text: In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution and learning, produces DPPNs to reconstruct an image. Our main result is that DPPNs can be evolved trained to compress the weights of a denoising autoencoder from 157684 to roughly 200 parameters, while achieving a reconstruction accuracy comparable to a fully connected network with more than two orders of magnitude more parameters. The regularization ability of the DPPN allows it to rediscover (approximate) convolutional network architectures embedded within a fully connected architecture. Such convolutional architectures are the current state of the art for many computer vision applications, so it is satisfying that DPPNs are capable of discovering this structure rather than having to build it in by design. DPPNs exhibit better generalization when tested on the Omniglot dataset after being trained on MNIST, than directly encoded fully connected autoencoders. DPPNs are therefore a new framework for integrating learning and evolution.
  @cite_19: Research in neuroevolution---that is, evolving artificial neural networks (ANNs) through evolutionary algorithms---is inspired by the evolution of biological brains, which can contain trillions of connections. Yet while neuroevolution has produced successful results, the scale of natural brains remains far beyond reach. This article presents a method called hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) that aims to narrow this gap. HyperNEAT employs an indirect encoding called connective compositional pattern-producing networks (CPPNs) that can produce connectivity patterns with symmetries and repeating motifs by interpreting spatial patterns generated within a hypercube as connectivity patterns in a lower-dimensional space. This approach can exploit the geometry of the task by mapping its regularities onto the topology of the network, thereby shifting problem difficulty away from dimensionality to the underlying problem structure. Furthermore, connective CPPNs can represent the same connectivity pattern at any resolution, allowing ANNs to scale to new numbers of inputs and outputs without further evolution. HyperNEAT is demonstrated through visual discrimination and food-gathering tasks, including successful visual discrimination networks containing over eight million connections. The main conclusion is that the ability to explore the space of regular connectivity patterns opens up a new class of complex high-dimensional tasks to neuroevolution.
  @cite_10: Legged robots can potentially venture beyond the limits of wheeled vehicles. While creating controllers for such robots by hand is possible, evolutionary algorithms are an alternative that can reduce the burden of hand-crafting robotic controllers. Although major evolutionary approaches to legged locomotion can generate oscillations through popular techniques such as continuous time recurrent neural networks (CTRNNs) or sinusoidal input, they typically face a challenge in maintaining long-term stability. The aim of this paper is to address this challenge by introducing an effective alternative based on a new type of neuron called a single-unit pattern generator (SUPG). The SUPG, which is indirectly encoded by a compositional pattern producing network (CPPN) evolved by HyperNEAT, produces a flexible temporal activation pattern that can be reset and repeated at any time through an explicit trigger input, thereby allowing it to dynamically recalibrate over time to maintain stability. The SUPG approach, which is compared to CTRNNs and sinusoidal input, is shown to produce natural-looking gaits that exhibit superior stability over time, thereby providing a new alternative for evolving oscillatory locomotion.
  @cite_11: Natural brains effectively integrate multiple sensory modalities and act upon the world through multiple effector types. As researchers strive to evolve more sophisticated neural controllers, confronting the challenge of multimodality is becoming increasingly important. As a solution, this paper presents a principled new approach to exploiting indirect encoding to incorporate multimodality based on the HyperNEAT generative neuroevolution algorithm called the multi-spatial substrate (MSS). The main idea is to place each input and output modality on its own independent plane. That way, the spatial separation of such groupings provides HyperNEAT an a priori hint on which neurons are associated with which that can be exploited from the start of evolution. To validate this approach, the MSS is compared with more conventional approaches to HyperNEAT substrate design in a multiagent domain featuring three input and two output modalities. The new approach both significantly outperforms conventional approaches and reduces the creative burden on the user to design the layout of the substrate, thereby opening formerly prohibitive multimodal problems to neuroevolution.
summary: In HyperNEAT @cite_19 , CPPNs are used as indirect compressed encodings of the weights of a larger neural network. The inputs to the CPPN are the coordinates of the presynaptic and postsynaptic neuron, and the output is the weight joining those two neurons. If a single CPPN must encode multiple layers of a deeper neural network then there are two possibilities, either an extra input is given signaling which layer of weights the CPPN is outputting @cite_10 , or the CPPN is constrained to always have multiple output nodes, with a specific node outputting the weight for its assigned layer @cite_11 .