The weight of the cow: Dealing with bias in datasets

One of the best science books I read this year is “Superforcasters”, by Philip Tetlock. The story of how this book got to be written is just about as fascinating as the book itself, and I strongly recommend it to both scientists and non scientists.

Today I would like to talk about something that I am surprised wasn’t discussed in the book. As many posts on this blog, this is something that may or may not be an original idea: all I know is that it occurred to me and I thought it was worth sharing, and I haven’t heard of it in the forecasting world.

How to pool forecasting data to reduce bias

Early in the book, Tetlock gives an example of the “wisdom of the crowd”. At a fair, people are asked to guess the weight of a cow. Taken individually, some guesses are quite far from the real value. But the average of all the guesses turns out to be almost exactly equal to the real weight of the cow.

He uses that example to illustrate the fact that individual people can be biased, but when you average all the guesses, the biases cancel each other. Imagine each guess as having two components: the signal and the noise. The signal represents all the valid reasons why a person might have a good estimation of the weight of the cow: they know what is a cow and what things weight in general, and maybe this particular person grew up in a farm and knows really well about cows, or maybe they’re a weightlifter and knows really well about weights. The noise represents all the reasons why they might be biased. Maybe they’re a butcher and often overestimate the weight of what they sell to increase the price. Maybe they raise pigs and underestimated the weight of the cow because it’s so much bigger than a pig.

By averaging all the guesses, you are making strong assumptions.
You assume that people’s biases are opposite and equivalent.
Therefore by averaging, the noise components should cancel each other out and you should be able to get only the signal: the wisdom of the crowd.


These are reasonable assumptions that are used by default in many different fields. Noise is supposed to be random, while the signal contains information about something, therefore not is not random. Most people know what a cow is and most people know roughly what things weight. But in the case of human-driven forecasting, these assumptions are not perfect.
1. There is no reason why the bias should be evenly distributed. (In sciency terms: the probability distribution of the noise might not be a uniform distribution). If your crowd is made of 30 cheating butchers (overestimating weights) and 10 greedy clients (underestimating weights), your biases may be opposite but they are not evenly distributed. Even if the clients bias happen to be exactly opposite to the butchers bias, averaging the 40 guesses will not give you the right answer, because you have many more butchers in your population. It will give you an overestimated weight. Instead you should pool the data: average the clients guesses (pool A), average the butchers guesses (pool B), and then take the average of the results of of pool A and B.
2. There is no reason why the biases should be exactly opposite. (The distribution of the noise might not be 0-mean).
Ideally, you would know by how much butchers tend to overestimate (say on average +5% of the total weight) and by how much the clients tend to underestimate (say -10%). If you have this information, you can use it to weight your pooled data before putting them together. In this example, you would want to give less weight to the clients pool because you know that usually, their bias is higher than that of the butchers.

So if you have some forecasting data and you want to get the best forecast out of it, there are two things you should do before making averages.
First, identify all possible sources of biases and form pools based on this information. Repeat this step as many times as needed for different repartitions. If you are doing political forecasting, people might be biased in favor of their candidate: divide your data in political parties (repartition A). If women tend to have different political biases than men for some reason, identify that reason and divide your pool in men and women (repartition B). The more (verifiable) causes for bias you can find, the more you will be able to cancel them out.
Second, quantify the bias so you can attribute weights to your pools. For that you will have to rely on previous data and make guesses.
Finally, make your averages per repartitions. You will have as many averages as the number of repartitions you made. You can decide to make a final average out of this data, or you can go meta and give weights to your repartitions. If you are quite sure that repartition A captures a real cause for opposite biases, but less sure about B, give less weight to B.

Now of course, it should be noted that it isn’t always worth doing all this work. If you have data about guessing a cow’s weight, maybe just do a simple average. The result might be good enough and the extra work is not worth your time.
But if you are gathering data about whether country A and country B are going to start a war in the next 3 months, it might be worth putting a little bit more effort into pooling your data. It doesn’t have to be data directly produced by people: it can be governmental data, numbers from different agencies, it can be you trying to predict what people you know will do next… There is always place for bias anyway.
In addition, clearly identifying the source of bias in your data allows you to notice what data may be missing (if all your pools are biased in the same direction), and it allows you to update your forecasts efficiently. When you come into possession of new data, it can be hard to decide how much it should change your original forecast. But if you can readily identify to which pools the data belongs, updating is much easier.

Happy forecasting! The Good Judgement Open project is a good place to start (you don’t have to be a scientist at all, just give your opinion).

Deep Irrationality Cares About Facts


Bansky – Geisha from “Better in than out” – Wikimedia commons


I think all decisions we take are based on irrationality — but this irrationality can appear at different levels.

Paradoxically, when irrationality is at a deep level, opinions are easier to change. When irrationality is at the very last of the decision process, it is very difficult, if not impossible to operate change.

One of my most irrational opinions is that I love living in Japan. It is irrational in the sense that there is no reason for that opinion. I can make up reasons, I can rationalize my decision to live here: It’s a good place to do AI research, it’s full of good people, it has nice scenery.
But I knew none of that when I first visited here at 19 yo, and decided that I wanted to live here. This irrationality drove, from the top, my decision process; it is therefore difficult to convince me of changing my decision by giving me reasons why I should not love Japan.

Take someone who loves pasta. “I don’t think it tastes particularly good, and I know it’s a bit boring, but I just love pasta.”
You could tell them that spaghetti gives cancer and is made from dead skunks, they would have a hard time just starting to hate spaghetti.
Now take someone whose irrationality is much deeper in the decision process. “I love food that is made of wheat, and I heard my great grandpa was Italian, so I love spaghetti.” If you convince them that spaghetti isn’t made of wheat and that their great grandpa was Irish, they might just lose all interest for pasta.
You can change “love” by “hate”, “fear”, or any other emotion in the above examples. The point is that the level at which your emotions guide some of your decision processes determines how much you can be swayed by new facts.

And as much as I don’t understand America’s recent choice of president, I think that might be part of it. No amount of facts about that candidate could convince his followers that he wasn’t to be trusted. Maybe they are just in love with him. He says something and they interprete it as what they want to hear, and that is enough. They say he is actually a good person, a smart man, a competent businessman, that he respects woman and is not racist. Even when he himself says the contrary.

Of course, my decision to live in Japan is not supposed to destroy the life of millions of people. And maybe all of Trump voters actually made a rational choice, which is both extremely scary and leaves place to hope. But the way that election unfolded suggest that their choice is not based on facts, and therefore as irrational as can be.

Next year are the German and French elections, and a survey already revealed that the majority of French people would have chosen Trump if they could vote in the US elections.
What can be done? Unfortunately I do not have an answer.

For the past few years I have tried to deal with the worst of my irrational opinions, and the news are not good. Facts do not work. Pushing contradictory emotions does not work. Taking a step back has mixed results, but how do you force people to take a step back from politics? Replacing one irrational behaviour by another might work, from what I hear. I have not tested it. But if it is true, does it mean that the Trump crowd could only have been swayed by a candidate that they find more charismatic?
Given what their idea of charisma seems to be, I don’t know what a “more charismatic” candidate would have looked like.

Maybe we will discover it next year. Or maybe we will have to bow to President Le Pen.

Evolutionary Stability of Altruism


Wolf pack surrounding a bison, via Wikimedia

Wikipedia cites altruism as “an evolutionary enigma”, because under current paradigms it is “evolutionary unstable”.

It means that when an altruistic individual appears in a group for the first time (by genetic mutation), its has a lower probability to pass its genes to the next generation, so altruism should always disappear shortly after appearing: altruism may benefit other members of the group but is detrimental for the altruistic individual itself. Even if altruism genes do spread in the whole group, if a single member evolves a selfishness gene, it will be advantaged by cheating on the other members and the gene for selfishness should take over the whole group.

Diverse models have been built to explain how altruism can have spread through a population, without disappearing from the start or from competition with selfishness. All are evolutionary unstable, so the puzzle is not solved.

Here is my model, and I do believe that it is evolutionary stable. Hopefully I will have time to code a simulation.

Hypothesis I: Vindictive behaviour is a precondition to the formation of societies.

Hypothesis II: A necessary condition for the apparition and continuation of altruistic behaviour is vindictive behaviour.

Hypothesis III: The individual cost of altruistic behaviour must always be balanced by the cost of retribution in case of non-altruistic behaviour.

These are three strong hypotheses… Let me explain what I mean by giving an example: food sharing in wolves. How could this real life behaviour have appeared?

Say you’re a lonely carnivore, ancestor of today’s wolves, but not living in groups. You hunt a prey and start eating, but then some creature comes and steals your food from you. Clearly, if your descendants evolve some genes that make them attack people who try or does steal their food, they will be better off than their naive conspecifics. It is even possible that the same genes that make you attack preys also make you attack other people, or other people’s preys… Maybe are you even one of the thieves that to steal other wolves’ preys in the first place? There is not much difference between a sick rabbit and a freshly killed rabbit, or between your dead rabbit and their dead rabbit… It is difficult to sort out the order in which these related behaviours (hunting, stealing, defending one’s food) appeared, and it is plausible that they all appeared conjointly.

Now say that for some reason, you find yourself stuck with several other pre-wolves on a small area. Maybe the population had a sudden increase in density. Maybe you’re all following the same herbivore migration. Anyway, now several of you have to eat their own prey at relatively short distance from each other. You’re not yet a society, but you do live together (think about today’s bears, who usually live alone or with their cubs but form big groups when it’s salmon season).

The first thing to happen might be that cubs stay closer to their mother, even as young adults, simply because there is not much space. Obviously mums share food with their cubs, but they also protect their cubs when they are eating. If, simply because they live close to each other, this behaviour persists once they are adult, the family will have an obvious evolutionary advantage by protecting each other’s food. They might even team up to steal solitary wolves’ food, or hunting bigger preys. On the other hand, those who don’t even bother to protect their own food don’t stand a chance in this new setting.

At this point, what prevents one member of the pack from cheating? You could eat more than your share, and stay away from battles to avoid danger. That would confer you a big advantage. This is what makes theories of altruism evolutionary unstable. Altruism should not be able to survive cheaters.

… Except if there is retribution. If you tend to take the biggest part of the prey and go away to eat it in peace, it might trigger the thief detector of your colleagues and they will attack you. If you don’t take part to the hunt, you may be considered as an outsider and attacked when you try to eat with the others. The apparition of such vindictive behaviour may not require much genetic change, but it has obvious advantages: it protects the group from cheaters, and it also represents a disadvantage for the cheater, who can be harmed, killed, or just starved as a result of its behaviour. In this group, cheating is the evolutionary unstable behaviour, while cooperation is stable.

But what about altruism? Imagine that instead of hunting all together, some wolves go hunting and then share with the whole pack (maybe because some members have to stay home to protect the cubs). In that case, they must obviously share with those who didn’t go hunting. Maintaining cheaters at bay means insuring that you don’t end up hunting alone while a whole group of lazy adult wolves wait for you to bring food, an easy way to game the system. Being vindictive or resentful is a defence mechanism that should bring the group to punish free riders before reaching that extreme situation.

Meanwhile, altruism should be partly motivated by the fear of social retribution, which is learned, and partly by genetic predispositions. I say that altruism should be learned, because cheating remains beneficial for a given individual, provided that the cheating is not big enough to be caught and punished and behaviours that are beneficial have not reason to disappear from the gene pool; but the punishment threshold depends on the current food resources and the character of other group members so it cannot be genetically encoded. Same goes for vindictive behaviour, which should be proportional to the offence to make evolutionary sense.

A consequence of this theory is that genes for the fear of social retribution should also be evolved, since it prevents the individual to get into too much trouble. At the same time, a race between better cheaters that don’t get caught and those who catch and punish them could also appear. Good cheaters will pass more genes on (and possibly also their tricks as knowledge), but they might also be better at catching members who use the same tricks as them, maintaining balance.

It is possible to game the system by not exhibiting vindictive behaviour. It is costly to monitor and punish cheaters, so you can try to count on others to do it for you and save your energy for more important things. Except of course if this kind of slacking is also punished (just think about all the people who get angry both at what they see as immoral behaviour and at those who refuse to be indignant at such behaviour). Who would have believed it! Vigilantism, self-righteousness, jealousy and charity, sharing, benevolence, all linked together… (I do not endorse vindictive behaviour, by the way.)

This walkthrough can, I think, be applied to most altruistic behaviours. Some howling monkeys give alarm calls when a predator approach the group, which make them more likely to be spotted and killed by said predator. This is a behaviour that is clearly very costly in terms of survival chances. The group can only resist to cheaters if there is a form of punishment that is even more costly (I don’t know if cheaters are punished in these groups of monkeys, but I expect so). The loss caused by altruistic behaviour must always be lower than the cost of retribution to maintain evolutionary stability.

Once it has appeared and found stability, altruistic behaviour can be enforced by other means than retribution, for example by ensuring that the individuals that have the possibility to cheat do not reproduce (like in social bees or mole rats). After all, it is also costly to the group to monitor and punish cheaters…

New York Public Library’s Fantastic Data

As you know, my passions in life are food and food. This blogpost is therefore about the taxonomy of window panes.

Sorry. This post is about FOOD! NYPL made a heap of information about New York food open access here; it’s the dataset I used to train my crazy twitter bot (@CrazyPoshCook), and you can find more examples of the bot’s output at the end of this post.

In their crowd-driven project, NYPL numerized data about more than 17 000 menus from NY restaurants between 1851 and 2012. There are regular menus, menus for special events, cruise menus… I delved into the data because I’m a serious scientist, not at all because I was hungry and bored. Here we go!

I first looked at which dish appeared more often in New York’s restaurants. To the surprise of no one, the most common menu item is… Coffee, with 8487 apparitions! In second position comes Tea (4769), then more surprisingly, Celery (4247), Olives (4554) and Radish (3349). NY people, you’re officially weird. The followers are somewhat more expected: mashed potatoes, milk, and boiled potatoes. Wait, who orders plain milk at a restaurant??


There are lots of items that appear only once, mostly dishes with really long names. Some dishes have a negative number of citations (that’s human error), like the awesome “Clam Fry (with Bacon)” from a 1914 menu (“-4” citations!).

The same kind of error popped up when I looked for the dish with the shortest name: it seems to be the mysteriously named “&”, which appeared on 4 different menus in 1901.
The dish with the longest “name” is a long ramble about tea that manages to include references to Elizabeth II and Lewis Caroll:

Afternoon Tea- A Great British Tradition- Tea, the most universally consumed of all drinks, is especially popular in Britain where the annual consumption is something in the region of 512 million cups. W. E. Gladstone observed “If you are cold, tea will warm you- if you are heated, it will cool you- if you are depressed, it will cheer you- if you are excited, it will calm you.” First brought to England c. 1559 by Giambattista Rusmusio, tea did not evolve into an afternoon meal until the end of the 18th century. Anna, Duchess of Bedford, invented afternoon tea to fill the long gap between early lunch and dinner which bored many house parties. It became a meal surrounded by etiquette and customs, delicate china, silver, cake stands and doilies- a time when friend and family meet. Famous tea parties include Mad Hatter’s (Alice’s Adventures in Wonderland by Lewis Carroll 1865), the Boston Tea Party, 1773, and not forgetting HM Queen Elizabeth II’s annual garden parties at Buckingham Palace. The Duke of Wellington declared that “Tea cleared my head and left no misapprehensions.” He was right- tea contains small amounts of two B vitamins, and has no calories, artificial flavourings or colourings. It is said to cure gout, apoplexy, epilepsy, gall stones and sleepiness, and one’s longevity is assured. “Thank God for Tea! What would the world do without tea?”- Sydney Smith

But that’s cheating – there’s nothing about the actual tea they serve you. So the real laureate is the famous Tour d’Argent of Paris, with this lengthy but delicious-sounding single dish from 1987:

Fresh Water Prawn Rampant, Baby White Fish, with Timbal of Transylvanian Macadamia Nuts, Sea Scallops, Two Gunkan Rolls of American Sturgeon and Salmon Caviars, served on Wasabi Sauce Rouille- The fresh water prawn is from an American based farm and is split and baked in a hot rouille sauce. One prawn is served along side the baked white fish. It is served under a timbal made with sea scallops and alongside two Chinese rice rolls filled with two caviars. Rouille is similar to a hot Hollandaise. The sauce is made with wasabi powder and cream.

Price unknown. Oh gods. While we’re on the subject, let’s have a look at the priciest items. Ordering by highest “highest_price” gave ludicrous results (a $2550 grape fruit… Is it from the Hesperides’ Garden?!?) so I ordered the data by highest “lowest_price” instead. The winner is some “Chicken Liver Omelette”, at $1035! Yes, I checked the currency. Here are the 10 priciest dishes:


Lots of champagne, and a… ham sandwich?

Next I liked at old dishes. The oldest entries are from 1851, but most of them appeared only once, so instead I looked for old dishes that lasted for more than a year. I thought they would be more representative of what food was common at the time:

We have some weird ones! My favorite is the stale bread. Next I wondered what were the dishes that had the longest lifespan:

Super boring, but those are some pretty expensive peaches 0_0
I had to Google “Charles Heidsieck”. It’s champagne. Oh, and mashed potatoes can cost you more if you ask it with a capital P.
The menus with the most gigantic number of dishes all come from “Waldof Astoria”, with more than 1000 dishes to choose from for a single occasion! Here is what a page looks like:



So that’s some tidbits about the dataset I used. The bot was super fun to train, here are some screenshots that made me cry laughing (because I’m a bit crazy too I guess).

See you next time!

This slideshow requires JavaScript.

Open Ended Evolution – At last, some data

Hi tweeps (I know most of you arrive here via Twitter (except for that one US bot who watches the same 10 pages every night (hi you!)))

So I’m sitting in the Tokyo-Sidney plane, which has no power plugs and broken headphones, and I thought, what can I do while waiting to land on the continent with the weirdest fauna in the world?

The answer is, talk about my own computer generated weird species of course. This post is the follow up to this one and this one, and to a lesser extent, this and this. Actually the results have been sitting in my computer since last summer; I posted a bit on twitter too.  In short, OEE is about building a living world that is “forever interesting”. Since you’ve got all the theory summed up in the previous posts, let’s go directly to the implementation and results.

To be honest, I don’t remember all the details exactly. But here we go!

Here is what the 1st batch looked like, at the very beginning of the simulation:


So you have an artificial world with individuals that we hope will evolve into something interesting through interactions with each other. The yellow individuals are how we input free energy in the system. It means that they appear every few steps, “out of nothing”. They cannot move, or eat, or do anything interesting really. They just contain energy, and when the energy is used up, they die. I call it “light”.

Then you have the mutants, which appear on the field like light, but with a random twist. Maybe they can move, or hypothetically store more energy. Mutants can produce one or more kids if they reach a given energy threshold (they do not need a mate to reproduce.) The kid can in turn be copy of their parents, or mutants of mutants.

Then you have the interesting mutants. These have sensors: if something has properties that their sensors can detect, they eat it (or try to). Eating is the only way to store more energy, which can then be used to move, or have kids, or just not die, so it’s pretty important.

Now remember that this sim is about the Interface Theory of Perception. In this case it means that each sensor can only detect a precise value of a precise property. For example, maybe I have a sensor that can only detect individuals who move at exactly 1 pixel/second. Or another sensor that detects individuals that can store a maximum of 4 units of energy. Or have 2 kids. Or have kids when they reach 3 units of energy. Or give birth to kids with a storage of 1 unit of energy.

A second important point is, you can only eat people who have less energy than you do, otherwise you lose energy or even die. BUT, to make things interesting, there is no sensor allowing you to measure how much energy this other guy has right now.

It sounds a bit like the real world, no? You can say that buffaloes that move slowly are maybe not very energetic, so as a lion, you should try to eat them. But there is no guarantee that you will actually be able to overpower them.

Before we get there, there is a gigantic hurdle. Going from “light” to lions or buffaloes is not easy. You need sensors, but sensors require energy. And mutations appear randomly, so it takes a lot of generations to get the first viable mutant: something that can detect and eat light, but doesn’t eat their own kids by mistake. Here is what the origin of life looks like in that world:


The Y axis is the ID of the oldest ancestor, and X is the time. Everything on the diagonal is just regular light. All the horizontal branches are mutant lineages; as you can see, there are lots of false starts before we get an actual species to get off! Then at a longer timescale this happens:


This is the same sim as before, but zoomed out. Lots of interesting stuff here. First, or previously successful descendants of #14000 go extinct just as a new successful lineage comes in. This is not a coincidence. I think either both species were trying to survive on the same energy source (light) and one starved out the other, or one just ate the other to extinction.

Seeing as the slope of the “light” suddenly decreases as species 2 starts striving, I think the 1st hypothesis is the right one.

Now the fact that our successful individuals all have the same ancestor doesn’t actually mean that they belong to the same species. Actually, this is what the tree of life looks like in my simulated worlds:

tree1 tree1b four_species

These images represent the distribution of individuals’ properties through time. I encoded 3 properties (don’t remember which) in RGB, so differences in colors also approximately represent different species, or variations in species.  In images 1 and 2, you can see 2 or 3 different branches with different ancestors. On these I was only looking at the max amount of energy that each individual can store, and how much of this energy is passed from the parent to its kids. If I had looked instead at speed, or at the number of sensors, we may have seen the branches divide in even smaller branches.

In the 3rd image, we see much more interesting patterns; the lower branch divides clearly in 2 species that have the same original ancestor; then one branch dies out, and the other divides again, and again! To obtain these results, I just doubled the area of the simulation, and maybe cranked up the amount of free energy too (the original one was extremely extremely tiny compared to what is used in Artificial Life usually. Even when doubling the area, I don’t think I ever heard about such a small scale simulation.).

Still, the area was bigger but one important motor of speciation was missing. In real life, species tend to branch out because they become separated by physical obstacles like oceans, mountains, or just distance. To simulate that, I made “mobile areas” of light. Instead of having a fixed square, I had several small areas producing light, and these areas slowly move around. It’s like tiny islands that get separated and sometimes meet each other again, and it looks like this:


Now the species have to follow the light sources, but they can also meet each other and “infect” each other’s islands, competing for resources (or just to eat each other). The trees you get with this are like this:

snake_tree wild

Even more interesting!  So many branches! And just looking at the simulation is also loads of fun. Each one is a different story. Sometimes there is drama…


I was rooting for the “smart guys” (fast and with many sensors) above, but they eventually lost the war and went extinct.

What do we take out of that? First, some of the predictions I made in previous posts got realised. The Interface Theory of Perception does allow for a variety of different worlds with their own histories. Additionally, refusing to encode species in the simulation does lead to interesting interactions, and speciation becomes an emergent property of the world. Individuals do not have a property names “species”, or a “species ID” written somewhere. Despite that we don’t end up with a “blob of life” with individuals spread everywhere, we don’t have a “tree of life” clean and straight like in textbooks. It’s more of a beautiful mutant broccoli of life, with blobs and branches. And this sim doesn’t even have sexual reproduction in it! That would make the broccoli even cooler.

The next step in the sim was to implement energy arrays, as I mentioned in an earlier post. I already started and then I kinda forgot. Hopefully I’ll find time to do it!

Conclusion: Did I build an OEE world? Ok, probably not. But I like it and it lived to my expectations.

An opinion on defining life, and a theory of emergence, embodied cognition, OEE and solving causal relationships in AI

Wikimedia Commons

Here comes a really long blog post, so I have included a very brief summary at the end of each section. You can read that and go for the long version after if you think you disagree with the statements!


  • Defining Life: A Depressing Opinion

Deciding what is alive and what is not is an old human pastime. A topic of my lab’s research is Artificial Life, so we also tend to be interested in defining life, especially at the level of categories. What is the difference between this category of alive things and this category of not-alive things? There are lots of definitions trying to pin down the difference, none of them satisfactory enough to convince everyone so far.

One thing we talked about recently is the theory of top down causation. When I heard it, it sounded like this: big alive things can influence small not-alive things (like you moving the molecules of a table by pushing said table away) and this is top down causation, as opposed to bottom up causation where small things influence big things (like the molecules of the table preventing your fingers to go through it via small scale interactions).
I’m not going to lie, it sounded stupid. When you move a table, it’s the atoms of your hands against the atoms of the table. When you decide to push the table, it’s still atoms in your brain doing their thing. Everything is just small particles meeting other small particles.

Or is it? No suspense, I still do not buy top-down causation as a definition of life. But I do think it makes sense and can be useful for Artificial Intelligence, in a framework that I am going to explain here. It will take us from my personal theory of emergence, to social rules, to manifold learning and neural networks. On the way, I will bend concepts to what fits me most, but also give you links to the original definitions.

But first, what is life?
Well here is my depressing opinion: trying to define life using science is a waste of time, because life is a subjective concept rather than a scientific one. We call “alive” things that we do not understand, and when we gain enough insight about how it works, we stop believing it’s alive. We used to think volcanoes were alive because we could not explain their behaviour. We personified as gods things we could not comprehend, like seasons and stars. Then science came along and most of these gods are dead. Nowadays science doesn’t believe that there is a clear-cut frontier between alive and not alive. Are viruses alive? Are computer viruses alive? I think that the day we produce a convincing artificial life, the last gods will die. Personally, I don’t bother to much about classifying things as alive or not; I’m more interested in questions like “can it learn? How?”, “Does it do interesting stuff?” and “What treatment is an ethical one for this particular creature?”. I’m very interested in virtual organisms — not so much in viruses. Now to the interesting stuff.

Summary: Paradoxically, Artificial Life will destroy the need to define what is “alive” and what is not.


  • A Theory of Emergence

Top-down causation is about scale, as its name indicates. It talks about low level (hardware in your computer, neurons in your brain, atoms in a table) and high level (computer software, ideas in your brain, objects) concepts. Here I would like to make it about dimensions, which is quite different.
Let’s call “low level” spaces with a comparatively larger number of dimensions (e.g. a 3D space like your room) and “high level” spaces with fewer dimensions (like a 2D drawing of your room). Let’s take low level spaces as projections of the high level spaces. By drawing it on a piece of paper, you’re projecting your room on a 2D space. You can draw it from different angles, which means that several projections are possible.
But mathematical spaces can be much more abstract than that. A flock of bird can be seen as a high dimensional space where the position of each bird is represented by 3 values on 3 bird-dependent axes: bird A at 3D position a1 a2 a3, bird B at position 3D b1 b2 b3 etc. That’s 3 axes per bird, already 30 dimensions even if you have only 10 birds! But the current state of the flock can be represented by a single point in that 30D space.
You can project that space onto a smaller one, for example a 2D space where the flock’s state is represented by one point of which position is just the mean of all bird’s vertical and horizontal position. You can see that the trajectory of the flock will look very different whether you are in the low or high dimensional space.

What does this have to do with emergence?
Wikipedia will tell you a lot about the different definitions and opinion about emergence. One thing most people agree about is that an emergent phenomena must be surprising, and arise from interactions between parts of a system. For example, ants finding the shortest path to food is an emergent phenomena. Each ant follows local interactions rules (explore, deposit pheromones, follow pheromones). That they can find the shortest path to a source of food, and not a random long winding way to it, is surprising. You couldn’t tell that it was going to happen just by looking at the rules. And if I told you to build an algorithm inside the ants heads to make them find the shortest path, that’s probably not the set of rules you would have gone for.

I think that all emergent phenomena are things that happen because of interactions in a high dimensional space, but can be described and predicted in a projection of that space. When there is no emergence, no projection is ever going to give a good description and predictability to your phenomenon. Food, pheromones, but also each ant is a part of the high dimensional original system. Each has states that can be represented on axes: ants move, pheromones decay. Ants interact with each other, which mean that their states are not independent from each other. The space can be projected onto a smaller one, where a description with strong predictive power can be found: ants find the shortest path to food. All ants and even the food have been smashed into a single axis. Their path is optimal or not. They might start far from 0, the optimal path, but you can predict that they will end up at 0. If you have two food sources, you can have two axes; the ants closeness tho the optimal solution depends to their position on these axes. Another example is insect architecture: termite mounds, bee hives. The original system includes interactions between particles of building material and individual termites, but can be described in much simpler terms: bees build hexagonal cells. Or take the flock of birds. Let’s say that the flock forms a big swarming ball that follows the flow of hot winds. The 2D projection is a more efficient way to predict the flock’s trajectory than the 30D space, or than following a single bird’s motion (combination of its trajectory inside the swarm-ball and on the hot winds). Of course, depending on what you want to describe, the projection will have to be different.

Here we meet one important rule: if there is emergence, the projection must not be trivial. The axes must not be a simple subset of the original space, but a combination (linear or not) of the axes of the high dimensional space.
This is where the element of “surprise” comes in. This is a rather nice improvement on all the definitions of emergence I’ve found: all talk about “surprise” but most do not define objectively what is considered as surprising. The rule above is a more practical definition than “an emergent property is not a property of any part of the system, but still a feature of the system as a whole” (wikipedia).

Follows a second implicit rule: trajectories (emergent properties) built in low dimensional spaces cannot be ported to high dimensional spaces without modification.
You could try to build “stay in swarm but also follow hot winds” into the head of each bird. You could try to build “find shortest path” into the head of each ant. It makes sense: that is the simplest description of what you observe. The problems starts when you try to build that with what you have in the real, high dimensional world. Each ant has few sensors. They cannot see far away. Implementing a high level algorithm rather than local interactions may sometimes work, but is not the easiest, more robust or more energy efficient solution. If you are building rules that depend explicitly on building high level concepts from low level high dimensional input, you are probably not on the right track. You don’t actually need to implement a concept of “shortest path” or “swarm” to achieve these tasks; research shows that you obtain much better results by giving these up. This is a well known problem in AI: complex high level algorithms do very poorly in the real world. They are slow, noise sensitive and costly.

However, I do not agree that emergent phenomena “must be impossible to infer from the individual parts and interaction”, as anti-reductionists say. Those that fit in the framework I have described so far can theoretically be inferred, if you know how the high dimensional space was projected on the low dimensional one. Therefore you can generate emergent phenomena by drawing a trajectory in the low dimensional space, and trying to “un-project” it to the high dimensional space. By definition you will have several possible choices, but it should not be a too big problem. I intuitively think this generative approach works and I tried it on a few abstract examples; but I need a solid mathematical example to prove it. Nevertheless, if emergent phenomena don’t always have to be a surprise and can be engineered using tools other than insight, it’s excellent news!

Summary: an emergent phenomenon is a simplification (projection to low dimensional space) of underlying complex (high dimensional) interactions that allows to predict something about the system faster than by going through all the underlying interactions, whatever the input.

Random thought that doesn’t fit in this post: If there were emergent properties of the system “every possible algorithm”, the halting problem would be solvable. There is not, so we actually have to run all algorithms with all possible inputs (see also Rice’s theorem).


  • Top-Down Causation and Embodied Cognition

So far we’ve discussed about interactions happening between elements of the low level high dimensional system, or between the elements of the high level low dimensional system. It is obvious that what happens down there influences what happens up here. Can what happens upstairs influence what goes on downstairs?
Despite my skepticism at what you can read about top-down causation here  and there, I think the answer is yes, in a very pragmatic way: if elements of the high dimensional space take inputs directly from the low dimensional space, top down causation happens. Until now the low-dim spaces were rather abstract, but they can exist in a very concrete way.

Take sensors, for example. Sensors reduce the complexity of the real world in two ways:
– by being imprecise (eyes don’t see individual atoms but their macro properties)
– by mixing different inputs into the same kind of output (although the mechanisms are different, you feel “cold” both when rubbing mint oil or an ice cube on your skin)
This reduction of dimensions is performed before giving your brain the resulting output. Your sensors give you input from a world that is a already a non-trivial projection of a richer world. Although your actions impact the entire, rich, high dimensional world, you only perceive the consequences of it through the projection of that world. Your entire behaviour is based on sensory inputs, so yes, there is some top-down causation going on. You should not take it as a definition for living organisms though: machines have sensors too. “sensor” is actually a pretty subjective word anyways.
You might not be convinced that this is top-down causation. Maybe it sounds to pragmatic and real to be top-down causation and not just “down-down” causation.

So what about this example: social rules. Take a group of humans. Someone decides that when meeting a person you know, bowing is the polite thing to do. Soon everyone is doing it: it has become a social rule. Even when the first person to launch this rule has disappeared from that society, the rule might continue to be applied. It exists in a world that is different from the high dimensional world in formed by all the people in that society, a world that is created by them but has some independence from each of them. I can take a person out and replace them by somebody from a different culture — soon, they too will be bowing. But if I take everyone out and replace them by different people, there is no chance that suddenly everyone will start bowing. The rule exists in a low dimension world that is inside the head of each member of the society. In that projection, each person that you have seen bowing in your life is mashed up in an abstract concept of “person” and used in a rule saying “persons bow to each other”. This low dimensional rule directs your behaviour in a high dimensional world where each person exists as a unique element. It’s bottom up causation (you see lots of people bowing and deduce a rule) that took its independence (it exists even if the original person who decided the rule dies, and whether or not some rude person decides not to bow) and now acts a top down causation (you obey the rule and bow to other people). When you bow, you do not do it because you remember observing Mike bow to John and Ann bow to Peter and Jake bow to Mary. You do it because you remember that “people bow to other people”. It is definitely a low dimensional, general rule dictating your interactions as a unique individual.

We have seen two types of top-down causation. There is a third one, quite close to number one. It’s called embodied cognition.
Embodied cognition is the idea that some of the processing necessary to achieve a task are delegated to the body of an agent instead of putting all the processing load on its brain. It is the idea that the through interactions with the environment, the body influences cognition, most often by simplifying it.
My favourite example is the swiss robot. I can’t find a link to the seminal experiment, but it’s a small wheeled robot that collects objects in clusters. This robot obeys fixed rules, but the results of its interaction with the environment depends on the placement of its “eyes” on the body of the robot. With eyes on the side of its body, the robots “cleans up” its environment. For other placements, this emergent behaviour does not appear and the robot randomly moves objects around.
Although the high level description of the system does not change (a robot in an arena with obstacles), changes in the interactions of the parts of the system (position of the eyes on the body) change the explanatory power of the projection. In one case, the robot cleans up. In the others, the behaviour defies prediction in a low dimensional space (no emergence). Here top-down causation works from the body of the robot to its interactions in a higher dimensional world. The low dimension description is “a robot and some obstacles”. The robot is made of physically constrained parts: its body. This body is what defines whether the robot can clean up or not — not the nature of each part, but how they are assembled. For the same local rules, interactions between the robot and the obstacles depend on the high level concept of “body”, not only on each separate part. The swiss robot is embodied cognition by engineered emergence.

In all the systems with top-down causation I have described so far, only one class falls into the anti-reductionist framework. Those where the state of the high level space are historically dependent on the low level space. These are systems where states in the low dimensional world depends not only on the current state of the high dimensional one, but also on its past states. If on top on that the high dimensional world takes input from the low dimensional one (for example because directly taking high dimensional inputs is too costly), then the system’s behaviour cannot be described only by looking at the interactions in the high dimensional world.
Simple example: some social rules depend not only on what people are doing now, but on what they were doing in the past. You wouldn’t be able to explain why people still obey archaic social rules just by looking at their present state, and these rules did not survive by recording all instances of people obeying them (high dimensional input in the past), but by being compressed into lower dimensional spaces and passed on from person to person in this more digestible form.
This top-down causation with time delay cannot be understood without acknowledging the high level, low dimensional world. It is real, even if it only exists in people’s head. That low dimensional world is where the influence of the past high dimensional world persists even if it has stopped in the present high dimensional world. Maybe people’s behaviour cannot be reduced to only physical laws after all… But there is still no magic in that, and we are not getting “something from nothing” (a pitfall with top-down causation).

A counter argument to this could be that everything is still governed by physical laws, both people and people’s brain, and lateral causation at the lowest level between elementary particles can totally be enough to explain the persistence of archaic social rules and therefore top-down causation does not need to exist.
I agree. But as soon as you are not looking at the lowest level possible, highest dimensional world (which currently cannot even be defined), top-down causation does happen. Since I am not trying to define life, this is fine with me!

Summary: Top-down causation exists when the “down” takes low dimensional input from the “top”. The key here is the difference in dimensions of the two spaces, not a perceived difference of “scale” as in the original concept of top-down causation. Maybe I should call it low-high causation?


  • Open Ended Systems

In this section I go back to my pet subject, Open Ended Evolution and the Interface Theory of Perception. You probably saw it coming when I talked of imprecise sensors. I define the relationship between OEE and top-down causation as: An open ended system is one where components take inputs from changing projected spaces. It’s top-down causation in a billion flavors.
These changes in projections are driven by interactions between the evolution of sensors and the evolution of high dimensional outputs from individuals.

Two types of projections can make these worlds interesting:
1. sensory projection (see previous section)
2. internal projections (in other words, brains).

The theoretical diversity of projections n.1 depends of the richness of the real world. How many types of energy exist, can be sensed, mixed and used as heuristics for causation?
N.2 depends on n.1 of course (with many types of sensors you can try many types of projections), but also on memory span and capacity (you can use past sensor values as components of your projections). Here, neurons are essentially the same as sensors: they build projections, as we will see in the next section. The main difference is that neurons can be plastic: the projections they build can change during your lifetime to improve your survival (typically, changes in sensors decrease your chances of survival…).
As usual, I think that the secret ingredient to successful OEE is not an infinitely rich physical world, even if it helps… Rather, the richness of choice of projected spaces (interfaces) is important.


  • Neural Networks

I will not go into great details in this section because it is kind of technical and it would take forever to explain everything. Let’s just set the atmosphere.
I was quite shocked the other day to discover that layered neural networks are actually the same thing as space projection. It’s so obvious that I’m not sure why I wasn’t aware of it. You can represent a neural network as a matrix of weights, and if the model is a linear one, calculate the output to any input by multiplying the input by the weight matrix (matrix multiplication is equivalent to space projection).
The weight matrix is therefore quite important: it determines what kind of projection you will be doing. But research has shown that when you are trying to apply learning algorithms to high dimensional inputs, even a random weight matrix improves the learning results, as long as it reduces the dimension of the input (you then apply learning to the low dimensional input).
Of course, you get even better results by optimizing the weight matrix. But then you have to learn the weight matrix first, and only then apply learning to the low dimensional inputs. That is why manifold learning has been invented, it seems. It finds you a good projection instead of using random stuff. Then you can try to use that projection to perform tasks like clustering and classification.

What would be interesting is to apply that to behavioural tasks (not just disembodied tasks) and find an equivalent for spiking networks. One possible way towards that is prediction tasks.

Say you start with a random weight matrix. You goal is to learn to predict what projected input will come after the current one. For that, you can change your projection: two inputs that you thought were equivalent because they got projected at the same point, but ended up having different trajectories, were probably not equivalent to begin with. So you change your projection as to have these two inputs projected at different places.

From this example we can see several things:
– Horror! layers will become important. Some inputs might require a type of projection, and some others a different type of projection. This will be easier implemented if we have layers (see here).
– A map of the learned predictions ( = input trajectories) will be necessary at each layer to manage weight updates. This map can take the form of a Self Organising Map, or more complex, a (possibly probabilistic) vector field where each vector points to the next predicted position. There are as many axes as neurons in the upper layer, and axes have as many values as neurons have possible values. (This vector field can actually be itself represented by a layer of neurons, with each lateral connection representing a probabilistic prediction). Errors in the prediction drive changes in the input weights to the corresponding layer (would this be is closer to Sanger’s rule than to BackProp?). Hypothesis: the time dependance of this makes it possible to implement using Hebbian learning.
– Memory neurons with defined memory span can improve prediction for lots of tasks, by adding a dimension to the input space. It can be implemented simply with LSTM in non-spiking models of NN, or with axonal delays for spiking models.
– Layers can be dynamically managed by adding connections when necessary, or more reasonably deleting redundant ones (neurons that have the exact same weights as a colleague can replace said weights by a connection to that colleague)
– Dynamic layer management will make a feedforward network into a recurrent one, and the topology of the network will transcend layers (some neurons will develop connections bypassing the layer above to go directly to the next). The only remain of the initial concept of layers will be the prediction vector map.
– Memory neurons in upper layers with connections towards lower layers will be an efficient tool to reduce the total number of connections and computational cost (See previous sections. Yes, top-down causation just appeared all of a sudden).
– Dynamic layer management will optimise resource consumption but make learning new things more difficult with time.
– To make the difference between a predicted input and that input actually happening, a priming mechanism will be necessary. I believe only spiking neurons can do that, by raising the baseline level of the membrane voltage of the neurons coding for the predicted input.
– Behaviour can be generated (1), as the vector field map tells us where data is missing or ambiguous and need to be collected.
– Behaviour can be generated (2), because if we can predict some things we can have anticipatory behaviour (run to avoid incoming electric shock)

Clustering and classification are useless in the real world if they are not used to guide behaviour. Actually, the concept of class is subjective to the behaviour it supports; here we take “prediction” as a behaviour, but the properties you are trying to describe or predict depends on which behaviour you are trying to optimise. The accuracy or form of the prediction depends on your own experience history, and the input you get to build predictions from depends on your sensors… Here comes embodied cognition again.

Summary: predictability and understanding are the same thing. Predictability gives meaning to things and thus allows to form classes. The difference between deep learning and fully recurrent networks is top-down causation.


  • Going further

It might be tempting to generalise top-down causation. Maybe projecting to lower dimensions is not that important? Maybe projecting to different spaces with the same number of dimensions, or projecting to higher dimensional spaces, enhances predictability. After all, top-down projection in layered networks is equivalent to projecting low dimensional input to higher dimensional space (see also auto-encoders and predictive recurrent neural networks). But if our goal is to make predictions in the less costly way possible (possibly at the cost of accuracy), then of course projection to lower dimensional spaces is a necessity. When predictions must be converted back to behaviour, projection to high dimensional spaces becomes necessary; but in terms of memory storage and learning optimisation, the lowest dimensional layer is the one that allows reduction of storage space and computational cost (an interesting question here is, what happens to memory storage when the concept of layer is destroyed?).

One possible exception would be time (memory). If knowing the previous values of an input improves predictability and you add neuron(s) to keep past input(s) as memory, you are effectively increasing the number of dimensions of your original space. But you use this memory for prediction (i.e. low dimensional projection) in the end. So yes, the key concept is dimension reduction.

A nice feature of this theory is that models would be able to capture causal relationships (something that deep learning cannot do, I heard). This whole post was about a concept called “top-down causation” after all. If an input improves predictability of trajectories in the upper layer, certainly this suggests a causal relationship. So what the model is really doing all the way is learning causal relationships.

Summary: dimension reduction is the key to learning causal relationships.
Wow, that was a long post! If you have come this far, thank you for your attention and don’t hesitate to leave a thought in the comments.

To: Google Scholar’s Dad — Data-driven science hypotheses

A week ago I sent an email to Anurag Acharia, the man behind “Google Scholar”. Scholar is a search engine that allows you to browse through scientific papers, a specialized version of Google. You can use it for free (although accessing the papers is often not free).


Scholar is an extraordinary tool. It does something that nobody else can right now. Which is why I think they can solve a weird issue of science: the way researchers come up with hypotheses is everything but scientific. It relies on the same methods that your grandma’s grandma used to cure a cold: tradition and gut feeling.

I believe that the generation of scientific hypotheses must be data-driven, just as science itself is. Here is what I wrote in my proposal (original PDF here). There was no answer, unsurprisingly: I can’t imagine what the timetable of someone like Anurag Acharya looks like. But I put this here in the hope that someone finds it worth debating.



By definition, science follows the scientific process. Hypotheses are adopted or discarded based on objective analysis of data. But surprisingly, the process of generating hypotheses itself is hardly scientific: it relies on hunches and intuition.

It often goes like this: a researcher gets an idea from reading a colleague’s paper or listening to a talk. Literature from the field is reviewed, which allows for refinement of the original idea. Then it is time for designing experiments, analysing data and writing a paper. If the researcher is actually a student, things can be more complicated. But in all cases, the original hypothesis relies tremendously on the researcher’s own subjective collection and appreciation of information, that must be selected from the gigantic amount of existing scientific papers.

Clearly, the fact that we now have access to all this scientific information is a giant leap from the situation of a few decades ago; and it has been made possible single-handedly by Google Scholar. But it is also a fact that researchers everywhere have more and more data to look at, and that “to look at” too often becomes “to subjectively pick from”.

Hypothesis generation is the basis of science – arguably the most crucial and exciting part of actually doing science. Yet it is not based on anything scientific. This document summarise 3 proposals to make of hypothesis generation a datadriven process. I believe this is not restricting the creativity of scientists, but enhancing it; that it can make science more efficient and limit the waste of time and resources caused by irrelevant, biased, or outdated hypotheses – especially for graduate students. Not only does this respect the philosophy of Google and more specifically Google Scholar, but Google Scholar is currently the only organism that has the resources to make it happen. Here are my 3 proposals, from the easiest to implement to the more hypothetical.

1. Paper Networks

Going through several dozen of references at the end of a paper is far from optimal: the reason why a paper is cited and the paper itself are not physically close; the authors tend to unconsciously cite papers that support their view; the place of the papers in the field and their relationship to each other are virtually inaccessible.

Numerous services suggest papers supposed to be close to the one you have just read, but this is not enough. We need, at a glance, to know which papers support each other’s views and which support conflicting opinions, and we need to know how many there are. A visual map, a graph of networks of papers or of clusters of papers could be the ideal tool to reach this goal. The benefits would go beyond simple graphical structuring of the information:

• Reducting confirmation bias. When we look for papers simply by inputting keywords in Google Scholar, the keyword choice itself tend to be biased. A Paper Network would make supporting and opposing papers equally accessible.

• Promoting interdisciplinarity. It’s easy to say that interdisciplinary approaches are good. It’s better to actually have the tools to make it happen. A Paper Network would make it clear which approaches are related in different fields.

• Sparking inspiration. Standard search methods tell us what is there. But science is about bringing forth what is not yet here. A Paper Network would show existing papers in different fields, helping us to avoid re-doing what has already been done. More importantly, it would make it visually clear where the gaps are, where some zones are still blank, and what may be needed to fill them.

2. Burst Detection

Artificial Intelligence, my field, has known several “winters” and “summers”: periods when it seemed like all had already been done and the field fell in hibernation, and periods when suddenly everyone seemed to do AI (now is such a period). I suspect that other field know these brisk oscillations as well: several teams announcing the same big discovery in parallel, or a rapid succession of findings that leads to revival of the field, or even spawn new specialised fields.

These bursts are most likely not completely random. If we could predict, even very roughly, when which field will boom, we could prepare for it, invest in it and even maybe make it happen faster. What are the factors influencing winters and summers? How many steps in advance can we predict? How many more Moore Laws are waiting to be discovered? Being able to predict winters would also be an asset, because we could look for the profound causes that force science to slow down and try to prevent it. Is it the lack of funds? Relying too much on major paradigms? Only analysing data from the past can transform hunches into successful policies for the advance of science.

3. Half Life of Facts

The destiny of scientific facts if to be overturned – it is the proof that science works. Better tools, better theories: these are obvious first level parameters influencing the shelf life of scientific papers. But we need to go deeper and look for meta-parameters: properties that allow us to predict this shelf life, and identify which papers, which parts of a theory are statistically more likely to be busted.

As anyone who has assisted to a heated scientific debate can testify, right now, the leading cause for accepting a non-trivial theory or choosing to challenge it is the researcher’s own “common sense”; yet all science is about is rejecting common sense as an explanation to anything and looking for facts in hard data. In these conditions, how can we continue to rely on gut feeling to justify our opinions? We need more sound foundations to our beliefs, even if in the absence of experimental verification they are just that: beliefs.

If a specific part of a theory looks perfectly sound but is statistically close to death, we must start looking at its opponents, or even better, think about what a good opponent theory would look like and choose research topics accordingly.

4. Conclusion

These proposals could change the way we, researchers, do science. They also come with a flurry of ethical issues: new tools would change the way resources (financial and human) are distributed, with desirable and undesirable outcomes. Just like prenatal genetic screening leads to difficult ethical questions, building tools allowing the hierarchisation of research projects should be a very careful enterprise.

But here is the catch: unlike genetic screening, new research tools have an objective component to them. These 3 proposals are about bringing more science to science: allowing the generation of science seeds to be data-driven. Science changes the world, every day. Any tiny improvement to the scientific process is worth striving for – and these 3 changes would, I believe, bring major improvements.