A New year’s post!

Kumbakarna

Kumbakarna

Happy new year all :) Belated wishes and wishes still even if somebody moved your new year to a different date :P On Vishu day, (apparently) it is tradition to pick a random chapter in the Ramayana early in the morning, and whatever is read is said to have some impact on the reader’s life in the coming year. I tried it yesterday and the chapter I picked was about Vibheeshana’s confrontation with Ravana. It was quite serendipitous as the event has constantly been a source of confusion to me. To elaborate …..,

Vibheeshana

Vibheeshana

Two of Ravana’s brother are source of particular interest – Kumbakarna and Vibheeshana. Both, at some point advise Ravana against a war with Rama. However Vibheeshana is shouted at for this advise and  leaves Lanka to join forces with Rama and betrays many of Lanka’s secrets to Rama. He is later anointed King of Lanka after Ravana’s death. Kumbakarna makes the same advice but follows it up by comforting Ravana speaking of an assured victory despite knowing fully well what was in store for him. Kumbakarna is eventually killed in battle.

Kumbakarna’s actions are all too familiar. Actions like his are replicated in the Mahabharatha and is generally seen as the nobler of the two courses. Vibheeshana is often criticized for betraying his King and is commonly seen as an usurper and traitor. So then what is the confusion? Vibheeshana is (at the end of the epic) ordered by Lord Vishnu in the original form to guide people towards Dharma. He also becomes an immortal joining the ranks of Hanuman, Parasurama and Mahabali. What the _?

For those of us who are used to seeing the epics in black and white (no, not literally) – and thanks to Ramanand Sagar for this - this situation is confusing. What is correct here? Too often in life we are faced with similar situations. When and why is it ever right to be a snitch!! And the epics seem to be of no help here – both courses are shown as good and not against Dharma. All along, Valmiki continually praises the qualities of Vibheeshana – he is at no point portrayed as greedy or selfish. Instead, the descriptions are

“Vibheeshana spoke to powerful Ravana the words convinced of reason and which were very much beneficial. He, who could discriminate between good and evil things in the world, having sought the favour from his eldest (half-) brother by means of soothing words arranged in an order, spoke in consonance with place, time and purpose.”

I am not still fully clear why this action is considered correct. I am not at that level yet. But the original author clearly seems to think so. Feel free to read the original text and make sense of it. If you come by interesting commentaries, I would love to be notified.

The intention that drives your action is perhaps more important than the action itself. From a different perspective, this episode reinforces the idea that there is no distinct line between black and white in such situations.

I want to make a special note of this because it is very easy to get lost in the strongly polar natures of the main characters in the epics. The epics would seem to be of no practical use as situations or characters as seen in them would never happen in real life. In fact however, there is a large trove of such useful tips and indicators buried within them. Many answers are here. So take a closer look.

References and Further reading:

Note: Nope, this is no longer going to be an exclusively tech blog. There is enough boring content on the net already. Time for some arbit content. Sure there’s enough of that too, but the world could always use more :P

On Tigers, diffusion and chaos

Tiger

RT @sanchan89 Always good to know that my mojo is still intact after 4 years :) Take a look http://bit.ly/bGv5su

So, after quite a while, I tried sketching again. And it came out pretty neat, I suppose. But then, I want this to be a tech blog, right?

We humans, have a somewhat dull skin[1]. It is completely bereft of any fur[2] and any pattern to be had on are to be painfully tattooed. Look, on the other hand , at the pervasive presence of spacial patterns on animal coats and flora. Most commonly seen in plants are the rosette patterns, and self replicating branching systems. Mammals and fishes are so much richer – their fur coats come with stripes, spots, rosettes, bands, blocks, combination of these  and in the case of some sea shells – Serpenski triangle! Even in animal behavior, there is so much elegance – if you have not seen the movements of large schools of fish or birds in flight, you have a serious problem and you should consult a psychotherapist. Even the inanimate desert sands are beautifully patterned with near parallel curves.

Spatial patterns collage

Spacial patterns collage

It makes us think, doesn’t it? How are these patterns formed?

If every skin cell were to take on either black or white color with a uniformly random probability, then a zebra would look like white noise. Try imagining one with a coat like that. No probabilistic distribution is ever going to generate patterns as fantastic as those on every tiger. Does every cell, then, have a global spacial view of itself? Is it possible that a single cell knows that it is a part of the stripe across the head of the tiger, and therefore, it should take on a black pigmentation? That seems like something phenomenally complex for a single living cell to know.

Related problems in developmental biology are cell differentiation, and Morphogenesis. Every cell in an embryo is the same. Embryos are homogenous; and yet without a single central controller, cells in different areas of the embryo develop into different parts of the body. Some develop into the the heart and lungs and others into brain and legs.

The first explanation for this phenomenon was provided by the British Mathematician, code breaker, logician, computer scientist ( and during the later days of his life, a chemist )  Alan Turing in his paper titled ‘The Chemical basis of Morphogenesis” in 1951.  ( This paper has its own wiki page ) The paper described mechanisms; borrowing heavily from concepts of self-organisation, well known in physics; by which non-uniformity may arise from uniform homogeneous states, and outlined the reaction-diffusion theory of morphogenesis. Reaction–diffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space.

Independently, around the same time a Russian biophysicist Boris Belousov discovered a reaction-diffusion system, now called the Belousov-Zhabotinsky reaction. Where Turing had proposed mathematical models, here was already a demonstration of the self-organizing tendencies of the non linear systems which he had proposed. Here’s a video of a BZ cocktail evolving

From a uniformly homogeneous solution – spirals, spots and expanding rings are formed. And no two instances of the same experiment will get you the exact same results. The equations that govern these reactions are so expressive that you can actually come up with results that show stripes and hexagons! Try it out yourself in this applet.

These two works are considered by some as the founding work on chaos theory. In a nutshell, Chaos theory deals with highly nonlinear and usually self looped systems that despite being fully deterministic, are subject to abrupt and seemingly random change. It is clear in this case -  In spite of explicitly and deterministically defined rules, the reaction-diffusion yields a uniquely different result every time. The source of all this chaos is, well…, in the source itself. The non-linearity of the system greatly magnifies even immeasurably small changes in the initial state. So, the next time you round up a value from 0.506127 to 0.506, be warned! As a sidenote, the phrase “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?“, is not a misunderstanding of chaos theory. It is in fact the title of the talk presented by Edward Lorenz at AAAS, 1972 on chaos theory. The title was the result of inferences from a run of the simulation he had built, when he changed one of the values of atmospheric conditions as stated above.

If you are interested in learning more about Chaos theory, there is a fantastic one hour program on BBC. No, it does not have equations ( well, maybe just one )

  1. Well, thats not entirely true! We have fingerprints. And they are beautiful and unique, but not colorful or macro. Guess that still qualifies as dull.
  2. This is interesting because, man is the only mammal; excluding those that are aquatic, that has no fur, check out the February 2010 edition of Scientific American

Further reading

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Vision and Cognition

Quite eventful, these past 3 months. I presented my first publication at the World Congress on Natural and Bio-Inspired Computing in December; attended the Microsoft Research India Winter school on machine learning and computer vision, followed by Kurukshetra, in January.

Some pics first – NaBIC 09, MSRI Winter School, Kurukshetra. Our NaBIC paper is here and our code is here. In short, we show that a simple iterative algorithm can find a very good photomosaic when compared to other population based methods like genetic algorithms. To induce some interest, here is one of our results.

Now that the pictures have spoken the thousand words……

Human Vision

I have been a follower of Predicatbly Irrational after watching Dan Ariely’s talks ( here and here ) on Ted.com. Both talks are delightfully entertaining and demonstrate with wonderful examples the fallibility of our own decision-making capacity. For a while after each talk, I spent a lot of time probing into every decision I make, usually ending up almost undecided. As an undergrad who has to choose between a career and higher education – it couldn’t have come at a worse time. I was already in doubt whether I was applying to graduate schools simply because it was what the best among us were doing. Equally, I didn’t know whether it was simply cold feet/cowardice or the safety of a job at Amazon India that was making me have second thoughts about higher education.

Coming back; Dan starts off by using visual illusions as a metaphor. Here’s an example:

The Grey square optical illusionSame color illusion proofTake a look at the image on the left. It seems absolutely impossible that squares marked A and B are the same. They seem to be opposing colors, but in fact they are exactly the same. The proof is on the image to the right. `What is gong on here? How can it be that we see wrong? How can it be that even after we are shown that these two patches are identical we still can’t see them accurately when look left again?`

Dan’s ( more colorful ) example is here. Quoting from his blog:

Now, vision is our best system. We have lots of practice with it (we see many hours in the day and for many years) and more of our brain is dedicated to vision than to any other activities. So consider this — if we make mistakes in vision, what is the chance that we would not make mistakes in other domains? Particularly in domains which are more complex (dealing with insurance, money, etc.), and ones in which we have less practice? Domains such as decision making and economic reasoning?

So a few thousand years of evolution of the visual cortex ( which by the way is the largest part of the human brain ) and eyes has given us a visual system that can’t even see the world for what it truly is even; after it is explicitly demonstrated? Not exactly…..,

Gestalt Theory

One of the plenary talks @ NaBIC was on Gestalt psychology. Gestalt in German means – shape of an entity’s complete form. The principle behind gestalt theory is that out brain is very holistic and understands more than what the sum of the parts indicate. The concept itself is somewhat difficult to put down in words, but a few examples expose some interesting aspects of our cognition system. For example, take a look at the following picture:

Emergence

If at first you cannot make sense of the image, take a second to look at it before continuing with the text. The picture demonstrates `emergence `. After a while the scene with the dalmatian dog sniffing the path emerges. One can even make out the fallen leaves, the crossroads and the trees in the background. We do not recognize the dog’s body parts and then put them together to form the concept of the dog! Instead we perceive the dog and then make sense of its parts. The gestalt psychology theory gives only a description of this phenomenon and does not provide any explanation as to how we do it ( and it has been zinged a lot for that ).

Reification

Reification

Another phenomenon is called `reification`. It is when we understand more than what we see. Look to the right. There is no triangle in A, but we perceive it, no rectangle in B, but we see it. We can sense the presence of a sphere in C and the (absent) surface of water over which the snake glides!

Multistability

Multistability

Before this post becomes a copy of the wiki page, one last example. This phenomenon is called `multistability`. As you keep looking at the images to the left, you keep shifting between two interpretations of the same image. The first image is the necker cube.

You can read more on Gestalt in its wiki page. For reviews of technical articles, see here.

There is already some criticism about the traditional statistics based approach to Computer Vision, and it seems almost impossible for any system now to truly replicate any of the phenomenon demonstrated above. But, there have been some attempts.

It is said that almost every branch of science follows a steep sigmoid. And there was consensus at the winter school ( which included Jitendra Malik, Yan LeCunYair Weiss, Martin Wainwright, Bruno Olhaussen, Richard Zemmel, William Freeman and Manik Varma — I am mentioning only the CV people here ) that computer vision is currently only at the bottom end on the verge of the steep rise; and that fifty years from now the best computer vision systems could be based on a completely different set of fundamentals.

Understanding Motion

Federer in action

Federer in action

Point light displays

Point light display

The next level is understanding videos, or at a least of sequence of images. But can’t we understand the action from a single image? Sure, if its an image like the one on the left, it says a lot about the action being performed and precludes the need to understand image sequences. But what about the image on the right? Umm., not so sure. Looks like a human, but its not trivially understood what it is or what it is doing.

Watch the related videos on youtube.

That makes it a lot clearer. Dr. Malik presented a video on the research work of one Dr. Johansson from the 1970s ( I have not been able to locate the original video. Its not on youtube). There has been a lot of work after that trying to understand our pre-disposition to recognize biological motion. Apparently babies only three months old can perceive as much. So can other mammals!

Some pages on biological motion detection:

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Computer Go (….continued)

The last post on Computer Go (about a year back) was a brief description of the game, and why it is very difficult to approach Go in the same way we tackled Chess.

In a 4 page article on IEEE spectrum, Feng – Hsiung Hsu – the architect and the principal designer of the IBM Deep Blue – discusses in some detail about how Go could be solved using brute force and variations of Min-Max search itself. The article does not go into great detail about the principal problem with computer Go – the evaluation of board positions. Also, one statement caught my eye:

On top of that, in 10 years Moore’s law is expected to present us with still another 100-fold speedup.

I was under the impression that Moore’s law had already reached its limit. However, by adding more and better processors, supercomputers, will undoubtedly be able to do more operations in parallel. In this article we take a look at the most successful technique that takes advantage of the massive parallel processing power of today’s supercomputers – Monte Carlo Techniques using UCT – and deal the advancements made to it in a later post.

As a side-note – For a while now, I had felt that these approaches are not the best way to tackle Go, and that systems that mimic the behavior of human pattern recognition and learning mechanisms are the way to go ( no pun intended ). There was recently a small discussion in the Go mailing list about the use of Neural Networks in tackling Go. This one remark by Alvaro Begue, has affected strongly my sentiments on the issue:

People tried to make flying machines by imitating birds for a long time. Planes and helicopters fly, but not like birds do it. Similarly, I believe that whenever we figure out how to make machines that play go well, they will not do it like a brain does it.

The point being made here is that the computing systems that we have today are very different from the wirings in our own brains. We do not have very good brain-like pattern recognition system. What we do have are really fast parallel systems that perform simple operations at an amazing speed. And our aim should be to learn to use that effectively.

Monte Carlo Go – MoGo and CrazyStone

The introduction of Monte Carlo methods was a great boost to Computer Go. Currently, the best Computer Go program is MoGo and it uses Monte Carlo evaluation with the UCT algorithm. MC-Go engines explore the game tree upto a certain depth and then use Monte Carlo simulation to evaluate the leaf positions. The biggest issue in computer Go is that there is no way to evaluate the resulting board position after the Min-max tree has been explored to a certain depth. Board evaluation is relatively easier in Chess. Positions and pieces directly give away the value of the board. There is no such simplicity in Go. Territories may change hands. And patterns formed initially may have complex implications across the board.

In Monte Carlo evaluation, multiple simulations are run to evaluate the board position. A stochastic player plays a number of random games against himself starting from this position; until the end, and the average of all the final scores is taken as an estimate of the board’s value. In some cases, the frequency of wins from the position is determined as the position’s value.

Something that we could improve is the stochastic player. Ideally, to effectively evaluate the board position, the stochastic player should model the opponent as closely as possible. This is understandably very difficult to achieve. Instead it is far more practical to make the stochastic player biased towards picking better moves ( as both players are in reality going to draw from a set of good moves ) instead of picking all moves uniformly randomly.

A naive implementation of Monte Carlo simulation based evaluation function, where every leaf is evaluated by running a constant number of simulations, will naturally waste simulations on poor board positions. Instead, its better distribute the available simulations properly to evaluate more promising moves more. This leads us to the Exploration vs Exploitation problem.

Exploration vs Exploitation problem

An intuitive example of this is the n-armed bandit problem. A gambler wants to maximize his winnings from a slot machine with n arms. Each arm has a different mean winning associated with it. Through repeated plays the gambler is to maximize his winnings by concentrating his plays on the best levers, except he doesn’t know which lever is the best. In the absence of this knowledge, the gambler’s choices are to choose between a greedy action (exploitation), where he selects the lever which has given him the maximum reward so far; or to explore and choose a different lever in the hope that it’ll give a greater reward. In MC-Go, during evaluation, every move is treated as different bandit problem.

Using UCT ( UCB1 applied to Trees ) in MC-Go

The UCB1 algorithm simply picks the move aj which maximizes this value UCB1 formula, where Xj is the average of all rewards obtained by selecting action aj, Tj is the number of times action aj was picked, and n is the total number of times any action was picked. It would be space-wise expensive if we were to maintain information about each bandit problem and its values. Therefore, both MoGo and CrazyStone do the Monte Carlo simulation in two phases. In the first phase, called Tree Policy UCB1 is followed, and in the other, a default policy ( using the stochastic player discussed earlier ) is used.

Starting from the board position to be evaluated as the root, MoGo selects a move according to UCB1. It then descends down the tree in a similar manner, until the selected node is not a part of the tree. MoGo then adds this node to the tree. The Tree Policy ends here. From here on the default policy using the stochastic player is used. The video shown illustrates the technique.

Resources for further reading

Most of the content here is from the slides of either Sylvian Gelly or Remi Coulom. Following up on the side-note, there are in fact two fairly strong Go programs built on neural networks – NeuroGo and Steenvreter. Lets see if I could read up on them and blog on it sometime. But soon, there’ll be a post on RAVE and hints on RL-Go.

Genetic Algorithms.., A Primer

It is Charles Darwin’s 200th birthday. So I guess there must be loads of posts on GA, strewn across the Internet. Genetic Algorithms are special to me because they are the prime reason why I am doing whatever it is that I am doing.

This post is a light intro to Genetic Algorithms, sans its terms. Genetic Algorithms are delightfully simple. GA is an approximation algorithm, that is, they are used in situations where either the optimal solution is unnecessary or the complexity of the problem does not permit it. Sometimes, the Genetic Algorithm may produce the most optimal result also. Since examples are the best way to learn an algorithm, here’s the example problem we are to solve.

Balancing moments

Balancing moments

Given to you is a configuration of balances as shown in the figure. The problem is to balance the configuration by adding weights on either side. You are provided with 10 weights measuring 1,2,3……10 kg each. Each weight is to be used exactly once. Thanks to GreatBG for this puzzle. His puzzles are always most entertaining. This can roughly be equated to the traveling salesperson problem. In the problem, the salesperson is to visit all cities (and comeback ), in such a sequence so as to minimize the total distance covered. The most naive solution is to try all possible sequences and see which one gives the minimum cost. For a map of n cities, that comes to n! combinations. A similar approach would work in our case also, but then, when the map or the number of weights is larger, the technique, takes so much more time. A more professional approach would be ruffle up your knowledge of elementary physics and reduce the problem to a set of linear equations and then solve them. Naaa.

Genetic Algorithms

My code, in C++, is here. Here’s the pseudo-code, sourced from wikipedia

  1. Choose initial population
  2. Evaluate the fitness of each individual in the population
  3. Repeat until termination: (time limit or sufficient fitness achieved)
    1. Select best-ranking individuals to reproduce
    2. Breed new generation through crossover and/or mutation (genetic operations) and give birth to offspring
    3. Evaluate the individual fitnesses of the offspring
    4. Replace worst ranked part of population with offspring

Initializing the Population

The algorithm maintains a set of solutions. Not optimal solutions, just solutions. For example, in the case of the TSP, it may be a set of random ordering of the cities. In our problem, a set of random configuration of weights. In the program, I maintain the configuration as a string, where the weight alloted to each slot is represented by a character, with ‘A’ being 1, ‘B’ being 2 and so on. The weights are added bottom to top and left to right. One point to be noted here is that all solutions in the set must stick to the constraints of the problem. No city must be re-visited, no weight can be added twice.

Evaluating the Population

This is the key part of the algorithm. Once a way is found to evaluate each member of the ‘population’, the problem is half complete already. In our case, the “fitness” will be based on the resultant moment in the system. Therefore, best solution will have 0 fitness, the resultant moment in the system would be zero.

Until the required precision is obtained, or a maximum limit on the number of iterations is reached, we continue by doing the following opertions.

Crossover

This is where we actually begin to understand why it is called Genetic Algorithms in the first place. According to Darwin’s thery of Natural Selection, the best members of the population mate to produce better offsprings. Similarly, in our algorithms, the best solutions found so far mate with each other to (hopefully) produce a better solution. In code, this translates as the merging of substrings from different members, chosen from among the best solutions found so far. Point to be noted is that if done improperly, this could result in an offspring, that is not even a valid member of the population. It might violate the problems’ constraints. In TSP, and in this case, the same city/weight might get listed again, which cannot be allowed. So we use a special crossover method called, Partially Matched Crossover(PMX in code) which is beyond the scope of a primer.

Mutation

Some members of the population are randomly chosen to be mutated. Mutation is a process by which the offsprings get a trait that is inherited neither from the father nor the mother.While translating into code, this simply means swapping two characters within the string. You can choose more complex mutation techniques if desired. Again, the problem constraints must be satisfied. Mutation is required mainly to increase the variety of solutions in the population. Variety is very important.

Natural Selection and Elitism

Once these operations are done on the parents, a new generation of solutions are born. To make sure that the best solution in this generation is atleast as good as the best one in the previous generation, we introduce “elitism”. Normally, all the individuals in the previous generation are replaced by the members from the newer generation. But by having a non zero elitism value, a small portion of the best solutions from the previous generation survive on in the next generation.

Going by the paradigm of survival of the fittest, we now select the best solutions from the both the generations and these form the actual next generation. (My code is slightly varied. It does not use natural selection, the members of the younger generation simply replace all but the elite members of the elder population)

Local Maxima

Genetic Algorithms suffer from the problem that it might converge to a non-optimal solution. Consider that we are looking for the solution that is at the top of a mountain. It is possible that the population end up on an elevated hill, far away form the mountain. This is possible if the various values are not tuned properly. The algorithm will not get out of this situation by itself. the best way to go in this kind of a scenario is to simply start again.

People, Blogs, Conferences and Applications

Game AI Development Event at Kurukshetra 09

College of Engineering, Guindy is organizing a game AI development event this time at  Kurukshetra, the annual International Techno-Management festival.

Kurukshetra 09

Kurukshetra 09

We wanted the event to reflect the current trends in the Game AI development industry. It is left to the participants to be the judge of to what extent the main goal is accomplished. The trends seem to be

  • Player specific content
  • A move away from hard-coded-rules based opponents.

We chose Lunar Lander to be the test game for both problem statements. Why? Lunar Lander was one of the earliest games to use Vector Graphics. But that’s not the reason why. Lunar Lander is simple, to code and to play. And.., it seemed to offer scope for hacking both problem statements. And now to the problem statements.

The First problem statement is a challenge to create a player that plays the Lunar Lander. You could try a rule based approach and try coding it. And you may succeed too. But I’ll bet the easier way out is to make your player learn how to handle the Lander. There are many situations where a rule based approach would fail. Consider the case of a car racing game, a rule based approach may satisfy the initial requirements of the game. Your racer may successfully out-race the human player, but it wouldn’t do well on tracks you, as its programmer would not have seen.  Because your AI doesn’t know how to ‘drive’. Well, that’s the motivation for this problem statement.

The second problem statement is with regards to content creation. Simple games such as Lunar Lander, I think deserve to engage the player for longer than 3 levels. The content of the game is very simple. It involves very little graphics. Is it possible to use modern / not-so-modern techniques to generate an infinite set of levels?? Theoretically, yes. Further, would these levels, ‘engage’ the player as much as hand-crafted levels would? It is definitely worth a try.

Well, if you are a Game AI developer PRO, and all this seems, well, ‘childish’ to you,  or in case you disagree with what we have identified as the current trend in the industry, try the third problem statement. If you have any innovative ideas on game AI, an implementation of your concept is most welcome. Although, we are not intending to accept any text-book based search algorithms. Even slightly modified but better versions are accepted.

This is the link to the event’s page. Please go through the problem statements again. This is the first time we are attempting such an event. Your comments and suggestions are welcomed. They would be most invaluable to making this a more successful event in the next editions of Kurukshetra. Have fun, Merry Christmas and Happy New Year!!!