The Creativity Code: How AI is learning to write, paint and think. Marcus Sautoy du

it would singularly fail for anyone outside this group, as no new citizen would have that passport number.

      Given ten points on a graph, it is possible to come up with an equation that creates a curve which passes through all the points. You just need an equation with ten terms. But, again, this has not really revealed an underlying pattern in the data that could be useful for understanding new data points. You want an equation with fewer terms, to avoid this over-fitting.

      Over-fitting can make you miss overarching trends by inviting you to model too much detail, resulting in some bizarre predictions. Here is a graph of twelve data points for population values in the US since the beginning of the last century. The overall trend is best described by a quadratic equation, but what if we used an equation with higher powers of × than simply x²? Taking an equation with powers all the way up to x¹¹ actually gives a very tight fit to the data, but extend this equation into the future and it takes a dramatic lurch downwards, predicting complete annihilation of the US population in the middle of October in 2028. Or perhaps the maths knows something we don’t!

      Algorithmic hallucinations

      Advances in computer vision over the last five years have surprised everyone. And it’s not just the human body that new algorithms can navigate. To match the ability of the human brain to decode visual images has been a significant hurdle for any computer claiming to compete with human intelligence. A digital camera can take an image with a level of detail that far exceeds the human brain’s storage capacity, but that doesn’t mean it can turn millions of pixels into one coherent story. The way the brain can process data and integrate it into a narrative is something we are far from understanding, let alone replicating in our silicon friends.

      Why is it that when we receive the information that comes in through our senses we can condense it into an integrated experience? We don’t experience the redness of a die and its cubeness as two different experiences. They are fused into a single experience. Replicating this fusion has been one of the challenges in getting a computer to interpret an image. Reading an image one pixel at a time won’t tell us much about the overall picture. To illustrate this more immediately, take a piece of paper and make a small hole in it. Now place the paper on an A4 image of a face. It’s almost impossible to tell whose face it is by moving the hole around.

      Five years ago this challenge still seemed impossible. But that was before the advent of machine learning. Computer programmers in the past would try to create a top-down algorithm to recognise visual images. But coming up with an ‘if …, then …’ set to identify an image never worked. The bottom-up strategy, allowing the algorithm to create its own decision tree based on training data, has changed everything. The new ingredient which has made this possible is the amount of labelled visual data there is now on the web. Every Instagram picture with our comments attached provides useful data to speed up the learning.

      You can test the power of these algorithms by uploading an image to Google’s vision website: https://cloud.google.com/vision/. Last year I uploaded an image of our Christmas tree and it came back with 97 per cent certainty that it was looking at a picture of a Christmas tree. This may not seem particularly earth-shattering, but it is actually very impressive. Yet it is not foolproof. After the initial wave of excitement has come the kickback of limitations. Take, for instance, the algorithms that are now being trialled by the British Metropolitan Police to pick up images of child pornography online. At the moment they are getting very confused by images of deserts.

      ‘Sometimes it comes up with a desert and it thinks it’s an indecent image or pornography,’ Mark Stokes, the department’s head of digital and electronics forensics, admitted in a recent interview. ‘For some reason, lots of people have screen-savers of deserts and it picks it up, thinking it is skin colour.’ The contours of the dunes also seem to correspond to shapes the algorithms pick up as curvaceous naked body parts.

      There have been many colourful demonstrations of the strange ways in which computer vision can be hacked to make the algorithm think it’s seeing something that isn’t there. LabSix, an independent student-run AI research group composed of MIT graduates and undergraduates, managed to confuse vision recognition algorithms into thinking that a 3D model of a turtle was in fact a gun. It didn’t matter at what angle you held the turtle – you could even put it in an environment in which you’d expect to see turtles and not guns.

      The way they tricked the algorithm was by layering a texture on top of the turtle that to the human eye appeared to be turtle shell and skin but was cleverly built out of images of rifles. The images of the rifle are gradually changed over and over again until a human can’t see the rifle any more. The computer, however, still discerns the information about the rifle even when they are perturbed, and this ranks higher in its attempts to classify the object than the turtle on which it is printed. Algorithms have also been tricked into interpreting an image of a cat as a plate of guacamole, but LabSix’s contribution is that it doesn’t matter at what angle you showed the turtle, the algorithm will always be convinced it is looking at a rifle.

      The same team has also shown that an image of a dog that gradually transforms pixel by pixel into two skiers on the slopes will still be classified as a dog even when the dog had completely disappeared from the screen. Their hack was all the more impressive, given that the algorithm being used was a complete black box to the hackers. They didn’t know how the image was being decoded but still managed to fool the algorithm.

      Researchers at Google went one step further and created images that are so interesting to the algorithm that it will ignore whatever else is in the picture, exploiting the fact that algorithms prioritise pixels they regard as important to classifying the image. If an algorithm is trying to recognise a face, it will ignore most of the background pixels: the sky, the grass, the trees, etc. The Google team created psychedelic patches of colour that totally took over and hijacked the algorithm so that while it could generally recognise a picture of a banana, when the psychedelic patch was introduced the banana disappeared from its sight. These patches can be made to register as arbitrary images, like a toaster. Whatever picture the algorithm is shown, once the patch is introduced it will think it is seeing a toaster. It’s a bit like the way a dog can become totally distracted by a ball until everything else disappears from its conscious world and all it can see and think is ‘ball’. Most previous attacks needed to know something about the image it was trying to misclassify, but this new patch had the virtue of working regardless of the image it was seeking to disrupt.