The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for scalable semi-supervised learning from multi-relational data. Key aspects of the novel GRNN architecture are the use of multi-relational graphs, the dynamic adaptation to the different relations via learnable weights, and the consideration of graph-based regularizers to promote smoothness and alleviate over-parametrization. Our ultimate goal is to design a powerful learning architecture able to: discover complex and highly non-linear data associations, combine (and select) multiple types of relations, and scale gracefully with respect to the size of the graph. Numerical tests with real data sets corroborate the design goals and illustrate the performance gains relative to competing alternatives.

Volumetric analysis of brain ventricle (BV) structure is a key tool in the study of central nervous system development in embryonic mice. High-frequency ultrasound (HFU) is the only non-invasive, real-time modality available for rapid volumetric imaging of embryos in utero. However, manual segmentation of the BV from HFU volumes is tedious, time-consuming, and requires specialized expertise. In this paper, we propose a novel deep learning based BV segmentation system for whole-body HFU images of mouse embryos. Our fully automated system consists of two modules: localization and segmentation. It first applies a volumetric convolutional neural network on a 3D sliding window over the entire volume to identify a 3D bounding box containing the entire BV. It then employs a fully convolutional network to segment the detected bounding box into BV and background. The system achieves a Dice Similarity Coefficient (DSC) of 0.8956 for BV segmentation on an unseen 111 HFU volume test set surpassing the previous state-of-the-art method (DSC of 0.7119) by a margin of 25%.

This study proposes a trainable adaptive window switching (AWS) method and apply it to a deep-neural-network (DNN) for speech enhancement in the modified discrete cosine transform domain. Time-frequency (T-F) mask processing in the short-time Fourier transform (STFT)-domain is a typical speech enhancement method. To recover the target signal precisely, DNN-based short-time frequency transforms have recently been investigated and used instead of the STFT. However, since such a fixed-resolution short-time frequency transform method has a T-F resolution problem based on the uncertainty principle, not only the short-time frequency transform but also the length of the windowing function should be optimized. To overcome this problem, we incorporate AWS into the speech enhancement procedure, and the windowing function of each time-frame is manipulated using a DNN depending on the input signal. We confirmed that the proposed method achieved a higher signal-to-distortion ratio than conventional speech enhancement methods in fixed-resolution frequency domains.

We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient iterative method (EigenPro). Due to the simplicity of this method, its hyper-parameters such as kernel bandwidth can be automatically and efficiently selected using line search with subsamples of training data. We observe an empirical correlation between the regression loss (mean square error) and regular metrics for speech enhancement. This observation justifies our training target and motivates us to achieve lower regression loss by training separate kernel model per frequency subband. We compare our method with the state-of-the-art deep neural networks on mask-based HINT and TIMIT. Experimental results show that our kernel method consistently outperforms deep neural networks while requiring less training time.

We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction---the random variable. Our lightweight implementation in TensorFlow enables numerous applications: a model-parallel variational auto-encoder (VAE) with 2nd-generation tensor processing units (TPUv2s); a data-parallel autoregressive model (Image Transformer) with TPUv2s; and multi-GPU No-U-Turn Sampler (NUTS). For both a state-of-the-art VAE on 64x64 ImageNet and Image Transformer on 256x256 CelebA-HQ, our approach achieves an optimal linear speedup from 1 to 256 TPUv2 chips. With NUTS, we see a 100x speedup on GPUs over Stan and 37x over PyMC3.

Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to memory constraints), high latency, and inefficiency at small batch sizes. All of these can be solved by more general distribution strategies (model-parallelism). Unfortunately, efficient model-parallel algorithms tend to be complicated to discover, describe, and to implement, particularly on large clusters. We introduce Mesh-TensorFlow, a language for specifying a general class of distributed tensor computations. Where data-parallelism can be viewed as splitting tensors and operations along the "batch" dimension, in Mesh-TensorFlow, the user can specify any tensor-dimensions to be split across any dimensions of a multi-dimensional mesh of processors. A Mesh-TensorFlow graph compiles into a SPMD program consisting of parallel operations coupled with collective communication primitives such as Allreduce. We use Mesh-TensorFlow to implement an efficient data-parallel, model-parallel version of the Transformer sequence-to-sequence model. Using TPU meshes of up to 512 cores, we train Transformer models with up to 5 billion parameters, surpassing state of the art results on WMT'14 English-to-French translation task and the one-billion-word language modeling benchmark. Mesh-Tensorflow is available at https://github.com/tensorflow/mesh .

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements. Unlike standard GANs relying only on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even for a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. We used three generators for the PI-GANs, two of them were feed forward deep neural networks (DNNs) while the other one was the neural network induced by the SDE. Depending on the data, we employed one or multiple feed forward DNNs as the discriminators in PI-GANs. Here, we have demonstrated the accuracy and effectiveness of PI-GANs in solving SDEs for up to 30 dimensions, but in principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and Hyperparameter optimization. Many algorithms have been devised to address this problem. In this paper we introduce a neural network architecture (Deep Genetic Network) which will optimize its parameters during training based on its fitness. Deep Genetic Net uses genetic algorithms along with deep neural networks to address the hyperparameter optimization problem, this approach uses ideas like mating and mutation which are key to genetic algorithms which help the neural net architecture to learn to optimize its hyperparameters by itself rather than depending on a person to explicitly set the values. Using genetic algorithms for this problem proved to work exceptionally well when given enough time to train the network. The proposed architecture is found to work well in optimizing hyperparameters in affine, convolutional and recurrent layers proving to be a good choice for conventional supervised learning tasks.

Stochastic gradient based methods are dominant in optimization for most large-scale machine learning problems, due to the simplicity of computation and their compatibility with modern parallel hardware, such as GPU. In most cases these methods use over-parametrized models allowing for interpolation, i.e., perfect fitting of the training data. While we do not yet have a full understanding of why these solutions generalize (as indicated by a wealth of empirical evidence, e.g., [22, 2]) we are beginning to recognize their desirable properties for optimization, particularly in the SGD setting [11]. In this paper, we leverage the power of the interpolated setting to propose MaSS (Momentum-added Stochastic Solver), a stochastic momentum method for efficient training of over-parametrized models. See pseudo code in Appendix A. The algorithm keeps two variables (weights)w andu .

We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively unit-tested implementations of these manifolds, together with useful Riemannian metrics and associated Exponential and Logarithm maps. The corresponding geodesic distances provide a range of intuitive choices of Machine Learning's loss functions. We also give the corresponding Riemannian gradients. The operations implemented in geomstats are available with different computing backends such as numpy, tensorflow and keras. We have enabled GPU implementation and integrated geomstats' manifold computations into keras' deep learning framework. This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.