend some time engineering a task-specific optimizer that will be better, but this is really premature optimization of my optimization and, as Knuth famously said: “About 97% of the time, premature optimization is the root of all evil”.The docker whale

Abstract starfish

This one is just for fun. There’s no deeper meaning, just a failed experiment that resulted in some cool looking pictures.

Abstract bear


You have just eaten the most delicious soup of your life. You beg the cook for a recipe, but soup makers are notoriously secretive and soup recipes are traditionally only passed on to the eldest heir. Surreptitiously and with extreme caution, you pour some soup into a hidden soup compartment in your pocket.

The Information Sieve

When you get back to your mad laboratory, you begin reverse engineering the soup using an elaborate set of sieves. You pour the soup through the first sieve which has very large holes. “Eureka! The first ingredient is an entire steak.” Pleased with yourself, you continue by pouring the soup through the next sieve with slightly smaller holes. “Mushrooms, of course!” You continue to an even smaller sieve, “Peppers, I knew it!”. Since it is not a just a laboratory, but a mad laboratory, you even have a set of molecular sieves that can separate the liquid ingredients so that you are able to tell exactly how much salt and water are in the soup. You publish the soup recipe on your blog and the tight-lipped chef is ruined and his family’s legacy is destroyed. “This is for the greater good,” you say to yourself, somberly, “Information wants to be free.”

This story is the allegorical view of my latest paper, “The Information Sieve“, which I’ll present at ICML this summer (and the code is here). Like soup, most data is a mix of different things and we’d really like to identify the main ingredients. The sieve tries to pull out the main ingredient first. In this case, the main ingredient is the factor that explains most of the relationships in the data. After we’ve removed this ingredient, we run it through the sieve again, identifying successively more subtle ingredients. At the end, we’ve explained all the relationships in the data in terms of a (hopefully) small number of ingredients. The surprising things are the following:

  1. We can actually reconstruct the “most informative factor”!
  2. After we have identified it, we can say what it means to “take it out”, leaving the “remainder information” intact.
  3. The third surprise is negative: for discrete data, this process is not particularly practical (because of the difficulty of constructing remainder information). However, an exciting sequel will appear soon showing that this is actually very practical and useful for continuous data.

Update: The continuous version is finally out and is much more practical and useful. A longer post on that will follow.