We all know that processing and representation are intimately linked.27 So, given this general fact, how does one get the representation correct for creativity? If the representations used by BRUTUS.1 are inadequate, what might work? What about creative processes in evolutionary computation? And what about marrying a new mode of representation to processing that is evolutionary in character, rather than (as in the case of BRUTUS.1) processing that is essentially theorem proving?
The first response to such questions is to observe that present systems of evolutionary computation would seem to squelch their capacity for creative processes because of their own impoverished representation schemes. Consider, for example, one of the standard processes of an evolutionary system: epigenesis -- the process in an evolutionary system that translates a given genotype representation into the phenotype representation.28 The present systems of evolutionary computation use parameterized computational structures to accomplish epigenesis: such systems use the genotype representation to encode levels of the parameters, and the phenotype representation becomes the direct output. The use of parameterized computational structures to formalize that which is within the reach of an evolutionary system works just as poorly as the methods behind BRUTUS.1. Pre-set parameterized computational structures are limited in their ability to map the levels of a finite number of parameters (even if the value of the parameters are infinite) onto a complete set of designs. Just as BRUTUS.1, for reasons discussed above, is tackling a space that probably can't be ``mastered" via parameterized computational structures, so too present evolutionary systems face the same uphill battle. If we consider not , the space of interesting short-short stories, but the space of interesting paintings, then Hofstadter has probably given us the key paper: he has argued in [Hofstadter, 1982] that when Knuth [Knuth, 1982] applied such a system to the design of fonts, he was bound to fail: the system could only cover a small portion of the set of all `As,' for example. (The wildly imaginative As drawn in Hofstadter's paper are reason enough to read it; see Figure 1.) The use of parameterized computational structures, if you will, requires describing the quintessence of the hoped-for design before the (evolutionary) system can seek a solution.
In our opinion, a system is creative only if it can somehow capture the quintessence of the space from which a particular design is is to come. On this view, creativity occurs outside of (at least most) current evolutionary systems. This is so because such systems, like the logic-based BRUTUS.1, are based on a pre-selected and bounded design space.
One of us (Noel), working with Sylvia Acchione-Noel, has created a system -- MONA-LISA -- that changes things: MONA-LISA uses an information-based representation that affects the resolution of the system (the ability to describe a wave form) but forces no feature-level dimension on the system. The representation is based on atomic or molecular representation, similar to the notions of atomic or molecular decomposition by Fourier analysis or wavelets [Meyer, 1993]. This new evolutionary system evolves patterns of pixelsinto any desired image. The use of a sub-feature representation requires the units evolve simultaneously en mass to generate both the features and the configuration of an image. The evolved image is not constrained at the feature level and can encode a dog, a tree, a car, or, just as easily, a face. (If there is anything to the view that the set of all As makes a productive set, such a view in connection with the set of all faces is hardly implausible. And of course we believe that this view on As is quite plausible. We direct readers to [Hofstadter, 1982] for the data and evidence. This paper includes an interesting collection of faces.) However, the resolution of the images is affected by the number of pixels or the atomic representation used in the system. For instance, the ``portrait" of Abraham Lincoln shown in Figure 2 was evolved in a 25-by-25 pixel space which can only represent images with 12.5 lines of resolution or less.
Traditional evolutionary programs use parameterized modeling to map between the genotype and the phenotype. The use of such models results in a direct mapping between the set of genes that comprise a parameter, and the level of the feature that the parameter models in the phenotype. There is no noise, no pheiotropy, no polygeny in the mapping. The system can only create objects within the parameterized space, and all objects evolved are members of that space. For instance, one might model a face by making a model in which some genes selected types of eyes, noise, lips, ears, face shape, hair, etc., and other genes arrange the features within configurations of a normal face. If one were using such a system, the population of the first generation would all look like faces. One would select the faces that are most like the intended face and use them for breeding the next generation. The impact of this is that one must constantly compare faces with the intended face to make decisions. One face might have the eye shape and size right, while another might have the distance between the eyes correct.
In our technique, the desired or intended image is considered the signal, and all other images are considered noise. The elicitation of the image is done by a biased selection of the objects that generate the greatest recognition, or signal to noise ratio, in each generation. In keeping with our example, consider evolving a face image. The first generation is pure noise, or in other words, all possible images are equally likely. The task of the evolver is to select the images for breeding that have the greatest signal (most like the face to be evolved) and therefore the least noise. At first, the probability of any image looking like a face, any face, is extremely unlikely. Most images look like the snow on a TV tuned to a channel without a station. However, one can select images whose pixels might give the impression of something rounded in the middle, dark in the area of hair, or light where cheeks may be. Since the images selected to parent the next generation have more of the signal and consequently less noise, it will give rise to a population of images whose mean signal to noise ratio will be greater than the previous generation. Eventually the signal to noise ratio is strong enough to elicit the intended image.
In our evolutionary system one only sees the face that one seeks. The face is seen in different amounts of noise, from high to low. In high noise conditions, only the lowest spatial frequency in low contrast can be imaged. As the image evolves, the level and contrast of detail increases. The end image is much like seeing the intended face in a cloud in that there are no distinct features, but a holistic precept. While the quality of the image is at present limited in resolution (about 15 to 20 lines of resolution), the reader should be reminded that the system can evolve any image that the pixels can represent. One could just as easily select to evolve a horse, a ball, a tree, etc. In the traditional approach one is limited to a domain and would require a new model for each new type of object to be evolved.
MONA-LISA is at present a two-dimensional system used by humans to create images, but it can be generalized to other domains. Humans were chosen to perform the judging and selecting.29 Evolutionary systems are not necessarily, by themselves, creative. Creativity in evolution presumably occurs through the interaction of the objects and their environment under the forces of natural selection. However, as we have said, evolutionary systems can preclude creativity -- by limiting and bounding the phenotype.30 MONA-LISA gives full rein to representational power to the user. It starts from scratch or from randomness, and it is truly general since the image's features are not pre-determined.31