Clune, Jeff, Charles Ofria, and Robert T. Pennock. “The sensitivity of HyperNEAT to different geometric representations of a problem.” In *Proceedings of the 11th Annual conference on Genetic and evolutionary computation* , pp. 675-682. 2009.

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HyperNEAT, a generative encoding for evolving artificial neural networks (ANNs), has the unique and powerful ability to exploit the *geometry* of a problem (e.g., symmetries) by encoding ANNs as a function of a problem’s geometry. This paper provides the first extensive analysis of the sensitivity of HyperNEAT to different geometric representations of a problem. Understanding how geometric representations affect the quality of evolved solutions should improve future designs of such representations. HyperNEAT has been shown to produce coordinated gaits for a simulated quadruped robot with a specific two-dimensional geometric representation. Here, the same problem domain is tested, but with different geometric representations of the problem. Overall, experiments show that the quality and kind of solutions produced by HyperNEAT can be substantially affected by the geometric representation. HyperNEAT outperforms a direct encoding control even with randomized geometric representations, but performs even better when a human engineer designs a representation that reflects the actual geometry of the robot. Unfortunately, even choices in geometric layout that seem to be inconsequential a *priori* can significantly affect fitness. Additionally, a geometric representation can bias the *type* of solutions generated (e.g., make left-right symmetry more common than front-back symmetry). The results suggest that HyperNEAT practitioners can obtain good results even if they do not know how to geometrically represent a problem, and that further improvements are possible with a well-chosen geometric representation.