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Some of you might have seen the movie “A Beautiful Mind” about John Nash, which was a professor at Princeton University and a Nobel prize winner for his contributions to game theory and mathematics. When I saw it many years ago, I was wondering why game theory is so important and what could be a practical application of it?  What and how can we use the “Nash Equilibrium” theory? Well, today we use it to generate synthetic images to be used to train Machine Learning models. Some uses are only for fun, like this example, while most others are for real-world applications. Here is an example of what a model can do when it reaches its “Nash Equilibrium” state with another AI.

I set up two neural networks to “fight” each other or play a non-cooperative game. One model knows what a real image is because I “showed” that AI those images. The other AI is generating images out of “thin air” and presents it to the first as being real images. The 1st will emphatically reject these images as being fake and back propagates all the errors, which are the differences in the image structure, patterns, features, and other details. So the 2nd AI corrects itself and tries again, to be rejected again and, so on for many, many cycles. This “game” goes on for hours or days but there comes a point when the images produced by the 2nd AI are so good that the 1st one is simply fooled and accepts the synthetic images as being real. At this point, we are at or near the Nash Equilibrium point and the practical results are the images generated by the 2nd AI (named Generator) which are so good that the 1st AI (named Discriminator) cannot tell them apart.

Some of the images generated as a result of the experiment I have done today are attached. I didn’t wait for the system to get to the equilibrium point, these were generated after 9hrs of training and the model was still improving. This is just for fun and visuals but nothing stops you to generate images of liver cancer, lung cancer, or any other medical condition which can be picked up by a CT scan and then using those hyper-realistic images to train another AI (yes, the 3rd one) to create a model for clinical use to analyse a CT Scan in 50ms, more accurately than a panel of 3 specialised doctors could do. Without the need for +20,000 CT scan images with cancer, all of them labelled by a specialist doctor as various cancer types and subtypes. Who is going to do that? Time, cost, privacy issues, etc. Massive roadblocks in developing ML systems that can help us humans and improve diagnostics and healthcare. This is just one example of how Nash Equilibrium and Game Theory can be used, thanks to Professor John Nash (1928-2015).

Original images labelled as real came from the work of the fantastic Leonora Carrington (1917-2011). This image was generated today by the process described above.

9brain Technologies provides bespoke dataset development services including generating synthetic images for the purpose of strengthening Machine Learning models and AI systems.

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