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_0: The ability of learning networks to generalize can be greatly enhanced by providing constraints from the task domain. This paper demonstrates how such constraints can be integrated into a backpropagation network through the architecture of the network. This approach has been successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service. A single network learns the entire recognition operation, going from the normalized image of the character to the final classification.
  @cite_1: Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that use backpropagation to learn their own programming. Despite their appeal NTMs have a weakness that is caused by their sequential nature: they are not parallel and are are hard to train due to their large depth when unfolded. We present a neural network architecture to address this problem: the Neural GPU. It is based on a type of convolutional gated recurrent unit and, like the NTM, is computationally universal. Unlike the NTM, the Neural GPU is highly parallel which makes it easier to train and efficient to run. An essential property of algorithms is their ability to handle inputs of arbitrary size. We show that the Neural GPU can be trained on short instances of an algorithmic task and successfully generalize to long instances. We verified it on a number of tasks including long addition and long multiplication of numbers represented in binary. We train the Neural GPU on numbers with upto 20 bits and observe no errors whatsoever while testing it, even on much longer numbers. To achieve these results we introduce a technique for training deep recurrent networks: parameter sharing relaxation. We also found a small amount of dropout and gradient noise to have a large positive effect on learning and generalization.
summary: A limitation of the CPPN approach is that weights are evolved rather than being learned by gradient-based methods that utilize backpropagation. Such methods scale better than evolutionary methods with respect to the number of parameters in the model. They are able to optimize millions of parameters at once, e.g. for convolutional neural networks for performing object classification on ImageNet @cite_1 . CPPNs and convolutional neural networks have previously been studied with CPPNs being used to evolve adversarial examples for convolutional network classifiers on ImageNet @cite_0 . However, in that work the CPPN is not modified by gradient descent.