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.
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.
@cite_0 @cite_1
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Deep convolutional neural networks have liberated its extraordinary power on various tasks. However, it is still very challenging to deploy state-of-the-art models into real-world applications due to their high computational complexity. How can we design a compact and effective network without massive experiments and expert knowledge? In this paper, we propose a simple and effective framework to learn and prune deep models in an end-to-end manner. In our framework, a new type of parameter – scaling factor is first introduced to scale the outputs of specific structures, such as neurons, groups or residual blocks. Then we add sparsity regularizations on these factors, and solve this optimization problem by a modified stochastic Accelerated Proximal Gradient (APG) method. By forcing some of the factors to zero, we can safely remove the corresponding structures, thus prune the unimportant parts of a CNN. Comparing with other structure selection methods that may need thousands of trials or iterative fine-tuning, our method is trained fully end-to-end in one training pass without bells and whistles. We evaluate our method, Sparse Structure Selection with several state-of-the-art CNNs, and demonstrate very promising results with adaptive depth and width selection. Code is available at: https: github.com huangzehao sparse-structure-selection. Multilayer Neural Networks (MNNs) are commonly trained using gradient descent-based methods, such as BackPropagation (BP). Inference in probabilistic graphical models is often done using variational Bayes methods, such as Expectation Propagation (EP). We show how an EP based approach can also be used to train deterministic MNNs. Specifically, we approximate the posterior of the weights given the data using a "mean-field" factorized distribution, in an online setting. Using online EP and the central limit theorem we find an analytical approximation to the Bayes update of this posterior, as well as the resulting Bayes estimates of the weights and outputs. Despite a different origin, the resulting algorithm, Expectation BackPropagation (EBP), is very similar to BP in form and efficiency. However, it has several additional advantages: (1) Training is parameter-free, given initial conditions (prior) and the MNN architecture. This is useful for large-scale problems, where parameter tuning is a major challenge. (2) The weights can be restricted to have discrete values. This is especially useful for implementing trained MNNs in precision limited hardware chips, thus improving their speed and energy efficiency by several orders of magnitude. We test the EBP algorithm numerically in eight binary text classification tasks. In all tasks, EBP outperforms: (1) standard BP with the optimal constant learning rate (2) previously reported state of the art. Interestingly, EBP-trained MNNs with binary weights usually perform better than MNNs with continuous (real) weights - if we average the MNN output using the inferred posterior. Although deep Convolutional Neural Network (CNN) has shown better performance in various computer vision tasks, its application is restricted by a significant increase in storage and computation. Among CNN simplification techniques, parameter pruning is a promising approach which aims at reducing the number of weights of various layers without intensively reducing the original accuracy. In this paper, we propose a novel progressive parameter pruning method, named Structured Probabilistic Pruning (SPP), which effectively prunes weights of convolutional layers in a probabilistic manner. Specifically, unlike existing deterministic pruning approaches, where unimportant weights are permanently eliminated, SPP introduces a pruning probability for each weight, and pruning is guided by sampling from the pruning probabilities. A mechanism is designed to increase and decrease pruning probabilities based on importance criteria for the training process. Experiments show that, with 4x speedup, SPP can accelerate AlexNet with only 0.3 loss of top-5 accuracy and VGG-16 with 0.8 loss of top-5 accuracy in ImageNet classification. Moreover, SPP can be directly applied to accelerate multi-branch CNN networks, such as ResNet, without specific adaptations. Our 2x speedup ResNet-50 only suffers 0.8 loss of top-5 accuracy on ImageNet. We further prove the effectiveness of our method on transfer learning task on Flower-102 dataset with AlexNet. Deep convolutional neural networks have liberated its extraordinary power on various tasks. However, it is still very challenging to deploy state-of-the-art models into real-world applications due to their high computational complexity. How can we design a compact and effective network without massive experiments and expert knowledge? In this paper, we propose a simple and effective framework to learn and prune deep models in an end-to-end manner. In our framework, a new type of parameter -- scaling factor is first introduced to scale the outputs of specific structures, such as neurons, groups or residual blocks. Then we add sparsity regularizations on these factors, and solve this optimization problem by a modified stochastic Accelerated Proximal Gradient (APG) method. By forcing some of the factors to zero, we can safely remove the corresponding structures, thus prune the unimportant parts of a CNN. Comparing with other structure selection methods that may need thousands of trials or iterative fine-tuning, our method is trained fully end-to-end in one training pass without bells and whistles. We evaluate our method, Sparse Structure Selection with several state-of-the-art CNNs, and demonstrate very promising results with adaptive depth and width selection.