ABC Easy as 42

Teacher’s gonna show you how to get an ‘A’

In 1989, IBM hired a team of programmers out of Carnegie Mellon University. As part of his graduate program, team leader Feng-hsiung Hsu (aka Crazy Bird) developed a system for computerized chess playing that the team called Deep Thought. Deep Thought, the (albeit fictional) original, was the computer created in Douglas Adam’s The Hitchhiker’s Guide to the Galaxy to compute the answer for Life, the Universe, and Everything. It was successful in determining the answer was “42,” although it remained unknown what the question was. CMU’s Deep Thought, less ambitiously, was a custom designed hardware-and-software solution for solving the problem of optimal chess playing.

Once at IBM, the project was renamed Deep Blue, with the “Blue” being a reference to IBM’s nickname of “Big Blue.”

On February 10th, 1996, Deep Blue won its first game against a chess World Champion, defeating Garry Kasparov. Kasparov would go on to win the match, but the inevitability of AI superiority was established.

Today, computer programs being able to defeat humans is no longer in question. While the game of chess may never be solved (à la checkers), it is understood that the best computer programs are superior players to the best human beings. Within the chess world, computer programs only make news for things like when top players may using programs to gain an unfair advantage in tournament play.

Nevertheless, a chess-playing computer was in the news late last year. Headlines reported that a chess playing algorithm based on neural networks, starting only from the rules of legal chess moves, in four hours created a program that could beat any human and nearly all top-ranked chess programs. The articles spread across the internet through various media outlets, each summary featuring their own set of distortions and simplifications. In particular, writers that had been pushing articles about the impending loss of jobs to AI and robots jumped on this as proof that the end had come. Fortunately, most linked to the original paper rather than trying to decipher the details.

Like most I found this to be pretty intriguing news. Unfortunately, I also happen to know a little (just a little, really) about neural networks, and didn’t even bother to read the whole paper before I started trying to figure out what had happened.

Some more background on this project. It was created at DeepMind, a subsidiary of Alphabet, Inc. This entity, formerly known simply as Google, reformed itself in the summer of 2015 with the new Google being one of many children of the Alphabet parent. Initial information suggested to me an attempt at creating one held company for each letter of the alphabet, but time has shown that isn’t their direction. As of today, while there are many letters still open, several have multiple entries. Oh well, it sounded more fun my way. While naming a company “Alphabet” seems a bit uninspired, there is a certain logic to removing the name Google from the parent entity. No longer does one have to wonder why an internet company is developing self-driving cars.

Google’s self driving car?

 

The last time the world had an Artificial Intelligence craze was in the 1980s into the early 1990s. Neural networks were one of the popular machine intelligence techniques of that time too. At first they seemed to offer the promise of a true intelligence; simply mimicking the structure of a biological brain could produce an ability to generalize intelligence, without people to craft that intelligence in code. It was a program that could essentially teach itself. The applications for such systems seemed boundless.

Unfortunately, the optimism was quickly quashed. Neural networks had a number of flaws. First, they required huge amounts of “training” data. Neural Nets work by finding relationships within data, but that source data has to be voluminous and it has to be suited to teaching the neural network. The inputs had to be properly chosen, so as to work well with the networks’ manipulation of that data and the data themselves had be properly representative of the space being modeled. Furthermore, significant preprocessing was required of the person organizing the training. Additional inputs would result in exponential increases in both the training data requirement and the amount of processing time to run through the training.

It is worthwhile to recall the computer power available to neural net programmers of that time. Even a high-end server of 35 years ago is probably put to shame by the Xbox plugged into your television. Furthermore, the Xbox is better suited to the problem. The mathematics capability of Graphical Processing Units (GPUs) is a more efficient design for solving these kinds of matrix problems. Just like Bitcoin mining, it is the GPU on a computer that is going to best be able to handle neural network training.

To illustrate, let me consider briefly a “typical” neural network application of the previous generation. One use is something called a “soft sensor.” Another innovation of that same time was the rapid expansion in capabilities of higher-level control systems for industrial processes. For example, some kind of factory wide system could collect real-time data (temperatures, pressures, motor speeds – whatever is important) and present them in an organized fashion to give an overview of plant performance and, in some cases, automate overall plant control. For many systems however, the full picture wasn’t always available in real time.

Let’s imagine the production of a product which has a specification limiting the amount of some impurity. Largely, we know what the right operating parameters of the system are (temperatures, pressures, etc) but to actually measure for impurities, we manually draw a sample, send it off to a lab for testing, and wait a day or two for the result. It would stand to reason that, in order to keep your product within spec, you must operate far enough away from the threshold that if it begins to drift, you would usually have time catch it before it goes out of spec. Not only does that mean you’re, most of the time, producing a product that exceeds specification (presumably at extra cost), but if the process ever moves faster than expect, you may have to trash a day’s worth of production created while you were waiting for lab results.

Enter the neural network and that soft sensor. We can create a database of the data that were collected in real time and correlate that data with the matching sample analyses that were available afterward. Then a neural network can be trained using the real-time measurements as input to produce an output predicting sample measurement. Assuming that the lab measurement is deducible from the on-line data, you now have in your automated control system (or even just as a presentation to the operators) a real time “measurement” of data that otherwise won’t be available until much later. Armed with that extra knowledge, you would expect to both cut operating costs (by operating tighter to specification) and prevent waste (by avoiding out of spec conditions before they happen).

That sounds very impressive, but I did use the word “assuming.” There were a lot factors that had to come together before determining that a particular problem was solvable with neural networks. Obviously, the result you are trying to predict has to, indeed, be predictable from the data that you have. What this meant in practice is that implementing neural networks was much bigger than just the software project. It often meant redesigning your system to, for example, collect data on aspects of your operation that were never necessary for control, but are necessary for the predictive functioning of the neural net. You also need lots and lots of data. Operations that collected data slowly or inconsistently might not be capable of providing a data set suitable for training. Another gotcha was that collecting data from a system in operation probably meant that said system was already being controlled. Therefore, a neural net could just as easily be learning how your control system works, rather than the underlying fundamentals of your process. In fact, if your control reactions were consistent, that might be a much easier thing for the neural net to learn that the more subtle and variable physical process.

The result was that many applications weren’t suitable for neural networks and others required a lot of prep-work. It might be necessary to rework your data collection system to get more and better data. It also was useful to pre-analyze the inputs to eliminate any dependent variables. Now, technically, that’s part of what the neural network should be good at – extracting the core dependencies from a complex system. However, the amount of effort – in data collected and training time – increases exponentially when you add inputs and hidden nodes, so simplifying a problem was well worth the effort. While it might seem like you can always just collect more data, remember that the data needed to be representative of the domain space.  For example, if the condition that results in your process wandering off spec only occurs once every three or four months, then doubling your complexity might mean (depending on your luck) increasing the data collection from a month or two to over a year.

Hopefully you’ll excuse my trip down a neural net memory lane, but I wanted to set your expectations of neural network technology where mine were, because the state of the art is very different than what it was. We’ve probably all seen some of the results with image recognition that seems to be one of the hottest topics in neural networks these days.

So back to when I read the article. My first thought was to think in terms of the neural network technology as I was familiar with it.

My starting point to design my own chess neural net has to be representations of the board layout. If you know chess, you probably have a pretty good idea how to describe a chess board. You can describe each piece using a pretty concise terminology . In this case, I figure it is irrelevant where a piece has been. So whether it started as a king’s knight’s pawn or a queen’s rook’s pawn, that doesn’t effect its performance. So you have 6 possible piece descriptors which need to be placed into the 64 squares that they could possibly reside upon. So, for example, imagine that I’m going to assign an integer to the pieces, and then use positive for white and negative for black:

Pawn Knight Bishop Rook King Queen
1 2 3 4 5 6

My board might look something like this 4,2,3,6,5,3,2,4,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0…-3,-2,-4

If I am still living in the 90s, I’m immediately going to be worried about the amount of data, and might wonder if I can compress the representation of my board based on assumptions about the starting positions. I’ve got all those zeros in the center of my matrix, and as the game progresses, I’m going to be getting fewer data and more zeros. Sixty-four inputs seems like a lot (double that to get current position and post-move position), and I might hope to winnow that down some manageable figure with the kind of efforts that I talked about above.

If I hadn’t realized my problem already, I’d start to figure it out now. Neural networks like inputs to be proportional. Obviously, binary inputs are good – something either affects the prediction or doesn’t. But for variable inputs, the variation must make sense in terms of the problem you are solving. Using the power output of a pump as an input to a neural network makes sense. Using the model number of that pump, as an integer, wouldn’t make sense unless there is happenstancial relationship between the serial number and some function meaningful to your process. Going back to my board description above, I could theoretically describe the “power” of my piece with a number between 1 and 10 (as an example), but any errors in my ability to accurately rank my pieces contribute to prediction errors. So is a Queen worth six times a pawn or nine? Get that wrong, and my neural net training has an inaccuracy built in right up front. And, by the way, that means “worth” to the neural net, not to me or other human players.

A much better way to represent a chess game to a mathematical “intelligence” is to describe the pieces. So, for example, each piece could be described with two inputs, describing its deviation from that piece’s starting position in the X and Y axes, with perhaps a third node to indicate whether the piece is on the board or captured. My starting board then becomes, by definition, 96 zeros, with numbers being populated (and generally growing) as the pieces move. It’s not terribly bigger (although rather horrifyingly so to my 90s self) than the representation by board, and I could easily get them on par by saying, for example, that pieces captured are moved elsewhere on the board, but well out of the 8X8 grid. Organizing by the pieces, though, is both non-intuitive for we human chess players and, in general, would seem less efficient in generalizing to other games. For example, if I’m modelling a card game (as I talked about in my previous post), describing every card, and each of their possible positions; that  is a much bigger data set than just describing what is in each hand and on the table. But, again, it should be clear that the description of the board going to be considerably less meaningful as a mathematical entity than the description creating working from the game piece.

At this point, it is worth remembering again that this is no longer 1992. I briefly mentioned the advances in computing, both in power and in structure (the GPU architecture as superior for solving matrix math). That, in turn, has advanced the state of the art in neural network design and training. The combination goes a long way in explaining why image recognition is once again eyed as a problem for neural networks to address.

Consider the typical image. It is a huge number of pixels of (usually) highly-compressible data. But compressing the data will, as described above, befuddle the neural network. On the other hand, those huge, sparse matrices need representative training data to evenly cover the huge number of inputs, with that need increasing geometrically. It can quickly become, simply, too much of a problem to solve in a timely manner no matter what kind of computing power you’ve got to throw at it. But with that power, you can do new and interesting things. A solution for image recognition is to use “convolutional” networks.

Not to try to be too technically correct, I’ll try to capture the essence of this technique. The idea is that the input space can be broken up into sub-spaces (in an image, small fractions of the image), that then feed a significantly smaller neural network. Then, one might assume that those small networks are all the same or similar to each other. For an image recognition, we might train 100s or even 1000s of networks operating on 1% of the image (in overlapping segments), creating a (relatively) small output based on the large number of pixels. Then those outputs feed a whole-image network. It is still a massive computational problem, but immensely smaller than the problem of training a network processing the entire image as the input.

Does that make a chess problem solvable? It should help, especially if you have multiple convolutional layers. So there might be a neural network that describes each piece (6 inputs for old/new position (2D) plus on/off board) and reduces it to maybe 3 outputs. A second could map similar pieces.. where are the bishops? where are the pawns? Another sub-network, repeated twice, could try just looking at one player at a time. It is still a huge problem, but I can see that it’s something that is becoming solvable given some time an effort.

Of course, this is Alphabet, Inc we are talking about. They’ve got endless supplies of (computing) time and (employee) effort, so if it is starting to look doable to a mere human like me, it is certainly doable for them.

At this point, I went back to the research paper wherein I discovered that some of my intuition was right, although I didn’t fully appreciate that last point. Just as a simple example, the input layer for the DeepMind system is to represent each piece as a board showing the position of the piece. So 32X a 64-by-64 positional grid. They also use a history of turns, not just current and next turn. It is orders-of-magnitude more data than I anticipated, but in extremely sparse data sets. In fact, it looks very much like image processing, but with much more ordered images (to a computer mind, at least). The paper states they are using Tensor Processing Units, a Google concoction meant to use hardware having similar advantages to the GPU and it’s matrix-math specialization, but further optimized specifically to solve this kind of neural network training problem.

So lets finally go back to the claim that got all those singularity-is-nigh dreams dancing in the heads of internet commentators. The DeepMind team were able to train in a matter of (really) twenty-four hours a superhuman level chess player with no a priori chess knowledge. Further, the paper states that the training set consists of 800 randomly-generate games (constrained only to be made up of legal moves), which seems like an incredibly small data set. Even realizing how big those representations are (with their sparse descriptions of the piece locations as well as per-piece historical information), it all sounds awfully impressive. Of course, that is 800 games per iteration. If I’m reading right, that might be 700k iterations in over 9 hours using hardware nearly inconceivable to we mortals.

And that’s just the end result of a research project that took how long? To get to that point where they could hit the “run” button took certainly months, and probably years.

First you’ve got to come up with the data format, and the ability to generate games in that format. Surprisingly, the paper says that the exact representation wasn’t a significant factor. I suppose that it an advantage of its sparseness. Next, you’ve got to architect that neural net. How many convolutions over what subsets? How many layers? How many nodes? That’s a huge research project, and one that is going to need huge amounts of data – not the 800 randomly generated games you used at the end of it all.

The end result of all this – after a process involving a huge number of PhD hours and petaFLOPS of computational power – you’ve created a brain that can do one thing; learn about chess games. Yes, it is a brain without any knowledge in it – a tabula rasa – but it is a brain that is absolutely useless if provided knowledge about anything other than playing chess.

It’s still a fabulous achievement, no doubt. It is also research that is going to be useful to any number of AI learning projects going forward. But what it isn’t is any kind of demonstration that computers can out-perform people (or even mice, for that matter) in generic learning applications. It isn’t a demonstration that neural nets are being advanced into the area of general learning. This is not an Artificial Intelligence that that could be, essentially, self-teaching and therefore life-like in terms of its capabilities.

And, just to let the press know, it isn’t the end of the world.

Known Bugs – Arab Israeli Wars

Arab Israeli Wars

Version 0.1.3.0. (April 22nd 2017)

  1. If you move a vehicle, and still have additional transfers left, but don’t want to use them, the system may wait forever for you to make another transfer. This doesn’t always happen, but if it does, moving a unit around within the same front will usually result in the prompt.
  2. If multiple informational displays are show simultaneously and overlapped, the hide button may show through the upper card from the lower card.