We propose the BinaryGAN, a novel generative adversarial network (GAN) that uses binary neurons at the output layer of the generator. We employ the sigmoid-adjusted straight-through estimators to estimate the gradients for the binary neurons and train the whole network by end-to-end backpropogation. The proposed model is able to directly generate binary-valued predictions at test time. We implement such a model to generate binarized MNIST digits and experimentally compare the performance for different types of binary neurons, GAN objectives and network architectures. Although the results are still preliminary, we show that it is possible to train a GAN that has binary neurons and that the use of gradient estimators can be a promising direction for modeling discrete distributions with GANs. For reproducibility, the source code is available at https://github.com/salu133445/binarygan .

Backpropagation over deep neural networks has as much to do with the way the brain learns as modern jet airplanes have to do with the way birds fly. Both jets and birds fly, but they do so using entirely different principles. Jets do things birds cannot (fly at 500 miles per hour carrying many passengers), birds do things jets cannot (take off instantly). Each neuron is sending out "da dit da" messages like Morse code to neighboring neurons. The transfer functions are entirely different from RLUs or sigmoid.

By and large, Backpropagation (BP) is regarded as one of the most important neural computation algorithms at the basis of the progress in machine learning, including the recent advances in deep learning. However, its computational structure has been the source of many debates on its arguable biological plausibility. In this paper, it is shown that when framing supervised learning in the Lagrangian framework, while one can see a natural emergence of Backpropagation, biologically plausible local algorithms can also be devised that are based on the search for saddle points in the learning adjoint space composed of weights, neural outputs, and Lagrangian multipliers. This might open the doors to a truly novel class of learning algorithms where, because of the introduction of the notion of support neurons, the optimization scheme also plays a fundamental role in the construction of the architecture.

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we present the first application of Implicit Stochastic Gradient Descent (ISGD) to train neural networks, a method known in convex optimization to be unconditionally stable and robust to the learning rate. Our key contribution is a novel layer-wise approximation of ISGD which makes its updates tractable for neural networks. Experiments show that our method is more robust to high learning rates and generally outperforms standard backpropagation on a variety of tasks.

In real-world scenarios, it is appealing to learn a model carrying out stochastic operations internally, known as stochastic computation graphs (SCGs), rather than learning a deterministic mapping. However, standard backpropagation is not applicable to SCGs. We attempt to address this issue from the angle of cost propagation, with local surrogate costs, called Q-functions, constructed and learned for each stochastic node in an SCG. Then, the SCG can be trained based on these surrogate costs using standard backpropagation. We propose the entire framework as a solution to generalize backpropagation for SCGs, which resembles an actor-critic architecture but based on a graph. For broad applicability, we study a variety of SCG structures from one cost to multiple costs. We utilize recent advances in reinforcement learning (RL) and variational Bayes (VB), such as off-policy critic learning and unbiased-and-low-variance gradient estimation, and review them in the context of SCGs. The generalized backpropagation extends transported learning signals beyond gradients between stochastic nodes while preserving the benefit of backpropagating gradients through deterministic nodes. Experimental suggestions and concerns are listed to help design and test any specific model using this framework.

We consider time-domain digital backpropagation with chromatic dispersion filters jointly optimized and quantized using machine-learning techniques. Compared to the baseline implementations, we show improved BER performance and 40% power dissipation reductions in 28-nm CMOS. Joint Filter Optimization using Deep Learning The system setup is shown in Figure 1, where the four quantization blocks can be ignored for now. Introduction Fiber nonlinearities impose a fundamental limitation on transmission performance and various nonlinear compensation schemes have been proposed. Our focus is on digital backpropagation (DBP) which emulates backward fiber propagation using digital signal processing (DSP).

We introduce backdrop, a flexible and simple-to-implement method, intuitively described as dropout acting only along the backpropagation pipeline. Backdrop is implemented via one or more masking layers which are inserted at specific points along the network. Each backdrop masking layer acts as the identity in the forward pass, but randomly masks parts of the backward gradient propagation. Intuitively, inserting a backdrop layer after any convolutional layer leads to stochastic gradients corresponding to features of that scale. Therefore, backdrop is well suited for problems in which the data have a multi-scale, hierarchical structure. Backdrop can also be applied to problems with non-decomposable loss functions where standard SGD methods are not well suited. We perform a number of experiments and demonstrate that backdrop leads to significant improvements in generalization.

Most successful machine intelligence systems rely on gradient-based learning, which is made possible by backpropagation. Some systems are designed to aid us in interpreting data when explicit goals cannot be provided. These unsupervised systems are commonly trained by backpropagating through a likelihood function. We introduce a tool that allows us to do this even when the likelihood is not explicitly set, by instead using the implicit likelihood of the model. Explicitly defining the likelihood often entails making heavy-handed assumptions that impede our ability to solve challenging tasks. On the other hand, the implicit likelihood of the model is accessible without the need for such assumptions. Our tool, which we call spectral backpropagation, allows us to optimize it in much greater generality than what has been attempted before. GANs can also be viewed as a technique for optimizing implicit likelihoods. We study them using spectral backpropagation in order to demonstrate robustness for high-dimensional problems, and identify two novel properties of the generator G: (1) there exist aberrant, nonsensical outputs to which G assigns very high likelihood, and (2) the eigenvectors of the metric induced by G over latent space correspond to quasi-disentangled explanatory factors.

Backpropagation-based visualizations have been proposed to interpret convolutional neural networks (CNNs), however a theory is missing to justify their behaviors: Guided backpropagation(GBP) and deconvolutional network (DeconvNet) generate more human-interpretable but less class-sensitive visualizations than saliency map. Motivated by this, we develop a theoretical explanation revealing that GBP and DeconvNet are essentially doing (partial) image recovery and thus are unrelated to the network decisions. Specifically, our analysis shows that the backward ReLU introduced by GBP and DeconvNet, and the local connections in CNNs are the two main causes of compelling visualizations. Extensive experiments are provided that support the theoretical analysis.