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.
Recent work applied CPPNs in the HyperNEAT framework to evolve the weights of the 5 layer LeNet-5 convolutional neural network for MNIST character recognition @cite_16 . Classification performance with HyperNEAT alone used to optimize the weights of this network was very poor after 2500 generations, with only 50 Previous work exists in evolving the topology of neural networks for learning. For example evolved the topology of the cells of an LSTM (Long Short Term Memory) recurrent neural network for sequence learning @cite_30 , and more recently explored the topology of LSTMs and GRUs improving on both @cite_5 .
@cite_30 @cite_5 @cite_16
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Long short-term memory (LSTM) is normally used in recurrent neural network (RNN) as basic recurrent unit. However, conventional LSTM assumes that the state at current time step depends on previous time step. This assumption constraints the time dependency modeling capability. In this study, we propose a new variation of LSTM, advanced LSTM (A-LSTM), for better temporal context modeling. We employ A-LSTM in weighted pooling RNN for emotion recognition. The A-LSTM outperforms the conventional LSTM by 5.5 relatively. The A-LSTM based weighted pooling RNN can also complement the state-of-the-art emotion classification framework. This shows the advantage of A-LSTM. A Long Short-Term Memory (LSTM) network is a type of recurrent neural network architecture which has recently obtained strong results on a variety of sequence modeling tasks. The only underlying LSTM structure that has been explored so far is a linear chain. However, natural language exhibits syntactic properties that would naturally combine words to phrases. We introduce the Tree-LSTM, a generalization of LSTMs to tree-structured network topologies. TreeLSTMs outperform all existing systems and strong LSTM baselines on two tasks: predicting the semantic relatedness of two sentences (SemEval 2014, Task 1) and sentiment classification (Stanford Sentiment Treebank). 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.