Human inventions find their inspiration from nature. Likewise, deep learning was an attempt to model the human brain, one of the most complicated structures in the universe. The attempt was not to mimic every detail of the brain. Instead, artificial neural networks were inspired by biological neural networks, eventually leading to deep learning. So what is deep learning?

Neural networks have gained importance as the machine learning models that achieve state-of-the-art performance on large-scale image classification, object detection and natural language processing tasks. In this paper, we consider noisy binary neural networks, where each neuron has a non-zero probability of producing an incorrect output. These noisy models may arise from biological, physical and electronic contexts and constitute an important class of models that are relevant to the physical world. Intuitively, the number of neurons in such systems has to grow to compensate for the noise while maintaining the same level of expressive power and computation reliability. Our key finding is a lower bound for the required number of neurons in noisy neural networks, which is first of its kind. To prove this lower bound, we take an information theoretic approach and obtain a novel strong data processing inequality (SDPI), which not only generalizes the Evans-Schulman results for binary symmetric channels to general channels, but also improves the tightness drastically when applied to estimate end-to-end information contraction in networks. Our SDPI can be applied to various information processing systems, including neural networks and cellular automata. Applying the SDPI in noisy binary neural networks, we obtain our key lower bound and investigate its implications on network depth-width trade-offs, our results suggest a depth-width trade-off for noisy neural networks that is very different from the established understanding regarding noiseless neural networks. Furthermore, we apply the SDPI to study fault-tolerant cellular automata and obtain bounds on the error correction overheads and the relaxation time. This paper offers new understanding of noisy information processing systems through the lens of information theory.

The success of neural networks in image classification has inspired various hardware implementations on embedded platforms such as Field Programmable Gate Arrays, embedded processors and Graphical Processing Units. These embedded platforms are constrained in terms of power, which is mainly consumed by the Multiply Accumulate operations and the memory accesses for weight fetching. Quantization and pruning have been proposed to address this issue. Though effective, these techniques do not take into account the underlying architecture of the embedded hardware. In this work, we propose PoET-BiN, a Look-Up Table based power efficient implementation on resource constrained embedded devices. A modified Decision Tree approach forms the backbone of the proposed implementation in the binary domain. A LUT access consumes far less power than the equivalent Multiply Accumulate operation it replaces, and the modified Decision Tree algorithm eliminates the need for memory accesses. We applied the PoET-BiN architecture to implement the classification layers of networks trained on MNIST, SVHN and CIFAR-10 datasets, with near state-of-the art results. The energy reduction for the classifier portion reaches up to six orders of magnitude compared to a floating point implementations and up to three orders of magnitude when compared to recent binary quantized neural networks.

Researchers at the Research Center for IT Innovation of Academia Sinica, in Taiwan, have recently developed a novel generative adversarial network (GAN) that has binary neurons at the output layer of the generator. This model, presented in a paper pre-published on arXiv, can directly generate binary-valued predictions at test time. So far, GAN approaches have achieved remarkable results in modeling continuous distributions. Nonetheless, applying GANs to discrete data has been somewhat challenging so far, particularly due to difficulties in optimizing the model distribution toward the target data distribution in a high-dimensional discrete space. Hao-Wen Dong, one of the researchers who carried out the study, told Tech Xplore, "I am currently working on music generation in the Music and AI Lab at Academia Sinica. In my opinion, composing can be interpreted as a series of decisions--for instance, regarding the instrumentation, chords and even the exact notes to use. To move toward achieving the grand vision of a solid AI composer, I am particularly interested in whether deep generative models such as GANs are able to make decisions. Therefore, this work examined whether we can train a GAN that uses binary neurons to make binary decisions using backpropagation, the standard training algorithm."

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 .